Out-of-Sample Equity Premium Prediction: Combination Forecasts and Links to the Real Economy

Source: Rapach, D. E., Strauss, J. K. & Zhou, G. (2010). Review of Financial Studies 23(2),

821–862.

TL;DR

A constructive answer to the Welch-Goyal pessimism: while individual predictors of the equity

premium fail out of sample, simple combinations of many individual forecasts (e.g., the mean of

predictors) deliver consistent, significant out-of-sample gains and are tied to the business cycle —

combination forecasts beat both the historical average and any single predictor.

Individual predictive regressions are unstable and overfit, so they fail out of sample. The paper asks

whether aggregating across many noisy predictors can recover real, usable predictability.

Combination forecasts (especially simple averages) produce positive out-of-sample R² where

individual models do not — they reduce forecast variance and are robust to model instability.

The predictability is countercyclical, strengthening in recessions, linking return predictability

to real-economic fluctuations.

Compute out-of-sample forecasts for many individual predictors, then combine them (mean, median,

trimmed mean, discounted MSE weights); evaluate with out-of-sample R² and utility gains against the

prevailing-mean benchmark.

Forecast combination / ensembling is a powerful antidote to overfitting — averaging many weak,

unstable signals beats betting on one.

Predictability is regime-dependent (stronger in bad times), which matters for timing and risk.

Rapach, D., Strauss, J. & Zhou, G. (2010) — Out-of-Sample Equity Premium Prediction: Combination Forecasts — Review of Financial Studies

Welch, I. & Goyal, A. (2008) — A Comprehensive Look at the Empirical Performance of Equity Premium Prediction — Review of Financial Studies

Timmermann, A. (2006) — Forecast Combinations — Handbook of Economic Forecasting