Conditional out-of-sample predictability of aggregate equity returns and aggregate equity return volatility using economic variables

Contrary to the myriad of studies that apply tests of unconditional predictive ability to quantify the out-of-sample predictive impact of economic variables on aggregate equity returns and aggregate equity return volatility, we evaluate the evidence of conditional predictive ability. Using monthly data from 1926m12 to 2019m12, we consistently fail to reject the equal unconditional predictive ability null hypothesis when predicting (forecasting) aggregate equity returns (aggregate equity return volatility) one-month ahead. In contrast, the equal conditional predictive ability null hypothesis is rejected more often. Upon rejection of the equal conditional predictive ability null hypothesis, we perform pseudo-real-time point prediction (forecast) selection, and find that it becomes possible to leverage certain variables into out-of-sample relative point prediction (forecast) accuracy gains. The statistical evidence of conditional predictive ability also translates to economic gains using the Value-at-Risk framework.