Value at Risk (VaR)

Value at risk (VaR) is a measure of how the market value of an asset or of a portfolio of assets is likely to decrease over a certain time, the holding period (usually one to ten days), under 'normal' market conditions. As such it is a measure of risk.

It is typically used by security houses or investment banks to measure the market risk of their asset portfolios.

Calculating VaR

Theory

VaR is measured by using normal distribution theory.

VaR = amount at risk to be lost from an investment under usual conditions over a given holding period, at a particular "confidence level".

Confidence levels are usually set at 95% or 99%,

i.e. for a 95% confidence level, the VaR will give the amount that has a 5% chance of being lost.

Illustration

A bank has estimated that the expected value of its portfolio in two weeks' time will be $50 million, with a standard deviation of $4.85 million.

Using a 95% confidence level, identify the value at risk.

Solution

A 95% confidence level will identify the reduced value of the portfolio that has a 5% chance of occurring.

From the normal distribution tables, 1.65 is the normal distribution value for a one-tailed 5% probability level. Since the value is below the mean,  -1.65 will be needed.

z = (x - µ)/s

(x - 50)/4.85 = -1.65

x = (-1.65 × 4.85) + 50 = 42

There is thus a 5% probability that the portfolio value will fall to $42 million or below.

A bank can try to control the risk in its asset portfolio by setting target maximum limits for value at risk over different time periods (one day, one week, one month, three months, and so on).

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