tag:blogger.com,1999:blog-7759671094740593352024-03-14T07:15:08.900-07:00Kevin On InvestingCovering the basics of rational investing for family and friends. Feel free to send questions to KevinOnInvesting@gmail.com.Unknownnoreply@blogger.comBlogger111125tag:blogger.com,1999:blog-775967109474059335.post-22283201075310808892017-04-27T16:00:00.000-07:002017-04-27T16:00:06.735-07:00Monitor Your CD Maturity Dates<div dir="ltr" style="text-align: left;" trbidi="on">
This is a quick reminder to those of you with CDs to monitor your CD maturity dates. I have an IRA CD maturing at a credit union in mid-May, and the rates there aren't great. So I logged on, and used online chat to request that the proceeds be deposited into my IRA savings account instead of being rolled into a new IRA CD (which is the default at most banks and credit unions). Within a few seconds, the rep responded that it had been done, and followed up with an email confirmation.<br />
<br />
Typically there's a 10-day grace period after the maturity date during which time you can cancel the renewal, but I prefer to do it in advance if possible. It turned out to be very easy at this credit union. Now I'll be hunting for a good IRA CD at a bank or credit union at which I don't already have an IRA CD (I typically put enough in these to get close to the federal deposit insurance limit, which I don't want to exceed). We've been seeing some pretty good deals in recent months, so I'm optimistic.</div>
Unknownnoreply@blogger.com10tag:blogger.com,1999:blog-775967109474059335.post-92110938385816395792017-04-25T19:09:00.000-07:002017-04-25T19:09:38.503-07:00Bond Basics: Part 7 (Duration)<div dir="ltr" style="text-align: left;" trbidi="on">
Toward the end of the last post in this series, <a href="http://www.kevinoninvesting.com/2017/01/bond-basics-part-6.html" target="_blank">Bond Basics: Part 6</a>, we saw that the change in the price of a bond, for a given change in yield, was related to the bond's term to maturity, and I mentioned that this was related to the bond concept of <i>duration</i>. In this post I'll discuss the concept of duration, especially as it relates to bond funds, which is the way you probably own bonds if you own them at all.<br />
<br />
In a nutshell, duration provides a way to calculate an approximate value for the change in bond or bond fund price for a given a change in bond or bond fund yield. In the previous posts in this series, we discussed how bond price and yield move in opposite directions--when one goes up, the other goes down, and vice versa. Duration gives us a simple way to quantify this relationship--at least approximately.<br />
<br />
<a name='more'></a>Also in the last post in this series, I said I'd discuss the online calculators and spreadsheet formulas you can use to calculate bond prices, but I've decided not to do that now, and instead will bring the discussion up to a higher level that's probably of more interest to most people. It's easy to find <a href="https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=bond+formulas+and+calculators" target="_blank">information on the web about bond formulas and calculators</a>, and maybe I'll come back to them later.<br />
<br />
If you use your web browser to navigate to the <a href="https://investor.vanguard.com/mutual-funds/list#/mutual-funds/asset-class/bond-attributes" target="_blank">Vanguard mutual funds webpage, with <span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">Bond attributes</span> selected in the <b>Show </b>drop-down box on the right</a>, you'll see <b>Duration</b> as one of the column headings. If you click on the <b>Duration </b>column heading, you'll see the following definition:<br />
<blockquote class="tr_bq">
<span style="background-color: white; color: #333333; font-family: "arial" , sans-serif; font-size: 14px;">A measure of the sensitivity of bond—and bond mutual fund—prices to interest rate movements. For example, if a bond has a duration of 2 years, its price would fall about 2% when interest rates rose 1 percentage point. On the other hand, the bond's price would rise by about 2% when interest rates fell by 1 percentage point.</span></blockquote>
So duration gives us a number we can use to approximate how much the value of a bond or bond fund will go up or down when the yield of the bond or bond fund goes down or up. A bond fund with a longer duration will lose more value when its average yield rises, and gain more value when its average yield falls.<br />
<br />
We can express this <i>duration approximation</i><b> </b>relationship between change in bond or bond fund yield and price mathematically with the following formula:<br />
<br />
dP% = -D * dY<br />
<br />
where dP% is the percentage price change, D is duration, and dY is the percentage point change in yield--and of course * is the multiplication operator. We put a minus sign in front of D since the percentage price change will be negative when the percentage point yield change is positive, and vice versa.<br />
<br />
Using the values in the Vanguard definition of duration quoted above, D = 2, dY = 1 for a yield <b>increase </b>of 1 percentage point, and we would calculate dP% as:<br />
<br />
dP% = -D * dY<br />
dP% = -2 * 1<br />
dP% = -2%<br />
<br />
Similarly, dY = -1 for a 1 percentage point <b>decrease</b> in yield, and the calculation would be:<br />
<br />
dP% = -D * dY<br />
dP% = -2 * -1<br />
dP% = 2%<br />
<div>
<br /></div>
If you scan down the list of bond funds on the <a href="https://investor.vanguard.com/mutual-funds/list#/mutual-funds/asset-class/bond-attributes" target="_blank">Vanguard mutual funds page</a> until you find Total Bond Market Index, which is a very popular bond fund among <a href="https://www.bogleheads.org/" target="_blank">Bogleheads</a>, you'll see the duration listed as 6.1 years, and you'll see a <b>Yield to maturity</b> of 2.6% (both of these values may be slightly different when you check, since they change somewhat over time). If you own a different Vanguard bond fund, you can scan the list until you find it, and you can relate this discussion to the duration and yield to maturity for the bond fund you own. From now on I'll abbreviate Total Bond Market Index as TBM.<br />
<br />
With a duration of 6.1 years, if the yield to maturity (YTM) of TBM <b>increased </b>by one percentage point, from 2.6% to 3.6%, the share price of the bond fund (and the value of your shares) would <b>decrease</b> by about 6.1%. Conversely, if the YTM <b>decreased</b> by one percentage point, from 2.6% to 1.6%, the share price of the fund would <b>increase</b> by about 6.1%.<br />
<br />
If you scan the list of bond funds on the Vanguard web page, you'll notice that funds with longer durations also have higher average maturities (listed in the column immediately to the right of Duration), and vice versa. In some cases duration and average maturity are quite close or even the same, and in other cases they are further apart. This is because duration is closely related to maturity, but there also are other factors that affect duration (which are beyond the scope of this discussion). Duration is the more relevant number when considering how much change in yield can affect the value of your bond fund.<br />
<br />
In other words, duration is the most relevant measure of <i>interest-rate risk</i>, which is the risk that the value of your bond or bond fund will lose value if the yield (interest rate) increases. Since duration is related to term to maturity, interest-rate risk also is referred to as <i>term risk</i>. In summary, the higher the duration, the higher the term risk.<br />
<br />
To see an example of how well the duration approximation formula works for a bond fund, we can use a fund's yields (to maturity) on two different dates, along with the fund's duration, to calculate the estimated percentage change in price, and then compare that to the actual percentage change in price.<br />
<br />
Vanguard reports yield to maturity and average duration of its bond funds in the fund's annual and semiannual reports. I'll use the yield to maturity values reported in the <a href="https://www.vanguard.com/funds/reports/q842.pdf" target="_blank">June 30, 2016 semiannual report</a> and the <a href="https://www.vanguard.com/funds/reports/q840.pdf" target="_blank">December 31, 2016 annual report</a> to calculate the change in yield between those two dates. The duration changed slightly between those dates, so I'll use the average of the two reported duration values.<br />
<br />
In the June 30 report, yield to maturity was reported as 1.90% and duration was 5.8 years. In the December 31 report, yield to maturity was reported as 2.60% and duration was 6.0 years. So, between June 30 and December 31, yield <b>increased </b>by 0.70 percentage points: dY = Y2 - Y1 = 2.60% - 1.90%. Since duration changed slightly, from 5.8 to 6.0, I'll use the average of these two values, 5.9, in the duration approximation formula.<br />
<br />
Plugging our values for D and dY into the duration approximation formula:<br />
<br />
dP% = -D * dY<br />
dP% = -5.9 * 0.70<br />
dP% = -4.13%<br />
<br />
The duration approximation formula gives us an estimated percentage price change of -4.13% for a yield percentage point change of +0.70%. (yield up, price down). How does this compare to the actual percentage price change?<br />
<br />
There are various ways to get historical share prices, but I'll use the <a href="https://personal.vanguard.com/us/funds/tools/pricehistorysearch?radio=1&results=get&FundType=VanguardFunds&FundIntExt=INT&FundId=0584&Sc=1&fundName=0584&fundValue=0584&radiobutton2=1&beginDate=06%2F30%2F2016&endDate=12%2F31%2F2016&year=#res" target="_blank">Vanguard price history search tool</a>, and search for prices of VBTLX, the Admiral shares class of TBM. The price was 11.09 per share on June 30, and 10.65 per share on December 30 (December 31 was a Saturday, so no price was quoted for that day).<br />
<br />
To get the percentage change in price (dP%), we subtract the old price (P1) from the new price (P2), divide by the old price (P1), then multiply by 100:<br />
<br />
dP% = (P2 - P1) / P1 * 100<br />
dP% = (10.65 - 11.09) / 11.09 * 100<br />
dP% = - 0.0397 * 100<br />
dP% = -3.97%.<br />
<br />
So the actual bond fund percentage share price change was -3.97%, which is very close to the value of -4.13% estimated by the duration approximation formula. In this case, the formula worked quite well.<br />
<br />
To help solidify the understanding of the duration approximation formula, we can use approximate values and do the arithmetic mentally. Duration is approximately 6 years (5.9 rounded to one significant figure). First we multiply duration by the change in yield of 0.7. Hopefully we remember that 6 * 7 = 42, so we can mentally calculate that 6 * 0.7 = 4.2, which rounded to one significant figure is 4. Since we know that price change is negative if yield change is positive, we take the opposite of 4, which we express as a percentage to give us an estimated price change of -4%. This is close enough to the value calculated with the formula, considering that the duration approximation formula only gives us an approximate value for percentage price change.<br />
<br />
So what relevance does duration have to our investment decisions, specifically with respect to selecting a bond fund?<br />
<br />
A bond fund with a longer duration has more term risk than a bond fund with shorter duration (we'll assume that the credit risk of the two bond funds is about the same; credit risk is based on the quality of the bonds in the fund). Because investors demand higher yield in compensation for more risk, the bond fund with more term risk will have a higher yield. Sometimes the higher term risk is rewarded, and the higher yields generate higher long-term returns, as is the case during periods of generally steady or falling yields. But sometimes the higher risk "shows up", as is the case during periods of generally rising yields, and the higher yields cannot compensate for the falling prices.<br />
<br />
We can see term risk both showing up and being rewarded by looking at the 1-year and 10-year returns of the Vanguard Short-Term, Intermediate-Term, and Long-Term Treasury funds. I'll use the values as of now on the <a href="https://investor.vanguard.com/mutual-funds/list#/mutual-funds/asset-class/month-end-returns" target="_blank">Vanguard mutual funds web page with Annual average month-end returns selected</a> in the Show drop-down box (the values may be different when you look). The Treasury funds are good to compare to each other because they all hold only the highest-quality bonds, U.S. Treasuries, so they all have the same credit risk (essentially none). I've also included the durations of the funds in the chart below.<br />
<style type="text/css"><!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}</style>
<br />
<table border="1" cellpadding="0" cellspacing="0" dir="ltr" style="border-collapse: collapse; border: none; font-family: arial,sans,sans-serif; font-size: 13px; table-layout: fixed;"><colgroup><col width="174"></col><col width="74"></col><col width="62"></col><col width="69"></col></colgroup><tbody>
<tr style="height: 21px;"><td style="padding: 2px 3px 2px 3px; vertical-align: bottom;"></td><td style="padding: 2px 3px 2px 3px; vertical-align: bottom;"></td><td colspan="2" data-sheets-value="{"1":2,"2":"Annual Returns"}" rowspan="1" style="font-weight: bold; padding: 2px 3px 2px 3px; text-align: center; vertical-align: bottom;">Annual Returns</td></tr>
<tr style="height: 21px;"><td data-sheets-value="{"1":2,"2":"Fund"}" style="font-weight: bold; padding: 2px 3px 2px 3px; text-align: center; vertical-align: bottom;">Fund</td><td data-sheets-value="{"1":2,"2":"Duration"}" style="font-weight: bold; padding: 2px 3px 2px 3px; vertical-align: bottom;">Duration</td><td data-sheets-value="{"1":2,"2":"1-year"}" style="font-weight: bold; padding: 2px 3px 2px 3px; vertical-align: bottom;">1-year</td><td data-sheets-value="{"1":2,"2":"10-year"}" style="font-weight: bold; padding: 2px 3px 2px 3px; vertical-align: bottom;">10-year</td></tr>
<tr style="height: 21px;"><td data-sheets-value="{"1":2,"2":"Short-Term Treasury"}" style="padding: 2px 3px 2px 3px; vertical-align: bottom;">Short-Term Treasury</td><td data-sheets-value="{"1":2,"2":"2.2 years"}" style="padding: 2px 3px 2px 3px; vertical-align: bottom;">2.2 years</td><td data-sheets-numberformat="{"1":3,"2":"0.00%","3":1}" data-sheets-value="{"1":3,"3":0.0011}" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.11%</td><td data-sheets-numberformat="{"1":3,"2":"0.00%","3":1}" data-sheets-value="{"1":3,"3":0.0223}" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2.23%</td></tr>
<tr style="height: 21px;"><td data-sheets-value="{"1":2,"2":"Intermediate-Term Treasury"}" style="padding: 2px 3px 2px 3px; vertical-align: bottom;">Intermediate-Term Treasury</td><td data-sheets-value="{"1":2,"2":"5.2 years"}" style="padding: 2px 3px 2px 3px; vertical-align: bottom;">5.2 years</td><td data-sheets-numberformat="{"1":3,"2":"0.00%","3":1}" data-sheets-value="{"1":3,"3":-0.0141}" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">-1.41%</td><td data-sheets-numberformat="{"1":3,"2":"0.00%","3":1}" data-sheets-value="{"1":3,"3":0.0432}" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">4.32%</td></tr>
<tr style="height: 21px;"><td data-sheets-value="{"1":2,"2":"Long-Term Treasury"}" style="padding: 2px 3px 2px 3px; vertical-align: bottom;">Long-Term Treasury</td><td data-sheets-value="{"1":2,"2":"16.7 years"}" style="padding: 2px 3px 2px 3px; vertical-align: bottom;">16.7 years</td><td data-sheets-numberformat="{"1":3,"2":"0.00%","3":1}" data-sheets-value="{"1":3,"3":-0.0504}" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">-5.04%</td><td data-sheets-numberformat="{"1":3,"2":"0.00%","3":1}" data-sheets-value="{"1":3,"3":0.0649}" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">6.49%</td></tr>
</tbody></table>
<br />
We see that the Short-Term Treasury fund, with the shortest duration (and least term risk), had the highest 1-year return (a small gain) and the lowest 10-year return. The Long-Term Treasury fund, with the longest duration (and most term risk), had the lowest 1-year return (a loss) and the highest 10-year return. The Intermediate-Term Treasury fund, with duration between the other two funds, had returns between the other two funds.
<br />
<div>
<br />
So over the 1-year period, the term risk showed up, and the longer the duration the lower the return, but over the 10-year period, the term risk was rewarded, and the longer the duration the higher the return.<br />
<br />
We need to be careful about extending this particular set of 10-year returns into the future. Yields have generally fallen over the last ten years, and this contributed to higher returns for bond funds with longer durations (more term risk) compared to funds with lower durations. Yields generally increased over the last year, which is why bond funds with longer durations had lower returns, but yields have been generally falling since 1982, which is longer than the Vanguard bond funds, and most bond funds, have existed.<br />
<br />
If we use simulated bond fund returns prior to 1982, there are 10-year periods, and longer, when yields generally increased, and short-term Treasuries did better than intermediate-term Treasuries, which did better than long-term Treasuries. Sometimes the risk shows up.</div>
</div>
Unknownnoreply@blogger.com24tag:blogger.com,1999:blog-775967109474059335.post-53682584470043438502017-01-23T18:29:00.000-08:002017-01-23T18:29:18.874-08:00Bond Basics: Part 6<div dir="ltr" style="text-align: left;" trbidi="on">In <a href="http://www.kevinoninvesting.com/2017/01/bond-basics-part-5.html" target="_blank">Part 5</a> of this series on bond basics, I derived the formula to calculate the price of a one-year bond in terms of its yield. I started by developing a formula to calculate something more familiar: the amount you end up with in a savings account after one year. In this part of the series I'll derive the formula to calculate the price of a bond with a term to maturity of more than one year, and again, I'll start with the more familiar concept of compound interest in a savings account.<br />
<br />
<a name='more'></a>We saw in <a href="http://www.kevinoninvesting.com/2017/01/bond-basics-part-5.html" target="_blank">Part 5</a> that we can calculate the amount we'll end up with in a savings account after one year with this <i>time value of money</i> (TVM) formula:<br />
<pre> FV = PV * (1 + i)
</pre>where FV is the Future Value, PV is the Present Value, and i is the annual interest rate (and * is the multiplication operator).<br />
<br />
If we left the money in the savings account for an additional year, we could apply this same formula to calculate the value at the end of the second year, but the starting value at the beginning of year 2 would be the value at the end of year 1. In other words, FV from our calculation for year 1 would be PV in our calculation for year 2. To get set up for the year 2 calculation, let's rewrite the TVM formula above as:<br />
<pre> FV1 = PV * (1+i) (Year 1)
</pre>where FV1 indicates the Future Value at the end of year 1.<br />
<br />
Since FV1 is the amount we end up with at the end of year 1, it is the amount we start with, the present value, in year 2. So we can use FV1 as PV in the year-2 formula:<br />
<pre> FV2 = FV1 * (1+i) (Year 2)
</pre>We can then substitute the right-hand side of the year-1 formula for FV1 in the year-2 formula as follows (from here on I'll use extra spaces and brackets to help clarify which expression is being substituted for another):<br />
<pre> FV2 = [ FV1 ] * (1+i)
FV2 = [ PV * (1+i) ] * (1+i)
FV2 = PV * (1+i) * (1+i)
</pre>As a numeric example, for a starting year-1 value of 100 (PV = 100 in the year-1 formula), and an interest rate of 1% (0.01), the value of our account at the end of two years (FV2) would be:<br />
<pre> FV2 = PV * ( 1 + i ) * ( 1 + i )
FV2 = 100 * ( 1 + 0.01 ) * ( 1 + 0.01 )
FV2 = 100 * 1.01 * 1.01
FV2 = 102.01
</pre>You will remember from elementary arithmetic that we can write a number multiplied by itself as that number squared, for example we can write 2*2 as 2<sup>2</sup>, or using ^ is the <a href="https://en.wikipedia.org/wiki/Exponentiation" target="_blank">exponentiation operator</a> (as used in spreadsheet formulas), we can write it as 2^2. Thus, we can write (1+i) * (1+i) as (1+i)^2, and rewrite the 2-year compound interest TVM formula as:<br />
<pre> FV2 = PV * [ (1+i) * (1+i) ]
FV2 = PV * [ (1+i)^2 ]
FV2 = PV * (1+i)^2
</pre>Note that the only difference between the 2-year and 1-year compound interest formulas is that we multiplied by an additional factor of (1+i) in the 2-year formula. We can use the same reasoning to extend the formula to any number of years. For example, the 3-year compound interest formula is:<br />
<pre> FV3 = PV * (1+i) * (1+i) * (1+i)
</pre>Just as we can write 2*2 as 2<sup>2</sup> or 2^2 (two squared), we can write 2*2*2 as 2<sup>3</sup> or 2^3 (two cubed), which means we can rewrite the 3-year compound interest formula as:<br />
<pre> FV3 = PV * [ (1+i) * (1+i) * (1+i) ]
FV3 = PV * [ (1+i)^3 ]
FV3 = PV * (1+i)^3
</pre>We can generalize this formula to any number of years, n, and write it as:<br />
<pre> FVn = PV * (1+i)^n
</pre>which usually is written simply as:<br />
<pre> FV = PV * (1+i)^n
</pre>We have derived the generic compound interest TVM formula used to calculate the future value after n years given a present value and an interest rate. I have found this to be the single most useful financial formula, whether used directly or used to derive a related TVM formula, as we'll do next.<br />
<br />
The formula above gives us future value in terms of present value, but we saw in <a href="http://www.kevinoninvesting.com/2017/01/bond-basics-part-5.html" target="_blank">Part 5</a> that bond price is related to a <b>present</b> value. So we want to rearrange the above formula, solving for PV in terms of FV, using the same simple algebra we used in <a href="http://www.kevinoninvesting.com/2017/01/bond-basics-part-5.html" target="_blank">Part 5</a>. Dividing both sides of the equation by (1+i)^n, and reversing the order of the equation, we get:<br />
<pre> PV = FV / (1+i)^n
</pre>As I explained in <a href="http://www.kevinoninvesting.com/2017/01/bond-basics-part-5.html" target="_blank">Part 5</a>, FV in a TVM formula can be referred to as a future cash flow. So we can say that the present value of a future cash flow is the future cash flow discounted by the discount rate (i). The discounting is done by dividing the future cash flow by the sum of 1 and the interest rate raised to the nth power, where n is the number of years over which we are compounding.<br />
<br />
The formula above is for a single future cash flow, FV, at the end of n years. This formula can be extended to calculate the present value of multiple annual cash flows over N years as follows:<br />
<pre> PV = CF1 / (1+i)^1 + CF2 / (1+i)^2 + ... + CFN / (1+i)^N
</pre>where CF1 is the cash flow received at the end of year 1, CF2 is the cash flow received at the end of year 2, and CFN is the cash flow received at the end of year N (the last year). The ellipses ( ... ) represent the cash flows between cash flow 2 and the last cash flow. So if we were solving this for a five-year period, there would be five terms in the right-hand side of the equation, one each for cash flow term CF1 through CF5. I'll refer to this formula as the <i><b>present value of discounted cash flows</b></i> formula.<br />
<br />
In <a href="http://www.kevinoninvesting.com/2017/01/bond-basics-part-5.html" target="_blank">Part 5</a> we saw that bond price is described in terms of bond yield as follows:<br />
<blockquote><b>A bond's price is the present value of its future cash flows discounted at a rate equal to the bond's yield.</b><br />
</blockquote>Looking at the present value of discounted cash flows formula, we see that the present value of each cash flow is the cash flow divided by the factor (1+i)^n, where i is the interest rate and n is the year in which the cash flow is received. For bonds, the analog of interest in a savings account is the bond's <i>yield</i>, so we'll use y to represent yield instead of i for interest rate, and rewrite the discount factor for year n as (1+y)^n.<br />
<br />
So in the the present value of discounted cash flows formula, the present value of each bond cash flow for year n can be written as:<br />
<pre> PVn = CFn / (1+y)^n
</pre>All future bond cash flows, except the last one, consist of an interest payment, also referred to as a <a href="https://en.wikipedia.org/wiki/Coupon_(bond)" target="_blank"><i>coupon payment</i></a>. The final cash flow consists of the final interest payment and the principal payment.<br />
<br />
Assuming annual interest payments, each interest payment is the interest rate (coupon rate) times the par value (face value) of the bond. For example, for a par value of 100 and a coupon rate of 1%, each annual interest payment would be 100 * 1% = 1. Using a par value of 100 and designating the coupon rate as <b>r</b>, each <b>annual interest payment cash flow</b> is:<br />
<pre> CFn = 100 * r
</pre>Substituting the right-hand side of this equation for CFn in the annual interest payment cash flow formula above:<br />
<pre> PVn = [ CFn ] / (1+y)^n
PVn = [ 100 * r ] / (1+y)^n
</pre>This formula gives us the <b>discounted cash flow for the annual interest payment</b> in year n for a bond with par value 100, coupon rate r, and yield y.<br />
<br />
The final cash flow also includes the principal payment, which for a bond with par value 100 is 100. This is discounted by the same discount factor, which for the last year, N, is (1+y)^N. We could just add the discounted principal payment as a final term in the discounted cash flow formula; this final term is:<br />
<pre> Discounted principal payment = 100 / (1+y)^N
</pre>Using this approach, the final cash flow would consist of two terms, one for the final interest payment and one for the principal payment. Designating the present value of this final cash flow in the last year, N, as PVN:<br />
<pre> PVN = [ 100 * r / (1+y)^N ] + [ 100 / (1+y)^N ]
</pre>Alternately, we can combine the final interest payment and the principal payment into a single cash flow, CFN, consisting of the principal payment of 100 plus the final interest payment of 100*r, and use the distributive property to simplify as follows:<br />
<pre> CFN = 100 + 100 * r
CFN = 100 * (1 + r)
</pre>We can then rewrite the final discounted cash flow formula in the simpler form:<br />
<pre> PVN = [ CFN ] / (1+y)^N
PVN = [ 100 * (1+r) ] / (1+y)^N
PVN = 100 * (1+r) / (1+y)^N
</pre>Combining the final discounted cash flow with the discounted cash flows for the annual interest payments, we can write the present value of discounted cash flows formula as:<br />
<pre> PV = [ CF1 ] / (1+y)^1 + [ CF2 ] / (1+y)^2 + ... + [ CFN ] / (1+y)^N
PV = [ 100*r ] / (1+y)^1 + [ 100*r ] / (1+y)^2 + ... + [ 100*(1+r) ] / (1+y)^N
</pre>Since <b>a bond's price is the present value of its future cash flows discounted at a rate equal to the bond's yield</b>, and since bonds are priced as a percent of par value (so a bond's price at maturity is 100), we have derived the formula for the price of a bond with with coupon rate r, yield y, and term to maturity N. So we can rewrite the present value formula as a <b>bond price formula</b> by using P for Price instead of PV for Present Value:<br />
<pre> P = 100*r / (1+y)^1 + 100*r / (1+y)^2 + ... + 100*(1+r) / (1+y)^N
</pre>As an example calculation, let's calculate the price of a 3-year bond (N=3) with a yield, y, of 1.5% (the yield of a 3-year Treasury as I write this), and a coupon rate, r, of 1.5%. Writing 1.5% in decimal form as 0.015, the bond price formula is:<br />
<pre> P = 100 * r / (1 + y )^1 + 100 * r / ( 1 + y )^2 + 100*( 1 + r ) / ( 1 + y )^3
P = 100*0.015 / (1+0.015)^1 + 100*0.015 / (1+0.015)^2 + 100*(1+0.015) / (1+0.015)^3
</pre>You can either copy and paste the right-hand side of the equation into a Google search box or into a spreadsheet (preceded by = to indicate that it's a formula), or use a calculator (careful with the parentheses) to determine that in this case P = 100.<br />
<br />
This result is not surprising if you recall from <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-2.html" target="_blank">Part 2</a> that with some reasoning about bond price and yield, we determined that yield equals coupon rate for a bond priced at par (100). In other words, bond price is 100 if yield equals coupon rate.<br />
<br />
We've learned in this series that bond price and yield move in opposite directions, and now we can verify this for a 3-year bond with the bond price formula. Let's assume that the 3-year Treasury yield jumps from 1.5% to 2.0% today. Coupon rate is fixed, so r would remain 1.5% (0.015), but the yield, y, increases to 2.0% (0.020), and our bond price formula becomes:<br />
<pre> P = 100 * r / (1 + y )^1 + 100 * r / (1 + y )^2 + 100*( 1 + r ) / (1 + y )^3
P = 100*0.015 / (1+0.020)^1 + 100*0.015 / (1+0.020)^2 + 100*(1+0.015) / (1+0.020)^3
</pre>Performing this calculation with one of the methods mentioned, the result is P = 98.56, which verifies that the bond price decreases when the yield increases.<br />
<br />
When the yield increases by 0.5 percentage points from 1.5% to 2.0%, the price decreases by 1.44% (98.56 / 100 - 1 = -1.44%). Note that the price percentage decrease is a little less than three times the percentage point increase (1.44 / 0.5 = 2.88), which is a little less than the bond maturity of three years. This is not a coincidence, but is related to the bond concept of <b><i><a href="https://en.wikipedia.org/wiki/Bond_duration" target="_blank">duration</a></i></b>, which I intend to discuss in a future post in this series.<br />
<br />
Although I think understanding the bond price formula is a great way to deepen one's understanding of the relationship between bond price and yield, the formula is cumbersome to use, especially for a bond with a long term to maturity; e.g., for a 20-year bond we'd have 20 discounted cash flow terms in the formula. Fortunately there are spreadsheet formulas and online calculators that can be used to easily calculate bond price, which I plan to discuss in the next post in this series.</div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-775967109474059335.post-61798918270577055132017-01-07T14:53:00.000-08:002017-01-07T14:53:04.373-08:00Bond Basics: Part 5<div dir="ltr" style="text-align: left;" trbidi="on">
