Quantitative Investing with Tail Behavior—A Distributional Approach

In previous chapters, we introduced classical mean–variance methodologies. Classical methodologies have been used widely in risk management, such as the use of standard deviation for risk; alpha models, such as the use of OLS for weighting schemes; and modern portfolio theory, such as the mean–variance optimization. However, these are all based on the assumption that the first two moments will capture most information about asset returns, which is usually not true of real-world finance data, where fat and long tails are often the case. In this chapter, we present a distributional approach to capture tail behaviors for quantitative investing. Quantile regression (QR), a frontier methodology that extends beyond the median into tail percentiles, provides a useful tool for incorporating tail information into portfolios. We explore how QR can be employed for risk management, alpha modeling, and portfolio construction. The last section introduces R codes and packages for QR.