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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...