Much of the discussion in this series on bond basics has been about the inverse relationship between bond yield and bond price: when one goes up, the other goes down, and vice versa. My goal in this post is to help you begin to understand the mathematical formula that specifies bond price in terms of bond yield, since understanding this can facilitate a deeper understanding of bond fundamentals. We can start by considering something familiar: earning interest in a savings account. We can develop the simple formula that describes this, then with some elementary algebra, we can build on it to develop the formula that gives us bond price in terms of bond yield.<br />
<br />
<a name='more'></a>In <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-1.html" target="_blank">Part 1</a> of this series, I explained that a bond is basically a loan from an investor to a corporation or government. Similarly, a savings account is essentially a loan from a saver to a bank (or credit union). The bank compensates the saver for the loan by paying interest, very much like the corporation or government compensates the bondholder by paying interest. The main difference is that the saver can take back all or part of the loan from the bank at any time by removing money from the savings account. In bond terms, the term to maturity of the savings account is zero years, so we can think of it as an extremely short-term bond.<br />
<br />
If you deposit $100 in a savings account with an annual interest rate of 1%, you will earn $1 in interest in one year, because 1% of $100 is $1 (taking percentages of 100 is trivial: 1% of 100 is 1, 10% of 100 is 10, 27.4% of 100 is 27.4, etc.). Adding this $1 in interest to your original $100 gives you a total of $101 in your account after one year. From now on I'm going to drop the dollar sign for convenience; e.g., 100 grows to 101 at the end of one year. Also, all interest rates will be understood to be annual interest rates.<br />
<br />
If we use FV to represent the Future Value of the savings account at the end of one year, we can write this equation to describe the future value in terms of the initial value of 100 and the interest rate of 1%:<br />
<br />
FV = 100 + 100 * 1%<br />
<br />
Here I'm using * for the multiplication operator, so 1% of 100 is written as 1% * 100, which also can be written as 100 * 1% (due to the <a href="https://www.google.com/search?q=commutative%20property&rct=j" target="_blank">commutative property</a> of multiplication).<br />
<br />
The right-hand side of the equation above can be evaluated directly in a spreadsheet formula or by Google (copy and paste it into a Google search box to verify). Some calculators have a % key that also would allow you to evaluate the expression as written. However, it is standard to write such expressions using decimal numbers rather percentages.<br />
<br />
In decimal form, 1% is 0.01. If you don't remember this from elementary school arithmetic, then consider that % can be interpreted as the arithmetic operation "divide by 100". Using / as the division operator, 1% = 1 / 100 = 0.01. Dividing by 100 is the same as moving the decimal point two places to the left (adding one or more zeros if necessary). So 100% = 1, 10% = 0.1 and 1% = 0.01.<br />
<br />
Rewriting the above equation using 0.01 instead of 1%:<br />
<br />
FV = 100 + 100 * 0.01<br />
<br />
Based on the <a href="https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-ditributive-property/a/distributive-property-explained" target="_blank">distributive property</a>, we can factor out the 100 in the expression on the right-hand side of this equation, and rewrite it as:<br />
<br />
FV = 100 * (1 + 0.01)<br />
<br />
If we want to be able to apply this formula to any starting amount, instead of just 100, we can designate the starting amount as PV, which stands for Present Value. Similarly, if we want to be able to apply the formula using any interest rate, instead of just 1%, we can designate the interest rate as <i>i</i> and rewrite the equation as:<br />
<br />
FV = PV * (1 + i)<br />
<br />
This is the basic <i><a href="https://www.google.com/search?q=time%20value%20of%20money&rct=j" target="_blank">time value of money</a></i> (TVM) formula that allows you to calculate the future value (FV) at the end of one year given a present value (PV) and an interest rate (i). We can easily extend this formula to calculate the future value at the end of any number of years, but for now I'll just stick with a one-year time period.<br />
<br />
We can use some simple algebra to rearrange the above equation to answer the question, "what is the present value that will result in a given future value at the end of one year?" For example, what value do I start with to end up with 101 at the end of one year at an interest rate of 1%? To derive the formula to answer questions like this, we simply divide both sides of the above equation by (1+i), and move each side of the equation to the other side, which gives us:<br />
<br />
PV = FV / (1+i)<br />
<br />
(Still using / as the division operator). In words, the present value is the future value divided by the sum of one and the interest rate.<br />
<br />
Of course if we substitute 101 for FV and 0.01 for i in this equation, and solve it, we will get 100 as the result for PV. We know this because we've already determined that 101 is the Future Value after one year given the Present Value of 100 and an interest rate of 1%. Just as we used some simple algebra to rearrange the TVM equation, we can rearrange our words to say that 100 is the Present Value given a Future Value of 101 and an interest rate of 1%.<br />
<br />
In this version of the one-year TVM formula, in which we solve for PV in terms of FV, <i>i</i> typically is referred to as the <i>discount rate, </i>since we discount the future value using this rate to determine the present value. Thus we can say that the present value equals the future value received one year from now discounted by the discount rate.<br />
<br />
How does this relate to bond price and yield? Before answering this, we must introduce one more TVM term: <i>cash flow</i>. In TVM lingo, FV in the equation above is referred to as a <i>cash flow</i>. In the simple example of our savings account, there is one future cash flow, which is the principal and interest payment we receive at the end of one year. Now we can define bond price in terms of bond yield using TVM terminology:<br />
<br />
<b>A bond's price is the present value of its future cash flows discounted at a rate equal to the bond's yield.</b><br />
<br />
That's a mouthful, but read it carefully while looking at the equation for present value in terms of future value and an interest rate (or discount rate) for a one-year period:<br />
<br />
PV = FV / (1+i)<br />
<div>
<br /></div>
<div>
For a one-year bond (term to maturity of one year), PV in the above equation is the bond's price, FV is the future cash flow (principal and interest), and i is the discount rate equal to the bond's yield. So the same formula we used to calculate the initial deposit into a savings account given the interest rate and the value after one year can be used to calculate the price of a bond given the yield and the principal and interest payment received at the end of one year.</div>
<br />
Now that we're talking about bonds, we'll replace PV with P (for Price), and replace i with y (for yield), and write it this way:<br />
<br />
P = FV / (1 + y)<br />
<br />
We can improve this further by expressing FV in terms of known bond characteristics.<br />
<br />
The Future Value when the bond matures after one year is the face value of the bond plus the interest earned in one year. We learned in <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-1.html" target="_blank">Part 1</a> that face value also is referred to as par value, or simply par. To avoid confusion between the terms future value and face value, I'll use the term par value or par from now on.<br />
<br />
Since bonds are priced as a percent of par value, we note the price of a bond valued at par is 100 (100% of par value). In our calculations, we will use 100 as par value, since this will give us a result consistent with the bond pricing convention. So 100 will be the principal portion of the cash flow we receive after one year.<br />
<br />
The interest earned in one year is the coupon rate times the par value of the bond, as discussed in <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-1.html" target="_blank">Part 1</a>. So for a bond with a coupon rate of 1%, the interest portion of our future cash flow will be 1% * 100 = 1.<br />
<br />
Putting this together, the future cash flow, FV in the equation, is:<br />
<br />
FV = 100 + 100 * 0.01<br />
<br />
Replacing 0.01 with the letter r, for coupon <b>r</b>ate, we can write this as:<br />
<br />
FV = 100 + 100 * r<br />
<br />
Which we can rewrite as:<br />
<br />
FV = 100 * (1+r)<br />
<br />
Substituting the right-hand side of the above equation for FV in our bond price formula:<br />
<br />
P = FV / (1+y)<br />
<div>
P = 100 * (1+r) / (1+y)</div>
<br />
In <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-2.html" target="_blank">Part 2</a> I used words and logic to explain that the yield equals the coupon rate for a bond priced at par. Now we can verify this with the one-year bond pricing formula we've developed. For a bond with a coupon rate of 1% and a yield of 1%:<br />
<br />
<div>
P = 100 * (1+r) / (1+y)</div>
P = 100 * (1 + 0.01) / (1 + 0.01)<br />
P = 100 * 1<br />
P = 100<br />
<br />
In <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-2.html" target="_blank">Part 2</a> I also used words and logic to explain that the price of a one-year bond with a yield of 2% and a coupon rate of 1% is about 99. Now we also can verify this with the one-year bond pricing formula we've developed. For a bond with a coupon rate of 1% and a yield of 2%:<br />
<br />
<div>
P = 100 * (1+r) / (1+y)</div>
P = 100 * (1 + 0.01) / (1 + 0.02)<br />
P = 100 * 1.01/1.02<br />
P = 100 * 0.99<br />
P = 99<br />
<div>
<br /></div>
Also in <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-2.html" target="_blank">Part 2</a>, we saw that the price of a bond with a coupon rate of 1% and a yield of 0% is 101; let's check that with our formula too:<br />
<br />
<div>
P = 100 * (1+r) / (1+y)</div>
P = 100 * (1 + 0.01) / (1 + 0)<br />
P = 100 * 1.01/1<br />
P = 100 * 1.01<br />
P = 101<br />
<div>
<br /></div>
<div>
We now have the formula to calculate the price of a one-year bond, and have verified that it gives results consistent with those we achieved through reasoning about equalizing the one-year returns of bonds with the same coupon rates but different yields. The formula is more powerful than the reasoning we used, because we can expand on it to derive a formula for bonds with more than one year to maturity, for which it would be difficult to determine the price based on the reasoning used in <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-2.html" target="_blank">Part 2</a>.</div>
<br />
In <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-3.html" target="_blank">Part 3</a> I mentioned that the inverse relationship between bond price and yield is related to the formula for bond price in terms of bond yield, because yield is in the denominator of the right-hand side of the equation. Now we can see this clearly, and can see that when y increases in the denominator of the expression, the value of the expression decreases, and thus P decreases, and vice versa.<br />
<br />
In the next part of this series on bond basics, I'll extend the simple one-year bond price formula to the general case of a bond with a term to maturity of any number of years.</div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-775967109474059335.post-27001553819892857502017-01-04T14:15:00.000-08:002017-01-04T14:15:09.205-08:00Bond Basics: Part 4<div dir="ltr" style="text-align: left;" trbidi="on">
I had planned to start digging into the mathematical formula that relates bond price and bond yield in this post, but first I want to discuss one more example related to the topic discussed in <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-3.html" target="_blank">Part 3</a> of this series. In that part, I explained that we can't make precise statements about the general relationship between interest rates and bond prices, because the yield (and price) of each bond changes differently depending on the bond market's assessment of the term risk and credit risk of that particular bond. Confusion about this is often exposed by questions about the impact of increases to the <a href="https://www.google.com/search?q=federal%20funds%20rate&rct=j" target="_blank">federal funds rate</a> (FFR) on the prices of bond funds. So following is a brief discussion of this, and then in Part 5 I'll pick up on deriving the formula for bond pricing.<br />
<br />
<a name='more'></a>If you follow financial news at all, you have heard that the Federal Open Market Committee (FOMC), often referred to simply as <i>the Fed</i>, recently increased the target federal funds rate by 25 basis points (0.25 percentage points), and that they intend to increase the target FFR several more times in 2017. A common question on the <a href="https://www.bogleheads.org/forum/search.php?search_id=active_topics" target="_blank">Bogleheads investment forum</a> is how increases in the FFR will affect the share price of a bond fund owned by the forum member.<br />
<br />
The short answer is that changes in the FFR are not of particular concern, since the FFR is a very short-term interest rate, and as discussed in Part 3, yields of different terms to maturity can change by different amounts and even in different directions. There is no direct relationship between the change in the FFR and the change in yield of an intermediate-term or long-term bond or bond fund.<br />
<br />
A dramatic example of this was the period between May 10, 2004 and September 1, 2005, during which the effective FFR <b>increased </b>from about 1% to about 3.5%, while the yield on the 10-year Treasury <b>decreased</b> from about 4.7% to about 4%. This is shown in the chart below.<br />
<br />
(If you have any trouble viewing the charts while reading this in your email, click on the blog title link, which should take you directly to the blog where you should be able to view the charts).<br />
<br />
<img alt="If not seeing the graph in email, click on the blog title to go directly to the blog" src="https://fred.stlouisfed.org/graph/fredgraph.png?g=cf4m" width="100%" /><br />
<br />
Note however that the yield on the 1-month Treasury, also shown in the graph, closely tracked the effective FFR, since both are short-term rates. Similarly, you can expect the yields on money market funds, which also are very short-term rates, to have a close relationship to the FFR, but the yields of intermediate-term and long-term bonds and bond funds can change very differently than changes in the FFR.<br />
<br />
As a more recent example, the Fed <b>increased </b>the FFR by 25 basis points in December 2015, but the yield on the 10-year Treasury <b>decreased </b>from about 2.3% at that time to about 1.4% in early July of 2016.<br />
<br />
I think of Fed changes to the FFR more as responding to the economy rather than driving bond yields, other than very short-term bond yields. It's the economy that drives interest rates in general. It's not particularly surprising that intermediate-term bond yields could be increasing at the same time the Fed increases the FFR, since both are related to prospects of the economy strengthening, but this doesn't mean that an increase in the FFR <b>causes</b> an increase in bond yields in general.<br />
<br />
Consider the period since shortly before the recent presidential election until now, as shown in the chart below. The yield on the 10-year Treasury gradually increased while the effective FFR was flat at about 0.4%. Then on November 9, the day after the election, the 10-year yield jumped from 1.88% to 2.07%, and then continued to climb, while the effective FFR remained flat at about 0.4%. On December 15, the effective FFR jumped to 0.66%, consistent with the increased Fed target of 0.5% to 0.75%, and although the 10-year yield also increased slightly that day, within a few days it was back down to its level before the FFR increase.<br />
<br />
<iframe allowtransparency="true" frameborder="0" scrolling="no" src="//fred.stlouisfed.org/graph/graph-landing.php?g=ch6X&width=600&height=400" style="height: 400px; overflow: hidden; width: 600px;"></iframe><br />
<br />
Although there are reasons to be concerned (or perhaps happy) about rising intermediate-term bond yields, what the Fed does with its target for the FFR is not one of them. Bond yields will increase, and prices will fall, if the economy strengthens and inflation expectations increase, and the Fed is likely to increase the target FFR due to the same factors. Correlation does not imply causation, and as we've seen, sometimes bond yields aren't even correlated to changes in the federal funds rate.</div>
Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-775967109474059335.post-16644222802732439612016-12-30T13:03:00.000-08:002016-12-30T13:04:01.676-08:00Bond Basics: Part 3<div dir="ltr" style="text-align: left;" trbidi="on">
In <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-2.html" target="_blank">Part 2</a> of this series on bond basics I explained the relationship between bond price and bond yield: when one goes up, the other goes down. However, I also stated that saying when interest rates rise, bond prices fall (or vice versa) is not really an accurate statement. This is because there are many different interest rates in our economy, and the price of a bond is only affected by the interest rate, or more precisely the yield, of that particular bond or bonds very similar to it. Below I'll discuss the precise relationship between the price and yield of a particular bond a bit more, then explain why the relationship between interest rates in general and bond prices in general is not so precise.<br />
<br />
<a name='more'></a>For a particular bond, price and yield are precisely related by a mathematical formula. Because of this precise relationship, price and yield are really two sides of the same coin--two different ways of expressing the value of a bond. So for a particular bond, it is absolutely true that when yield increases, price decreases, and vice versa.<br />
<br />
Although it's not a perfect analogy, this analogy may help. You can express mileage as miles per gallon (mpg) or gallons per mile (gpm): 20 mpg is the same as 1/20 gpm (or 0.05 gpm, since 1/20 = 0.05). We can express this generically as mpg = 1/gpm, or equivalently, gpm = 1/mpg. If the denominator on the right-hand side of either of these equations increases, the value of the left-hand side of the equation decreases, and vice versa. In other words, mpg and gpm are inversely related.<br />
<br />
The mathematical formula relating bond price and bond yield is more complex, but the mathematical foundation for the inverse relationship between bond price and yield is similar. In a subsequent post I'll get into more detail about the formula that relates bond price and yield, but for now I'll just note that in the equation that expresses bond price as a function of bond yield, yield is in the denominator of the right-hand side of the equation. As with the mpg vs. gpm example, this is the mathematical foundation for the inverse relationship between bond price and yield.<br />
<br />
The yield of a bond is related to the riskiness of the bond: a riskier bond will have a higher yield than a less risky bond. Since bond price is inversely related to bond yield, we can also say that a riskier bond will have a lower price than a less risky bond (assuming both bonds have the same coupon rate). Risk is proportional to the uncertainty that the expected return will be realized. For a bond we can think of the yield as a reasonable measure of the annualized expected return. There are two dominant factors that contribute to the riskiness of a bond; i.e., the uncertainty that an investor will earn the yield of the bond.<br />
<br />
The two main risk factors for bonds are credit quality, a measure of default risk, and term to maturity, which affects term risk, commonly referred to as interest-rate risk. Credit quality is a measure of the certainty that the bond issuer will make interest and principal payments (or make them on time). As explained in Part 1, term to maturity is the number of years until a bond matures and repays its principal.<br />
<br />
An investor will demand a higher yield for a bond with lower credit quality to compensate for the higher uncertainty that interest and principal payments will be received (or received on time). If a bond issuer defaults on interest or principal payments, the investor will not earn the original yield (yield at the time the bond was purchased).<br />
<br />
Investors usually demand higher yields for bonds with longer terms to maturity. Although the investor will receive face value for the bond at maturity, assuming no default, that may not be the case if the bond is sold before maturity. The longer the term to maturity, the longer the investor must bear the uncertainty of having to sell before maturity and receive a price other than face value. Also, the longer the term to maturity, the higher the uncertainty of the impact of unexpected inflation on the purchasing power of the bond's interest and principal payments.<br />
<br />
A standard benchmark for bond yields for different terms to maturity are the yields of U.S. Treasuries, published by the U.S. Department of the Treasury. You can find the latest published yields as well as historical yields here: <a href="https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield">Daily Treasury Yield Curve Rates</a>. If you click on the link, you'll see yields for terms to maturity from 1 month to 30 years, and as of this writing you'll see that yield increases as term to maturity increases, which is typical. For example, yields on the 1-year, 5-year and 10-year Treasuries as of December 29, 2016 are 0.85%, 1.96% and 2.49% respectively.<br />
<br />
Incidentally, the U.S. Treasury Department uses the terms <i>bills</i>, <i>notes </i>and <i>bonds</i> to refer to U.S. Treasuries of maturities of up to 1 year, 1-10 years, and more than 10 years respectively. This distinction is not particularly useful for our purposes, since the bond basics being discussed in this series are the same for all of them. It is common to refer to a Treasury security as simply a <i>Treasury</i>, whether referencing a bill, note or bond, but I also will use the generic term <i>bond</i> to refer to all of them.<br />
<br />
Since U.S. Treasuries generally are considered to have no default risk, the Treasury yield curve gives us insight into the term risk the bond market is assessing for different terms to maturities. The degree to which longer-term Treasuries have higher yields is referred to as the steepness of the yield curve.<br />
<br />
With this background, we can now start to understand the imprecision of simply saying that bond prices fall when interest rates rise, or vice versa. First let's look at this just from the perspective of term to maturity, and consider U.S. Treasuries since they have no default risk.<br />
<br />
Yields on Treasuries of different maturities change every day, and they change by different amounts. The price of a Treasury of a given term to maturity is directly related to the yield of that Treasury, but not necessarily related to the yield of a Treasury of a different term to maturity. For example, looking at the current <a href="https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield" target="_blank">Treasury yield curve</a>, we see that between December 28 and 29 of 2016, the yield of the 6-month Treasury did not change at all--it was 0.62% on both days--but the yield on the 5-year Treasury fell by 6 <a href="https://www.google.com/search?q=basis%20point&rct=j" target="_blank">basis points</a>--from 2.02% to 1.96%. So the price of the 5-year Treasury increased due to the decrease in the 5-year yield, but the price of the 6-month Treasury did not change since its yield did not change.<br />
<br />
Although over long time periods, yields of all maturities tend to move up and down together, over shorter time periods this is not necessarily the case, since the yield curve can steepen or flatten as yields for different maturities change at different rates and even in different directions. This is an example of why it is imprecise to simply refer to bond prices falling due to interest rates rising, or vice versa.<br />
<br />
For non-Treasury bonds, such as corporate and municipal bonds, the bond market's changing assessment of credit risk also can cause changes in yields. For example, the yield on a certain 5-year corporate bond could increase or decrease on a day when the 5-year Treasury yield did not change, resulting in a change in price for the 5-year corporate bond but no change in price for the 5-year Treasury. This is another example of why we can't accurately specify the relationship between bond prices and interest rates (yields) without specifying which bond or bonds we're talking about.<br />
<br />
In the example in Part 2 of this series, I used a bond with a 1-year term to maturity to explain the inverse relationship between price and yield for a particular bond. In this part I've explained that prices and yields of bonds with different terms to maturity and different default risks can change by different amounts and even in different directions. So although the relationship between price and yield for a particular bond is mathematically precise, there is no such precise relationship between bond prices and yields (or interest rates) in general.<br />
<br />
In the next part of this series I'll start getting into more advanced bond topics, such as the mathematical formula that determines the relationship between bond price and bond yield.</div>
Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-775967109474059335.post-53542384832570003112016-12-28T17:56:00.000-08:002016-12-28T17:56:17.864-08:00Bond Basics: Part 2<div dir="ltr" style="text-align: left;" trbidi="on">
In <a href="http://www.kevinoninvesting.com/2016/12/bond-basics-part-1.html" target="_blank">Part 1</a> of this series I described how a bond is basically a loan, or more precisely, the contract defining the terms of a loan, where you are the lender and a company or government entity is the borrower. I explained that the terms of this loan contract, or bond, include the principal amount, referred to as the face value, an interest rate, referred to as the coupon rate, a payment schedule for the coupon payments, typically every six months, and a due date for the final coupon payment and repayment of principal, referred to as the maturity date.<br />
<br />
Toward the end of Part 1 I introduced the concept of yield to maturity (YTM), often simply referred to as <i>yield</i>. A bond's yield incorporates both the coupon rate and the change in bond price between the day you buy the bond and the day the bond matures. A bond's yield provides a reasonable measure of the rate of return you can expect for a bond held to maturity. I explained that the market price of a bond may be different than the face value of the bond, that bond yield is inversely related to bond price, and said that I would explain all of this with an example in Part 2. Read on for the explanation.<br />
<br />
<a name='more'></a>As explained in Part 1, although bonds typically are sold in increments of $1,000, bond prices are quoted as a percent of face value (also referred to as <i>par value</i>, or simply <i>par</i>). So in the examples that follow, when I say you pay 100 for a bond, or that a bond's price is 100, it means that the bonds price is 100% of face value, or $1,000 per bond. Similarly, a bond price of 99 means that the bond's price is 99% of par, or $990 per bond, and a price of 101 means that the bond's price is 101% of par, or $1,010 per bond.<br />
<br />
Say you buy a bond today at par value, with a coupon rate of 1%, that matures in one year. At issuance this bond has a price of 100, and it also will have a price of 100 at maturity; i.e., you will get back the same amount of principal that you paid for the bond. So for every $100 of bond value that you buy, you will receive $1 in interest, in the form of coupon payments (1% of $100 equals $1), and at maturity you also will receive the principal amount of $100. At issuance the yield (YTM) of the bond also is 1%; since you paid 100 for the bond, and the price at maturity also is 100, the coupon rate of 1% comprises the entire rate of return for the bond--there is no price change to factor into the yield.<br />
<br />
We can generalize the information in the previous paragraph, and say that for a bond priced at par (or simply <i>a par bond</i>), the yield equals the coupon rate. However, a bond priced above or below par will have a yield that is lower or higher than the coupon rate. Here's how this works.<br />
<br />
Say that the day after you buy the 1-year par bond with the 1% coupon rate, the coupon rate on new 1-year bonds bought at face value increases to 2%. The buyer of that bond will earn $2 in coupon payments for every $100 of bond value, so the yield also is 2%. Since investors can now earn 2% in one year by buying this new bond, no one would pay you 100 for your bond with a coupon payment of only 1%. They will pay you an amount that equalizes the rate of return, or yield, for the two bonds.<br />
<br />
Your bond pays only 1% in coupon payments, but an investor will only pay you a price for the bond that will give them a 2% return over the one year until maturity. Since they need an extra 1% in return to give them the same 2% return they can get on the new bond with the 2% coupon rate, the price of your bond will fall by about 1% to about 99.<br />
<br />
Now someone who buys your bond for about 99 will earn 1% in coupon payments and 1% in price appreciation (since the bond will mature at 100), giving them the same 2% <a href="https://www.google.com/search?q=total%20return&rct=j" target="_blank">total return</a> at the end of one year. The yield of both bonds is 2%; the new bond pays the 2% return through the 2% in coupon payments, and your bond pays the 2% return through 1% in coupon payments and 1% in price appreciation.<br />
<br />
