Value at risk
VaR redirects here. For the statistical technique VAR, see Vector autoregression. For the statistic denoted Var or var, see Variance.In financial mathematics and financial risk management, value at risk (VaR) is a widely used risk measure of the risk of loss on a specific portfolio of financial exposures. For a given portfolio, time horizon, and probability p, the p VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is p. This assumes mark-to-market pricing, and no trading in the portfolio.For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% probability). A loss which exceeds the VaR threshold is termed a ""VaR break.""VaR has four main uses in finance: risk management, financial control, financial reporting and computing regulatory capital. VaR is sometimes used in non-financial applications as well.Important related ideas are economic capital, backtesting, stress testing, expected shortfall, and tail conditional expectation.