VaR (value at risk) was invented by JP Morgan in 1994 as a general risk management tool and has now become the industry standard for risk. It has become a popular and important risk measure primarily because of the Basel Committee, who standardise international banking regulations and practises.
VaR lets an investor know in monetary terms how much one’s portfolio can expect to lose, for a given cumulative probability and for a given time horizon.
For example, for a cumulative probability of 99% over a period of 1 day, the VaR amount would tell us the amount by which one would expect the portfolio to lose e.g. $100. Mathematically we express this as.
Pr [portfolio loss · VaR] = 0.95%
Pr [portfolio loss · $100] = 0.95%
Note that Pr [. . .] denotes “cumulative probability of [. . .]” and is measured over the same time period as the loss.
VaR can be calculated by simulation using historical data or some mathematical formula. VaR can also be calculated by the “variance-covariance method” (also known as the delta-normal method) but makes unrealistic assumptions about portfolio returns e.g. returns are normally distributed.
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