Here we see that when the 1-year-bond <b>yield </b><b>increased, </b>the existing 1-year-bond <b>price decreased. </b>The price of the existing bond decreased by an amount that caused the yield to increase to the new market rate of 2%, so that buyers of either the new bond or the existing bond would earn the same rate of return.<br />
<br />
We can use similar reasoning to work out the approximate <b>price increase </b>for a one percentage point <b>yield decrease</b> in a 1-year bond, from 1% to 0%. If the one-year <b>yield decreased </b>to 0% the day after you bought your bond with the 1% coupon rate, your bond <b>price would increase</b> to about 101. Your bond would earn 1% in coupon payments and lose 1% in price depreciation, earning the same 0% as the buyer of the new bond with a coupon rate of 0%. The price of your 1% coupon bond increased so that the yield is 0%, the same as the 0% yield of the new bond with the 0% coupon rate.<br />
<br />
This brings us full circle to the observation I shared in Part 1, which was that a <a _blank="" href="http://www.usfinancialcapability.org/downloads/NFCS_2015_Report_Natl_Findings.pdf" style="background-color: white; color: #6e7abb;">National Financial Capability Study</a> found that only 28% of American adults understand the relationship between interest rates and bond prices. Here is the question as it was asked in the study:<br />
<br />
<b><i>If interest rates rise, what will typically happen to bond prices? Rise, fall, stay the same, or is there no relationship?</i></b><br />
<br />
Hopefully you are now in the 28% of American adults that can correctly answer, "Fall". Here is the explanation provided in the <a href="http://www.usfinancialcapability.org/quiz.php" target="_blank">online quiz</a> that asks the questions asked in the study:<br />
<br />
<b><i>When interest rates rise, bond prices fall. And when interest rates fall, bond prices rise. This is because as interest rates go up, newer bonds come to market paying higher interest yields than older bonds already in the hands of investors, making the older bonds worth less.</i></b><br />
<br />
The example in this post went through some simple bond math that explains this. However, the question and answer in the study and online quiz are not very precise, and don't really accurately describe the relationship between bond prices and bond yields. The reason is that there are many different interest rates in our economy, and the only interest rate relevant to the price of a particular bond is the yield of bonds that are similar to the bond in question. I'll discuss this in more detail in Part 3 of this series.</div>
Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-775967109474059335.post-43390321013288813992016-12-22T13:41:00.000-08:002016-12-22T13:41:53.255-08:00Bond Basics: Part 1<div dir="ltr" style="text-align: left;" trbidi="on">
One of Warren Buffett's famous maxims is, "Never invest in a business you cannot understand." I would expand on this to say that you shouldn't invest in <b>anything</b> you don't understand. An annual <a href="http://www.usfinancialcapability.org/downloads/NFCS_2015_Report_Natl_Findings.pdf" target="_blank">National Financial Capability Study</a> has found that only 28% of American adults understand the relationship between interest rates and bond prices, yet bonds comprise one of the major asset classes that most investors own. My goal in this blog post series is to aquaint you with the basics of bonds so that you can make informed decisions about including bonds in your investment portfolio.<br />
<br />
<a name='more'></a>If you own bonds, you probably own them in the form of a bond mutual fund (or simply <i>bond fund)</i>, which basically is a collection of individual bonds. It's easier to understand an individual bond than a bond fund, so I'll start with the basics of individual bonds.<br />
<br />
A bond is basically a loan in which you are the lender, and a corporation or government entity is the borrower. You probably are more familiar with a loan in which you are the borrower and a bank is the lender, such as a car loan, student loan, or home mortgage, but a bond basically is the same thing in reverse. From the bank's perspective the loan you get from it is a bond. The bank may even sell this loan to another entity who then packages your loan with other loans, and then sells the package as a special type of bond known as a <a href="https://www.google.com/search?q=mbs&oq=mbs&ie=UTF-8" target="_blank">mortgage backed security (MBS)</a> or <a href="https://www.google.com/search?q=mbs&oq=mbs&ie=UTF-8#q=asset+backed+security" target="_blank">asset backed security (ABS)</a>.<br />
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When you want to borrow money you typically borrow it from a bank. When a government or company wants to borrow money they may do so by selling (issuing) bonds to investors. One of the biggest borrowers (sellers/issuers of bonds) is the US government; the US Treasury held 272 public auctions to sell bonds in 2015.<br />
<br />
To define it more precisely, a bond is a contract that defines the terms of a loan. Historically bonds were issued as paper certificates that stated the terms of the loans, and the lender received this certificate in exchange for lending money to the bond issuer. Of course now all of this is handled electronically.<br />
<br />
Any loan has terms that specify a principal amount, which is the amount originally borrowed, an interest rate, a payment schedule, and a date by which the loan must be repaid in full. This is true for bonds as well, but bonds have their own language to describe these characteristics.<br />
<br />
With a typical loan, each payment consists of interest plus a repayment of a small portion of the principal, but this isn't always the case. There also are interest-only loans, where you make only interest payments, and then pay back all the principal on the due date. A typical bond is more like an interest-only loan.<br />
<br />
For a bond, the principal amount is called the <i>face value</i>. When bonds were issued in paper form, this was the value that was printed on the face of the bond. Another term used for this is <i>par value</i> or simply <i>par</i>.<br />
<br />
Bonds typically are sold in increments of $1,000, so the face value of one bond typically is $1,000. However, bond prices typically are quoted as a percent of face value (percent of par). So when the bond is initially sold at face value its price would be quoted as 100, which means 100% of face value. A bond price of 99 would mean that the bond's market value is $990, or 99% of the $1,000 face value, and a bond price of 101 would mean that the bond's market value is $1,010, or 101% of $1,000. In the next post in this series, I'll explain why market value can be different than face value.<br />
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The payment due date for a bond is called the <i>maturity date</i> or simply <i>maturity</i>, and the amount of time left until maturity is called the <i>term to maturity, </i>or simply <i>term. </i>Bonds sometimes are referred to using term to maturity, so a 5-year bond is a bond with five years remaining until maturity.<br />
<br />
The annual interest rate for a bond is called the <a href="https://en.wikipedia.org/wiki/Coupon_(bond)" target="_blank">coupon</a> rate, and interest payments are called <i>coupon payments</i> or simply <i>coupons</i>. Historically coupons were printed on the bond, and were detached (or <i>clipped</i>) and presented to collect the interest when it was due. Of course now all of this is handled electronically. So a bond with a face value of $1,000 and a coupon rate of 2% will pay $20 per year in interest, since 2% of $1,000 equals $20.<br />
<br />
The loans you are familiar with typically have monthly payments, but a bond typically pays interest every six months, with the full principal amount due at maturity (again, like an interest-only loan). So our example bond with a face value of $1,000 and a coupon rate of 2% would issue a coupon payment of $10 every six months for a total of $20 in interest each year.<br />
<br />
If you own a bond fund, you might be thinking, "But my bond fund pays monthly dividends." This is true, but it's also true that the individual bonds held by the bond fund typically pay interest every six months. The bond fund holds many bonds with coupon payments on different dates, and they distribute these interest payments monthly in the form of dividends.<br />
<br />
In addition to buying bonds directly from the issuer, such as from the US Treasury through one of the US Treasury auctions, bonds also are bought and sold after issuance in the <a href="https://en.wikipedia.org/wiki/Secondary_market" target="_blank">secondary bond market</a>. The price of a bond will vary due to changing interest rates and declining term to maturity, which I'll explain in the next blog post in this series, so in addition to a face value, a bond has a market value which could be lower or higher than the face value.<br />
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In addition to coupon rate, bonds also are characterized by their yield to maturity (YTM), which factors in the difference between the market price and the face value of a bond to provide a more meaningful measure of the <a href="https://en.wikipedia.org/wiki/Rate_of_return" target="_blank">rate of return</a> a bond holder will receive if the bond is held to maturity. The YTM of a bond often is referred to simply as the <i>yield</i> of the bond, so if the term <i>yield </i>is used in reference to a bond, it's usually the YTM that's being referenced.<br />
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At maturity the bond holder collects the face value of the bond. If the market price of the bond is less than face value, the yield to maturity will be higher than the coupon rate. This incorporates the price appreciation the investor will receive into the rate of return, or yield, of the bond. Similarly, if the market price of the bond is greater than the face value, the YTM will be less than the coupon rate, since this incorporates the price depreciation into the rate of return, or yield, of the bond.<br />
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So YTM (or simply yield) incorporates both the coupon rate and the price appreciation or depreciation to provide a meaningful rate of return for a bond held to maturity. As explained in the previous paragraph, yield and market price are inversely related--when one is higher the other is lower. But why would the market price of a bond be different than the face value? This is best explained with an example, which I'll provide in Part 2 of this series.<br />
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<br /></div>
Unknownnoreply@blogger.com5tag:blogger.com,1999:blog-775967109474059335.post-21934049112868668392016-11-04T14:31:00.000-07:002016-11-04T16:34:09.959-07:00Calculating Required Retirement Savings Rates: Part 5<div dir="ltr" style="text-align: left;" trbidi="on">
In <a href="http://www.kevinoninvesting.com/2016/10/calculating-required-retirement-savings.html" target="_blank">Part 1</a> of this series on calcluating required retirement savings rates, I stated this assumption:<br />
<ul>
<li>The remainder of your retirement living expenses will be covered by annual, inflation-adjusted withdrawals of 4% of your retirement savings.</li>
</ul>
In this post I'll explain what this means, evaluate whether or not this assumption is reasonable, and discuss a few different ways to think about this.<br />
<br />
<a name='more'></a>The statement about the 4% withdrawal rate can be interpreted in different ways, but the most common interpretation is that you withdraw an inflation-adjusted 4% of your <b>original </b>retirement savings each year. So if you had $1,000,000 of retirement savings when you first retired, your withdrawal in the first year would be $40,000 (4% x $1M). If inflation was 2% in your first year of retirement, your withdrawal in the second year would be $40,800 (1.02 x $40,000), regardless of the size of your portfolio at the beginning of year two. The purpose of withdrawing a constant, inflation-adjusted amount is to allow you to maintain a similar lifestyle throughout retirement, regardless of the change in purchasing power of your dollars due to inflation.<br />
<br />
This approach for retirement income planning is widely used and written about by financial planners. The approach has its origins in studies published by various financial planners and academics in the 1990s. These studies showed that this approach would have enabled a balanced portfolio of US stocks and bonds to have survived the worst 30-year period since 1926. In other words, 4% would have been a safe withdrawal rate (SWR) for a 30-year retirement starting in any year since 1926, and you would not have run out of money even if you retired at the beginning of the worst 30-year period of real returns for stocks and bonds. At least 50% of the retirement portfolio had to be in stocks; failure rates were higher at lower stock allocations.<br />
<br />
A second school of thought about retirement planning is that it is imprudent to rely on historical stock and bond returns for retirement planning purposes, and that you should not depend on returns from risky assets, like stocks, for retirement income. Instead, you should either keep your retirement savings in safe assets, or purchase an annuity that guarantees a set level of income for life. Of course the safe assets or annuity should ideally be inflation protected.<br />
<br />
In Part 1 of this series I explained that an initial withdrawal rate of 4% implies that your initial retirement savings equals 25 years of residual retirement expenses (retirement expenses not covered by Social Security benefits or a pension). This means that if you earned a steady 0% real return in safe assets, and withdrew an inflation-adjusted 4% annually, you would run out of money in 25 years. What real rate of return on safe assets would be required for the portfolio to last 30 years? We can answer this with the following spreadsheet RATE formula:<br />
<br />
=RATE(30, 4, -100, 0)<br />
<br />
In this formula, 30 is the number of years, and you can interpret the 100 as 100% of your retirement savings at the beginning of the 30-year period, the 0 as 0% of your retirement savings at the end of the 30-year period, and the 4 as a withdrawal rate of 4% per year. This formula returns 1.2% as the required real rate of return (you can copy the formula and paste it into a Google Sheets or Excel spreadsheet to verify it for yourself).<br />
<br />
You can change the number of years in the formula to determine the required real rate of return to support different length retirements. Plugging in 25 as the number of years gives a required real return rate of 0%, as expected. Plugging in 40 years gives a required real return rate of 2.5%. What guaranteed, real rate of return can you earn in the current economic environment with historically low interest rates?<br />
<br />
The only investments I know of that guarantee a real (inflation-adjusted) rate of return for US investors are TIPS (Treasury Inflation Protected Securities). You can look up the current TIPS interest rates (yields) here: <a href="https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=realyield">Daily Treasury Real Yield Curve Rates</a>. Currently I see a rate of 0.75% for the 30-year TIPS, with lower rates for shorter maturities, and negative real rates for maturities of 7 years or less. So currently you cannot earn even 1% real with TIPS, which means that you cannot count on TIPS for a 30-year retirement at a 4% withdrawal rate.<br />
<br />
Just as we easily calculated that a 0% real rate of return would support a 25-year retirement at a 4% withdrawal rate (since 1/25 = 4/100 = 4%), we can easily calculate the withdrawal rate that will support a 30-year retirement at a 0% real rate of return as 1/30 = 3.33/100 = 3.33%. We can verify this with the spreadsheet PMT formula:<br />
<br />
=PMT(0%, 30, -100, 0)<br />
<br />
This returns a value of 3.33, which we can interpret as the expected 3.33% withdrawal rate. We can replace the 0% in the formula with different return rates to determine withdrawal rates that would support a 30-year retirement. For example, assuming we could earn an average real rate of 0.5% from a 30-year TIPS ladder, with one TIPS maturing each year to cover our residual living expenses. we can use this formula to calculate the withdrawal rate<br />
<br />
=PMT(0.5%, 30, -100, 0)<br />
<div>
<br /></div>
<div>
This returns 3.6, which we can interpret as a 3.6% withdrawal rate. We already used the spreadsheet RATE formula to determine that a 1.2% real rate of return would support a 30-year retirement at a 4% withdrawal rate, and we can plug 1.2% into the PMT formula to verify this; it returns 4.0 as expected.</div>
<div>
<br /></div>
<div>
Of course to support longer retirements requires either lower withdrawal rates or higher rates of return. For example, to retire at age 50 with the expectation of living until age 90, we could use this PMT formula to determine the supported withdrawal rate for 40 years at a 0.5% real rate of return:</div>
<div>
<br /></div>
<div>
=PMT(0.5%, 40, -100, 0)</div>
<div>
<br /></div>
<div>
This formula returns 2.8, which we can interpret as a 2.8% withdrawal rate. This means that with an initial retirement savings amount of $1,000,000, residual living expenses would be funded with annual retirement savings withdrawals of $28,000, adjusted for inflation.</div>
<div>
<br /></div>
<div>
The conclusion is that using only safe assets for retirement income for a 30-40 year retirement implies safe withdrawal rates of closer to 3% than 4%.</div>
<div>
<br /></div>
<div>
Some financial planners and investment experts suggest that with current, historically low real interest rates, it is imprudent to assume that even a balanced portfolio of stocks and bonds will support the historically-justified 4% safe withdrawal rate, and that it is more prudent to use something like 3% as a safe withdrawal rate for retirement planning purposes. So although I used a 4% withdrawal rate in the calculations in the prior posts in this series, it may be prudent to re-run the savings calculations with a 3% withdrawal rate, which will result in higher required savings rates.<br />
<br />
As an example, let's consider a 25-year old earning a constant, inflation-adjusted salary of $60,000, retiring at age 65, and earning a real return of 4% during the working years. Assuming $20,000 of annual Social Security benefits in today's dollars, at a retirement savings safe withdrawal rate (SWR) of 4% I calculate a required savings rate of about 14%. Lowering the SWR to 3% increases the required savings rate to about 17%.</div>
</div>
Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-775967109474059335.post-28571846651311774722016-10-15T13:27:00.002-07:002016-10-15T16:36:21.763-07:00Calculating Required Retirement Savings Rates: Part 4<div dir="ltr" style="text-align: left;" trbidi="on">
In the prior posts in this series I outlined a method for estimating <a href="http://www.kevinoninvesting.com/2016/10/calculating-required-retirement-savings.html" target="_blank">how much you should be saving for retirement</a>, discussed how to <a href="http://www.kevinoninvesting.com/2016/10/calculating-required-retirement-savings_4.html" target="_blank">estimate expenses in retirement</a>, and discussed how to <a href="http://www.kevinoninvesting.com/2016/10/calculating-required-retirement-savings_6.html" target="_blank">estimate your Social Security retirement benefit</a>. In this post I'll discuss how to estimate a reasonable range for real rates of return on your investments. There's a lot of uncertainty in the rate of return you'll be able to earn on your investments over the next 30 or 40 years, yet that rate of return has significant impact on how much you must save. The lower the rate of return, the more you must save, and vice versa. In the prior posts in the series I assumed a 4% real rate of return. Is that reasonable?<br />
<br />
<a name='more'></a>We can estimate a lower bound for the range of long-term real rates of return by looking at the yield on the 30-year Treasury Inflation Protected Security (TIPS). TIPS yields are by definition real yields, since you will receive the stated yield plus adjustments of principal and interest based on the inflation rate. For TIPS and other Treasury bonds held to maturity, the yield is a very good approximation of rate of return, with the only uncertainty being the rates at which you can reinvest the interest payments. I'm using the term "yield" here to mean yield to maturity (YTM).<br />
<br />
The yield on the 30-year TIPS as of 10/13/2016 was 0.71% (<a href="https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=realyield" target="_blank">Daily Treasury Real Yield Curve Rates</a>), so assuming that you can reinvest your interest payments at the same real yield of 0.71%, you're real rate of return over the 30-year holding period will be 0.71%. This is as close as you can get to a risk-free 30-year rate of return for money invested today.<br />
<br />
To put this real yield of 0.71% into perspective, the (nominal) yield on the 30-year nominal Treasury bond on 10/13/2016 was 2.48% (<a href="https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield" target="_blank">Daily Treasury Nominal Yield Curve Rates</a>). The difference between the nominal yield and the real yield, 1.77% (2.48% - 0.71%), is referred to as the breakeven inflation rate, and can be viewed as an approximation of the bond market's estimation of the average inflation rate over the next 30 years. If average inflation over the next 30 years is 1.77%, then the TIPS and nominal Treasury bonds will have the same real return of about 0.71% (and same nominal return of about 2.48%). TIPS will earn a higher return if average inflation is higher than 1.77% over the next 30 years, and nominal Treasury bonds will win if average inflation is lower than 1.77%.<br />
<br />
The 0.71% expected real return of the 30-year Treasury is quite a bit lower than the 4% real return I assumed in the prior posts in this series. Before discussing why using a higher assumed real return could make sense, let's look a little more into the 30-year TIPS yield.<br />
<br />
The yield I'm quoting is a good estimate of the real return you'd earn for a TIPS bought today, but if you are 25 and plan to retire at 65, you would be buying TIPS or other investments over the next 40 years. We can look at historical 30-year TIPS yields to get a sense of the range of yields we might expect.<br />
<br />
Looking at <a href="https://fred.stlouisfed.org/graph/?g=7Jpj" target="_blank">this chart</a> of historical 30-year TIPS yields from the Federal Reserve Economic Database (FRED), we see a high yield of about 2.3% in 2010. We also see that the yield was above 1.3% as recently as December 2015, and above 1.6% as recently as December 2013. FRED has <a href="https://fred.stlouisfed.org/graph/?g=7JH1" target="_blank">another 30-year TIPS series</a> that allows us to look at yields as far back as 1998, shortly after TIPS were introduced, and we can see real yields above 4%.<br />
<br />
So a conservative estimate for long-term TIPS yields in the coming years might be about 1%, with perhaps about 2% being somewhat more optimistic.<br />
<br />
What happens if we plug the conservative estimate of 1% real return into our savings rate spreadsheet? Using our 25-year old earning $50,000 annually, planning to retire at age 65, with an estimated Social Security benefit of $19,020/year (from <a href="http://www.kevinoninvesting.com/2016/10/calculating-required-retirement-savings_6.html" target="_blank">Part 3</a>), and assuming a 4% safe withdrawal rate in retirement, I calculate a required savings rate of about 21% of pre-tax income. This is much higher than the 13% required savings rate calculated assuming a real rate of return on investments of 4%.<br />
<br />
Repeating the calculation for the higher annual income of $100,000 with an estimated annual Social Security benefit of $27,276 (from Part 3), I calculate a required savings rate of almost 25% of pre-tax income. Again, this is much higher than the required savings rate of 15% calculated assuming a 4% real rate of return.<br />
<br />
So to have much hope of retiring comfortably while saving only about 15% (instead of 20-25%) of your annual income starting at age 25, you have to take some risk to shoot for higher return. This requires owning stocks, which have higher expected returns and much more risk than safe TIPS. How can we estimate expected returns for stocks?<br />
<br />
In his short booklet <a href="https://dl.dropboxusercontent.com/u/29031758/If%20You%20Can.pdf" target="_blank"><i>If You Can</i></a> (which you definitely should read), William Bernstein explains that long-term stock returns can be estimated as the sum of the current dividend yield and the long-term, real dividend growth rate of about 1.5%. The dividend yield is about 2% for US stocks and about 3% for international stocks. So this gives an estimated, expected real return of about 3.5% for US stocks and 4.5% for international stocks. Using this estimation approach, a portfolio of 100% stocks split evenly between US and international has an estimated expected return of about 4%, which is the value I used in the prior posts in this series.<br />
<br />
(The link provided above links to a PDF version of <i>If You Can</i>, which Bernstein kindly makes available for free. If you'd like the convenience of reading a Kindle version, you can <a href="https://smile.amazon.com/If-You-Can-Millennials-Slowly-ebook/dp/B00JCC5JKI?sa-no-redirect=1" target="_blank">purchase it from Amazon</a> for the princely sum of $0.99).<br />
<br />
These return estimates may seem lower than values you may have read about elsewhere. Here are several things to keep in mind related to these estimates.<br />
<br />
The historical, long-term real return of US stocks has been about 7%, but the average dividend yield for US stocks has been much higher, about 4.4%, than the current dividend yield of about 2%. Since dividends have contributed a significant portion of the historical return, it seems reasonable to lower our return expectations going forward. Here's a useful tool to review historical returns for US stocks: <a href="http://politicalcalculations.blogspot.com/2006/12/sp-500-at-your-fingertips.html" target="_blank">Political Calculations: The S&P 500 at Your Fingertips</a>.<br />
<br />
The figures calculated using Bernstein's approach are expected returns, not guaranteed returns. There is quite a bit of uncertainty that the realized returns will match these estimates of expected returns. In researching this, I found <a href="http://raddr-pages.com/research/gordon.htm" target="_blank">this paper</a>, which I think does a pretty good job of demonstrating the uncertainty in using this approach.<br />
<br />
If you are like most people, you probably will not want to hold a portfolio of 100% stocks until you retire. Including some bonds in your portfolio will lower your expected return. If we assume that your portfolio consists of 1/3 each of US stocks, international stocks, and bonds, as recommended by Bernstein in his booklet, and if we use Bernstein's estimated real returns for stocks and a conservative estimate of 1% for the expected real return of bonds, the estimated portfolio expected real return is 3% (1/3 x 3.5% + 1/3 x 4.5% + 1/3 x 1%).<br />
<br />
So here we've seen estimates for long-term, expected real returns of anywhere from 1% to 7%, depending on the riskiness of one's portfolio and one's optimism or pessimism about future returns. The safest course is to have a very high savings rate and invest conservatively, but many people will find it difficult if not impossible to save 25% of their income for retirement. Most people will have to take more risk to have a shot at a decent retirement, so will want to have a healthy allocation to stocks, especially when young. Combine this with fairly conservative estimates about future returns, and the resulting required savings rate is likely to work out well for you.<br />
<br />
As discussed in <a href="http://www.kevinoninvesting.com/2016/10/calculating-required-retirement-savings.html" target="_blank">Part 1</a>, I've been using a safe withdrawal rate (SWR) of 4% in the required savings rate calculations. In Part 5 I'll discuss whether or not this SWR is reasonable, and explore the impact of different SWR assumptions.</div>
Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-775967109474059335.post-1598757318929075552016-10-06T17:43:00.000-07:002016-10-06T17:51:55.178-07:00Calculating Required Retirement Savings Rates: Part 3<div dir="ltr" style="text-align: left;" trbidi="on">
In <a href="http://www.kevinoninvesting.com/2016/10/calculating-required-retirement-savings.html" target="_blank">Part 1</a> of this series I outlined a method for estimating how much you need to save to have a good shot at a financially secure retirement. I put this in terms of a retirement savings rate, calculated as your required annual savings divided by your gross (before tax) annual income. For example, if your gross annual income is $50,000 and you estimate that you must save $7,500 annually, your required savings rate is 15% (7,500 / 50,000).<br />
<br />
In <a href="http://www.kevinoninvesting.com/2016/10/calculating-required-retirement-savings_4.html" target="_blank">Part 2</a> I discussed how to estimate living expenses in retirement, and gave a few examples of how this affects the retirement savings calculations. In this post I'll discuss how to estimate your Social Security retirement benefit, since this can have a significant impact on how much you need to save for retirement.<br />
<br />
<a name='more'></a>The <a href="https://www.ssa.gov/" target="_blank">Social Security Administration (SSA) website</a> provides several ways to estimate your Social Security retirement benefits. The best thing to do is to create a "<a href="https://www.ssa.gov/myaccount/" target="_blank"><i>my</i> Social Security</a>" account, which you can use to get customized benefits estimates whenever you want. This enables you to easily use your actual earnings history to estimate your benefits.<br />
<br />
The SSA website also provides a variety of <a href="https://www.ssa.gov/planners/benefitcalculators.html" target="_blank">calculators</a> you can use to estimate retirement benefits and other related things. These calculators do not require creating a <i>my </i>Social Security account, but some of them either access your earnings record or allow you to enter detailed earnings.<br />
