In a recent blog post, I reviewed a new book on the future of the Equity Risk Premium (ERP). For those who are not familiar with the ERP, it is the additional return that investors expect to receive for bearing the risk of owning company stock vs. owning a low-risk asset like government bonds. As readers of the book, *Rethinking the Equity Risk Premium* will discover, there is little agreement on how the ERP should be measured historically and even less consensus on how to estimate the future ERP.

We all know that there is no guarantee that stocks will deliver higher returns than bonds. In fact, at the depths of the last market crash (think back to early 2009) bonds had out-performed stocks over a trailing period of more than 40 years. If markets are at all rational, it would make sense that investors who own stock in companies should tend to be rewarded beyond those who own bonds. Stocks are (in general) riskier and we hope that stock investors will receive higher returns to compensate for the additional risk. If you read the book, you will find that there is broad agreement on the fact that its rational to expect stocks to return more than other less risky asset classes. However, you'll also see there is also an emerging consensus that the ERP will vary over time. If you buy into the market when prices are low relative to earnings or dividends, you can rationally expect to have a higher return on your equities than if you invest when prices are high relative to earnings and dividends. This makes perfect sense to me.

## Expected Value vs. Real Life Returns

It is crucial to understand that even if you have a perfect estimate of the *expected* return for stocks vs. bonds, there is no guarantee that you will actually end up with an *actual* return equal to the *expected* return.

For example, let’s imagine that the expected return of the S&P 500 is 8% per year, with annualized volatility (i.e., risk) of 15% per year. Every year, your best estimate for the return of the S&P 500 is that you will gain 8%, plus or minus 15% (in fact, two-thirds of the time, you'll find that the actual returns from the S&P 500 will fall into this range). Roughly one-sixth of the time the return of the S&P 500 will be above 23% (8%+15%) and one-sixth of the time the return will be below -7% (8%-15%). On average, you are going to make approximately 8% per year. If you were to invest and wait ten years, you'll have a one-in-twenty chance of ending up with an aggregate **loss** of around -10% at the end of that period.

We can account for the risk associated with varying returns from stocks from year to years. Indeed, this is precisely what Monte Carlo simulation is used for (for more on my Monte Carlo simulation, see "Risk, Return and Low Beta Stocks"). The problem here is that one of the key numbers that determines the outcomes from Monte Carlo simulations is the assumed ERP. This is why I call the ERP the *biggest unknown in financial planning*. In my recent book review, I note that experts come up with a wide range of estimates of the expected returns from stocks and bonds. It is crucial, however, to take the next step and to examine how different estimates of the ERP impact real-world financial plans.

Let’s look, for example, at how different ERP numbers impact the amount of income that an investor can expect to be able to safely draw from her retirement portfolio. Technically speaking, the ERP is defined as the additional return that equity investors can expect to receive beyond some very low-risk benchmark (the lack of a common benchmarks is discussed in the above book review). For this discussion purposes, let’s simplify the problem to estimating the expected future return of the S&P 500.

## How Much Income is Considered "Safe"?

One of the core issues that retirees face is determining how much income that they can safely draw from their portfolios. This so-called Safe Withdrawal Rate (SWR) is obviously going to be impacted by the expected future return of equities and I will use the S&P 500 as a proxy for equities. (The term "safe" is not meant to imply without risk).

Let’s examine the case of a recent retiree, Sue, who retired in 2011 at age 65 and is going to draw income from her portfolio starting in 2012. She holds a portfolio that is 50% in an S&P 500 stock fund and 50% in an aggregate bond fund. Both are low-cost index funds (Vanguard's Total Bond Market Index Fund (VFINX) or SPDR S&P 500 (SPY) for the stock fund and Vanguard's total Bond Market Index fund (VBMFX) and iShares Barclays Aggregate Bond Fund (AGG). I have run Monte Carlo simulations using an assumed 8.3% expected return for the S&P 500 (the baseline setting for Quantext Portfolio Planner, the Monte Carlo model that I designed) and calculated an SWR for the 50/50 portfolio. I then reduced the expected (average) annual return for equities and re-calculated the SWR. Before continuing, I will note that 8.3% in average annual return is fairly optimistic, but this estimate is well below the value that Peng Chen, the president of Ibbotson Associates, comes up with in his chapter in the ERP book.

So, if Sue follows the "4% rule," she will be able to draw 4% of the current value of her portfolio this year, and then escalate that amount to keep up with inflation at an assumed 3% increase in income each year. The Monte Carlo simulation suggests that Sue will be quite safe following this type of constant draw rate, although not perfectly safe. The Monte Carlo simulations suggest that Sue will have a 10% chance of completely exhausting this portfolio by age 88. For the purposes of this article, I will not ask whether this is an appropriate risk for Sue to take. I will just assume that this risk level is what Sue is targeting.

What if the "correct" estimate for the expected return of the S&P 500 is actually 6.3% rather than 8.3%? To have the same confidence in being able to fund a constant inflation-adjusted income stream from this portfolio, Sue must reduce here income draw to 3.4% of the value of her portfolio at the start of 2012. If the "correct" estimate for the expected return of the S&P 500 is 4.3% per year, she can only draw an income equal to 3% of the value of her portfolio at the start of 2012. (I have varied the historical periods used to initialize the model, including using the trailing 3-, 5-, and 20-year periods and the results are remarkably stable). Over the past ten years, the S&P 500 has provided a compound annual return (source: Morningstar) of about 4.2%. When I calculate a simple arithmetic annual return, I get a trailing 10-year average annual return of around 5.2%. Over the past 20 years, the S&P 500 has provided an arithmetic annual return of 9.3%.

## Substantial Uncertainty Ahead

Looking forward, many people believe that the future returns of stocks will be well below the levels seen in the last 20 years but, hopefully, above the levels in the last ten years. Frighteningly enough, however, the volatility level of the S&P 500 over the past 20 years is pretty low and is below the future expected level predicted by Ibbotson. Given the magnitudes of the boom and bust cycles that we have experience in this period, this should give investors pause. There is substantial uncertainty in our estimates for the future expected return of stocks and, as I have shown with my results in this article, there is consequently substantial variability in the amount of income that retirees can plausibly plan for.

While recent research has highlighted how uncertainty in estimating the expected future return for stocks impacts investment risk, there has been surprisingly little analysis of how this "estimation risk" impacts long-term savings requirements, investing strategy, and sustainable income. In this article, I have obviously just scratched the surface of this crucial problem. Given that estimation risk is an unavoidable part of investing, the best approach is to stress test your own retirement plans.

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