Cape vs the fed model: comparative analysis of the out-of-sample performance in predicting future stock returns

Abstract

The goal of this thesis is to compare the out-of-sample performance in predicting future stock returns of the Fed model and Shiller's cyclically adjusted price-to-earnings ratio (CAPE). The two models are also augmented with 10-year Treasury bond yield. Additionally, a version of CAPE that uses after-tax corporate pro ts and a Fed model adjusted for perceived risk are analyzed. The four models are tested using US market time series in a period ranging from 1871 to 2016 using regression analysis and compared using visual inspection of plots, forecast statistics, and forecast equivalence tests. We nd that in-sample and out-of-sample tests show low R2, which may still have economic signi cance for risk-averse investors. Versions of CAPE model dominate the Fed model alternatives in-sample. Out-of-sample, traditional CAPE exhibits very limited ability to generate accurate forecasts for long investment horizons of 20 years, while Fed model performs better at 1-year horizon. Alternative versions of the two models do not exhibit signi cant improvement in equity return predictability. So, for strategic asset allocation, CAPE and Fed should be used with caution as complementary tools and in conjunction with diversi cation.