<br />
To get some rough estimates of Social Security benefits for purposes of illustration, we can use the Social Security retirement benefit <a href="https://www.ssa.gov/OACT/quickcalc/index.html" target="_blank">Quick Calculator</a>. I'll start by using this calculator for our hypothetical 25-year-old with an annual income of $50,000 who plans to retire at age 65. You might learn more if you click the <a href="https://www.ssa.gov/OACT/quickcalc/index.html" target="_blank">Quick Calculator</a> link and follow along by entering the numbers yourself.<br />
<br />
I make the following entries into the <a href="https://www.ssa.gov/OACT/quickcalc/index.html" target="_blank">Quick Calculator</a>:<br />
<ul style="text-align: left;">
<li>Birth date: 10/6/1991. This is 25 years before today. </li>
<li>Current salary: $50,000. </li>
<li>Last year and amount of covered earnings: 2016 and $50,000</li>
<li>Month and year of retirement: 10 and 2056. This is 40 years from now. </li>
<li>Leave the default of "today's dollars" selected for the benefit estimate, because we are calculating our retirement savings numbers in real dollars (which is the same as today's dollars). </li>
</ul>
Then I click Submit request, and a results page is displayed that says my estimated monthly benefit amount is $1,585 (in today's dollars).<br />
<br />
I also see a button labeled "See the earnings we used", so I click it. On the earnings page I see that some earnings were assumed starting in 2009, when I would have been age 18. There are other things you can do on this page to change the assumptions, but for now I'll just delete the earnings before 2016 to see what the impact is. I leave the default "Enter the amounts you want to change ...", delete all earnings before 2016, then click "Submit earnings information".<br />
<br />
There is no change in the benefit estimate of $1,585 per month. This is because the Social Security retirement benefit is based on the 35 years with the highest earnings, so years before 2016 aren't included. This also means that even though the benefit calculation assumes no earnings in the year of retirement, the retirement benefit would be the same if earnings in the retirement year were included, since the earnings over the 35-year period used in the benefit calculation would be the same.<br />
<br />
I multiply by 12 to get an annual benefit amount of $19,020 (1,585 x 12). This is is 38% of my assumed annual earnings of $50,000.<br />
<br />
In Parts 1 and 2, I assumed an annual Social Security retirement benefit of only $14,000, so based on the calculator, this estimate is too low. However, some people are pessimistic that they'll actually receive the full benefit, with SSA itself warning that only 79% of the estimated benefit will be covered by payroll taxes by 2034. If we are slightly more pessimistic, and assume only 75% of the benefit will be received, we get $14,265 (19,020 x 0.75), which I rounded down to $14,000.<br />
<br />
You can make any assumptions you want to develop estimates for different scenarios. Personally I think that laws will be changed to keep Social Security solvent, and able to pay 100% of estimated benefits beyond 2034. Changes could include increasing the cap on salary that is subject to Social Security tax, increasing the Social Security tax rate, and increasing full retirement age. Legislative changes like this have been made in the past, which is why, for example, full retirement age for people born in 1967 or later is 67, while it was age 65 for those born in 1937 or earlier (see <a href="https://www.ssa.gov/planners/retire/agereduction.html" target="_blank">this chart</a> to determine your full retirement age).<br />
<br />
As a more recent example, legislation was passed last year that reduces the amount of benefits that a married couple can receive by using certain claiming strategies (this actually affects my spouse and me, reducing the benefits we could have received before the change). Note however that this legislation has no impact on the Social Security benefit of each person based on their own earnings, so it would not affect the calculations we're doing here.<br />
<br />
Now let's rerun the <a href="https://www.ssa.gov/OACT/quickcalc/index.html" target="_blank">Quick Calculator</a> assuming annual earnings of $100,000. We can do this quickly by clicking "See the earnings we used" on the SSA web page showing the estimated benefits we already generated, changing the 2016 earnings amount to $100,000, then clicking "Submit earnings information". This generates an estimated monthly retirement benefit of $2,273, which is an annual benefit of $27,276 (2,273 x 12). This is about 27% of our assumed $100,000 annual earnings (27,276 / 100,000).<br />
<br />
Note that a much smaller percentage of earnings is covered at $100,000 (27%) than at $50,000 (38%) of annual earnings. This is due to the progressive nature of the Social Security retirement benefit, which is intended to provide a higher percentage of replacement income for people who have lower incomes. If we rerun the calculation assuming annual earnings of $25,000, the estimated monthly benefit is $1,007, which is $12,084 per year--an even higher replacement income of about 48% (12,084 / 25,000).<br />
<br />
The implication is that people who make more money must save a higher percentage of their incomes to be able to maintain a comparable lifestyle in retirement, assuming that our other assumptions also are the same. Of course using the same assumptions for lower incomes and higher incomes may not be reasonable. For example, we saw in Part 2 that buying a home and paying off the mortgage before retirement can reduce the required retirement savings rate, and a higher income could make doing this more feasible.<br />
<br />
With these caveats in mind, let's redo the calculations we did in Part 1 for annual incomes of $50,000 and $100,000, using the retirement benefit estimates generated by the <a href="https://www.ssa.gov/OACT/quickcalc/index.html" target="_blank">Quick Calculator</a>.<br />
<br />
Plugging the estimated annual Social Security benefit of $19,020 for annual earnings of $50,000 into my spreadsheet, with a little trial and error I get a savings rate of about 13%. As expected, since we are assuming a higher Social Security retirement benefit, the calculated savings rate is slightly lower than the 14% we calculated in Part 1.<br />
<br />
Plugging the estimated annual Social Security benefit of $27,276 for annual earnings of $100,000 into my spreadsheet, with a little trial and error I get a savings rate of about 15%. This is a slightly higher rate than the 14% we calculated in Part 1, but in Part 1 we assumed that Social Security retirement benefit would cover 35% of our retirement living expenses regardless of income. By using the Quick Calculator, we've learned that our Social Security retirement benefit will be a smaller percentage of our annual earnings at higher incomes, and thus cover a smaller percentage of our retirement living expenses if we keep all other assumptions the same.<br />
<br />
Of course there are many other variables you can play with when it comes to Social Security. You can begin collecting retirement benefits as early as age 62, but will receive more the longer you delay, until age 70 at which point your retirement benefit reaches it's maximum value. If you can afford to do it, it's probably a good idea to wait as long as possible to start collecting your Social Security retirement benefit, since this provides you with about the best inflation-adjusted longevity insurance you can get; i.e., if you live longer than predicted by the expected-lifetime tables used by the Social Security Administration, you will be very happy that you're collecting a much larger monthly retirement benefit that is guaranteed to keep pace with inflation.<br />
<br />
In the next post in this series I'll discuss how to come up with a range of reasonable estimates for the real rate of return you can expect on your investments. The higher the rate of return, the lower the required savings rate, and vice versa.</div>
Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-775967109474059335.post-60051868957697017212016-10-04T10:34:00.001-07:002016-10-05T08:29:48.342-07:00Calculating Required Retirement Savings Rates: Part 2<div dir="ltr" style="text-align: left;" trbidi="on">
In <a href="http://www.kevinoninvesting.com/2016/10/calculating-required-retirement-savings.html" target="_blank">Part 1 of this series</a> I outlined how to estimate the savings rate required to ensure a financially secure retirement. The required savings rate estimate depends a lot on various projections and assumptions that I outlined in Part 1. In this post I'll discuss how to estimate your expenses in retirement. In subsequent posts in the series I'll discuss how to estimate your Social Security retirement benefits, how to estimate the expected rate of return on your investments, and how much you should expect to be able to safely withdraw from your retirement savings each year.<br />
<a name='more'></a><br />
Remember that we are doing these calculations in real dollars, and we're assuming that your income increases at the same rate as inflation from when you start saving at age 25 until you retire at age 65. So if your current annual income is $50,000, and we assume that your retirement expenses will be 80% of this, your annual retirement expenses will be $40,000 in real dollars.<br />
<br />
Here's quick refresher on the difference between real dollars and nominal dollars. In Part 1 I explained that at an annual average inflation rate of 2%, you multiply real dollars by about 2.2 to get the equivalent number of nominal dollars in 40 years. So your annual income in nominal dollars just before you retire in 40 years would be about $110,000 (2.2 x $50,000), and your estimated annual expenses in in nominal dollars in your first year of retirement would be about $88,000 (2.2 x $40,000, or 80% x $110,000) . In other words, you would see a gross year to date income of $110,000 on your last pay stub before you retired in 40 years, but this amount of nominal dollars would only have the purchasing power that $50,000 has today.<br />
<br />
So is 80% of your income a reasonable estimate for living expenses in retirement? It's a fairly common number used by financial planners. You can verify this by doing a Google search something like this: <a href="https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=+retirement+living+expense+80%25">retirement living expense 80%</a>. Reading some of the articles that come up in a search like this will give you some insight into how people come up with estimates for expenses in retirement.<br />
<br />
Why might your expenses be less in retirement than while working? One obvious reason is that you won't be saving for retirement once you retire. If we use the 14% savings rate we calculated in Part 1, you can subtract that, getting to 86% of income (100% - 14%). You may also have lower commuting costs, clothing costs, and other costs related to working, which could get you down to the 80% number.<br />
<br />
But this percentage can vary a lot, depending on costs that you have now that you won't have in retirement, or vice versa. If you have a mortgage that you plan to pay off before retiring, that will significantly reduce your expenses in retirement. If you plan to travel a lot or expect higher health care costs in retirement, that could significantly increase your retirement living expenses. So the best way to estimate your retirement living expenses is to work through the differences in your own living expenses before retirement and expected living expenses after retirement. If you find this too difficult, then you can just plug a range of numbers into the calculations to get a range of savings rates based on different assumptions. Let's do that.<br />
<br />
Let's say that you own your home and are spending 30% of your gross income on mortgage payments. This 30% figure does not include property taxes, insurance, and maintenance, since these expenses will continue after the mortgage is paid off. If you plan to pay off the mortgage before retiring, then your retirement spending will be reduced by 30% of gross income due to the elimination of the mortgage payment expense.<br />
<br />
We assume that you are able to to save enough for retirement, on top of the incremental expenses of home ownership (a challenge in itself). We'll calculate your required retirement savings rate assuming no other changes in retirement living expenses compared to pre-retirement living expenses, other than elimination of the mortgage expense and the expense of saving for retirement, while keeping all other assumptions the same.<br />
<br />
Since we haven't calculated the required savings rate yet, we don't know how much to reduce estimated retirement spending due to the elimination of the retirement saving expense, but with a spreadsheet set up to do the calculations, it's quite easy to use trial and error to quickly figure out the required savings rate. The required savings rate comes out to about 9%, with retirement living expenses at about 61% of pre-retirement living expenses (100% minus 30% mortgage expense minus 9% retirement savings expense). Let's run through the calculations like we did in Part 1 to check this.<br />
<br />
Assuming a real annual income of $50,000, our estimated real annual retirement living expense is $30,500 (61% x $50,000). In Part 1 we assumed that Social Security benefits would cover $14,000 of our annual retirement living expenses. We aren't changing any assumptions that affect estimated social security benefits, so we can subtract this same assumed annual Social Security benefit from our estimated annual living expenses to calculate our annual residual living expenses (RLE) of $16,500 ($30,500 - $14,000).<br />
<br />
As in Part 1, we are assuming that we can safely withdraw an inflation-adjusted 4% annually from our retirement savings to cover our annual RLE. In Part 1 we determined that this implies that we must accumulate 25 times our annual RLE before retiring. Thus we calculate that we must accumulate $412,500 (25 x $16,500) <b>in real dollars</b> before retirement.<br />
<br />
As in Part 1, we plug into the spreadsheet PMT function our assumed real rate of return of 4% on the investments that will generate our retirement savings, the 40 years between ages 25 and 65 that we will be saving, our current savings of $0, and the required amount of $412,500 that we must save:<br />
<br />
=PMT(4%, 40, 0, -412500)<br />
<br />
This PMT formula returns the required annual savings amount of $4,341, which is 8.7% of our assumed $50,000 annual income (4,341 / 50,000), and we can round this to approximately 9%, the required savings rate. So being able to buy a house and pay off the mortgage before retirement could lower the required savings rate from about 14% to about 9%, given our other assumptions.<br />
<br />
As a final example, let's calculate the required savings rate assuming that retirement living expenses will be 100% of pre-retirement living expenses, with all other assumptions the same. This basically means that you will be spending enough more on travel, medical care, and other retirement living expenses to offset any reductions, such as eliminating the retirement saving expense. For this scenario I calculate a required savings rate of about 19% of gross income. Let's check this.<br />
<br />
With post retirement living expenses at 100% of pre-retirement expenses, your RLE is $36,000 ($50,000 minus $14,000 in annual Social Security benefits). Multiplying by 25 (based on our 4% safe withdrawal rate assumption) gives $900,000 in required savings at retirement. Plug this into the PMT function:<br />
<br />
=PMT(4%, 40, 0, -900000)<br />
<div>
<br /></div>
<div>
The result is $9,471 in required annual savings, which is 18.94% of gross income (9,471 / 50,000), which we can round to 19%.</div>
<div>
<br /></div>
<div>
So with various assumptions about post-retirement spending as a percent of pre-retirement spending, we've come up with required savings rates anywhere from about 9% to about 19%. For a gross annual income of $50,000, this corresponds to real savings at retirement of anywhere from $412,500 to $900,000. Remembering that these are real dollars, we multiply by 2.2 to get nominal dollars in 40 years at 2% inflation, so you'd actually need to see values of your retirement accounts between $907,500 ($412,500 x 2.2) and $1,980,000 ($900,000 x 2.2).</div>
<div>
<br /></div>
<div>
Keep in mind that the savings rate calculations so far have been based on certain assumptions about Social Security retirement benefits, the real rate of return you can expect on your investments, and a safe withdrawal rate from your retirement savings. In Part 3 of this series I'll discuss how to come up with an estimate of your Social Security retirement benefit, since this is a key factor in determining your residual living expenses in retirement. In Part 4 I'll discuss how to evaluate reasonable estimates for the real rate of return on your investments, since this has significant impact on how much savings you'll end up with given a certain savings rate. In Part 5 I'll discuss the 4% safe withdrawal rate assumption. At least that's my plan.</div>
</div>
Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-775967109474059335.post-91123122588791295722016-10-01T14:54:00.000-07:002016-10-01T16:18:59.243-07:00Calculating Required Retirement Savings Rates: Part 1<div dir="ltr" style="text-align: left;" trbidi="on">
In <a href="http://www.kevinoninvesting.com/2009/12/college-graduate-first-job-how-to-get.html" target="_blank">one of my early blog posts</a>, written in December 2009 for recent college graduates , I wrote, "<span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px;">You must manage your spending so that you can save a significant portion of your income -- at least 10%, and more if possible." </span>How do we determine if 10% is enough, or could it even be more than you really need to save? Although there are too many unknowns to answer this precisely, we can make various assumptions to calculate a range of savings rates that are likely to enable you to enjoy a financially secure retirement.<br />
<br />
In this post I'll show how we can calculate that a savings rate of about 14% of gross (before-tax) income is required, given the following facts and assumptions:<br />
<ul style="text-align: left;">
<li>Current savings: $0.</li>
<li>Current age: 25.</li>
<li>Retirement age: 65.</li>
<li>A steady income with annual raises equal to the annual inflation rate.</li>
<li>A 4% annualized real rate of return on your investments.</li>
<li>Annual living expenses in retirement will be 80% of your current salary (adjusted for inflation).</li>
<li>Social Security benefits will cover 35% of your living expenses.</li>
<li>The remainder of your retirement living expenses will be covered by annual, inflation-adjusted withdrawals of 4% of your retirement savings.</li>
</ul>
So the 10% savings rate I mentioned in my 2009 post was too low given these facts and assumptions. I'll discuss the assumptions listed above in subsequent posts in this series, and make some different assumptions to see what other required savings rates we come up with.<br />
<br />
<a name='more'></a>Note that the figures above are stated in percentage terms, so the required 14% savings rate applies whether your annual earnings are $50,000, $100,000, or any other amount. For example, with annual earnings of $100,000, we assume that your annual living expenses in retirement will be $80,000 (80% x $100,000), that Social Security will fund $28,000 of that (35% x $80,000), and we calculate that you will need to save $14,000 per year (14% x $100,000), which is $1,167 per month. For an annual salary of $50,000, just cut these numbers in half.<br />
<br />
In working on a problem like this, we first need to figure out how to handle inflation. With an annual inflation rate of 2%, after one year it will take about $102 to buy what you can buy with $100 today. This reduction in purchasing power compounds over the years. At an average annual inflation rate of 2%, it will take about $220 in 40 years to buy what you can buy today for $100.<br />
<br />
If your earnings keep pace with inflation, then in 40 years you will earn about $220 for every $100 you earn today. Since $100 worth of goods in today's dollars will cost about $220 in 40 years, your earnings in 40 years will have about the same purchasing power they have today. Another way to say this is that in 40 years, $100 of earnings in today's dollars will buy $100 of goods in today's dollars.<br />
<br />
If we assume that earnings and the cost of goods both increase at the average inflation rate, then we can just work the problem in today's dollars. Today's dollars also are referred to as "real dollars", while future dollars are referred to as "nominal dollars". So 100 real dollars is equal to 100 nominal dollars today and 220 nominal dollars in 40 years (again, assuming an average annual inflation rate of 2%). To convert any real dollar amount to nominal dollars in 40 years at a 2% inflation rate, multiply by 2.2. For example, $100,000 in real dollars is about $220,000 in nominal dollars in 40 years at a 2% inflation rate, and $50,000 in real dollars is about $110,000 in nominal dollars.<br />
<br />
Similarly, we can refer to nominal or real rates of return on investments and savings. The real rate of return is approximately equal to the nominal rate of return minus the inflation rate (the exact calculation is slightly more complex, but this approximation is close enough for the type of calculation we're doing here). So assuming an inflation rate of 2%, a nominal return rate of 6% is approximately equal to a real return rate of 4% (the exact value to two decimal places is 3.92%). At these rates, $100 of investments will grow in one year to $106 in nominal dollars and about $104 in real dollars.<br />
<br />
As another example using the same inflation rate assumption, a 2% nominal rate of return equals a 0% real rate of return, and with these rates of return, $100 of investments today will be worth $100 in real dollars at any time in the future. In other words, with a 2% inflation rate, you need to earn a nominal return of 2% just to keep up with inflation and maintain your purchasing power.<br />
<br />
Remembering that we're working in real dollars, the assumption that your living expenses in retirement will be 80% of your current salary means that with an annual salary of $50,000, your annual living expenses in retirement will be $40,000 (80% x $50,000). Our assumption is that Social Security will cover 35% of this, or $14,000 (35% x $40,000). This leaves $26,000 of annual residual living expenses (RLE) to be funded with withdrawals from your retirement savings ($40,000 - $14,000). We can calculate that to fund the annual RLE of $26,000 with annual inflation-adjusted withdrawals of 4% from your retirement savings requires that you accumulate $650,000 in retirement savings during the 40 working years before you retire.<br />
<br />
How do we calculate this required retirement savings value of $650,000 based on the 4% withdrawal rate? Hopefully you recall from your elementary-school math classes that 4% can be written as the fraction 4/100, which can be reduced to the fraction 1/25. So a 4% withdrawal rate means that you will start by withdrawing 1/25 of your retirement savings in your first year of retirement, which means that you will need retirement savings equal to 25 times the annual withdrawal amount of $26,000. Multiplying $26,000 by 25 gives us the required retirement savings value of $650,000.<br />
<br />
Now that we've figured out how much you'll need in accumulate in retirement savings to retire in 40 years (using the listed facts and assumptions), we can use our assumed 4% real rate of return on investments (6% nominal rate of return minus 2% inflation) to calculate how much we'll need to save each year. We could do this by entering 40 rows of data into a spreadsheet, with each row calculating how much we'd have at the end of each year given a specified amount of savings along with our 4% real rate of return, and then use trial and error until we find the annual savings amount that gets us to $650,000 after 40 years. But there's an easier way.<br />
<br />
Spreadsheets like Excel and Google Sheets provide a "payment" function, PMT, that we can use to calculate the required annual savings amount directly. We plug into the spreadsheet PMT function our 4% assumed real rate of return, number of periods = 40 (years), a starting value of $0, and a future value of $650,000. The PMT function then calculates the required annual savings amount of $6,840.<br />
<br />
Dividing $6,840 by our $50,000 annual salary gives us a savings rate of 13.68%, which we can round to 14%. Again, this same savings rate applies to any annual salary given the assumptions we're using here; if we double the annual salary to $100,000, the required savings at retirement doubles to $1,300,000, and the annual savings amount doubles to $13,680, which is 13.68% of $100,000.<br />
<br />
If you want to try this yourself, open up an Excel or Google Sheets spreadsheet, and enter this formula into any cell:<br />
<br />
=PMT(4%, 40, 0, -650000)<br />
<br />
Note that the cash flow convention used by these types of spreadsheet functions requires a minus sign in front of the future value of 650000 if we want to get a positive value for the annual savings amount (payment).<br />
<br />
Using this PMT formula, you can enter different numbers to determine the required annual savings amount based on different assumptions. For example, to retire in 30 years assuming a 3% real rate of return and $50,000 of current savings, with all other facts and assumptions the same, we would use this formula:<br />
<br />
=PMT(3%, 30, 50000, -650000)<br />
<br />
This returns an annual savings amount of $11,112, which is a savings rate of about 22% (11,112 / 50,000). This is much larger than the 14% savings rate calculated based on our initial facts and assumptions, and illustrates the wide range of savings rates we can come up with depending on our assumptions.<br />
<br />
In the next article in this series, we'll start looking at factors to consider in coming up with reasonable assumptions to use in calculating a required annual savings rate. For example:<br />
<br />
<ul style="text-align: left;">
<li>How to estimate your living expenses in retirement.</li>
<li>How to estimate how much you'll receive in Social Security benefits.</li>
<li>How to determine a reasonable assumption for the rate of return on your investments.</li>
<li>How to determine a reasonable assumption for a safe withdrawal rate from your retirement savings.</li>
</ul>
</div>
Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-775967109474059335.post-78538916901163440752016-07-13T12:39:00.000-07:002016-07-13T12:39:40.331-07:00CD Rates Falling, But Yield Premiums Still Attractive<div dir="ltr" style="text-align: left;" trbidi="on">
Rates on several 5-year CDs I've been monitoring have fallen in recent weeks, but good CD (<a href="https://en.wikipedia.org/wiki/Certificate_of_deposit" target="_blank">Certificate of Deposit</a>) deals still are available, and the yield premiums of good CDs over Treasuries of the same maturities still are attractive. Ally Bank recently dropped its 5-year CD rate from 2.00% to 1.75% <a href="https://www.google.com/search?q=apy&oq=apy&aqs=chrome..69i57j69i61j69i60l2j69i61l2.630j0j4&sourceid=chrome&ie=UTF-8" target="_blank">APY </a>(1.70% if less than $25,000), and more recently Barclays Bank dropped its 5-year CD rate from 2.05% to 1.75%. The rate on the Synchrony Bank 5-year CD still is relatively attractive at 2.05% (2.00% if less than $25,000), but Synchrony recently increased the <a href="https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=CD+early+withdrawal+penalty" target="_blank">early withdrawal penalty</a> (EWP) on its 5-year CDs from 180 days of interest to 365 days of interest, so even this CD is somewhat less attractive than it was before this change.<br />
<br />
<a name='more'></a>It's not particularly surprising that 5-year CD rates have been generally declining, since <a href="https://fred.stlouisfed.org/graph/fredgraph.png?g=5pkn" target="_blank">5-year Treasury rates have been generally declining this year,</a> from a fairly-recent high of 1.80% on December 29, 2015 to a more-recent low of 0.94% on July 5, 2016. So even at 1.75%, a 5-year CD purchased directly from a bank or credit union ("direct CD") with an EWP of 180 days of interest is a good deal compared to the recent 5-year Treasury yield of about 1%. That's a yield premium of about 0.75 percentage points (75 basis points).<br />
<br />
Of the three CDs mentioned above, the Synchrony Bank 5-year CD with a rate of 2.05% provides a yield premium over the 5-year Treasury of about 1 percentage point (100 basis points), or to put it another way, the yield is about twice that of a 5-year Treasury. So even with the higher EWP compared to a few months ago, this CD is pretty attractive.<br />
<br />
Coupled with the early withdrawal option of a direct CD, which significantly decreases the risk of losing money if interest rates increase (interest-rate risk, also referred to as term risk), the much higher yields on good direct CDs make them an extremely attractive fixed-income option for individual investors who can take advantage of FDIC deposit insurance (for banks) or NCUA deposit insurance (for credit unions). Institutional investors with millions or billions to invest cannot take advantage of this federal deposit insurance due to insurance limits in the hundreds of thousands of dollars, and thus must be content with Treasury rates if they do not want to take credit risk (the risk of a bond not paying its interest, and possibly not paying back some or all of the original investment as well). The inability of large, institutional investors to take advantage of the federal deposit insurance is one reason these attractive rates remain available to smaller investors.<br />
<br />
Even better CD deals are available if you're willing to join a credit union. I recently purchased a 7-year IRA CD with an APY of 3.00% and an early withdrawal penalty (EWP) of 180 days of interest from Andrews Federal Credit Union, using a custodian-to-custodian transfer of the proceeds from an Ally Bank IRA CD that matured a couple of months ago. I am in the process of doing another such transfer from the proceeds of an Ally Bank IRA CD that matured yesterday.<br />
