Jeremy Siegel’s dictum – to invest in stocks for the long run – faces a new challenge. A recent paper by Robert Stambaugh, a Wharton colleague, and Lubos Pastor of the University of Chicago says that once you take into account the uncertainty of estimating future returns, stocks are not nearly as attractive to retirement-oriented investors as Siegel has claimed.
I’ll look at Pastor and Stambaugh’s research, but first I’ll review the rationale behind Siegel’s reasoning and explain why this is important to investors with long-time horizons.
American investors have an equity-oriented retirement model and increasingly fund their retirements through defined contribution plans. The conventional wisdom is that equities should play a major role in the asset allocation. Siegel is perhaps the best-known advocate for an equity-centric approach to asset allocation for retirement savings.
If we assume that stocks will return 8% per year with a 15% annualized volatility, for example, we can immediately see the virtues of Siegel’s argument. As one’s holding period increases, the probability that stocks will underperform bonds or risk-free assets diminishes.
But many investors are questioning whether they have the risk tolerance to hold substantial allocations in stocks given the volatility in equity markets in recent years, despite the long-term evidence that equities justify their volatility. Siegel steadfastly stands by his argument in favor of stocks.
Pastor and Stambaugh’s recent study presented a challenge to the case for equities. They approached this issue from a new angle in a 2009 paper titled Are Stocks Really Less Volatile In The Long Run? This paper is now listed as forthcoming in the Journal of Finance on Pastor’s website.
Pastor and Stambaugh argue that Siegel falsely assumes that investors can be highly confident that equities will outperform in the future because they have in the past. The problem is that investors never know with a high degree of certainty what the average return will be for stocks or other risky asset classes, nor can investors be very certain what future volatility will be. In other words, there is substantial estimation risk in addition to market risk. As Pastor said in a 2009 interview:
We are not interested in the backward-looking historical volatility but in the volatility that matters to forward-looking investors. Historical volatility is somewhat relevant to investors, but it does not fully capture all the uncertainties that investors face. Investors care not only about historical estimates but also about the uncertainty associated with those estimates. That uncertainty, which is sometimes called “estimation risk,” is included in the forward-looking measures of volatility that we compute. We find that estimation risk rises rapidly with the investment horizon, pushing up long-run volatility.
Siegel’s argument that the expected return of stocks justifies their risks relies on the fact that U.S. stocks have delivered remarkably high (6% real) average annual returns going back as far as 1802. He assumes that this risk premium will persist and that we can estimate the expected future return of stocks on this basis.
Could investors have known ahead of time that the average real return from stocks would have been this high? Pastor and Stambaugh argue that they could not. Can investors plausibly use a very long period of history as the basis for an accurate expected return as we look into the future? Once again, Pastor and Stambaugh argue that this is not reasonable. Because of uncertainty about estimating expected returns, investors looking forward face a higher level of risk as the time horizon increases. In practical terms, this means that if we use an expected return that is too high, the impact of the estimation error grows in time due to compounding.
The challenge of estimating return and volatility for a portfolio through time is considerably harder than the problem Pastor and Stambaugh describe. They are only estimating expected return for equities as a broad asset class. For real-world portfolios, we need to estimate risk and return for a series of asset classes (at the very least for stocks and bonds) and the expected correlations between them.
There are a variety of ways to accomplish this task. (For a review of the various formal methods, see this paper by Ibbotson) For a methodology for projecting portfolio return and risk to be considered reasonable, it must take into account more than historical data; you need to test any formalism that purports to do so. It is not enough, for example, to say that stocks have generated outsized returns relative to risk over some arbitrary number of years and then to extrapolate this into the future. You must also show that this approach has led to good decisions on a rolling basis.
I have studied the problem of portfolio estimation risk using a Monte Carlo asset allocation that I designed called Quantext Portfolio Planner (see this paper, for example). I have found that my system and others like it lead to considerably improved asset-allocation decisions and higher risk-adjusted returns, even in light of estimation risk.
Even if the risk associated with stocks is higher than previously thought in the long run, for example, what about the estimation risks with bonds or inflation? In his 2009 interview, Pastor tacitly acknowledges this dilemma:
Q. If someone were to act on your findings and reduce his or her equity exposure in favor of bonds, how could he or she hedge the risk of inflation eating into the nominal value of the returns?
A. They could buy TIPS. But we have not analyzed the long-horizon volatility of bonds, so I do not wish to give any investment advice on stock-bond allocations.
This is a crucial element that is missing from Pastor and Stambaugh’s findings, which hinders its applicability to portfolio management. To make the best investing decisions, we must consider estimation risks across all applicable asset classes. While stocks may be riskier than previously thought, so might bonds and cash.
