Professor Robert Shiller’s work and his famous CAPE (cyclically-adjusted price-to-earnings) ratio is well known among the investment community. His methodology for assessing a valuation of the U.S. equity market is not the first one but is surely the most cited and the most discussed. There are numerous papers that tweak or adjust Shiller’s methodology to assess better if U.S. equities are under- or over-valued. We recommend the work of Wang, Ahluwalia, Aliaga-Diaz, and Davis (all from The Vanguard Group ) in which they use a combination of machine learning and a regression-based approach to obtain forecasted CAPE ratio, and subsequently, U.S. stock market returns, more accurately.
Authors: Wang, Ahluwalia, Aliaga-Diaz, Davis
Title: The Best of Both Worlds: Forecasting US Equity Market Returns using a Hybrid Machine Learning – Time Series Approach
Machine-learning forecasts have similar forecast errors to a traditional return forecast model based on lagged CAPE ratios. However, machine-learning forecasts have higher forecast errors than the regression-based, two-step approach of Davis et al  that forecasts the CAPE ratio based on macroeconomic variables and then imputes stock returns. When we combine our two-step approach with machine learning to forecast CAPE ratios (a hybrid ML-VAR approach), U.S. stock return forecasts are statistically and economically more accurate than all other approaches. We discuss why and conclude with some best practices for both data scientists and economists in making real-world investment return forecasts.
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