<br />
With the yield on a 7-year Treasury at 1.35% yesterday, a 7-year CD at 3% provides a yield premium of 1.65 percentage points (165 basis points). That's pretty outstanding. My average yield premium for CDs purchased in the last 5.5 years or so is about 115 basis points, and my average premium for CDs I still have open is about 130 basis points. Adding another CD with a premium of 165 basis points will nudge that average higher.<br />
<br />
For non-IRA accounts, a couple of credit unions to look at for good 5-year CD deals are Mountain America Credit Union (MACU) and Northwest Federal Credit Union (NWFCU), both of which I am already a member of, having become a member to purchase attractive CDs previously. Yield on the <a href="https://www.macu.com/rates#TermDeposit-Tab" target="_blank">MACU</a> 5-year CD currently is 2.30% APY, and according to the following blog post at <a href="https://www.depositaccounts.com/" target="_blank">DepositAccounts</a>, you can earn as much as 2.47% on the 5-year CD at NWFCU: <a href="https://www.depositaccounts.com/banks/northwest-fcu/offers/">Northwest FCU Offers Bonus Rate On Share Certificates</a>.<br />
<br />
With the latter, be careful about exceeding the NCUA insurance limit of $250K in an IRA, since the minimum deposit to earn the 2.47% rate on this CD is $250K. In an IRA, your principal would be insured, but your interest would not be insured if you reinvested your interest in the CD or in any other IRA account at MACU (since your IRA account value would then exceed the $250K limit). There are a number of ways to get more than $250K of NCUA insurance in a taxable (non-IRA) account using different ownership categories. For example, a joint account for spouses is insured up to $500K, and using a trust or payable on death (POD) account, you are insured up to $250K per beneficiary up to five beneficiaries (and even more, but the rules are more complicated for more than five beneficiaries).<br />
<br />
So the great CD deals are becoming fewer, but they're still out there, and even the OK CD deals are a good deal compared to marketable securities with no credit risk (i.e., Treasuries). Assuming an efficient bond market, and I believe that the bond market is quite efficient, CDs being a good deal compared to Treasuries on a pure yield basis make them a good deal to <b>any </b>bonds or bond funds on a risk-adjusted basis, since in an efficient market, higher yield means proportionally higher risk. For more thoughts on the superiority of the risk-adjusted yields of direct CDs, read my 3-part blog series on the 5-year returns of CDs compared to other fixed-income investments:<br />
<br />
<ul style="text-align: left;">
<li><a href="http://www.kevinoninvesting.com/2015/10/cd-5-year-report-card-part-1.html">CD 5-Year Report Card: Part 1</a>.</li>
<li><a href="http://www.kevinoninvesting.com/2015/10/cd-5-year-report-card-part-2-risk-and.html">CD 5-Year Report Card: Part 2 (Risk and Return)</a></li>
<li><a href="http://www.kevinoninvesting.com/2015/11/cd-5-year-report-card-part-3.html">CD 5-Year Report Card: Part 3</a></li>
</ul>
</div>
Unknownnoreply@blogger.com10tag:blogger.com,1999:blog-775967109474059335.post-65679395513834611932016-06-25T14:43:00.001-07:002016-06-26T12:24:17.768-07:00Brexit and Stock Market Volatility<div dir="ltr" style="text-align: left;" trbidi="on">
You probably heard the news about the <a href="https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=brexit" target="_blank">Brexit vote</a> results on Friday, June 24, in which a majority of United Kingdom voters voted to leave the European Union (EU). If you caught any financial news, you heard that global stock markets dropped a lot in response. I'll discuss the stock market reaction in more detail below, but the most important message for long-term investors is to not worry about daily stock market volatility. As I've <a href="http://www.kevinoninvesting.com/2010/02/financial-news-worse-than-useless.html" target="_blank">discussed before,</a> worrying about daily financial and economic news can be detrimental to your emotional health, and if you <b>act </b>on scary-sounding news or daily stock market volatility based on emotions, it also can be detrimental to your wealth.<br />
<br />
<a name='more'></a>US financial news tends to focus on US stock markets, and although the one-day drop in US stocks on Friday was relatively large, the drop in international stocks, especially European stocks, was much larger. So although you may have heard that "the Dow " (Dow Jones Industrial Average) dropped more than 600 points, the more rational way to talk about the change in stock values is in terms of the percentage change in the stock funds that you are invested in; very few people invest in "the Dow".<br />
<br />
If you follow my advice, you probably own something like the Vanguard Total Stock Market Index Fund (VTSMX/VTSAX/VTI) and the Vanguard Total International Stock Index Fund (VGTSX/VTIAX/VXUS). I'm showing the "<a href="https://www.google.com/search?q=ticker+symbol&oq=ticker+symbol&aqs=chrome..69i57l2j69i65j69i60l3.2508j0j9&sourceid=chrome&ie=UTF-8" target="_blank">ticker symbols</a>" for the three share classes of these funds in parentheses, which are Investor Shares, Admiral Shares, and ETF shares respectively. Admiral Shares and ETF shares have slightly lower <a href="https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=expense%20ratio" target="_blank">expense ratios</a>, but all share classes of a fund hold exactly the same stocks. Below are Friday's change in values for the Admiral Share class of these two funds (minimum investment $10,000):<br />
<br />
VTSAX: -3.65% (US stocks)<br />
VTIAX: -7.09% (International stocks)<br />
<br />
So here we see that international stocks dropped almost twice as much as US stocks. Although most people don't (and probably shouldn't) own a separate European stock fund, we can look at Friday's change in the value of Vanguard European Stock Index Fund (VEURX/VEUSX/VGK) to see that the drop was even more dramatic for European stocks:<br />
<br />
VEUSX: -10.56% (European stocks)<br />
<br />
This is a really big one-day drop, and although it may be difficult not to react to it emotionally, it helps to put this in perspective by looking at a slightly longer time period. As recently as June 14, less than two weeks ago, VEUSX share price was 56.99, so the Friday share price of 55.99 is only about 1.8% lower than that. So rather than freak out about a one-day drop of more than 10%, you could reframe it as a drop of less than 2% in a little less than two weeks.<br />
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Similarly, VTIAX share price was 23.28 on June 14, so Friday's price of 23.08 represents a drop in the total international stock market of less than 1% in a little less than two weeks. If you hold 40% of the stocks in your portfolio in the total international stock market (as do the Vanguard Target Retirement and LifeStrategy funds, which I highly recommend), and stocks are 80% of your portfolio, then this represents a drop of less than 0.3% of your portfolio in a little less than two weeks--hardly worth losing any sleep over.<br />
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Looking at a slightly longer time period, on February 11, a little more than four months ago, VEUSX share price was 54.70, so even with Friday's dramatic drop, this European stock fund is almost 2.4% <b>higher </b>than it's low point for the year.<br />
<br />
Similarly, VTIAX share price on February 11 was 21.34, so Friday's price of 23.08 for this total international stock fund, which is more likely what you own, is more than 8% <b>higher </b>than it's low price of the year. So by reframing your perspective from the one-day change to the change over a few months, you have a <b>gain </b>of more than 8% instead of a loss of about 7%.<br />
<br />
It is widely expected that the prospect of Britain exiting the EU will continue to result in relatively high volatility in global stock markets, so we shouldn't be surprised to see more big down days (and some big up days) in the coming days and weeks. Although it's unlikely that Friday's drops were enough to trigger any <a href="https://www.bogleheads.org/wiki/Rebalancing" target="_blank">rebalancing </a>or <a href="https://www.bogleheads.org/wiki/Tax_loss_harvesting" target="_blank">tax loss harvesting</a>, because of gains earlier in the year, further decreases in stock prices could do so. If you have an <a href="http://www.kevinoninvesting.com/2015/08/the-value-of-investment-policy.html" target="_blank">investment policy</a>, which you should, then you can ignore daily volatility, other than possibly as a reminder to check your portfolio values to see if any policy rebalancing has been triggered.<br />
<br /></div>
Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-775967109474059335.post-24456602576241802472015-11-09T10:56:00.000-08:002015-11-09T10:56:59.102-08:00New Online CD Management Functionality at Ally Bank<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: "arial" , "helvetica" , sans-serif;">Only a few days after I published a blog post on how to give advance instructions to Ally Bank to not renew a CD (</span><a href="http://www.kevinoninvesting.com/2015/11/advance-request-to-not-renew-ally-bank.html" target="_blank">Advance Request to Not Renew Ally Bank CDs at Maturity</a>)<span style="font-family: arial, helvetica, sans-serif;">, Ally has added functionality to its online banking interface to allow modifying what happens to the CD proceeds of </span><b style="font-family: arial, helvetica, sans-serif;">taxable</b><span style="font-family: arial, helvetica, sans-serif;"> CDs at maturity. So although the instructions in the previous blog post still will work, it now is much easier to make changes to taxable CDs using the new online functionality. </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;">The new functionality also allows changing the interest disbursement option (reinvest, mail a check, or distribute to another Ally or non-Ally account), and changing the term of the CD if you choose to renew. </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;">For IRA CDs, you still must call or use online chat to make changes.</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"></span><br />
<a name='more'></a><span style="font-family: "arial" , "helvetica" , sans-serif;">(Reminder: Any screen shots in this post may not appear properly, if at all, in email, so email subscribers should click on the blog post title link in the email to read the post directly on the blog website.)</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br />
</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">This morning, I received an email from Ally Bank with the subject "Funds transfer reminder". On opening the email, I saw "Your CD transfer is scheduled" in large letters at the top of the message, and below that I saw "At maturity: Close CD". OK, so far no surprises, since I had </span><span style="font-family: arial, helvetica, sans-serif;">used the steps documented in the previous blog post to </span><span style="font-family: arial, helvetica, sans-serif;">instruct Ally to close this CD at maturity.</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br />
</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">Reading further, I saw the surprise:</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="background-color: #eeeeee; color: #505050; font-family: "helvetica neue" , "arial" , "helvetica" , "geneva" , sans-serif; font-size: 16px;">To edit this transfer or make other changes to your CD: </span><br />
<table border="0" cellpadding="0" cellspacing="0" style="color: #505050; font-family: 'Helvetica Neue', Arial, Helvetica, Geneva, sans-serif; font-size: 16px; width: 100%px;"><tbody>
<tr><td align="right" style="margin: 0px; padding: 10px 10px 0px 0px; text-align: right;" valign="top" width="50">•</td><td align="left" style="margin: 0px; padding: 10px 0px 0px 10px;">Log in to online banking</td></tr>
<tr><td align="right" style="margin: 0px; padding: 10px 10px 0px 0px; text-align: right;" valign="top" width="50">•</td><td align="left" style="margin: 0px; padding: 10px 0px 0px 10px;">Go to the <b>Main Menu</b> <img border="0" class="CToWUd" height="20" src="https://blogger.googleusercontent.com/img/proxy/AVvXsEiyGo1ak9SNV3D2k-ZpZAIZkuN7WEQ8gGjpCpkke5XK2RHgX_1taBkS74_o16gM6pCaNflyF1N7PoWO2piC4jmjkschIfNvFVKuCcuirJVUDwQu4i-79dyuUylZfZXfCmedpZFZkaRcX1koYk74NUxDjTG8YD2wlSbMkhlmPYwCvaghCdr6ZUXTs-AA-TxHrc8Lhw=s0-d-e1-ft" style="display: inline-block; vertical-align: middle;" width="20" /></td></tr>
<tr><td align="right" style="margin: 0px; padding: 10px 10px 0px 0px; text-align: right;" valign="top" width="50">•</td><td align="left" style="margin: 0px; padding: 10px 0px 0px 10px;">Select <b>Manage CDs</b></td></tr>
</tbody></table>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;">Huh? What's this?</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;">I knew Ally had done some upgrades of their online banking site over the weekend, since a warning about this had been splashed on the Accounts Summary page each time I logged on during the previous week or so, so I figured this must have been one of the upgrades.</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;">I logged on, followed the email instructions to navigate to the Manage CDs functionality, and checked it out.</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u>Manage CDs</u></b></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;">On the <b>Manage CDs</b> page, there are three choices: </span><br />
<br />
<ul style="text-align: left;">
<li><span style="font-family: arial, helvetica, sans-serif;">Renewal Options</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">Interest Disbursement</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">Early Withdrawal</span></li>
</ul>
<div>
<b style="font-family: arial, helvetica, sans-serif;"><u>Renewal Options</u></b></div>
<div>
<b style="font-family: arial, helvetica, sans-serif;"><br /></b></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">The default screen is <b>Renewal Options</b>. On this screen there is a drop-down selection box to select the CD to manage, and your current renewal options are displayed, along with the current CD balance, original term to maturity (e.g., 5 years), and interest disbursement selection.</span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">Importantly, I also see a link to the right of the CD selection box that says "<span style="color: #0b5394;">Looking for your IRA CD?</span>". Clicking this link pops up a small window that says:</span></div>
<div>
<span style="background-color: white; color: #505050; font-family: sans-serif; font-size: 16px; line-height: 22.4px;"><br /></span></div>
<div>
<span style="background-color: white; color: #505050; font-family: sans-serif; font-size: 16px; line-height: 22.4px;">To make changes to your IRA CD, call us at 1-877-247-ALLY (2559). If you don’t make any changes, your IRA CD will automatically renew into the same term on the renewal date.</span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">So you <b>cannot use the new manage CDs functionality to manage IRA CDs</b>. That's too bad, but it still can be done with a phone call or online chat.</span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">There is a large </span><b><span style="font-family: Arial, Helvetica, sans-serif;">Make Changes</span></b><span style="font-family: arial, helvetica, sans-serif;"> button below the list of renewal options; you may have to scroll down to see it. After clicking this button, several drop-down selection boxes appear. The first selection box shows the following selections:</span></div>
<div>
<ul style="text-align: left;">
<li><span style="font-family: arial, helvetica, sans-serif;"> Transfer Funds/Close CD</span></li>
<ul>
<li><span style="font-family: arial, helvetica, sans-serif;">Rollover balance</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">Add funds to this balance</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">Withdraw partial amount</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">Close my CD at maturity</span></li>
</ul>
</ul>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><b>Rollover balance</b> is the default selection, and with this choice selected, additional drop selection boxes appear that allow you to select the term of the new CD (e.g., 5-year, 3-year, etc.), and to select the disbursement frequency (annually, semi-annually, quarterly, monthly) and </span><span style="font-family: arial, helvetica, sans-serif;">disbursement </span><span style="font-family: arial, helvetica, sans-serif;">method for the new CD.</span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">For annual disbursement frequency, the disbursement choices are </span><span style="font-family: Arial, Helvetica, sans-serif; font-size: xx-small;"><b>Credit to CD</b></span><span style="font-family: arial, helvetica, sans-serif;"> (i.e., reinvest interest), <b><span style="font-size: xx-small;">Send me a check</span></b>, or <b><span style="font-size: xx-small;">Deposit into an account</span></b>. If you select <b><span style="font-size: xx-small;">Send me a check</span></b>, the mailing address is verified, with a note indicating that you can change this in your profile. If <b><span style="font-size: xx-small;">Deposit to an account</span></b> is selected, a drop-down selection box is displayed, and you can select any of your Ally checking, savings or money market accounts, or any of your linked non-Ally accounts.</span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">For monthly, quarterly, or semi-annual disbursement frequencies, the only disbursement method choices are <b><span style="font-size: xx-small;">Send me a check</span></b> or <b><span style="font-size: xx-small;">Deposit into an account</span></b>.</span></div>
<div>
<br /></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">If you select a <b>renewal option other than Rollover Balance</b>, the selection boxes shown are modified accordingly. </span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">For example, if you select <b><span style="font-size: xx-small;">Close my CD at maturity</span></b>, you are shown a selection box to <b><span style="font-size: xx-small;">Transfer Amount By</span></b> either <span style="font-size: xx-small;"><b>Online transfer</b> </span>or <b><span style="font-size: xx-small;">Check</span></b>. For online transfer, you can transfer to an Ally account or linked non-Ally account. This is the option you would use instead of the process I documented in the previous blog post.</span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">After making changes to the renewal options, you click the </span><b style="font-family: arial, helvetica, sans-serif;">Submit Changes</b><span style="font-family: arial, helvetica, sans-serif;"> button to save them, or click the </span><b style="font-family: arial, helvetica, sans-serif;">Cancel</b><span style="font-family: arial, helvetica, sans-serif;"> link to cancel any changes.</span></div>
</div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><b><u>Interest Disbursement</u></b></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">This choice is used to change the interest disbursement frequency and method for your existing CD. The choices are the same as those documented in the previous section for changing these options for the CD at renewal. </span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">Being able to easily change this online is a great feature for someone who decides they'd like to have their interest disbursed to them instead of having it reinvested. I would only choose this if I could earn more interest elsewhere, or needed the money for living expenses.</span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><b><u>Early Withdrawal</u></b></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">This choice allows you to do an early withdrawal online. This is a nice option for those who prefer to do things online rather than talk to a person on the phone, and who don't want to bother answering questions like "why are you doing this?" It will probably will take less time than the 5-10 minute phone call to do an early withdrawal, which is what I've done previously. It also reinforces my confidence that Ally Bank will not disallow an early withdrawal request, although of course they could remove this functionality at some point in the future.</span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">The current balance + accrued interest is displayed for the selected CD, along with the early withdrawal penalty amount and the balance after penalty amount. As with the disbursement method, you can choose to transfer the balance by online transfer or by check.</span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><b><u>Setting a taxable CD to not renew at maturity</u></b></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: arial, helvetica, sans-serif;">So the steps to set your <b>taxable</b> CD to be closed (not renew) at maturity are now:</span></div>
<div>
<ol style="text-align: left;">
<li><span style="font-family: arial, helvetica, sans-serif;">Log on to online banking for your Ally account.</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">Select <b>Manage CDs</b> from the main menu (three horizontal lines at top right).</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">Select the CD from the drop-down selection box.</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">Click the <b>Make Changes</b> button.</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;"> Select <b><span style="font-size: x-small;">I Want To: </span><span style="font-size: xx-small;">Close my CD at maturity</span></b>.</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">Select to <b><span style="font-size: x-small;">Transfer Amount By: </span><span style="font-size: xx-small;">Online transfer</span></b> or <b><span style="font-size: xx-small;">check</span></b>.</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">For online transfer, select the Ally account or linked non-Ally account you want the proceeds deposited to upon maturity.</span></li>
<li><span style="font-family: arial, helvetica, sans-serif;">Click the <b>Submit Changes</b> button to save your changes.</span></li>
</ol>
<div>
<span style="font-family: arial, helvetica, sans-serif;">Very cool!</span></div>
</div>
</div>
Unknownnoreply@blogger.com7tag:blogger.com,1999:blog-775967109474059335.post-29122132092120514622015-11-08T10:36:00.000-08:002015-11-08T10:36:04.418-08:00Reading Blog Posts in Email<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: Arial, Helvetica, sans-serif;">If you are an email subscriber and tried to read the last blog post in email, you may have noticed that it was garbled. If so, this is because the screen shots don't appear in email, and instead you see either nothing or a bunch of garbled text. The fix is simple: click on the blog post title at the beginning of the email, and because the title is a link to the blog, a new window or tab should open showing the blog post directly on the blog, and the screen shots will appear properly. If for some reason the link doesn't work, simply type <a href="http://www.kevinoninvesting.com/" target="_blank">KevinOnInvesting.com</a> into your <a href="https://www.google.com/#q=browser+address+bar" target="_blank">browser address bar</a> to take you to the blog, and you can then read any of the blog posts.</span></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-775967109474059335.post-24050760169126820422015-11-06T13:33:00.000-08:002015-11-06T13:34:52.653-08:00Advance Request to Not Renew Ally Bank CDs at Maturity<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: "arial" , "helvetica" , sans-serif;">As a follow up to my post about <a href="http://www.kevinoninvesting.com/2015/10/what-to-do-with-maturing-cds.html" target="_blank">what to do with maturing CDs</a>, I wanted to share that you <b>can</b> request <b>in advance</b> that your CDs at Ally Bank <b>not</b> be renewed at maturity. I think you can do this by phone, but I have only done it using online chat. In this post I describe how I've done it, and how you can too.</span><br />
<br />
<a name='more'></a><span style="font-family: "arial" , "helvetica" , sans-serif;">I like to do this with online chat, because I can copy the account numbers from my online account summary and paste them into the chat window, and because I can multi-task and do things in other windows at the same time, or even talk on the phone, while waiting for the chat representative to complete their tasks and respond in the chat window. Here are the steps to do this.</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>Log on to your Ally Bank account.</b> You'll then see all of your accounts, including CDs, on the account summary screen. You might have to scroll down to see your CDs if you have multiple checking and savings accounts. The last four digits of each account number are displayed, and this is the only account info you'll need to provide instructions to the chat rep.</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>Open a chat window</b>. To do this, click <span style="color: #0b5394;">Help</span> near the top right of the accounts summary screen, below and to the left of the </span><span style="font-family: "arial" , "helvetica" , sans-serif;">tools menu </span><span style="font-family: "arial" , "helvetica" , sans-serif;">gear</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span><span style="font-family: "arial" , "helvetica" , sans-serif;">icon ... </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;"><img src="data:image/png;base64,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" /></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>
<span style="font-family: "arial" , "helvetica" , sans-serif;">... then click <span style="color: #0b5394;">Chat</span> at the bottom of the Help & FAQs pop-up screen, to the right of the phone number:</span><br />
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" 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" /></span><br />
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" /></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>Type in your request</b> to not renew the selected CDs, then click the Send button when ready to transmit your request. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The chat rep will ask for the last four digits of the account number for the CD you want to close, so to save time you can just include this in your initial request, either by typing it in, or copying it from your accounts summary page, and pasting it into your request in the chat window. Here is an example of an instruction I used today for two CDs:</span><br />
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<span id="docs-internal-guid-f2ed94e4-de6e-7614-9ab3-afe7e3e9d133"><span style="font-size: x-small;"><span style="background-color: white; color: #5fbbb4; font-family: "arial"; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Kevin: </span><span style="background-color: white; color: #650360; font-family: "arial"; vertical-align: baseline; white-space: pre-wrap;">I would like to not renew CDs maturing on Nov 9, ending in 1234 and 5678, but have proceeds deposited into my savings account ending in 4321 (at maturity)</span></span></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">They will ask you why you don't want to renew, so </span><span style="font-family: "arial" , "helvetica" , sans-serif;">to save time, </span><span style="font-family: "arial" , "helvetica" , sans-serif;">you can just provide a reason before they even ask. They also may tell you about the 0.05% loyalty reward they offer if you renew, so you can also tell them you know about this to save time.</span><br />
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<span style="font-size: x-small;"><span style="background-color: white; color: #5fbbb4; font-family: "arial"; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Kevin: </span><span style="background-color: white; color: #650360; font-family: "arial"; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">reason is better rate elsewhere</span></span></div>
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<span style="font-size: x-small;"><span style="background-color: white; color: #5fbbb4; font-family: "arial"; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Kevin: </span><span style="background-color: white; color: #650360; font-family: "arial"; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">and I do know about the 0.05% loyalty rate bump</span></span></div>
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<span style="background-color: white; color: #650360; font-family: "arial"; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
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<span style="background-color: white; color: #650360; font-family: "arial"; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: black; font-family: "arial" , "helvetica" , sans-serif; line-height: normal; white-space: normal;">They also will ask for your phone number. I just wait for them to ask, since they may also ask for other information to verify your identity.</span></span></div>
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<span id="docs-internal-guid-f2ed94e4-de73-5ea9-44b8-ed88c353572d"><span style="font-size: x-small;"><span style="background-color: white; color: #610485; font-family: "arial"; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Travis: </span><span style="background-color: white; color: #650360; font-family: "arial"; vertical-align: baseline; white-space: pre-wrap;">I can certainly make a request to close your CDs ending in 1234 and 5678 at maturity and transfer the funds to your Online Savings Account ending in 4321. May I confirm your phone number, please?</span></span></span></div>
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<span style="background-color: white; font-family: "arial" , "helvetica" , sans-serif; line-height: normal;">Note that the chat rep, Travis, has confirmed my request, so I double-check the account numbers, and verify that the confirmation acknowledges that I am requesting to transfer funds to savings or checking account <b>at maturity</b>; I want to make sure the rep understands that I am <b>not requesting an early withdrawal</b>, although I haven't seen a rep make that mistake in doing this three times so far.</span></div>
