What performance should investors expect from the S&P 500 Index based on price-to-earnings (P/E) and Cyclically-Adjusted Price-to-Earnings (CAPE, or P/E10)? In their November 2020 paper entitled “Extreme Valuations and Future Returns of the S&P 500”, Shaun Rowles and Andrew Mitchell take a layered “regression upon a regression” approach to predict S&P 500 Index returns and level. First, to estimate future returns, they run a linear regression on P/E, P/E10, S&P 500 dividend yield, inflation, 10-year U.S. Treasury note yield, historical 1-year, 3-year, 5-year and 10-year S&P 500 Index returns and percentiles of many of these variables within their respective historical distributions. Then, they run separate linear regressions to predict 1-year, 3-year, 5-year and 10-year future annualized returns. Finally, they run a linear regression to model current S&P 500 Index level for comparison to actual current level. Using Robert Shiller’s U.S. stock market and economic data spanning January 1871 through June 2020, they find that:
- As of June 2020:
- P/E is 32.2, at the 98th percentile of full-sample monthly values, with all higher values occurring since January 1999, mostly during June 2001-December 2002 and November 2008-January 2009. These higher values follow crashes and are (unexpectedly?) attractive market entry points.
- P/E10 is 28.8, at the 94th percentile of full-sample monthly values. The 94 months with higher values occur during July 1929-October 1929, February 1997-April 2002 and March 2017-February 2020.
- Regarding accuracy of predicted returns:
- At a 1-year horizon, R-squared is 0.27 with standard error 0.17 (not effective).
- At a 3-year horizon, R-squared is 0.41 with standard error 0.09 (not very reliable).
- At a 5-year horizon, R-squared is 0.39 with standard error 0.06 (a little better).
- At a 10-year horizon, R-squared is 0.60 with standard error 0.03 (much better).
- S&P 500 Index level predictions produce a very high 0.93 R-squared, with predicted returns forward from June 2020 as follows:
- 1-year return through June 2021: 13.6%.
- 3-year annualized return through June 2023: 8.4%.
- 5-year annualized return through June 2025: 7.1%.
- 10-year annualized return through June 2030: 6.8%.
In summary, evidence indicates predictability of future U.S. stock market returns based on regressions of historical market and economic variables.
Cautions regarding findings include:
- The sample period is not long in terms of number of independent 10-year intervals. Moreover, relationship between economic and market conditions and future returns may change across generations.
- The degree to which the methodology is in-sample is not clear. Regressions may use full-sample values of variables (e.g. percentile ranks) in regressions, thereby incorporating look-ahead bias.
- The S&P 500 Index time series is not stationary, but instead generally rising. Applying simple regressions to non-stationary series can produce dramatically spurious results.
- The paper does not test any strategies for exploiting findings of predictability.
For related research, see results of this search, especially “CAPE (P/E10) Version of Fed Model?”.
