A Comprehensive Look at the Empirical Performance of Equity Premium Prediction

Source: Goyal, A. & Welch, I. (2008) · Review of Financial Studies 21(4), 1455–1508 · doi:10.1093/rfs/hhm014

TL;DR

A systematic out-of-sample test of the variables claimed to predict the equity premium — dividend

yield, earnings/payout ratios, book-to-market, interest rates and spreads, net issuance, cay — finds

that, despite often-strong in-sample fits, **not a single one would have helped a real-world investor

beat the prevailing historical-average benchmark out of sample**, and most would have hurt. A landmark

demonstration that in-sample predictability routinely fails honest OOS evaluation.

Decades of studies reported in-sample regressions Rₘ(t)−R_f(t) = γ₀ + γ₁·x(t−1) + ε(t) in which various

ratios predict excess returns. Goyal and Welch ask the only question that matters for an investor:

using only data available in real time, would these signals have beaten the prevailing-mean forecast

out of sample? They score forecasts by out-of-sample ΔRMSE / ΔMAE versus the prevailing mean (a

negative number means the predictor underperformed the mean).

Data/sample: monthly, quarterly and annual series; annual data back to 1872, monthly from 1927;

out-of-sample forecasts typically begin in 1965 (some panels begin forecasts in 1964).

Headline result: out of sample, essentially every predictor **underperforms the prevailing

mean** — e.g. at annual frequency the large majority of regressions deliver negative ΔRMSE.

In-sample performance is unstable, often driven by a few episodes (e.g. the 1973–75 oil shock)

and not robust across subperiods; underperformance occasionally reaches ~2–3% per annum.

Reply: Campbell & Thompson (2008) show economically motivated sign/magnitude restrictions

recover a small but real OOS R² (on the order of ~0.5% per month for some predictors) — enough to

matter for a mean-variance investor.

Always evaluate out of sample; a high in-sample R² or t-statistic is not evidence of a usable

signal. Use the prevailing mean as the benchmark to beat.

Economic restrictions and shrinkage toward sensible priors improve real-time forecasts.

Conclusions concern the aggregate equity premium, not cross-sectional anomalies.

OOS power depends on split date and estimation window; the published RFS (2008) version updates the

NBER w10483 (2004) working paper. Results are about predictability of the market, not about whether

the premium exists.

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

Campbell, J. & Thompson, S. (2008) — Predicting Excess Stock Returns Out of Sample — Review of Financial Studies

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

Provenance: verified/generated from the paper's full text.