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<span style="background-color: white; font-family: "arial" , "helvetica" , sans-serif; line-height: normal;">That's it!</span></div>
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<span style="background-color: white; font-family: "arial" , "helvetica" , sans-serif; line-height: normal;">It can take up to two business days for the proceeds to be transferred into your account when the CD matures, so don't worry if you still see the CD in your account on the maturity date (with a new maturity date five years hence). Do check back within two business days to make sure that the CD is gone, and the proceeds are in your savings or checking account. I have seen it happen as late as one business day later, but also have seen it happen on the maturity date.</span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-775967109474059335.post-39998925486506728192015-11-02T19:37:00.003-08:002015-11-04T01:49:46.719-08:00CD 5-Year Report Card: Part 3<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: "arial" , "helvetica" , sans-serif;">In the first two posts in this series, I compared the 5-year return of a 5-year direct CD to a 5-year Treasury security, and provided a fairly detailed explanation of how to evaluate risk and return of fixed-income investments, such as CDs, bonds (including Treasuries), and bond funds. In this post, I conclude the series by presenting the 5-year returns of various Vanguard bond funds, and by comparing these results to the CD and Treasury in terms of risk as well as return.</span><br />
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<a name='more'></a><span style="font-family: "arial" , "helvetica" , sans-serif;">The comparisons in this post are for the 5-year period ending September 30, 2015 for the bond funds, and September 15, 2015 for the 5-year CD and 5-year Treasury note. The bond fund average annual returns were conveniently obtained directly from the <a href="https://investor.vanguard.com/mutual-funds/vanguard-mutual-funds-list#tab=averageAnnualMonthEnd" target="_blank">Vanguard web site</a> </span><span style="font-family: "arial" , "helvetica" , sans-serif;">during October 2015, when the returns ending September 30, 2015 were displayed (a</span><span style="font-family: "arial" , "helvetica" , sans-serif;">s I write this, the returns shown are for the period ending October 31, 2015). </span><span style="font-family: "arial" , "helvetica" , sans-serif;">Although the holding period for the bond funds doesn't exactly match that for the CD and Treasury, I think that they're close enough for a reasonable comparison.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The bond fund returns are for the Admiral shares class, with a minimum investment of $50,000 for all funds compared here, except the Total Bond Market Index fund, which has a minimum investment of $10,000.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The comparison table shown later in the post has quite a few columns, but if you read <a href="http://www.kevinoninvesting.com/2015/10/cd-5-year-report-card-part-2-risk-and.html" target="_blank">Part 2</a> of this series, you should be able to understand the table contents with a little additional explanation. The table lists the securities (CD and Treasury) and funds, the average annual returns, several risk-related measures, and the difference between the return of each security or fund and that of the CD.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">From <a href="http://www.kevinoninvesting.com/2015/10/cd-5-year-report-card-part-2-risk-and.html" target="_blank">Part 2</a> of this series, you'll recognize the terms <i><b>Credit risk</b></i> and <i><b>Term risk</b></i>, the headers of two of the columns in the comparison table.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><i>Note that on the <a href="https://investor.vanguard.com/mutual-funds/vanguard-mutual-funds-list#tab=averageAnnualMonthEnd">Vanguard web site</a>, if you use the left navigation bar to select</i> Bond <i>as the asset class, you can filter the bond funds by credit risk (Credit quality) and term risk (Maturity).</i></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The </span><b style="font-family: arial, helvetica, sans-serif;">credit risk</b><span style="font-family: "arial" , "helvetica" , sans-serif;"> value shown in my comparison table for each fund is a numerical approximation of the average credit quality rating provided by Morningstar (M*), but with some adjustments applied. Other than the adjustments, explained below, I use a scheme based on the </span><a href="https://en.wikipedia.org/wiki/Bond_credit_rating#Credit_rating_tiers" style="font-family: arial, helvetica, sans-serif;" target="_blank">credit rating tiers shown in a Wikipedia article on bond credit rating</a><span style="font-family: "arial" , "helvetica" , sans-serif;"> to translate the letter-based credit ratings to numeric values, as follows:</span><span style="font-family: "arial" , "helvetica" , sans-serif;"><br />
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<table border="1" cellpadding="0" cellspacing="0" dir="ltr" style="border-collapse: collapse; border: 1px solid rgb(204, 204, 204); font-family: arial, sans, sans-serif; font-size: 13px; table-layout: fixed; text-align: center;"><colgroup><col width="94"></col><col width="59"></col></colgroup><tbody>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"M* avgerage credit quality"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">M* average credit quality</td><td data-sheets-value="[null,2,"Numeric rating"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Numeric rating</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"AAA"]" style="font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">AAA</td><td data-sheets-numberformat="[null,2,"#,##0",1]" data-sheets-value="[null,3,null,0]" style="font-size: 100%; padding: 2px 3px; text-align: center; vertical-align: bottom;">0</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"AA"]" style="font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">AA</td><td data-sheets-numberformat="[null,2,"#,##0",1]" data-sheets-value="[null,3,null,1]" style="font-size: 100%; padding: 2px 3px; text-align: center; vertical-align: bottom;">1</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"A"]" style="font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">A</td><td data-sheets-numberformat="[null,2,"#,##0",1]" data-sheets-value="[null,3,null,2]" style="font-size: 100%; padding: 2px 3px; text-align: center; vertical-align: bottom;">2</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"B"]" style="font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">B</td><td data-sheets-numberformat="[null,2,"#,##0",1]" data-sheets-value="[null,3,null,5]" style="font-size: 100%; padding: 2px 3px; text-align: center; vertical-align: bottom;">5</td></tr>
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">So the larger the number, the higher the credit risk. Note that there's a larger numerical gap between A and B than between AAA and AA or between AA and A. This is because a</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> credit quality rating of B actually is quite a bit lower than a rating of A, which you can see in the <a href="https://en.wikipedia.org/wiki/Bond_credit_rating#Credit_rating_tiers" target="_blank">Wikipedia article on bond credit rating</a>.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">M* assigns an average credit</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span><span style="font-family: "arial" , "helvetica" , sans-serif;">quality</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> rating of AA to the <b>Vanguard Treasury funds</b>, I assume because one of the credit rating agencies (S&P) downgraded the US from AAA (outstanding) to AA+ (excellent) in 2011. My sense is that most investors still consider US debt obligations to be essentially risk free, so I assigned a value of 0 to all federally-backed securities (Treasury note and CD) and funds that include only Treasuries (all Treasury funds).</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">M* also assigns </span><span style="font-family: "arial" , "helvetica" , sans-serif;">an average credit</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span><span style="font-family: "arial" , "helvetica" , sans-serif;">quality</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> rating of AA to </span><span style="font-family: "arial" , "helvetica" , sans-serif;"><b>Vanguard Total Bond Market Index fund</b>, but this fund holds <a href="https://personal.vanguard.com/us/funds/snapshot?FundId=0584&FundIntExt=INT#tab=2" target="_blank">about 35% of its portfolio in corporate bonds</a>, so it has more credit risk than a fund that holds only Treasuries. So I rated this a 1 for credit risk.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">M* </span><span style="font-family: "arial" , "helvetica" , sans-serif;">assigns </span><span style="font-family: "arial" , "helvetica" , sans-serif;">an average credit</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span><span style="font-family: "arial" , "helvetica" , sans-serif;">quality</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> rating of A to</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> all of the <b>Vanguard investment-grade bond funds</b>, so these are all rated a 2 using my scheme.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">Finally, M* gives an average credit quality rating of B to <b>Vanguard High-Yield Corporate Bond fund</b>, so the numerical rating is 5.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">I'll show the table of results now, and will explain the other risk columns below.</span><br />
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<tr style="height: 21px;"><td data-sheets-value="[null,2,"Security or fund"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Security or fund</td><td data-sheets-value="[null,2,"Credit risk"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Credit risk</td><td data-sheets-value="[null,2,"Term risk (duration)"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Term risk (duration)</td><td data-sheets-value="[null,2,"Overall risk"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Overall risk</td><td data-sheets-value="[null,2,"Return / Risk"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Return / Risk</td><td data-sheets-value="[null,2,"Avg annual return"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Avg annual return</td><td data-sheets-value="[null,2,"Return vs. CD"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Return vs. CD</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"5-year direct CD"]" style="background-color: lime; color: #5b0f00; font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">5-year direct CD</td><td data-sheets-value="[null,3,null,0]" style="background-color: lime; font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0</td><td data-sheets-formula="=60/365*R[0]C[3]*100" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,0.45041095890410954]" style="background-color: lime; font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.5</td><td data-sheets-formula="=SUM(R[0]C[-2]:R[0]C[-1])" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,0.45041095890410954]" style="background-color: lime; font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.5</td><td data-sheets-formula="=R[0]C[1]/R[0]C[-1]*100" data-sheets-numberformat="[null,2,"#,##0.00",1]" data-sheets-value="[null,3,null,6.083333333333334]" style="background-color: lime; font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">6.08</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0274]" style="background-color: lime; font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2.74%</td><td style="background-color: lime; padding: 2px 3px 2px 3px; vertical-align: bottom;"></td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"5-year Treasury Note"]" style="color: #5b0f00; font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">5-year Treasury Note</td><td data-sheets-value="[null,3,null,0]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0</td><td data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,2]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2.0</td><td data-sheets-formula="=SUM(R[0]C[-2]:R[0]C[-1])" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,2]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2.0</td><td data-sheets-formula="=R[0]C[1]/R[0]C[-1]*100" data-sheets-numberformat="[null,2,"#,##0.00",1]" data-sheets-value="[null,3,null,0.73]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.73</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0146]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1.46%</td><td data-sheets-formula="=R[0]C[-1]-R2C[-1]" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,-0.0128]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">-1.28%</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"High-Yield Corporate fund (VWEAX)"]" style="color: #5b0f00; font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">High-Yield Corp. fund (VWEAX)</td><td data-sheets-value="[null,3,null,5]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">5</td><td data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,4.6]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">4.6</td><td data-sheets-formula="=SUM(R[0]C[-2]:R[0]C[-1])" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,9.6]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">9.6</td><td data-sheets-formula="=R[0]C[1]/R[0]C[-1]*100" data-sheets-numberformat="[null,2,"#,##0.00",1]" data-sheets-value="[null,3,null,0.6583333333333334]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.66</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0632]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">6.32%</td><td data-sheets-formula="=R[0]C[-1]-R2C[-1]" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.035800000000000005]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3.58%</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"Int-Term Invest-Grade fund (VFIDX)"]" style="color: #5b0f00; font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">Int-Term Invest-Grade fund (VFIDX)</td><td data-sheets-value="[null,3,null,2]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2</td><td data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,5.5]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">5.5</td><td data-sheets-formula="=SUM(R[0]C[-2]:R[0]C[-1])" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,7.5]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">7.5</td><td data-sheets-formula="=R[0]C[1]/R[0]C[-1]*100" data-sheets-numberformat="[null,2,"#,##0.00",1]" data-sheets-value="[null,3,null,0.5666666666666667]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.57</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0425]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">4.25%</td><td data-sheets-formula="=R[0]C[-1]-R2C[-1]" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.015100000000000002]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1.51%</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"Int-Term Treasury fund (VFIUX)"]" style="color: #5b0f00; font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">Int-Term Treasury fund (VFIUX)</td><td data-sheets-value="[null,3,null,0]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0</td><td data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,5.1]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">5.1</td><td data-sheets-formula="=SUM(R[0]C[-2]:R[0]C[-1])" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,5.1]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">5.1</td><td data-sheets-formula="=R[0]C[1]/R[0]C[-1]*100" data-sheets-numberformat="[null,2,"#,##0.00",1]" data-sheets-value="[null,3,null,0.5352941176470589]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.54</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0273]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2.73%</td><td data-sheets-formula="=R[0]C[-1]-R2C[-1]" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,-0.0000999999999999994]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">-0.01%</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"Short-Term Invest-Gr fund (VFSUX)"]" style="color: #5b0f00; font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">Short-Term Invest-Gr fund (VFSUX)</td><td data-sheets-value="[null,3,null,2]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2</td><td data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,2.6]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2.6</td><td data-sheets-formula="=SUM(R[0]C[-2]:R[0]C[-1])" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,4.6]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">4.6</td><td data-sheets-formula="=R[0]C[1]/R[0]C[-1]*100" data-sheets-numberformat="[null,2,"#,##0.00",1]" data-sheets-value="[null,3,null,0.47391304347826096]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.47</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0218]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2.18%</td><td data-sheets-formula="=R[0]C[-1]-R2C[-1]" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,-0.005600000000000001]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">-0.56%</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"Total Bond Market Index fund (VBTLX)"]" style="color: #5b0f00; font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">Total Bond Mkt Index fund (VBTLX)</td><td data-sheets-numberformat="[null,2,"#,##0",1]" data-sheets-value="[null,3,null,1]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">1</td><td data-sheets-value="[null,3,null,5.7]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">5.7</td><td data-sheets-formula="=SUM(R[0]C[-2]:R[0]C[-1])" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,6.7]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">6.7</td><td data-sheets-formula="=R[0]C[1]/R[0]C[-1]*100" data-sheets-numberformat="[null,2,"#,##0.00",1]" data-sheets-value="[null,3,null,0.4447761194029851]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.44</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0298]" style="background-color: white; color: #333333; font-size: 100%; padding: 2px 3px; text-align: right; vertical-align: bottom; word-wrap: break-word;">2.98%</td><td data-sheets-formula="=R[0]C[-1]-R2C[-1]" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0023999999999999994]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.24%</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"Long-Term Invest-Gr fund (VWETX)"]" style="color: #5b0f00; font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">Long-Term Invest-Gr fund (VWETX)</td><td data-sheets-value="[null,3,null,2]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2</td><td data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,13]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">13.0</td><td data-sheets-formula="=SUM(R[0]C[-2]:R[0]C[-1])" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,15]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">15.0</td><td data-sheets-formula="=R[0]C[1]/R[0]C[-1]*100" data-sheets-numberformat="[null,2,"#,##0.00",1]" data-sheets-value="[null,3,null,0.436]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.44</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0654]" style="font-size: 100%; padding: 2px 3px; text-align: right; vertical-align: bottom; word-wrap: break-word;">6.54%</td><td data-sheets-formula="=R[0]C[-1]-R2C[-1]" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.038]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3.80%</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"Short-Term Treasury fund (VFIRX)"]" style="color: #5b0f00; font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">Short-Term Treasury fund (VFIRX)</td><td data-sheets-value="[null,3,null,0]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0</td><td data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,2.2]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2.2</td><td data-sheets-formula="=SUM(R[0]C[-2]:R[0]C[-1])" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,2.2]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">2.2</td><td data-sheets-formula="=R[0]C[1]/R[0]C[-1]*100" data-sheets-numberformat="[null,2,"#,##0.00",1]" data-sheets-value="[null,3,null,0.41818181818181815]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.42</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0092]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.92%</td><td data-sheets-formula="=R[0]C[-1]-R2C[-1]" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,-0.0182]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">-1.82%</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"Long-Term Treasury fund (VUSUX)"]" style="color: #5b0f00; font-size: 100%; padding: 2px 3px 2px 3px; vertical-align: bottom;">Long-Term Treasury fund (VUSUX)</td><td data-sheets-value="[null,3,null,2]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0</td><td data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,16.1]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">16.1</td><td data-sheets-formula="=SUM(R[0]C[-2]:R[0]C[-1])" data-sheets-numberformat="[null,2,"#,##0.0",1]" data-sheets-value="[null,3,null,18.1]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">16.1</td><td data-sheets-formula="=R[0]C[1]/R[0]C[-1]*100" data-sheets-numberformat="[null,2,"#,##0.00",1]" data-sheets-value="[null,3,null,0.33756906077348064]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">0.38</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0611]" style="border-bottom-color: rgb(217, 217, 217); border-bottom-style: solid; border-bottom-width: 1px; font-size: 100%; padding: 2px 3px; text-align: right; vertical-align: bottom; word-wrap: break-word;">6.11%</td><td data-sheets-formula="=R[0]C[-1]-R2C[-1]" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0337]" style="font-size: 100%; padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">3.37%</td></tr>
</tbody></table>
<br />
<span style="font-family: "arial" , "helvetica" , sans-serif;">The securities and funds are sorted by decreasing values in the <b>Return / Risk</b> column, which I'll explain after explaining the other risk columns to the left of it.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><i><b>Update</b>: an astute Boglehead pointed out that I mistakenly assigned a credit-risk rating of 2 to the Long-Term Treasury fund in the comparison table, which also resulted in a slightly higher value for overall risk, and a slightly lower value for Return / Risk. I have modified the credit-risk rating to the correct value of 0, and updated the other values accordingly. It does not change the rank order of funds in the table though.</i></span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">To quantify <b>term risk for the funds</b>, I used the <b>duration</b> values from Vanguard's web site. Duration is an approximate measure of the percentage decrease (increase) in fund value (or share price) for each</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> percentage point</span><span style="font-family: "arial" , "helvetica" , sans-serif;"> </span><span style="font-family: "arial" , "helvetica" , sans-serif;">increase (decrease) in the </span><span style="font-family: "arial" , "helvetica" , sans-serif;">yields of all bonds in the fund. For example, if the yields of all bonds in the Total Bond Market Index fund increased by one percentage point, the value of the fund would fall by about 5.7%.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">The <b>duration of the 5-year Treasury note</b> is calculated with a spreadsheet duration formula, using a term to maturity of 2.5 years, since that's the average maturity over the 5-year life of the bond. The duration is as high as 4.8 at time of purchase, but declines to 1.0 after four years, and approaches 0 as the bond nears maturity. So the bond is much riskier early in the holding period, but the average duration of 2.0 over the entire 5-year holding period is a better value for comparing with the funds (for which duration is roughly constant over time).</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">Coming up with a <b>duration value for the direct CD</b> is kind of a finger-in-the-wind exercise, because the liquidation value of the CD does not change as interest rates change--it always equals the value of the principal and earned interest minus the early withdrawal penalty (EWP) until the day of maturity, at which time the EWP no longer applies. The number shown is approximately the value of the EWP in percent, which would be a reasonable number for comparison with the funds assuming a one percentage point change in yields. For smaller changes in yield, the CD would lose more than indicated by the duration value shown, and for larger changes it would lose less--potentially much less.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">This particular CD had an EWP of about two months of interest, so the percentage loss would be about 2 / 12 * 2.74% = 0.46%. This is rounded and expressed in percent for an estimated duration of 0.5.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">To derive an <b>overall risk</b> measure, I simply add the credit risk and term risk numeric values. This is a very rough risk measure, and I'm sure that someone else could justify something different. As always, I welcome comments on this and everything else I post.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">Note that the very <b>high term risk for the long-term bond funds causes these funds to end up with the highest overall risk ratings</b>--even higher than the High-Yield Corporate Bond fund, which some might think would be higher risk. However, another common risk measure is the <b><a href="http://www.morningstar.com/InvGlossary/standard_deviation.aspx" rel="nofollow" target="_blank">standard deviation</a></b> (SD) of returns, and over the five year period being evaluated, the SDs of the long-term Treasury (12.03%), long-term investment-grade (8.35%), and high-yield corporate (5.35%) funds do correlate fairly well with my overall risk numbers. I use <a href="https://www.portfoliovisualizer.com/backtest-portfolio?s=y&allocation2_2=100&lastMonth=9&symbol1=VUSUX&endYear=2015&symbol3=VWEAX&frequency=4&symbol2=VWETX&inflationAdjusted=true&annualAdjustment=0&showYield=false&startYear=2010&rebalanceType=0&timePeriod=2&annualPercentage=0.0&allocation1_1=100&allocation3_3=100&annualOperation=0&firstMonth=10&reinvestDividends=true&initialAmount=10000" target="_blank">Portfolio Visualizer to determine the SD values</a>; Portfolio Visualizer is a very nice, free, web-based tool with which you can do many kinds of historical investment returns analysis.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">The </span><b style="font-family: Arial, Helvetica, sans-serif;">Return / Risk </b><span style="font-family: "arial" , "helvetica" , sans-serif;">values are calculated as <b>average annual return divided by overall risk</b>. This is very similar in concept to <a href="http://www.investopedia.com/terms/s/sharperatio.asp" target="_blank">Sharpe ratio</a>, a measure that is widely used to evaluate the <b>risk-adjusted return</b> of investments and portfolios.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">I think it's very important to think in terms of risk-adjusted return. Although some of the bond funds had higher average annual returns than the CD, these higher returns were obtained only by taking considerably more risk. </span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">Sometimes risk pays off, and sometimes it "shows up". It so happens that over the 5-year period examined here, both term risk and credit risk generally were rewarded within the bond fund universe. This can be seen by examining the relative returns of the funds for a given level of credit risk, or for a given level of term risk, or simply by observing that higher <b>overall risk</b> </span><span style="font-family: "arial" , "helvetica" , sans-serif;">generally </span><span style="font-family: "arial" , "helvetica" , sans-serif;">resulted in higher average annual return.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">To see a recent example of when bond risk showed up, take a look at the bond fund returns for 2013, when interest rates increased enough to make a significant difference in returns. For example, the total return for the fund with the highest overall risk of the funds evaluated here, the <a href="https://personal.vanguard.com/us/funds/snapshot?FundId=0583&FundIntExt=INT#tab=1a" target="_blank">Long-Term Treasury fund</a>, was -12.94% (that's <b>minus</b> 12.94%) in 2013.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">One of the most striking results in the comparisons shown in the table above is that the <b>risk-adjusted return (return / risk) of the direct CD is an order of magnitude larger than for the Treasury note or any of the bond funds.</b> This is why I favor direct CDs so much, and why they now comprise about 75% of my fixed income.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">On the other hand, since taking more risk sometimes pays off, I've hedged my bets by keeping some of my fixed income in bond funds, including some of those shown in the comparison table. I now have about 25% of my fixed income in bond funds.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">An interesting exercise is to compute the metrics I've used here for a combination of 75% in the CD and 25% in the Intermediate-Term Investment-Grade Bond fund. This is a fund I'd recommend, especially in a tax-advantaged account (IRA or 401k/403b), and preferably in conjunction with direct CDs or other safe, high risk-adjusted return fixed-income investments (like the TSP G fund, or a good stable value fund). Computing the metrics for this combination is a simple arithmetic calculation, but since this post already is so long, I'll leave this to the interested reader, or perhaps will show these results in another post.</span></div>
