A Proposal for Evaluating Value-at-Risk Models

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La Trobe University--Australia

Value-at-risk (VAR) models are used to measure the market risk of financial assets or portfolios of assets. Specifically, they are used to measure the potential loss resulting from an adverse market movement with a given probability. While the use of VAR models is increasing, a question arises as to how well they perform in practice because these models are based on different approaches (parametric, historical, and simulation approaches). Moreover, even within one approach, several varieties may appear, depending, for example, on how the portfolios standard deviation is measured (equally weighted, exponentially weighted, and so on). Since these different models produce different results, criteria must be found by which the best model is selected.

For this purpose, Hendricks [Economic Policy Review, 1996] uses nine criteria to evaluate performance based on how closely the risk measures produced by the various models correspond to actual outcomes. Some of these criteria are the mean relative bias, root mean square relative bias, fraction of outcomes covered, and correlation between risk measures and absolute value of outcome. The problem with this approach is that the conclusions are based on the numerical value rather than the statistical significance of the criteria. For example, how does one know if the difference between the mean relative biases of the two models is statistically significant?

The alternative procedure suggested here allows for deriving inference about the statistical significance of the relative performance of two competing VAR models. It is based on the test suggested by Ashley et al. …