Chapter 11
Risk Management: Value at Risk
Value at risk (VaR) is a useful tool for assessing the financial risk in a portfolio of risky assets, and it is widely used to manage portfolio risk. After various financial disasters during 1993–1995, many banks began to adopt VaR as a key tool to manage market risk. The Basel Committee on Banking Supervision also adopted VaR as the international standard for regulatory purposes.1 Basel II defines three major components of risk that a financial institution will face: credit risk, operational risk, and market risk. The preferred approach to measure the market risk is VaR. Nonfinancial industries such as energy, agriculture, and airline industries also use VaR for risk management.
11.1 VaR of a Single Asset
Many portfolio managers interested in estimating the potential maximum loss over a given planning horizon at some given confidence level use VaR. VaR is the maximum expected loss that will not be exceeded with a specified probability over a predetermined time horizon. For example, with a 95 percent (equals 
) confidence level, VaR should exceed 5 percent (equals 
) of the total number of observations in the distribution. Popular choices of the confidence level are 95 percent and 99 percent, but the choice is arbitrary.
The formal definition ...
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