Horizon effect in the term structure of long-run risk-return trade-offs

The horizon effect in the long-run predictive relationship between market excess return and historical market variance is investigated. To this end, the asymptotic multivariate distribution of the term structure of risk-return trade-offs is derived, accounting for short- and long-memory in the market variance dynamics. A rescaled Wald statistic is used to test whether the term structure of risk-return trade-offs is flat, that is, the risk-return slope coefficients are equal across horizons. When the regression model includes an intercept, the premise of a flat term structure of risk-return relationships is rejected. In contrast, there is no significant statistical evidence against the equality of slope coefficients from constrained risk-return regressions estimated at different horizons. A smoothed cross-horizon estimate is then proposed for the trade-off intensity at the market level. The findings underscore the importance of economically motivated restrictions to improve the estimation of intertemporal asset pricing models.