A New Measure of Cross-Sectional Risk and its Empirical Implications for Portfolio Risk Management

Abstract

Litterman, Scheinkman, and Weiss (1991) and Engle and Ng (1993) provide empirical evidence of a relation between yield curve shape and volatility. This study offers theoretical support for that finding in the general context of cross-sectional time series. We introduce a new risk measure quantifying the link between cross-sectional shape and market risk. A simple econometric procedure allows us to represent the risk experienced by cross-sections over a time period in terms of independent factors reproducing possible cross-sectional deformations. We compare our risk measure to the traditional cross-yield covariance according to their relative performance. Empirical investigation in the US interest rate market shows that 1) cross-shape risk factors outperform cross-yield risk factors (i.e., yield curve level, slope, and convexity) in explaining the market risk of yield curve dynamics; 2) hedging multiple liabilities against cross-shape risk delivers superior trading strategies compared to those stemming from cross-yield risk management.

Keywords: Risk Measures, Risk Management, Factor Analysis, Cross-Sections, Interest Rates

JEL Classification: C31, E43, G11