Value at Risk (VaR) is a measure of the risk of investments. It estimates how much a set of investments might lose, given normal market conditions, in a set time period
such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses.
In financial mathematics and financial risk management
, VaR is defined as: 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, that means that 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.