A commonly used methodology for estimating market risk that has been endorsed by regulators and financial industry advisory groups is value at risk (VaR). Financial institutions with significant trading and investment volumes have adopted the VaR methodology in their risk management operations; corporations have used VaR for risk reporting. In general, VaR estimations can aid in decisions involving capital resource allocation, setting position limits, and performance evaluation.
The standard VaR computation (e.g., delta-normal VaR) requires that the underlying return generating processes for the assets of interest be normally distributed, where the moments are time invariant and can be estimated with historical data. Neftci (2000) points out that extreme events are structurally different from the return-generating process under normal market conditions. Höchstötter et al. (2005) and Rachev et al. (2005b, 2007b) make the same argument, focusing on the stylized fact that returns are heavy tailed. Brooks et al. (2005) argue that heavy tailedness might lead to an underprediction of both the size of extreme market movements and the frequency with which they occur. Khindanova et al. (2001) propose a methodology for computing VaR based on the stable distribution.
Despite the increased use of the VaR methodology, it does have well-known drawbacks. VaR is not a coherent risk measure and does not give any indication of the risk beyond the quantile. Beder (1995) has empirically demonstrated how different VaR models can lead to dramatically different VaR estimates. Moreover, when employing the VaR methodology, it is possible for an investor, unintentionally or not, to decrease portfolio VaR while simultaneously increasing the expected losses beyond the VaR (i.e., by increasing the “tail risk” of the portfolio). There are superior measures to VaR for measuring market risk. Expected tail loss (or expected shortfall), for example, is a coherent risk measure that overcomes the conceptual deficiencies of VaR.
Even with these well-known limitations, however, VaR remains the most popular measure of market risk employed by risk managers. Dowd (2002) identifies two characteristics of VaR that make it appealing to risk managers. First, VaR provides a common consistent measure of risk across different positions and risk factors. Second, it takes account of the correlation between different risk factors. Dowd also offers an explanation for the popularity of VaR given its well-documented limitations and the superiority of risk measures such as expected tail loss. First, it is a simple measure of expected tail risk. Second, VaR is often needed to estimate the expected tail loss if there is no formula to calculate expected tail loss directly.
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A New Approach for Using Lévy Processes for Determining High- Frequency Value-at-Risk Predictions
