Estimating the correlation of asset returns: A quantile dependence perspective

Abstract

In the practice of risk management, an important consideration in the portfolio choice problem is the correlation structure across assets. However, the correlation is an extremely challenging parameter to estimate as it is known to vary substantially over the business cycle and respond to changing market conditions. Focusing on international stock markets, I consider a new approach of estimating correlation that utilizes the idea that the condition of a stock market is related to its return performance, particularly to the conditional quantile of its return, as the lower return quantiles reflect a weak market while the upper quantiles reflect a bullish one. Combining the techniques of quantile regression and copula modeling, I propose the copula quantile-on-quantile regression (C-QQR) approach to construct the correlation between the conditional quantiles of stock returns. The C-QQR approach uses the copula to generate a regression function for modeling the dependence between the conditional quantiles of the stock returns under consideration. It is estimated using a two-step quantile regression procedure, where in principle, the first step is implemented to model the conditional quantile of one stock return, which is then related in the second step to the conditional quantile of another return. The C-QQR approach is then applied to study how the US stock market is correlated with the stock markets of Australia, Hong Kong, Japan, and Singapore.