Conditional Correlation via Generalized Random Forests; Application to Hedge Funds

Abstract

This paper introduces a simple yet powerful methodology for estimating the conditional correlation between financial assets given market variables. Using recent developments in decision trees, we produce a consistent estimator of the conditional correlation with wide and deep implications for analyzing financial markets. To better understand the methodology and its accuracy, we use well-known settings via simulation, demonstrating the differences between constant and non-constant correlations and regression coefficients. We then provide some insights into 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 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.

Keywords: Heterogeneous correlation; Random Forests; Decision Trees; Conditional Correlation

JEL Classification: C14, C58, G11