Three Essays on Variance Risk and Correlation Risk

Abstract

This thesis focuses on variance risk and correlation risk in the equity market, and consists of three essays. The first essay demonstrates that the variance risk, mea- sured as the difference between the realized return variance and its risk-neutral expectation, is an important determinant of the cross-sectional variation of hedge fund returns. Empirical evidence shows that funds with significantly higher loadings on variance risk outperform lower-loading funds on average. However, they incur severe losses during market downturns. Failure to account for variance risk results in overestimation of funds' absolute returns and underestimation of risk. The results provide important implications for hedge fund risk management and performance evaluations. The second essay examines the empirical properties of a widely-used correlation risk proxy, namely the dispersion trade between the index and individual stock options. I find that discrete hedging errors in such trading strategy can result in incorrect inferences on the magnitude of correlation risk premium and render the proxy unreliable as a measure of pure exposure to correlation risk. I implement a dynamic hedging scheme for the dispersion trade, which significantly improves the estimation accuracy of correlation risk and enhances the risk-return profile of the trading strategy. Finally, the third essay aims to forecast the average pair-wise correlations between stocks in the market portfolio. I investigate a comprehensive list of forecasting models and find that past average correlation and the option-implied correlation provide superior out-of-sample forecasting performance compared to other predictors. I provide empirical evidence showing that the forecasts of average correlation can improve the optimal portfolio choices and substantially enhance the performance of active correlation trading strategies.