## Saturday, October 15, 2016

### Calculating Required Retirement Savings Rates: Part 4

In the prior posts in this series I outlined a method for estimating how much you should be saving for retirement, discussed how to estimate expenses in retirement, and discussed how to estimate your Social Security retirement benefit. 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?

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).

The yield on the 30-year TIPS as of 10/13/2016 was 0.71% (Daily Treasury Real Yield Curve Rates), 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.

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% (Daily Treasury Nominal Yield Curve Rates). 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%.

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.

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.

Looking at this chart 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 another 30-year TIPS series 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%.

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.

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 Part 3), 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%.

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.

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?

In his short booklet If You Can (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.

(The link provided above links to a PDF version of If You Can, which Bernstein kindly makes available for free. If you'd like the convenience of reading a Kindle version, you can purchase it from Amazon for the princely sum of \$0.99).

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.

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: Political Calculations: The S&P 500 at Your Fingertips.

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 this paper, which I think does a pretty good job of demonstrating the uncertainty in using this approach.

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%).

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.

As discussed in Part 1, 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.

#### 1 comment:

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