Tuesday, April 25, 2017

Bond Basics: Part 7 (Duration)

Toward the end of the last post in this series, Bond Basics: Part 6, 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 duration. 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.

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.

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 information on the web about bond formulas and calculators, and maybe I'll come back to them later.

If you use your web browser to navigate to the Vanguard mutual funds webpage, with Bond attributes selected in the Show drop-down box on the right, you'll see Duration as one of the column headings. If you click on the Duration column heading, you'll see the following definition:
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.
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.

We can express this duration approximation relationship between change in bond or bond fund yield and price mathematically with the following formula:

  dP% = -D * dY

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.

Using the values in the Vanguard definition of duration quoted above, D = 2,  dY = 1 for a yield increase of 1 percentage point, and we would calculate dP% as:

  dP% = -D * dY
  dP% = -2 * 1
  dP% = -2%

Similarly, dY = -1 for a 1 percentage point decrease in yield, and the calculation would be:

  dP% = -D * dY
  dP% = -2 * -1
  dP% = 2%

If you scan down the list of bond funds on the Vanguard mutual funds page until you find Total Bond Market Index, which is a very popular bond fund among Bogleheads, you'll see the duration listed as 6.1 years, and you'll see a Yield to maturity 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.

With a duration of 6.1 years, if the yield to maturity (YTM) of TBM increased by one percentage point, from 2.6% to 3.6%, the share price of the bond fund (and the value of your shares) would decrease by about 6.1%. Conversely, if the YTM decreased by one percentage point, from 2.6% to 1.6%, the share price of the fund would increase by about 6.1%.

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.

In other words, duration is the most relevant measure of interest-rate risk, 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 term risk. In summary, the higher the duration, the higher the term risk.

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.

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 June 30, 2016 semiannual report and the December 31, 2016 annual report 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.

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 increased 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.

Plugging our values for D and dY into the duration approximation formula:

  dP% = -D * dY
  dP% = -5.9 * 0.70
  dP% =  -4.13%

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?

There are various ways to get historical share prices, but I'll use the Vanguard price history search tool, 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).

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:

  dP% = (P2 - P1) / P1 * 100
  dP% = (10.65 - 11.09) / 11.09  * 100
  dP% = - 0.0397 * 100
  dP% = -3.97%.

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.

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.

So what relevance does duration have to our investment decisions, specifically with respect to selecting a bond fund?

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.

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 Vanguard mutual funds web page with Annual average month-end returns selected 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.

Annual Returns
FundDuration1-year10-year
Short-Term Treasury2.2 years0.11%2.23%
Intermediate-Term Treasury5.2 years-1.41%4.32%
Long-Term Treasury16.7 years-5.04%6.49%

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.

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.

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.

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.

18 comments:

  1. So if 10 year bonds are only yielding 2.3% right now. If interests rates increase by 1% (which is historically likely), than I will lose 10% of my money...? Why in the world would anyone take on that much downside risk for 2.3% per year...? Why not just buy a 5 year CD with the same 2.3% yield, but with a defined early withdrawal penalty of only 1.15%.....
    Doesn't make any sense...? What am I missing?

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    1. Good question, and as readers of this blog know, I'm a big fan of direct CDs with competitive yields and low early withdrawal penalties, since you get higher yield with less risk compared to Treasuries. So personally, I would not buy a 10-year Treasury, or any other 10-year bond, in preference to a good CD.

      Before answering why someone might prefer the 10-year Treasury to the 5-year CD, I'll discuss how much you'd actually lose (or gain) in a few scenarios.

      The duration of a 10-year bond with a yield and coupon of 2.3% is closer to 9 years than 10 years, so the duration approximation would be a loss of about 9%. This is an approximation, and the actual loss for an immediate 1 percentage point increase in yield would be 8.4%.

      If the 1 percentage point increase occurred after one year, duration would have decreased since maturity would then be 9 years, and you'd lose about 7.7% in principal value. But, you would have received 2.3% in interest, reducing your overall loss to about 5.4%.

      Of course if you continued to hold to maturity, the value of the bond would recover to its original face value, and you'd end up earning about 2.3% annualized, assuming you could reinvest the interest payments at 2.3%.

      Of course you still do better with the 5-year CD at 2.3%, assuming you could reinvest at a higher rate when the CD matured in five years. If you could reinvest in another 5-year CD at 3.3% when the first CD matured, your overall annualized yield over the 10 years would be 2.8%.

