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### Finally, a model that accounts for mean-reverting margins and valuations.

Estimating future market returns is complex. Dr. John P. Hussman has popularized an approach that looks at currently observed valuations, inputs a steady-state earnings growth projection, and plugs in a future valuation. The Hussman forecast can be represented by the following equation:

Long term total returns =(1+g)(future CAPE / current CAPE)^(1/T)–1+dividend yield(current CAPE / future CAPE+1)/2, where CAPE=Cyclically adjusted Price to Earnings (i.e., "Shiller P/E").

Historically, this simple, yet elegant, technique has done a decent job bracketing realized long-term returns. By construction, the model has failed when valuations move to extremes, nonetheless, the methodology is fairly robust across time. In the figure below we calculate projected 10-year nominal S&P 500 returns with potential exit valuations of CAPE=5 (cheap) or an exit valuation of CAPE=10 (expensive). Peak-to-peak earnings growth is 6%. We also plot realized 10-year returns. Our approach is roughly analogous to Dr. Hussman.

While the Hussman model is a useful tool for predicting long-term returns, the method is unable to effectively model the real-world dynamics for parameters that matter to future returns. For example, the Hussman model makes an assumption of 6% peak to peak earnings growth. But is this a reasonable assumption if, for example, profit margins are at all-time highs and known to mean-revert? A more sophisticated model is needed to capture the mean-reverting dynamics of profit margins, as well as others. Another downfall of the simple Hussman approximation, is an inability to shed light on the distribution of future returns under different economic regimes. For example, plugging historical inputs into a model may be representative of the past, but are they relevant for the future? And if we change a model's parameters to reflect a "new normal," what do future returns look like?

**A Better Approach for Understanding Long-Term Returns**

Our approach to the long-term estimation problem begins with a 40,000 foot view of the drivers of long-term returns: revenue growth, profit margins, and valuations. These are uncontroversial and widely accepted factors that contribute to future returns. We conjecture that any long-term return projection models need to account for the empirically-observed dynamics of these variables. For each variable we run 1000 simulations of revenue growth, profit margins, and valuations to gain insight on the distribution of possible long-term returns under different scenarios. In particular, revenue growth is modeled by a stable growth pattern, but with bumps along the road. We model this "bump" aspect by adding a random volatility component in our simulations.

For profit margins, the dynamic is a bit different. Whereas revenues tend to grow over time, margins tend to mean-revert, in other words, currently high margins systematically drift back to the long-term average and currently low margins drift up to the long-term average. This mean-reversion reflects the competitive dynamics in the economy.

Finally, valuations are modeled in a similar fashion to margins—mean-reverting. Higher valuations are typically not followed with even higher valuations in the future (unless we are reliving the Internet Bubble).

For a more detailed explanation of our simulation model, please see our detailed report.

We conduct 1000 simulation of revenues, margins, and valuations associated with two states of the world: a "Good" case, which is characterized by inputs that represent historical averages (and where mean reversion occurs, but is not very aggressive), and a "Bad" case, which is characterized by inputs that reflect lower growth, lower valuations and margins, and higher volatility than observed historically (and where the mean reversion effect is more aggressive). The good state is meant to capture the status quo; the bad state reflects the possibility that government debt overhang causes growth in the future to be lower and more volatile, long-term steady-state valuations compress, and government intervention in the private sector causes businesses to earn lower steady-state margins.

In order to generate our estimates of long-term nominal 10-year returns for the S&P 500, we run 1,000 simulations of revenue growth, profit margins and valuations and generate 1,000 possible 10-year total return projections for each of our two regimes, the Good and Bad. The graph below highlights the histogram of possible 10-year total returns under our Good and Bad regimes:

Upon reviewing the output of our method simulations, we see that under Good conditions, one can expect to earn a 6.86% nominal compound annual growth rate (CAGR) over the next 10 years. Under Bad conditions, the expected CAGR drops to 3.43% and the distribution of CAGRs increases.

The approach we present is far from perfect. After all, we utilize a model, which by definition is not reality. Nonetheless, our systematic approach is comparatively free of the kinds of behavioral bias that affect "pundit predictions," which are often skewed by behavioral bias such as groupthink, overconfidence, anchoring, and so forth. We believe our estimation approach goes a long way towards accounting for the market's dynamic sensitivity to several potential outcome regimes, involving revenues, margins and valuations, and provides an additional level of insight into potential downside scenarios. We hope these observations can assist you in setting expectations for yourself and those who benefit from your investing.

Our estimations for potential long-term returns are not especially rosy, neither are they highly pessimistic. It is also important to highlight the return on bonds: 10-year bonds earn less than two percent and are less tax-efficient. How pension funds will hit 5 percent—let alone eight percent—bogeys will be interesting. Perhaps everyone will buy into the risk parity approach and create massively leveraged positions in treasury bonds. Good luck with that approach (and glad I'm not invested in a defined benefit pension plan).

*Wesley R. Gray, Ph.D. is a finance professor at Drexel University and the Executive Managing Member of Empiritrage, LLC, and SEC registered investment advisor. Wes is the co-author of Quantitative Value: A Practitioner's Guide to Automating Intelligent Investment and Eliminating Behavioral Errors. He has a BS from The Wharton School, University of Pennsylvania, and an MBA and a PhD in finance from the University of Chicago Booth School of Business.*