An Introduction to Value-at-Risk

An introduction to Value-at-Risk

Learning Curve

September 2003

Value-at-Risk

The introduction of Value-at-Risk (VaR) as an accepted methodology for quantifying

market risk is part of the evolution of risk management. The application of VaR has

been extended from its initial use in securities houses to commercial banks and

corporates, and from market risk to credit risk, following its introduction in October

1994 when JP Morgan launched RiskMetrics™. VaR is a measure of the worst

expected loss that a firm may suffer over a period of time that has been specified by

the user, under normal market conditions and a specified level of confidence. This

measure may be obtained in a number of ways, using a statistical model or by

computer simulation.

VaR is a measure of market risk. It is the maximum loss which can occur

with X% confidence over a holding period of n days.

VaR is the expected loss of a portfolio over a specified time period for a set level of

probability. For example if a daily VaR is stated as £100,000 to a 95% level of

confidence, this means that during the day there is a only a 5% chance that the loss the

next day will be greater than £100,000. VaR measures the potential loss in market

value of a portfolio using estimated volatility and correlation. The “correlation” referred

to is the correlation that exists between the market prices of different instruments in a

bank’s portfolio. VaR is calculated within a given confidence interval, typically 95%

or 99%; it seeks to measure the possible losses from a position or portfolio under

“normal” circumstances. The definition of normality is critical and is essentially a

statistical concept that varies by firm and by risk management system. Put simply

however, the most commonly used VaR models assume that the prices of assets in the

financial markets follow a normal distribution. To implement VaR, all of a firm’s

positions data must be gathered into one centralised database. Once this...