Long-run risk-return trade-offs

Excess market returns are correlated with past market variance. This dependence is statistically mild at short horizons (thereby leading to a hard-to-detect risk-return trade-off, as in the existing literature) but increases with the horizon and is strong in the long run (i.e., between 6 and 10 years). From an econometric standpoint, we find that the long-run predictive power of past market variance is robust to the statistical properties of long-horizon stock-return predictive regressions. From an economic standpoint, we show that, when conditioning on past market variance, conditional versions of the traditional CAPM and consumption-CAPM yield considerably smaller cross-sectional pricing errors than their unconditional counterparts.