Journal of Risk

Evaluating covariance matrix forecasts in a value-at-risk framework

Jose A. Lopez, Christian A. Walter


Covariance matrix forecasts of financial asset returns are an important component of current practice in financial risk management. A wide variety of models are available for generating such forecasts. In this paper, the relative performance of different covariance matrix forecasts are evaluated using standard statistical loss functions and a value-at-risk (VaR) framework. Using a foreign exchange portfolio, it is found that covariance matrix forecasts generated from option prices perform best under statistical loss functions, such as mean-squared error. Within a VaR framework, the relative performance of covariance matrix forecasts depends greatly on the VaR models' distributional assumptions. Of the forecasts examined, simple specifications, such as exponentially weighted moving averages of past observations, perform best with regard to the magnitude of VaR exceptions and regulatory capital requirements. The results provide empirical support for the commonly used VaR models based on simple covariance matrix forecasts and distributional assumptions.

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