Some simulation examples
To make the issues more concrete, let’s look at a specific example. Consider the typical retirement portfolio below:
This portfolio has 45% equities, 45% fixed income and 10% real estate. To estimate the future risks and returns associated with this portfolio is a somewhat involved process. The starting point is to specify the equity risk premium — the excess return (above a risk-free asset) that investors can expect for bearing the risks associated with equities. The baseline assumption that I used was an 8.3% nominal average annual return for the S&P 500 and 15.1% annualized volatility. The forward-looking projection is that this portfolio will provide 7.5% in average annual return with expected volatility of 12.3%. All simulations used market data available through May 2011 in deriving the forward-looking projections.
As an alternative case, we might consider a 100% bond portfolio:
This portfolio of bonds has an expected return of 3.9% with expected volatility of 4.8%.
Not surprisingly, over extended investment horizons, the model portfolio looks more attractive than the bond portfolio, even though the latter out-performed the former in recent years.
A great deal hinges on the starting assumption for the equity risk premium. As a stress test, then, let’s look at the projections if the S&P 500 has a nominal expected return of 5.3% per year rather than 8.3% per year. We consider an investor who starts with zero and invests $10,000 per year, adjusting the annual investment upwards by 3% per year to keep up with inflation for 20 years.
These results are quite striking. Even if we over-estimated the return of equities quite dramatically for the model portfolio, an expected annual return of 5.3% for equities results in a median portfolio value that is higher than the bond portfolio. Not surprisingly, in the worst 20th percentile (1-in-5) outcome, the bond portfolio outperforms the model portfolio, but the difference is small. The ending portfolio value of the model portfolio is 12.2% lower than the value of the bond portfolio in the 1-in-5 worst case.
Under what circumstances would these results suggest that a long-term investor would prefer the bond portfolio to the model portfolio, if the goal is to have the highest probability of accumulating a substantial nest egg? For the all-bond portfolio to look attractive, one would need to have a very bearish view on the long-term returns of equities or believe that the estimation risk associated with bonds is low (which in turn means assuming that interest rate risk is low).
Additional thoughts on estimation error
There is no reason to believe that estimation risk is the same across all investments. This is an important theme that I have not seen discussed in any of the research. Some investments are very likely to have lower estimation risk than others, and vice versa. Pastor alluded to this in the quote above. Given that stock prices in a rational market are determined by the discounted value of future earnings, more consistent earnings should correspond to less uncertainty in calculating expected returns.
Research by Douglas Skinner at the University of Chicago and Eugene Soltes at Harvard found that dividend-paying stocks had more consistent earnings (e.g., higher earnings quality) than non-dividend payers. This implies that dividend-paying stocks will have lower estimation risk in their future total returns, too.
Siegel acknowledged that stocks that pay dividends are more attractive than those that do not, but his argument is based on the value effect rather than estimation risk. (The value effect assumes that stocks with lower P/E ratios — in this case, also dividend-payers — generate higher returns.)
The one argument I have found that stocks benefit from lower estimation risk is the consistent assertion by Jeremy Grantham, head of GMO, that the only really attractive asset class is what he calls high-quality stocks. Those stocks have more predictable earnings and often pay dividends, which reduces the estimation risk in forecasting expected return. I have previously written that this effect may be a key factor in making income-oriented strategies attractive, because they may have less estimation error.
Conclusions
Pastor and Stambaugh’s analysis of the importance of estimation error is very timely, given that many individuals and institutions are re-evaluating their investment strategies. But dealing with estimation risk should not pose a paralyzingly daunting challenge for investors. We cannot assume that stocks will provide a 6% real return simply because they have done so in the past (although Siegel made this argument as recently as July 2010). On the other hand, it is quite straightforward to test models for asset allocation in a way that takes estimation error into account.
The idea that we need to account for estimation risk may be novel in asset allocation, but it is well-known in other fields (such as weather and climate forecasting). Pastor and Stambaugh’s research helps to place this issue on more formal grounds in the investing literature, which is why it is so important. Their results are consistent with common sense. It makes no sense to look at the average return of stocks and bonds over 50 or 100 years and assume that investors could have made rational a priori assumptions about the future returns.
Even if we substantially reduce our equity risk premium assumptions, there is still a strong argument to be made that long-term investors should substantially allocate to equities. I have shown only one example, but the broader message is evident. If there is an equity risk premium (and we have reason to believe that there will be a meaningful equity risk premium in the future), the best decision for long-term investors will be to maintain exposure to equities. We must always be mindful that the best way of maximizing the probability of future well being also exposes us to the possibility of a bad outcome, as Bodie has argued.
Pastor and Stambaugh’s work on estimation risk is crucial for investors allocating their life savings. While focusing on total return is standard practice today, introducing estimation risk raises a compelling argument in favor of income-oriented investing, an approach that will benefit from lower estimation risk.
Geoff Considine is the founder of Quantext, Inc. and the developer of Quantext Portfolio Planner (QPP), a portfolio management tool for advisors. More information is available at www.quantext.com.
Quantext is a strategic adviser to FOLIOfn,Inc. (www.foliofn.com), an innovative brokerage firm specializing in offering and trading portfolios for advisors and individual investors.
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