Economic value of modeling the joint distribution of returns and volatility: leverage timing

We propose a joint modeling strategy for timing the joint distribution of the returns and their volatility. We do this by incorporating the potentially asymmetric links into the system of 'independent' predictive regressions of returns and volatility, allowing for asymmetric cross-correlations, denoted as instantaneous leverage effects, in addition to cross-autocorrelations between returns and volatility, denoted as intertemporal leverage effects. We show that while the conventional intertemporal leverage effects bear little economic value, our results point to the sizeable value of exploiting the contemporaneous asymmetric link between returns and volatility. Specifically, a mean-variance investor would be willing to pay several hundred basis points to switch from the strategies based on conventional predictive regressions of mean and volatility in isolation of each other to the joint models of returns and its volatility, taking the link between these two moments into account. Moreover, our findings are robust to various effects documented in the literature.