# Handbook of Research Methods and Applications in Empirical Finance

## Handbooks of Research Methods and Applications series

## Edited by Adrian R. Bell, Chris Brooks and Marcel Prokopczuk

# Chapter 15: Quantifying the uncertainty in VaR and expected shortfall estimates

## Silvia Stanescu and Radu Tunaru

## Extract

Since it was first proposed in 1996 by the RiskMetrics Group of J.P. Morgan, valueat-risk (VaR) has become the standard market risk metric. Assuming that the losses and profits given by a chosen portfolio are measured relative to a time horizon h, the VaR_,h of that portfolio is the monetary amount such that a loss more severe than VaR_,h can occur only with a probability smaller than _. In other words, the investor or risk manager is 100(1 _ _)% confident that losses larger than VaR_,h will not materialize at the horizon h. For example, if, for a portfolio, we consider _ = 5% and h = 1 year and VaR5%,1yr is equal to £1 million, then there should be only a 5 per cent chance of losing £1 million or more over a one year period. An important point to make is that the definition of VaR is given under normal market conditions so that if extreme market conditions appear before the end of the horizon then large losses may materialize that could decimate the value of the portfolio. Hence, VaR is a measure of market risk but one should bear in mind that other types of risk, such as operational risk or credit risk, may impact negatively on the value of the portfolio. Calculating VaR is a forecasting exercise by nature and one may wonder what is the performance of this type of forecast.

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