      This raises the point that the 5-year CD has reinvestment risk compared to the 10-year Treasury. If good 5-year CD rates were lower than 2.3% when the CD matured in five years, you'd end up earning less by rolling the 5-year CD into a new 5-year CD and holding to maturity.

      It's not forordained that interest rates will rise. Although the 10-year Treasury yield, now at 2.35%, is a little higher than it was five years ago (about 2%), it's about the same as it was in mid-March 2011, and it was almost 3% in September 2013.

      One reason people give for preferring Treasuries to CDs, at least for part of the fixed-income portion of the portfolio, is that in a financial crisis, like we saw in late 2008, Treasuries can increase in value when stocks decrease in value, allowing you to sell the Treasuries at a profit to rebalance into stocks.

      My response to that is that the yield premium of a good CD more than makes up for the relatively small "rebalancing bonus" you get by rebalancing when Treasuries rise and stocks fall. Still, CDs are not the best fixed income to use for rebalancing, so you may want to keep something in a bond fund, or even cash, for rebalancing when stocks tank. During late 2008, Treasuries would have been the best bonds to own for this, since even high-quality corporate bonds lost value then.

      Still, you give up a lot of yield by holding Treasuries for this purpose, so I have not been doing so. It wouldn't be that big of a deal to pay a 1-2% early withdrawal penalty to redeem a CD early to buy stocks that had fallen 30% or more in value--you'd make that up in a year or two, compared to Treasuries of the same maturity, due to the higher yield of CDs of the same maturity.

      Finally, institutional investors can't take advantage of the federal deposit insurance for CDs, due to the relatively low limits, so for them, CDs have credit risk, unlike for retail investors who aren't investing billions of dollars in fixed income. So institutional investors have no choice if they want fixed income backed by the U.S. government.

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    2. Impressive response, thanks!

      PS. Is there any issue with getting banks to redeem a CD early in the midst of a moment like 2008? Have you ever actually tried it? I haven't ever tried but thought this might be part of the reason to opt for bonds vs CD's....

      P.P.S. Still a little confused why the duration of a 10 yr bond is closer to 9 years than 10....Apologize if you already covered this, but I must have missed it...?

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    3. More good questions.

      Early withdrawals
      -----------------

      I did early withdrawals from 2% CDs at Ally Bank and Barclays bank in late 2013 to buy 3% CDs from PenFed. It took about five minutes on the phone or using live chat, and money was available the next day.

      There often is language in the CD disclosure that allows the bank or credit union to disallow an early withdrawal or change the terms of existing CDs, but that has only happened in a couple of cases that I'm aware of. My general policy is to assume the worst case, and that I won't be able to do an early withdrawal, so I keep enough liquidity in bond funds, cash and CDs that will mature sooner to cover any expected an unexpected cash needs.

      I consider the early withdrawal option to be a valuable benefit that I probably, but not certainly, will be able to take advantage of if the situation warrants it.

      Duration vs. Maturity
      ---------------------

      I mentioned briefly in the blog post that duration was closely related to maturity, but that there are other factors involved (beyond the scope of the post). I also noted that for some Vanguard bond funds, duration and maturity are not the same. So I didn't really cover it in any depth.

      Another factor that affects duration is coupon rate. For a zero-coupon bond, coupon rate = 0%, and duration = maturity. Higher coupon rates lower duration, since more of your money is returned to you before maturity. At a coupon rate of 2.3% and yield of 2.3%, duration of a 10-year bond is 9 years. Raising the coupon rate to 3.3% lowers the duration to 8.7 years.

      Another minor factor is that there are different durations. The duration that's relevent here is modified duration (spreadsheet function MDURATION), which is slightly lower than Macaulay duration (spreadsheet function DURATION), but the difference is small enough to ignore, especially at low yields. So I usually just use DURATION, but technically we should use MDURATION for the price sensivity to yield change measure.

      Finally, modified duration is an approximation of the price change / yield change relationship, since it is essentially the straight-line tangent to a curve at a certain point on the curve (i.e., the derivative at a point on the curve). To determine the actual price change for a given yield change we can use the PV or PRICE functions for the two different yields. The result will be a bit different than that predicted by MDURATION, and the difference increases as the yield change increases (because you move further from the original tangent point on the curve).

