We develop a new framework for multivariate intertemporal portfolio choice that allows us to derive optimal portfolio implications for economies in which the degree of correlation across industries, countries, or asset classes is stochastic. Optimal portfolios include distinct hedging components against both stochastic volatility and correlation risk. We find that the hedging demand is typically larger than in univariate models, and it includes an economically significant covariance hedging component, which tends to increase with the persistence of variance–covariance shocks, the strength of leverage effects, the dimension of the investment opportunity set, and the presence of portfolio constraints.

Using a novel data set on correlation swaps, we study the relation between correlation risk, hedge fund characteristics, and their risk-return profile. We find that the ability of hedge funds to create market-neutral returns is often associated with a significant exposure to correlation risk, which helps to explain the large abnormal returns found in previous models. We also estimate a significant negative market price of correlation risk, which accounts for the cross-section of hedge fund excess returns. Finally, we detect a pronounced nonlinear relation between correlation risk exposure and the tail risk of hedge fund returns.