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Unknownnoreply@blogger.com10tag:blogger.com,1999:blog-775967109474059335.post-24428218289145069602015-10-31T11:06:00.000-07:002015-10-31T11:06:27.310-07:00CD 5-Year Report Card: Part 2 (Risk and Return)<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: "arial" , "helvetica" , sans-serif;">In my previous blog post, <a href="http://www.kevinoninvesting.com/2015/10/cd-5-year-report-card-part-1.html" target="_blank">CD 5-Year Report Card: Part 1</a>, I compared the 5-year annualized return of a CD I bought about five years ago to the 5-year annualized return of a 5-year Treasury security (Treasury bond, or more formally, Treasury note) I could have bought on the same date. Although that's the most relevant comparison, it's not particularly interesting, since the annual percentage y<b>ield</b> (APY) of the CD and the <b>yield</b> to maturity (YTM) of the Treasury basically predetermine the returns at time of purchase (assuming the CD or Treasury is held to maturity). </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">(From now on, the term <i>yield</i> refers to yield to maturity (YTM) for a Treasury, other bond, or <b>brokered</b> CD (purchased through a broker), and it refers to the annual percentage yield (APY) for a <b>direct</b> CD (purchased directly from a bank or credit union). Also, the term <i>return </i>refers to annualized return).</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">In my next post, I'll review the 5-year returns for various bond funds, and compare them to the 5-year return of the CD. However, to evaluate these returns rationally, it's necessary to understand the relationship between risk and return for fixed-income securities, which is what I'll examine in this post.</span><br />
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<a name='more'></a><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u>Risk, return, yield</u></b></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The <b>expected return</b> of an investment typically is <b>related to to the risk</b> of the investment; </span><span style="font-family: arial, helvetica, sans-serif;">the</span><b style="font-family: arial, helvetica, sans-serif;"> higher the expected return, </b><span style="font-family: arial, helvetica, sans-serif;">the </span><b style="font-family: arial, helvetica, sans-serif;">higher the risk</b><span style="font-family: arial, helvetica, sans-serif;">. In other words, for a </span><b style="font-family: arial, helvetica, sans-serif;">higher risk</b><span style="font-family: arial, helvetica, sans-serif;"> investment, there is </span><b style="font-family: arial, helvetica, sans-serif;">less certainty</b><span style="font-family: arial, helvetica, sans-serif;"> that the </span><b style="font-family: arial, helvetica, sans-serif;">realized return</b><span style="font-family: arial, helvetica, sans-serif;"> will equal the </span><b style="font-family: arial, helvetica, sans-serif;">expected return</b><span style="font-family: arial, helvetica, sans-serif;">. Due to this </span><b style="font-family: arial, helvetica, sans-serif;">greater uncertainty</b><span style="font-family: arial, helvetica, sans-serif;">, investors demand a </span><b style="font-family: arial, helvetica, sans-serif;">higher expected return for riskier investments</b><span style="font-family: arial, helvetica, sans-serif;">.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">So, <b>investment risk is the uncertainty that an investment will earn its expected return over the time period of interest</b>. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">There is very little uncertainty about whether or not a 5-year Treasury or 5-year federally-insured CD <b>held to maturity </b>will earn a return equal to its initial yield. Therefore, these investments are essentially risk-free over a 5-year holding period. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Note that here I'm discussing risk in terms of <a href="http://financial-dictionary.thefreedictionary.com/Nominal+Returns" target="_blank">nominal return</a>, not <a href="http://www.investopedia.com/terms/r/realrateofreturn.asp" target="_blank">real return</a>. Real return is important, since it accounts for inflation, but in comparing various nominal fixed-income investments (as opposed to <a href="https://www.treasurydirect.gov/indiv/research/indepth/ibonds/res_ibonds.htm" target="_blank">I Bonds</a> or <a href="https://www.treasurydirect.gov/indiv/products/prod_tips_glance.htm" target="_blank">TIPS</a>, which are real fixed-income investments), we can focus on nominal returns, since inflation affects all of these investments similarly.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">For fixed-income investments, like bonds or bond funds, <b>yield is an indicator of expected return</b>, and <b>higher yield typically means higher risk</b>. Higher yield doesn't <b>ensure</b> a higher <b>realized return</b>, but investors demand a higher yield to compensate for the greater uncertainty that the fixed-income investment will earn the expected return</span><span style="font-family: "arial" , "helvetica" , sans-serif;">.</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u>Yield, risk and return for CDs</u></b></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">CDs are somewhat of an exception to the general relationship between yield or return and risk. For the last five years, good 5-year CDs generally have offered higher yields (and higher essentially risk-free returns) than 5-year Treasuries. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The primary reason for this is that institutional investors (insurance companies, pension funds, mutual funds, etc.) cannot take advantage of the limited FDIC insurance; since institutions buy and sell hundreds of millions if not billions of dollars worth of fixed-income securities, the $250,000 federal insurance limit does not insure them against bank </span><span style="font-family: arial, helvetica, sans-serif;">defaults</span><span style="font-family: arial, helvetica, sans-serif;">. </span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">So CDs are not risk-free to institutional investors like they are to retail investors who can keep the amount of their deposits at a particular bank or credit union at or below the FDIC insurance limit. Therefore, institutional investors cannot <a href="https://www.google.com/search?q=arbitrage" target="_blank">arbitrage</a> away the yield premiums of CDs over Treasuries.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">A <b>brokered</b> 5-year <b>CD</b> (purchased from a broker) has about the same risk as a 5-year Treasury, since its price is determined by CD rates on the secondary CD market (where investors can buy and sell previously issued CDs). But a good <b>direct CD</b> (purchased directly from a bank or credit union) has less risk because of the early withdrawal option, which I explain in more detail below.</span><br />
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</span><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u>Two main types of risk for fixed income</u></b></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">A bond or bond fund has two primary types of risk:</span><br />
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<li><span style="font-family: "arial" , "helvetica" , sans-serif;"><i>Credit risk</i>, also known as <i>default risk</i></span></li>
<li><span style="font-family: "arial" , "helvetica" , sans-serif;"><i>Interest-rate risk</i>, also known as <i>term risk</i></span></li>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b>Credit risk</b> (<b>default risk</b>) depends on the credit-worthiness of the institution that issues the bond or other fixed-income security being evaluated, and this is inversely related to the possibility that the institution will <b>default</b> on payments of interest or principal. </span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">The US government typically is regarded as one of the most credit-worthy institutions in the world (despite having it's <a href="https://en.wikipedia.org/wiki/United_States_federal_government_credit-rating_downgrades" target="_blank">credit rating downgraded from AAA to AA+ by Moody's in 2011</a>). Therefore, <b>US Treasury securities and federally-insured CDs have essentially no credit risk</b>. Similarly, a Treasury bond <b>fund</b> has essentially no credit risk.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">However, corporate bonds and bond funds that own them do have credit risk. A bond fund can hold just Treasuries, just corporate bonds, or a combination of both. The corporate bonds in a bond fund can be of various qualities, thus affecting the credit risk of the bond fund. The bond funds I'll examine in the next post span the credit quality range from high to low.</span></div>
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</b></span> <span style="font-family: "arial" , "helvetica" , sans-serif;"><b>Interest-rate risk (term risk)</b> is the risk that the value of a bond, CD or bond fund will decrease or increase due to an increase or decrease in the relevant interest rate or yield. Note that price moves in the opposite direction of yield or interest rate.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">Even though the 5-year return of a 5-year Treasury held to maturity is essentially certain, the return over a shorter period is uncertain (e.g., if the bond were sold before maturity). If the yield of a 5-year Treasury were to <b>increase</b> from 2% to 3% shortly after purchase, the value of the Treasury would <b>decrease</b> by about 4.6%. If held to maturity, it still would earn its initial expected return of 2%, but someone who bought a 5-year Treasury after the rate increase would earn 3% over the five-year holding period. Being stuck earning 2% when the market rate increases to 3% is sometimes referred to as <i>opportunity cost</i>.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">If the original owner sells the bond at a 4.6% loss to invest in a new 5-year bond with a 3% yield, the annualized return over five years still will be 2%, so there's no advantage in doing this. So the buyer of a 5-year bond with a 2% original yield will earn pretty much 2% over the five year term regardless of what is done.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">Interest-rate risk is higher for longer terms to maturity, which is why it also is referred to as <b>term risk</b>. Therefore, bonds with longer terms to maturity will have larger price swings as interest rates change. </span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">For example, if the yield of a <b>10-year</b> Treasury were to increase from 2% to 3% shortly after purchase, the value would decrease by about 9%--a much larger price change than the 4.6% change for the 5-year Treasury.</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Since term risk is proportional to term to maturity, the <b>term risk of a bond declines as it approaches maturity</b>. The market price of a 3-year bond will decline less if the 3-year yield increases by 1% than will the price of a 5-year bond if the 5-year yield increases by 1%. After two years, a bond with an initial term to maturity of five years has three years left to maturity, and thus the price will change based on the change in 3-year yields.</span></div>
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">All of the above also applies to a brokered CD. Since a brokered CD is a marketable fixed-income security (i.e., it can be bought and sold through a broker), its price is determined by market participants, and will be inversely related to prevailing yields for CDs of the same term to maturity. The annualized return of a brokered CD will equal its initial yield if held to maturity (ignoring <a href="http://www.investopedia.com/terms/r/reinvestmentrisk.asp" target="_blank">reinvestment risk</a>), but could earn more or less over a shorter time period (e.g., if sold before maturity).</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: arial, helvetica, sans-serif;"><b><u>Term risk of direct CDs</u></b></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Things are different for a direct CD. The <b>early withdrawal option of a good direct CD lowers the term risk significantly</b>. If the 5-year CD rate were to increase from 2% to 3% immediately after purchase, an early withdrawal could be done from a direct CD at a cost of about 1% (assuming an early withdrawal penalty of six months of interest). Contrast this to the 4.6% price decrease of a 5-year Treasury or other bond.</span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">So the direct CD owner has the possibility of earning an annualized return that is higher than the initial yield if CD rates were to increase enough, unlike the bond or brokered CD owner. <b>This is the key advantage of direct CDs over brokered CDs.</b></span><br />
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</span><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u>Term risk of bond funds</u></b></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The above discussion of term risk does not apply directly to a bond fund, because the typical bond fund has no maturity date. A bond fund is similar to a rolling <a href="http://www.investopedia.com/terms/b/bondladder.asp" target="_blank">bond ladder</a>, in which bonds with a variety of maturities are purchased, and as each bond matures the proceeds are "rolled" into a new bond of the longest maturity in the ladder. Therefore, <b>with a bond fund or rolling bond ladder, the term risk does not decline as time passes.</b></span><br />
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</span> <span style="font-family: "arial" , "helvetica" , sans-serif;">Note that this also is true for a rolling ladder of <b>brokered</b> CDs (purchased through a broker, instead of directly from a bank). Since there is no early withdrawal option for brokered CDs, they will decline in value just like Treasuries or other bonds if interest rates increase. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u>Term risk of direct CDs vs. bond funds</u></b></span><br />
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</span><span style="font-family: "arial" , "helvetica" , sans-serif;">Just as an individual direct CD has less term risk than a bond of the same maturity, a rolling ladder of good <b>direct</b> CDs has less term risk than a rolling ladder of bonds of the same maturities. The early withdrawal option of a good direct CD limits the downside term risk of each CD in the ladder to a relatively small fixed amount, so the CD ladder has correspondingly lower term risk. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Si</span><span style="font-family: arial, helvetica, sans-serif;">nce a bond fund is similar to a rolling bond ladder, a good direct CD generally has lower term risk than a bond fund. The longer the average maturity or </span><a href="http://www.investopedia.com/terms/d/duration.asp" style="font-family: arial, helvetica, sans-serif;" target="_blank">duration</a><span style="font-family: arial, helvetica, sans-serif;"> of the bond fund, the higher the term risk compared to a good direct CD.</span><br />
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<span style="font-family: arial, helvetica, sans-serif;">One caveat is that banks and credit unions often reserve the right to <a href="https://www.depositaccounts.com/blog/2011/11/inflation-dangerous-banks-those-that-could-refuse-cd-early-withdrawals.html" target="_blank">refuse early withdrawals, or to change the early withdrawal terms of existing CDs</a>. In practice, this has hardly ever occurred, but some investors are concerned that it might be more common if interest rates were to increase a lot. However, I heard no reports of this happening when interest rates increased significantly in 2013, when the 5-year Treasury yield increased by 1.2 percentage points in about four months, from a low of 0.65% on 5/2/2013 to a high of 1.85% on 9/5/2013).</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u>Direct CD ladder vs. direct 5-year CD</u></b></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The low term risk of direct CDs is a reason to consider buying only 5-year direct CDs instead of constructing a 5-year ladder of direct CDs. A typical 5-year CD ladder would have CDs maturing in 1, 2, 3, 4 and 5 years. Since the term risk of a good direct 5-year CD already is so low, there's not much point in buying shorter-term CDs at lower yields to reduce term risk.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Aside from the risk of being denied an early withdrawal, you often come out ahead by doing an early withdrawal from a good 5-year direct CD rather than holding shorter-term CDs. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">For example, if you do an early withdrawal from a 5-year 2.25% CD with an early withdrawal penalty (EWP) of six months of interest, you earn an annualized return of 1.70%, which you can see using the <a href="https://www.depositaccounts.com/tools/ewp-calculator.aspx?ids=5207,264557" target="_blank">DepositAccounts.com early withdrawal calculator</a>. This is a higher return than the the 1.5% annualized return that you'll earn on a <a href="https://www.depositaccounts.com/cd/2-year-cd-rates.html" target="_blank">good 2-year CDs</a> (remember that the annualized return of a CD held to maturity is equal to the yield).</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">So you can think of a portfolio of good direct 5-year CDs as a 5-year CD ladder, but with higher average yield than an actual ladder. If you need the money for some reason before maturity, you can do an early withdrawal and probably earn more than you would from a maturing shorter-term CD. If you don't need the money before maturity, you end up earning even more than the 1-5 year ladder.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><b><u>Next up</u></b></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">With these basics out of the way, we can proceed to rationally evaluate the return and risk of bond funds with all combinations of low, medium and high term risk, and low, medium and high credit risk, compared to the return and risk of a the direct CD. This is what I'll cover in my next blog post.</span></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-775967109474059335.post-62728973292933639432015-10-26T19:56:00.001-07:002015-10-31T08:06:41.512-07:00CD 5-Year Report Card: Part 1<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: Arial, Helvetica, sans-serif;">Now that the 5-year CDs I bought about five years ago are maturing, I thought it would be interesting to compare the 5-year CD returns to the 5-year returns of some other fixed-income alternatives I could have invested in five years ago. All we should really have to do is compare the APY (Annual Percentage Yield) of the 5-year CD to the YTM (yield to maturity) of the 5-year Treasury at the time of purchase, since that's the most appropriate comparison in terms of risk and expected return for the forward-looking 5-year period. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Looking at past returns raises the issue of hindsight bias, or as Larry Swedroe refers to it, confusing strategy with outcome. Nevertheless, people seem to have a hard time not using past returns to evaluate their investments, so I'll compare some of the more relevant returns in this and the next one or two blog posts.</span><br />
<a name='more'></a><br />
<span style="font-family: Arial, Helvetica, sans-serif;">The most common way to express returns is using average annual return, also referred to as annualized return or compound annual growth rate (CAGR). For a direct CD (purchased directly from a bank or credit union) in which interest is reinvested, the annualized return will exactly equal the annual percentage yield (APY), so we know in advance the annualized return just by looking at the APY.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Similarly, the annualized return of a typical Treasury security held to maturity will be approximately the yield to maturity (YTM) when the Treasury is purchased. This is not as precise a predictor as the APY of a CD, because the interest rate at which the Treasury interest is reinvested is not known in advance (reinvestment risk). However, at current low interest rates, this won't have a huge impact on the return, so I'll use the YTM of the Treasury as the annualized return.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">The APY of the CD I purchased on September 15, 2010 (and that matured on September 15, 2015) was 2.74%, and this was the 5-year annualized return of the CD. The YTM of the</span><span style="font-family: Arial, Helvetica, sans-serif;"> 5-year Treasury on the date I bought the CD was 1.46%, which you can see in <a href="http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yieldYear&year=2010" target="_blank">this table of Treasury rates</a> provided by the US Department of the Treasury, and this was the annualized 5-year return of the Treasury. So we know that the average annual return of the CD was about 1.28% higher, </span><span style="font-family: Arial, Helvetica, sans-serif;">since 2.74 - 1.46 = 1.28</span><span style="font-family: Arial, Helvetica, sans-serif;"> (technically it is 1.28 percentage points or 128 basis points higher, but it is common to refer to it as a percentage, so I'll do that here).</span></div>
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</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Below is a tabular summary of what I've discussed above, but showing the annualized return of the 5-year Treasury compared to the 5-year CD (so it's a negative number; i.e., 1.46 - 2.74 = -1.28). This is the convention I'll be using in subsequent tables in this post and the subsequent 5-year report card posts.</span></div>
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</span></div>
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<table border="1" cellpadding="0" cellspacing="0" dir="ltr" style="border-collapse: collapse; border: 1px solid rgb(204, 204, 204); font-size: 13px; table-layout: fixed;"><tbody>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"Security or fund"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;"><span style="font-family: Arial, Helvetica, sans-serif;">Security or fund</span></td><td data-sheets-value="[null,2,"Average annual return"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;"><span style="font-family: Arial, Helvetica, sans-serif;">Average annual return</span></td><td data-sheets-value="[null,2,"Compared to CD"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;"><span style="font-family: Arial, Helvetica, sans-serif;">Compared to CD</span></td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"5-year CD"]" style="font-weight: bold; padding: 2px 3px; vertical-align: bottom;"><span style="font-family: Arial, Helvetica, sans-serif;">5-year CD</span></td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0274]" style="padding: 2px 3px; text-align: right; vertical-align: bottom;"><span style="font-family: Arial, Helvetica, sans-serif;">2.74%</span></td><td></td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"5-year Treasury"]" style="font-weight: bold; padding: 2px 3px; vertical-align: bottom;"><span style="font-family: Arial, Helvetica, sans-serif;">5-year Treasury</span></td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.0146]" style="padding: 2px 3px; text-align: right; vertical-align: bottom;"><span style="font-family: Arial, Helvetica, sans-serif;">1.46%</span></td><td data-sheets-formula="=R[0]C[-1]-R12C2" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,-0.0128]" style="padding: 2px 3px; text-align: right; vertical-align: bottom;"><span style="font-family: Arial, Helvetica, sans-serif;">-1.28%</span></td></tr>
</tbody></table>
</div>
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</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Another way to express return is as a cumulative return, either in terms of percent or dollars; e.g., the growth of $10,000. With some simple bond math, we can calculate cumulative return from annualized return. For the </span><span style="font-family: Arial, Helvetica, sans-serif;">5-year CD and </span><span style="font-family: Arial, Helvetica, sans-serif;">5-year Treasury, the 5-year cumulative returns in percentage terms are </span><span style="font-family: arial, sans, sans-serif; text-align: right;">14.47% </span><span style="font-family: arial, sans, sans-serif; text-align: right;">and </span><span style="font-family: arial, sans, sans-serif; text-align: right;">7.52% </span><span style="font-family: arial, sans, sans-serif; text-align: right;">respectively--a difference of 6.96%. Growth of $10,000 is </span><span style="font-family: arial, sans, sans-serif; text-align: right;">$11,447</span><span style="font-family: arial, sans, sans-serif; font-size: 13px; text-align: right;"> </span><span style="font-family: arial, sans, sans-serif; text-align: right;">for the CD and </span><span style="font-family: arial, sans, sans-serif; text-align: right;">$10,752 for the Treasury</span><span style="font-family: arial, sans, sans-serif; text-align: right;">--a difference of $696.</span></div>
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<span style="font-family: arial, sans, sans-serif; text-align: right;"><br />
</span></div>
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<span style="font-family: arial, sans, sans-serif; text-align: right;">The table below shows these cumulative results.</span></div>
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</span></div>
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<table border="1" cellpadding="0" cellspacing="0" dir="ltr" style="border-collapse: collapse; border: 1px solid #ccc; font-family: arial,sans,sans-serif; font-size: 13px; table-layout: fixed;"><colgroup><col width="205"></col><col width="100"></col><col width="100"></col><col width="100"></col><col width="100"></col></colgroup><tbody>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"Security or fund"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Security or fund</td><td data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,2,"Cumulative 5-year return"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Cumulative 5-year return</td><td data-sheets-value="[null,2,"Compared to CD"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Compared to CD</td><td data-sheets-numberformat="[null,4,"\"$\"#,##0",1]" data-sheets-value="[null,2,"Growth of $10K"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Growth of $10K</td><td data-sheets-numberformat="[null,4,"\"$\"#,##0",1]" data-sheets-value="[null,2,"Compared to CD"]" style="background-color: #eae5da; border-right-color: rgb(255, 255, 255); border-right-style: solid; border-right-width: 1px; color: #333333; font-size: 100%; font-weight: bold; padding: 2px 3px; text-align: center; vertical-align: middle; word-wrap: break-word;">Compared to CD</td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"5-year CD"]" style="font-weight: bold; padding: 2px 3px 2px 3px; vertical-align: bottom;">5-year CD</td><td data-sheets-formula="=(1+R[-8]C[0])^5-1" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.14471614188664028]" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">14.47%</td><td></td><td data-sheets-formula="=10000*(1+R[0]C[-2])" data-sheets-numberformat="[null,4,"\"$\"#,##0",1]" data-sheets-value="[null,3,null,11447.161418866403]" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">$11,447</td><td data-sheets-numberformat="[null,4,"\"$\"#,##0",1]" style="padding: 2px 3px 2px 3px; vertical-align: bottom;"></td></tr>
<tr style="height: 21px;"><td data-sheets-value="[null,2,"5-year Treasury"]" style="font-weight: bold; padding: 2px 3px 2px 3px; vertical-align: bottom;">5-year Treasury</td><td data-sheets-formula="=(1+R[-8]C[0])^5-1" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,0.07516294920931044]" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">7.52%</td><td data-sheets-formula="=R[0]C[-1]-R10C[-1]" data-sheets-numberformat="[null,3,"0.00%",1]" data-sheets-value="[null,3,null,-0.06955319267732984]" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">-6.96%</td><td data-sheets-formula="=10000*(1+R[0]C[-2])" data-sheets-numberformat="[null,4,"\"$\"#,##0",1]" data-sheets-value="[null,3,null,10751.629492093105]" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">$10,752</td><td data-sheets-formula="=R[0]C[-1]-R10C[-1]" data-sheets-numberformat="[null,4,"\"$\"#,##0",1]" data-sheets-value="[null,3,null,-695.5319267732975]" style="padding: 2px 3px 2px 3px; text-align: right; vertical-align: bottom;">-$696</td></tr>
</tbody></table>
</div>
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</span></div>
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<span style="font-family: arial, sans, sans-serif; text-align: right;">So, as we knew would be the case, the 5-year CD provided a significantly higher 5-year return than the 5-year Treasury, regardless of how we measure it. </span></div>
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</span></div>
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<span style="font-family: arial, sans, sans-serif; text-align: right;">Also, it's important to point out that the CD, which was a direct CD (purchased directly from a bank), provided the higher return with less risk. If interest rates had increased significantly, especially early in the term, I could have done an early withdrawal from the CD at a cost of only two months of interest, or about 0.5%, to reinvest at the higher rate. On the other hand, the Treasury could have experienced a much larger decline in value, proportional to the amount by which Treasury rates increased.</span></div>
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<span style="font-family: arial, sans, sans-serif; text-align: right;">In the third post in this series, I'll review the 5-year returns of some bond funds that I might have invested in instead of the CD, including some bond funds that I <b>did</b> invest in <b>in addition</b> to the CD. </span><span style="font-family: arial, helvetica, sans-serif;">However, for those results to make sense, it's necessary to understand the relationships between </span><b style="font-family: arial, helvetica, sans-serif;">yield</b><span style="font-family: arial, helvetica, sans-serif;">, </span><b style="font-family: arial, helvetica, sans-serif;">expected return, risk</b><span style="font-family: arial, helvetica, sans-serif;"> and</span><b style="font-family: arial, helvetica, sans-serif;"> realized return</b><span style="font-family: arial, helvetica, sans-serif;">, which is what I'll examine in my next post.</span></div>