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    4. thanks for the quick and comprehensive response!

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  2. Do you have any thoughts on deciding when to hold cash in a mmf at say 1%, versus buying a 5 yr CD?
    I seem to be perpetually debating this decision.
    Let's say for example, a 5 yr CD yields 2%, and has a 6 month EWP.
    So in round numbers, the breakeven is ~ 1 yr if you could get 1% in MMF.
    Ok, so now what?
    Assuming your only goal is to maximize long term yield, which is the better choice...? Do you apply some kind of probability that interest rates will go up or down within a year? Or do you just accept that can't predict interest rates and always opt for the CD in this example?
    You seem like a very smart guy so just wondering how you think about this?

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    1. Good question, and one that fixed-income investors always are faced with. In a nutshell, are you better off rolling shorter-term securities for N years or buying an N-year security? Should I roll 1-year Treasuries for five years or buy a 5-year Treasury? Should I roll 1-year CDs for five years or buy a 5-year CD? Should I roll a 0-year security (a money market or savings account) for 365 days or buy a 1-year CD?

      If we knew the answer to that, the yield curve would be such that either solution would provide the same return. Investors would drive the prices/yields to ensure it. This actually is the basis of the expectations hypothesis to explain the yield curve.

      However, since we don't know the answer, there are other factors that affect the yield curve, such as term risk--i.e., investors want higher yields for the greater uncertainty of investing further out on the curve. The formal name for this is liquidity preference.

      Unfortunately, we don't know how much of each factor is influencing the yield curve, so we really just don't know which is the best course.

      I do accept that I can't predict interest rates--I don't think anyone can. I try to position myself so that I won't get hurt too bad if rates generally increase--I may even benefit--and I'll also do OK if rates are flat or drop.

      Good direct CDs seem to be the best ticket for that, considering that my average yield premium over Treasuries of same maturity is over 1 percentage point (e.g., CD at 3% if Treasury yield at 2%) for CDs bought over the last 6.5 years. I'll earn more than the Treasury held to maturity no matter what (well, unless the bank/CU fails, in which case I may have to take my money back early, and reinvest it at a lower rate, but this is very low probability if you look at bank failure rates), and if rates increase enough, I might earn more (as in the case of redeeming my 2% CDs early and buying 3% CDs).

      For your particular dilemma, you can almost always earn more in a good CD after doing an early withdrawal after one year than you earn at 1% in a savings account or money market fund. For example, now I could buy a 5-year CD at 2.75% with an early withdrawal penalty (EWP) of six months of interest. This pulls ahead of a 1% savings account by 10 months (after paying the EWP), and by one year will have earned 1.37% after EWP. Maybe the savings account rate will increase enough over the year to match that, but I doubt it.

      Even an Ally Bank 5-year CD at 2.25% with an EWP of five months of interest earns 1.31% if you do an early withdrawal after one year.

      At two years you're up to 1.79% or 2.08% after EWP with the two CDs mentioned. Your savings account rate would need to increase to 2.6-3.2% after one year to beat the CD after two years. I wouldn't bet on that.

      If you're uncomfortable relying on the early withdrawal option, you could look at laddering your CDs. I see 1-year CDs in the 1.4-1.5% range, so a decent premium over 1% to lock your money up for one year.

      As a retiree, I generally like to keep enough in cash to cover at least a few months of expected and unexpected expenses. But I don't like to sell shares of my bond funds after they've dropped 3-4%, or my stocks after they've dropped 10-20% (unless I'm tax-loss harvesting), and I'd rather not lose 1-1.5% to do an early withdrawal unless I'm doing it to reinvest at a higher rate. Others don't have this concern, and would rather keep a bare minimum in cash earning 1%, and I can't argue too much with that.

      Cash hasn't done well at all in recent years compared to bonds or CDs, but as I mentioned at the end of the blog post, if we look at periods prior to 1982 when rates were rising, cash did better than bonds over a number of fairly long periods. Good CDs with low EWPs might do better than cash in scenarios like this, as long as banks continued to offer them and didn't clamp down on early withdrawals.

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    2. One other thought: if you're unsure, do some of each. Keep half in a savings account a 1%, and put the other half into a good CD with a low EWP. This lowers your return but also lowers your term risk. At least this is a way to help get over your analysis paralysis.

