Return Predictability from Realized and Option-Implied Moments

In this paper we test which computational method, of computing statistical moments, yields time series that contain most information on future equity returns. The methods we consider are the realized, autoregressive forecasted realized (AR), and option-implied method, the latter both model-free and derived from a Generalized Beta Distribution of the Second Kind (GB2Q). Using a static time series regression, we find a significant positive relation between the volatility of the AR315d (estimated on 315 trading-days), modelfree, and GB2Q method and subsequent excess returns. We do not find any relation using the skewness, and kurtosis. The rolling window regressions show that the coefficients vary substantially over time. Furthermore, these results indicate that the higher moments do not improve the accuracy of forecasting the excess return, and that we lack the statistical support to prefer one method over another in terms of forecasting accuracy. In measuring the performance of trading strategies, created using an utility framework, we find that the model-free and AR315d method perform best, with Sortino ratios of 0.30, compared to 0.24 of the S&P 500 index. Second best is the GB2Q method, followed by the realized and AR15m method (estimated on 15 months). Measured in alpha, the AR315d method performs better than the model-free method. The performance of the daily AR method is enhanced when increasing the estimation window when estimating the AR coefficients. Imposing an upper bound constraint on the optimal weight, slightly improves the performance of all methods. Furthermore, we find that the contribution of the third and fourth moment are economically not significant, that none of the methods perform consistently over time, and that the performance is insensitive to changes in the relative risk aversion parameter.