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Unknownnoreply@blogger.com2tag:blogger.com,1999:blog-775967109474059335.post-84220912878609940662015-10-22T20:17:00.000-07:002015-10-22T20:35:11.748-07:00What To Do With Maturing CDs?<div dir="ltr" style="text-align: left;" trbidi="on">
I started buying 5-year CDs directly from banks and credit unions ("direct CDs") about five years ago, because I learned about the advantages in terms of risk and expected return compared to bonds or bond funds. Perhaps you did too, either based on my musings or those of bloggers from whom I learned about direct CDs, like <a href="https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=%22allan+roth%22+CD+site:www.cbsnews.com" target="_blank">Allan Roth</a> and <a href="https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=CD+site%3Athefinancebuff.com" target="_blank">The Finance Buff</a>. Now that our CDs are starting to mature, what should we do?<br />
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<a name='more'></a>First, you should be sure you are keeping track of your CDs and their maturity dates. I track mine in a <a href="https://www.google.com/sheets/about/" target="_blank">Google Sheets</a> spreadsheet, but I also enter the maturity dates in my <a href="https://calendar.google.com/calendar/" target="_blank">Google Calendar</a>, set up with email alerts to notify me a few days before each CD matures.<br />
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You probably will receive an email or letter from the bank or credit union, notifying you a month or so before your CD matures, but I would keep track of your CD maturity dates just to be safe.<br />
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You have several choices about what to do with your maturing CD, and what you choose depends on a number of factors. Some of the factors depend on whether the CD is in a taxable account or an IRA account. Examples of taxable accounts are individual, joint, trust, and Payable on Death (POD) accounts. The factors related to IRAs are the same for traditional or Roth IRAs, so I'll just refer to these as IRAs.<br />
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I'll discuss the alternatives below, and since I bought my first direct CDs from Ally Bank, and those are the ones that are maturing, I'll use Ally Bank to provide examples.<br />
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The first choice is to ...<br />
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<b><u>Do Nothing</u></b><br />
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Typically CDs are set up to renew at maturity. This means that the proceeds of the maturing CD are "rolled" (deposited) into a new CD with the same term to maturity. So if you do nothing, a 5-year CD maturing on November 1, 2015 will roll into a new 5-year CD maturing on November 1, 2020. Although the term to maturity of the new CD is the same, the interest rate probably is lower, since rates generally are lower now than they were five years ago. Also, there may be better rates elsewhere.<br />
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For example, a 5-year Ally CD I bought on November 1, 2010 has a <a href="https://en.wikipedia.org/wiki/Nominal_interest_rate#Nominal_versus_effective_interest_rate" target="_blank">nominal interest rate</a> of 2.46%, which is an APY of 2.49% (APY, or <a href="https://en.wikipedia.org/wiki/Annual_percentage_yield" target="_blank">Annual Percentage Yield</a>, is slightly higher than the nominal interest rate because of daily compounding), but a 5-year CD at Ally now has an APY of only 2.00%, so about half a percent less per year.<br />
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So if you do nothing, your 5-year Ally Bank CD with an APY of 2.49% will roll into a new 5-year CD with an APY of 2.00%, but Ally Bank may increase the APY to 2.05% as a loyalty reward.<br />
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The <i>Do Nothing</i> choice is pretty much the same for a taxable account or IRA, but is it the right choice? To answer that, we have to consider the alternatives, which brings us to choice #2 ...<br />
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<b><u>Use the proceeds from the maturing CD to buy a new CD somewhere else</u></b><br />
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This is much easier to do in a taxable account than in an IRA, so I'll discuss taxable accounts first.<br />
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Currently you can buy a 5-year CD from Synchrony Bank with an APY of 2.25%, so about a quarter percent higher than the Ally Bank CD--about 0.20% higher if you get the 2.05% loyalty rate from Ally Bank. The Synchrony Bank rate is competitive; I've purchased Synchrony Bank CDs for myself, and have helped friends and family members buy them, so let's use a Synchrony Bank CD as an example.<br />
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Assuming you get the loyalty 5-year APY of 2.05% from Ally Bank, I show below how much more you'll earn on various amounts in a Synchrony Bank CD with an APY of 2.25%, assuming you hold it to maturity:<br />
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<ul style="text-align: left;">
<li>$10,000 CD: $22 more per year, so about $109 more over five years</li>
<li>$50,000 CD: $109 more per year, so about $544 more over five years</li>
<li>$100,000 CD: $218 more per year, so about $1,089 more over five years</li>
</ul>
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These numbers show the additional interest before income taxes, so for the after tax difference, multiply the above numbers by one minus your marginal tax rate. Assuming 25% federal and 5% state marginal tax rates, so 30% total, multiply by (1-0.30) = 0.70. So that would be an after-tax five-year premium of $762 over five years for a $100,000 CD.</div>
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You may be able to find a better deal, by looking at the <a href="https://www.depositaccounts.com/cd/5-year-cd-rates.html" target="_blank">5-year CD rates</a> on <a href="http://depositaccounts.com/">DepositAccounts.com</a>. Currently the highest rate for a nationally available 5-year CD is 2.45% APY on an eloan CD, but the early withdrawal penalty (EWP) is very steep at 730 days of interest (about 4.9%), compared to the EWP of 180 days of interest on the Synchrony Bank CD (about 1.13%). I would stick with the Synchrony Bank CD.</div>
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How hard is it to open a taxable account and buy a CD at Synchrony Bank? I think it is very easy, but different people have different abilities and tolerances for dealing with any issues that arise. I think it would take me about 10-15 minutes to open the account and buy the CD, entirely online, but it might take someone else 30 minutes or longer, depending on their abilities. You also can do it by phone, and it shouldn't take much longer than doing it online. I just prefer typing to talking, so I usually try to do these things online, but I don't hesitate to pick up the phone if I run into any issues, or am confused about something.</div>
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So to me, it is well worth the few minutes is takes to open a new account to buy a CD at a higher rate. I earn more than $1,000 more (before taxes) over five years for a few minutes work. However, for a $10,000 CD, it may not be worth it to you to bother with it to earn the extra $109 over five years.</div>
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More work is required to move the proceeds from a maturing CD in an IRA to another bank or credit union to buy an IRA CD with a higher rate. I recently did this, and published a blog post on it, so you can read that to get a sense of what's involved: <a href="http://www.kevinoninvesting.com/2015/07/i-recently-completed-my-first-transfer.html">Kevin On Investing: First bank-to-bank IRA transfer from a maturing IRA CD</a>. </div>
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Obviously it was worth it to me to do this, and I plan to do it with other Ally Bank IRA CDs that will mature next year. On the other hand, I had a relatively small Ally Bank IRA CD that matured recently, and it wasn't worth it to me to do the IRA transfer, so I just let it roll over to a new Ally Bank 5-year IRA CD. They gave me the loyalty rate of 2.05% APY.</div>
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<b><u>Other Alternatives</u></b></div>
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You may have other uses for some or all of the proceeds from the maturing CD, other than letting it roll into a new CD, or buying a better CD elsewhere. You may want to spend some of the money, use it for rebalancing into stocks, or put some of it in a savings account to earn a bonus. For any of these alternatives, you close the CD the same as if you were moving the proceeds to another bank or credit union. Closing the CD is discussed in the last section.</div>
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I just transferred most of the proceeds of an Ally Bank CD that matured into a new <a href="https://home.capitalone360.com/lp-savingsbonus500" target="_blank">CapitalOne360 savings account</a>, because I will receive a bonus of up to $500 if I leave the money in the account for 90 days. This comes out to an APY of 4.89%, which is better than any CD deal. So I think of it as a 3-month CD earning 4.89% APY on up to $50,000, which you can't come close to with a competitive 3-month CD earning about 0.5% APY, or in an online savings account earning about 1%.</div>
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After the 90-day period is up, I'll move the money from the CapitalOne360 savings account to the <a href="http://www.kevinoninvesting.com/2015/10/northwest-fcu-3-year-304-add-on-cd.html" target="_blank">3-year "add-on" CD</a> that I recently opened at Northwest Federal Credit Union (NWFCU) (it was a great deal with an APY of 3.04%). Unfortunately, this deal is no longer available, but it was a great choice for someone with CDs maturing soon, since you can make additional deposits to the CD as your existing CDs mature, up to the $100,000 limit.</div>
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Actually, I'll probably fill up the NWFCU CD with proceeds from other CDs maturing before the 90-day period is up, but maybe another good CD deal will pop up by then. I'll be keeping my eye out for great CD deals at <a href="http://depositaccounts.com/">DepositAccounts.com</a> as CDs mature over the next few months.</div>
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I'll also probably use some of proceeds from CDs maturing over the next few months to rebalance back to my target allocations for my stock funds, unless stocks have gone up enough by then to get me back to my target allocations. If stocks go down more, I'll use more of the proceeds from maturing CDs to buy more shares of my stock funds.</div>
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Depending on the premiums of good direct CDs over Treasuries of the same maturities, I'll probably move the bulk of the proceeds from maturing CDs into more 5-year CDs. Currently the <a href="http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield" target="_blank">5-year Treasury yield</a> is about 1.4%, so at 2.25%, a good direct CD is earning a premium of about 0.85% (85 basis points), which is quite good, so CDs still look better than bonds to me. Of course as you can see from this post, managing direct CDs can be more work than just using a bond fund, so if simplicity is of paramount importance to you, just use a bond fund.</div>
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If bond yields were to rise much, decreasing the value of my bond funds accordingly, I'd probably use some of the maturing CD proceeds to buy more shares of them, assuming the best available CD rates didn't also rise proportionally.</div>
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If some or all of these alternatives sound too complicated, remember, you can always keep it simple, do nothing, and let the CD roll over into a new CD at the same bank or credit union, as long as you don't need the money for something else.</div>
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<b><u><br /></u></b></div>
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<b><u>Closing the CD</u></b></div>
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If you decide to pursue one of the alternatives other than doing nothing, you must notify the bank or credit union that you want to close the CD--i.e., not have it roll over to a new CD. With Ally Bank, I notify them of this on the day the CD matures using online chat; you also can do it by phone. You have 10 days from the maturity date to do this without incurring an early withdrawal penalty (the "grace period"). </div>
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I notify them that I want to close the CD that matured today, providing the last four digits of the CD account number, and that I want the proceeds deposited into my savings account or checking account, providing them with the last four digits of that account too. They ask a few questions, like why I'm closing the CD (better rate elsewhere), what is my phone number and social security number, etc. It takes about 5-10 minutes, and since I'm doing it using online chat, I can do something else in another window at the same time, keeping an eye on the chat window in the corner of my screen.</div>
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You may be able to notify your bank or credit union ahead of time to close the CD at maturity, but Ally Bank told me to just do it within the 10-day grace period of the maturity date, so that's what I do.</div>
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Closing the CD works the same in a taxable account or IRA. Just be sure that in an IRA you have the proceeds deposited into an IRA savings account within the same IRA at the bank or credit union. You don't want to unintentionally take an IRA distribution. </div>
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You can then transfer the money from the savings or checking account elsewhere if so desired, but for an IRA you'll want to do a direct, custodian-to-custodian IRA transfer. An alternative is to do an IRA transfer directly from the maturing CD into a new CD elsewhere, which is what I described in the blog post I referenced above (<a href="http://www.kevinoninvesting.com/2015/07/i-recently-completed-my-first-transfer.html">Kevin On Investing: First bank-to-bank IRA transfer from a maturing IRA CD</a>).</div>
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Hopefully this is enough information to help you to decide what to do with your maturing CD, and how to do it. If not, don't hesitate to ask questions, either in comments to this blog post, by email, or on the <a href="https://www.bogleheads.org/" target="_blank">Bogleheads forum</a>. I've done a <a href="https://www.bogleheads.org/forum/viewtopic.php?f=2&t=176245" target="_blank">Bogleheads forum post</a> linking to this blog post, so Bogleheads can post additional comments or questions there, and we can learn from each other.</div>
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Unknownnoreply@blogger.com5tag:blogger.com,1999:blog-775967109474059335.post-27886715579017556762015-10-01T18:36:00.000-07:002015-10-02T17:03:22.535-07:00Northwest FCU 3-year 3.04% Add-On CD<div dir="ltr" style="text-align: left;" trbidi="on">
Today someone asked a question on the <a href="https://www.bogleheads.org/forum/" target="_blank">Bogleheads forum</a> about saving for a house down payment in 3-5 years from now, so as part of answering the question, I checked the 3-year CD rates at <a href="https://www.depositaccounts.com/" target="_blank">DepositAccounts.com</a>. I was flabbergasted to see a rate of 3.04% APY at the top of the list (with the closest competition at 1.85%). This is a <a href="https://www.nwfcu.org/Personal_Services-Savings_Accounts-Certificates/" target="_blank">promotional CD special</a> ("Dream Fund Certificate") offered by <a href="https://www.nwfcu.org/" target="_blank">Northwest Federal Credit Union</a> (NWFCU), with a minimum deposit of $10,000 and maximum of $100,000. After finishing up <a href="https://www.bogleheads.org/forum/viewtopic.php?f=1&t=174871&p=2642367#p2642306" target="_blank">my answer</a> to the forum question, I quickly investigated the CD deal, then proceeded to complete the online application to join the credit union, open an account, and buy this CD. It took about 15 minutes.<br />
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<a name='more'></a>This CD has a relatively unique feature, in that you can make additional deposits to it at any time. This works out perfectly for me, because I have another CD maturing in a couple of weeks, so I was able to open the CD with some available cash, and will deposit more to it when my existing CD matures.<br />
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After reading the DepositAccounts.com <a href="https://www.depositaccounts.com/blog/2015/10/northwest-fcu-limited-time-top-rate-3year-addon-cd.html" target="_blank">blog post and comments</a> about this CD deal, I went to the NWFCU web site, and read the <a href="https://www.nwfcu.org/WorkArea/DownloadAsset.aspx?id=2287" target="_blank">disclosure document</a> (clicking on the link downloads a PDF file with the disclosure); I was impressed that they had a link to the disclosure in the short paragraph describing the CD deal, since the disclosure document often is not easy to find, if available at all, on a bank or credit union web site.<br />
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The disclosure lays out the terms pretty clearly. One term of note is that they explicitly state that early withdrawals are allowed:<br />
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: xx-small;"><b>Transaction Limitations</b>: Within the first 30 days that the certificate is open, the Credit Union will require 30 days’ notice of intent to withdraw funds as permitted in our Bylaws. <b>You may otherwise make withdrawals subject to the early withdrawal penalties stated below</b>.</span></div>
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<span style="font-family: inherit;">The early withdrawal penalty (EWP) is 366 days of interest, which is larger than the 180 days of interest that I consider the current standard for a good CD, but with only a 3-year term and this exceptional rate, the EWP doesn't bother me. If you did an early withdrawal after two years, you'd earn about 1.5% per year, which is competitive with top-tier 2-year CDs.</span><br />
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<span style="font-family: inherit;">One caution: some of the comments on the DepositAccounts.com blog post about this CD indicated that if the balance hits the maximum of $100,000, including reinvested interest, interest is no longer earned. That doesn't make sense to me, but unless verified otherwise, I would limit the maximum deposit to about $91,000, which will keep the value with reinvested interest under $100,000 at the end of three years.</span><br />
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<span style="font-family: inherit;"><b>UPDATE: </b>Several Bogleheads have posted in the Bogleheads forum that NWFCU customer service reps have told them that you can deposit the full $100,000 and still earn interest. I was also informed of the same thing via a private message (PM) from a Boglehead. The misinformation in the previous paragraph seems to have been just a misunderstanding about the CD disclosure statements by someone who commented on the </span>DepositAccounts.com blog post<span style="font-family: inherit;">. The Boglehead who sent me the PM also said the service rep said that the $15,000 limit on the initial deposit could be overridden by instructing them in an email to transfer a larger amount, up to the maximum $100,000.</span></div>
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<span style="font-family: inherit;">To get an idea of how good a CD rate is, I always compare it to the yield of a Treasury security of the same maturity. Currently the 3-year Treasury yield is 0.92%, so this CD rate is more than 2% (200 basis points) higher. For the CDs I've bought over the last five years, the average CD premium over Treasuries of the same maturities has been a little more than 100 basis points, and currently a good 5-year CD at 2.25% has a premium over a 5-year Treasury of about 90 basis points, so this is a fantastic deal.</span></div>
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<span style="font-family: inherit;">I am buying this CD in a taxable account. I did not investigate whether or not this CD can be bought in an IRA, and whether or not NWFCU will lock the rate during the 2-3 weeks it typically takes to complete an IRA transfer. Doing an IRA transfer for a CD special can be risky if the bank or credit union won't guarantee the rate, since these promotional rates typically don't last long.</span></div>
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The membership application can be completed entirely online, and as mentioned, it only took me about 15 minutes to do so, including the time to enter the information for my beneficiaries (so this is a Payable on Death or POD account). Some documents to be signed electronically will be emailed. This is exactly the same process used by USAlliance Financial--the credit union <a href="http://www.kevinoninvesting.com/2015/08/usalliance-financial-2-year-cd-227-apy.html" target="_blank">I recently posted about</a> joining to buy their 25-month CD special.</div>
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Based on what I read in the DepositAccounts.com blog post, I selected to join the Financial Awareness Network to meet the credit union eligibility requirements (for a one-time $10 fee). There are hundreds of organizations that qualify for membership, so you can scan the list to see if you are an employee or member of any of them, and if not, just select Financial Awareness Network.</div>
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As part of the online application, I selected to make my initial deposit to the CD with an electronic transfer from my checking account. The maximum initial deposit from an external account is $15,000, so apparently the only way get close to the maximum of $100,000 is to make additional deposits later, which is what I planned to do anyway.</div>
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I'm grateful to the Boglehead forum member who asked the question about saving for a 3-5 year period, as I may not have learned about this CD otherwise!</div>
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Unknownnoreply@blogger.com29tag:blogger.com,1999:blog-775967109474059335.post-57686680552387558712015-08-21T17:25:00.000-07:002015-08-21T17:25:00.492-07:00The Value of an Investment Policy<div dir="ltr" style="text-align: left;" trbidi="on">
If you've paid any attention to financial markets lately, days like today and weeks like this week provide examples of the value of establishing and following an Investment Policy (IP). Among other things, an IP establishes your target asset allocation and rebalancing policy. So when stocks drop much, all you do is check your current asset allocation to determine if your rebalancing policy requires shifting some money from fixed income (CDs, bonds, cash) to stocks.<br />
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If you're really lazy, which isn't necessarily bad when it comes to investing, your investment policy could include something as simple as contributing a certain percent of income to your 401k or 403b plan at work, and holding everything in a target date retirement fund. In this case, there is no need to check your portfolio or pay attention to financial news, since no rebalancing ever is required--the fund does it for you.<br />
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Or maybe you have one or two stock funds and a bond fund, and your rebalancing policy is to rebalance once per year on your birthday, or on some other set date. Then you can ignore your portfolio and financial markets except for that one day each year.<br />
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Another common approach is to use more than one fund, and rebalance when your actual asset allocation (AA) deviates from target by more than a predetermined amount. For example, you could have a target allocation of 70% stocks and 30% fixed income, with a rebalancing policy of rebalancing back to target if your asset allocation deviates by 5% or more from target. So you would sell stocks and buy fixed income if your AA hit 75/25, or vice versa if it hit 65/35.<br />
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If you hear or see that stocks have dropped a lot, it might be worth checking your AA against target. Using the example in the previous paragraph, if you check today and see that your AA is 67/33, you've done your financial work for the day, and can get on with other things, since your rebalancing band has not been breached.<br />
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Having an Investment Policy and sticking to it helps remove the emotion from investing, which almost always is a good thing.</div>
Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-775967109474059335.post-63991887521182890492015-08-16T21:31:00.000-07:002015-08-16T21:31:05.512-07:00Consumption Smoothing and Adjusting Your Frugality Setting<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;"><a href="http://www.investopedia.com/terms/c/consumption-smoothing.asp" target="_blank">Consumption smoothing</a></b><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;"> is the economic concept used to express the desire of people to have a stable path of </span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">consumption throughout their lifetimes</span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">. </span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">The ideal consumption smoothing case, assuming no bequest motives, is to save just enough during your working years to be able to spend your retirement savings to fund about same lifestyle in your retirement years, and to die broke.</span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;"> </span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">Of course since we don't know how long we'll live, or exactly what our expenses will be in retirement, this is a difficult ideal to achieve.</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">To give yourself a reasonable margin of safety for retirement, you may need to be </span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;"><b>more frugal</b> </span><b style="color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">in your accumulation years </b><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">than you want to be</span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">. </span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">Conversely, if your investment returns were better than expected, or perhaps you were just more frugal than you had to be while working and saving, it might be reasonable to be </span><b style="color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">less frugal</b><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;"> <b>in your</b> </span><b style="color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">retirement years</b><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;"> than you disciplined yourself to be in your accumulation years. Your consumption smoothing may not end up being ideal, but perhaps it then makes sense to work on overcoming your previously virtuous frugality, and spending more to enjoy your remaining years more.</span><br />
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<span style="background-color: white;"><span style="color: #222222; font-family: arial, sans-serif;"><span style="font-size: 16px; line-height: 19.2000007629395px;">I see some working people being less frugal than I think is prudent, and this may result in significant reductions in their lifestyles when they retire. They probably need to think more about consumption smoothing. But I also see some retired people being overly frugal after many years of </span></span></span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">assiduously </span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">developing and practicing great savings habits during their accumulation years. Consequently, they may be depriving themselves and perhaps their significant others of the fruits of their many years of working and saving. </span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">It's hard for most working people to save too much these days, so most of them should be saving as much as they possibly can for retirement. But for those of us who have been frugal, have saved diligently during our accumulation years, and perhaps have achieved good investment returns, it might take some work to shift the frugality gear down a notch or two in retirement.</span><br />
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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.2000007629395px;">I've seen more than one <a href="https://www.bogleheads.org/wiki/Bogleheads%C2%AE_investment_philosophy" target="_blank">Boglehead</a> post about the challenges of shifting from the frugality mentality of the accumulation years to a less frugal mentality, once they've realized that they've accumulated more wealth than they need to last them the rest of their lives. I've had to work on this myself, and it's still a work in progress.</span><br />
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<span style="background-color: white;"><span style="color: #222222; font-family: arial, sans-serif;"><span style="font-size: 16px; line-height: 19.2000007629395px;">So all of you working folks, please keep saving as much as you can for retirement. For those of us who've spent many years living below our means so that we can ensure a financially secure retirement, let's remind ourselves that we've met our retirement savings goal, and that we might want to work on developing different spending habits, lest we deprive ourselves and our significant others of enjoying our golden years as much as possible.</span></span></span></div>
Unknownnoreply@blogger.com3