Conditional Correlation via Generalized Random Forests with Application to Hedge Funds

This paper introduces a simple yet powerful methodology for estimating correlations conditional on extra variables. Using recent developments in decision trees, we produce a consistent estimator of the conditional correlation with important implications in many applied areas, in particular financial markets. To gain a better understanding of the methodology and its accuracy, we simulate well-known settings to demonstrate the differences between constant correlation, non-constant correlations, and regression coefficients. We then provide some insights into financial asset behavior across market conditions by computing the correlation between the returns of the S&P 500 and different classes of hedge funds, conditioning on a popular financial factor, the VIX index. In particular, we find that some hedge-fund classes are indeed safe haven in times of high variance in the market. In general, we conclude that well-selected financial factors have explanatory power on the dependence structure between financial assets, revealing statistically significant non-constant conditional correlations, which further implies non-linear relations and non-Gaussian dependence structures among assets.