A counterfactual valuation of the stock index as a predictor of crashes

Stock market fundamentals would not seem to meaningfully predict returns over a shorter-term horizon - instead, I shift focus to severe downside risk (i.e., crashes). I use the cointegrating relationship between the log S&P Composite Index and log earnings over 1871 to 2015, combined with smoothed earnings, to first construct a counterfactual valuation benchmark. The price-versus-benchmark residual shows an improved, and economically meaningful, logit estimation of the likelihood of a crash over alternatives such as the dividend yield and price momentum. Rolling out-of-sample estimates highlight the challenges in this task. Nevertheless, the overall results support the common popular belief that a higher stock market valuation in relation to fundamentals entails a higher risk of a crash.