Ultra-Simple Shiller’s CAPE : How One Year’s Data Can Predict Equity Market Returns Better Than Ten

Campbell and Shiller average 10 years of real S&P 500 earnings to construct its Cyclically Adjusted P/E ratio, or CAPE, which they then use to forecast its future 10-year returns. In essence, Campbell and Shiller kill two birds with one large stone - they use the 10-year average to reduce noise and also to obtain a measure of where in the economic cycle we currently are. We start by providing a theoretical foundation for the CAPE methodology, and demonstrate that the standard CAPE methodology does not accurately predict returns when CAPE is very depressed - an additional non-linear term is called for. In addition, we separate the problems of noise reduction and cyclicality, and kill three birds (noise reduction, cyclicality and nonlinearity) with three small stones. First, by eliminating the worst quarter's earnings each year, we reduce the noise in earnings by about 40%. Next, we measure our current position in the economic cycle using the Sales-to-Price ratio. Finally, we use a quadratic term to pick up the nonlinearity in the relationship between earnings yields and future returns, and use robust regression to minimize the impact of outliers.Our method provides significantly better out-of-sample forecasts of the return of the S&P 500 than does CAPE, while using less data and greatly reducing computational effort - there is, for example, no need to obtain data on CPI, or to average past earnings. We also avoid using traditional measures of significance such as t-statistics, and instead evaluate models using the correlation between their out-of-sample predictions of the future returns of the S&P 500 and its actual realized returns. Finally, we estimate the significance level of each predictor's predictions using simulation, freeing us from the tyranny of correcting t-statistics for endogeneity and overlapping observations