      If rates increase enough, you'll be glad you kept some in reserve at the lower rate to invest at the subsequent higher rate. If they don't, you'll be glad you put some into the CD.

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  3. Thanks for the great comments, Kevin.
    Nice to be reassured that not missing something out in left field somewhere.
    Will stay the course with CD's....at least until Equities get interesting again ....but that's looking like it might be a while....
    Happy retirement, Frank

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    1. I've had a 30% target allocation to equities for some years now, so I hold stocks whether they're interesting or not. The CDs came out of my bond funds, so now I have about 30% stocks, 50% CDs, and 20% bonds.

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    2. With equity valuations at historically high levels, I understand being light on equities right now. But if you don't mind my asking, is your plan to bring that back to 50 or 60% eventually?

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    3. No--I have no plans to increase my stock allocation to 50-60%. My asset allocation (AA) is based on ability, willingness, and need to take risk. I don't need to take more risk in stocks to ensure a comfortable retirement. I probably have the ability to take more risk, but during the financial crisis of 2008/2009, I learned a lot about my willingness to take risk, and decided that 30% in stocks was enough. It was pretty scary watching a large chunk of my wealth evaporate after having recently retired, and although I kept rebalancing into stocks as they continued to decline, it was quite difficult emotionally to do so.

      I believe my willingness to take risk has increased since then, due to more study and more experience following a disciplined investment policy that includes a policy asset allocation target and a rebalancing policy. However, I don't think I'll really know for sure until we have another severe bear market, and we haven't had one since the financial crisis.

      So, an element of my policy is to revisit my target stock allocation when we have another severe bear market, with a drop of 30-40% in the equity portion of my portfolio, which is 60% U.S. stocks, 40% international stocks, and is tilted to small-value. I'll then reevaluate my ability and willingness to take risk, and consider not only rebalancing back to my target allocation to stocks of 30%, but also increasing that allocation. Until then, my plan is to stay at 30%.

      Another way to approach your AA in retirement it is to have enough in safe assets to fund your residual living expenses (RLE) in retirement. RLE are expenses not covered by social security and other reliable income streams. This portion of your AA is sometimes referred to as the liability matching portfolio (LMP). You can invest the rest in a risk portfolio (RP), that could be a combination of stocks and bonds, or even 100% stocks.

      The LMP/RP approach leads me to the same conclusion as the ability, willingness and need to take risk framework. During the next really big stock decline, I'll take a closer look at how large my LMP needs to be. If my emotional reactions (willingness to take risk) allow it, and I decide I have more in safe assets than I need for my LMP, then I may increase my target allocation to stocks, and thus increase my RP.

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    4. Interesting discussion you have going.

      Did you apply some process to arrive at 30% equity threshold?

      I ask because as of recently, I'm down to 4% equity. I started reducing from 50% equity in 2013 and have procedurally brought it down with the latest sale today.
      There just isn't any rationale I can see for the current level of the market. PE10=29, etc, etc.
      I really hadn't planned to ever go beneath 25% equity (per Ben Graham), but can't stop myself from taking the profits when it feels the market is again a house of cards.
      Similar to you, I actually have enough to carry us through retirement without much stock exposure, but my plan is to get back in when valuation ratios return to more historically normal levels.
      Therefore, per your framework of "need to take risk", I guess mine is zero. But I don't fully accept that investing in the stock market = "taking risk"--Just as long as you don't buy when history says you shouldn't.
      Any thoughts on your 30% threshold would be appreciated as I like the disciplined approach you are following.

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    5. Honestly, I didn't arrive at 30% in stocks through a highly analytical process. I was "value averaging" cash from some real estate sales into stocks and bonds when 2008 hit, and I just kept at it, and somehow ended up at 30%.

      My need to take risk probably justifies a 0% stock allocation, and my ability to take risk probably justifies something higher than 30%. My willingness to take risk, tested severely in late 2008 / early 2009, helped me settle on 30%.

      I just don't trust my ability to time the market, whether by using PE10 or any other method, so the farthest I push it is to rebalance back down to 30% more aggressively than waiting to hit 35%. So that's my form of "taking profits" as U.S. stocks keep soaring to new heights.

      One probelem with using something like PE10 to market time is deciding what's "normal". We haven't had "historically normal" PE10 levels in quite a few years, yet stocks have had decent returns while PE10 levels have remained at historically high levels. If we continue to have decent stock returns despite historically high PE10 levels, I'll be glad I've maintained at least a 30% allocation to stocks. When stocks eventually tank, I'll be glad that I had only a 30% allocation to stocks.

