Estimating a Covariance Matrix for Market Risk Management and the Case of Credit Default Swaps

Abstract

We analyze correlation matrix estimation from the perspective of market risk management, where the goal is to obtain accurate estimates of portfolio risk across essentially all portfolios — even those with small standard deviations. We use the portfolio perspective to determine estimators, loss functions and regularizers particularly suitable for market risk management. We propose several specialized loss functions, and a simple but effective visualization tool to assess estimators. Proper regularization of the correlation matrix significantly improves dynamic covariance models. These methods are applied to credit default swaps (CDS), for which correlation matrices are used to set portfolio margin requirements for central clearing. Among the methods we test, the graphical lasso estimator performs particularly well. The graphical lasso and a hierarchical clustering estimator also yield economically meaningful representations of market structure through a graphical model and a hierarchy, respectively. We find that credit default swap log-differences are driven by a strong market factor. The additional effect of natural candidates for other observable market factors is small, but there are latent factors and direct pairwise dependencies at play. We also examine the relationship between credit default swap correlations and implied correlations extracted from equity prices through distance-to-default measures. The difference between actual and implied log-differences is driven by a common factor that may reflect a premium for risk and possibly liquidity.