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    6. Interesting.

      As they say, maybe its more important to pick and stick to a specific plan than it is to waste too much time worrying about which plan to pick.

      I know in the past when I've made mistakes, it normally has something to do with changing my plan midstream (often as "justification" for doing what feels good at the new moment).

      Its these memories that have me second guessing my decision to take profits rather than staying at 50% --undeterred.

      But then again, if someone was offering to pay me $100K for a car that I bought for $30K, I wouldn't hesitate to sell.

      So even if I could wait a little longer and maybe sell it for $150K, I'm still pretty darn happy to take the money and run.

      Good luck and thank you for setting up this site and sharing all your impressive knowledge.

      Good stuff.

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  4. Kevin - Here's an observation:

    I've studied the goody out of Buffett's investment process for analyzing equities. I've read Ben Grahams books, etc, etc....Then after all that analysis, Buffett concludes, everyone should just buy an S&P500 index fund and forget about it....Even backs up his comment with his now famous "bet"....

    Similarly, you've laid out this beautiful series to describe how bonds work....I actually learned a lot about the mechanics of the process from you....
    But in parallel to the Buffett conclusion, it sounds like the conclusion on the fixed income side is that we should just all buy 5 yr CD's and forget about it...

    So would we really have all been smarter over the years to just set up a 50-50 portfolio that holds the S&P500 and 5 yr CD's, and forget about it....?

    Maybe we're all just victims of the salesmen (eh hem, I mean financial advisors) from Fidelity, Vanguard, etc in making us think there's more to investing than just implementing a very simple plan and forgetting about....

    After all, why do I need Fidelity's expertise to buy the SPY and a few 5 yr CDs...?

    Thank you for shining a light on this...!

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    1. Agreed that we don't need advice from financial advisors if we're willing to learn and follow the fundamentals of investing--especially if their interests aren't aligned with ours, as would be the case with Fidelity. By contrast, Vanguard is likely to put you into a simple, low-cost portfolio of index funds, but I don't see much point in paying them for that (other than the small amount they get from the fund expenses). However, even Vanguard is not going to recommend that you buy CDs directly from a bank or credit union, and that's a blind spot of theirs.

      So Vanguard, Buffett, and those of us who follow the low-cost index fund approach are on the same page when it comes to stock funds. Vanguard and I would generally prefer a total stock market index fund to an S&P 500 index fund, because we want some exposure to small-cap stocks, but the difference is immaterial compared to high-cost actively managed funds. Many of us, including Vanguard, also think it's rational to hold international stocks as well.

      Although I think good direct CDs clearly are a better deal than bonds, especially on a risk-adjusted basis, taking some term risk and even credit risk in bonds sometimes pays off. I've earned more from my bond funds over the last 6.5 years than I have from my CDs, but that's mostly due to the credit risk being rewarded, with less contribution from the term risk (I haven't used Treasury funds).

      It's obvious that CDs have done and will do better than Treasuries of the same maturity if held to maturity, since the yield premiums have been very rich most of the time over the last 6.5 years, and currently are quite good. It's less certain with an intermediate-term Treasury fund, which doesn't hold its bonds to maturity, since it's uncertain how much you'll gain or lose from the price-change component of return as bonds "roll down the yield curve", yields/prices change, and the change in valuations is incorporated into the fund value.

      Over the last 6.5 years I figure I've averaged about 2.5% annually from my CDs, while the Vanguard Intermediate-Term Treasury fund (VFIUX for Admiral shares) has returned 2.23%. Of course the CD return was achieved with much less term risk, and if/when the term risk finally shows up for more than a year or two, the CD advantage will be more clear.

      As an example of credit risk being rewarded, my Vanguard Intermediate-Term Investment-Grade fund (VFIDX for Admiral shares) has returned 4.05% during the same period. So I'm glad I continued to hold some of that, and some other bond funds with some credit risk and at least intermediate-term term risk.

      But we shouldn't confuse strategy with outcome, so we don't want to pile into a bond fund just because it's had better returns over the last 5-6 years. If we were going to do that, we might as well go 100% stocks, since they've had much higher returns over that time period.

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    2. Well summarized!
      Thank you for the insights

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