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The 5% Value at Risk of a hypothetical profit-and-loss probability density function. Value at risk (VaR) is a measure of the risk of loss of investment/capital.It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day.
An immediate consequence is that value at risk might discourage diversification. [1] Value at risk is, however, coherent, under the assumption of elliptically distributed losses (e.g. normally distributed) when the portfolio value is a linear function of the asset prices. However, in this case the value at risk becomes equivalent to a mean ...
Expected shortfall is also called conditional value at risk (CVaR), [1] average value at risk (AVaR), expected tail loss (ETL), and superquantile. [ 2 ] ES estimates the risk of an investment in a conservative way, focusing on the less profitable outcomes.
A set-valued risk measure is a function :, where is a -dimensional Lp space, = {: = (+)}, and = where is a constant solvency cone and is the set of portfolios of the reference assets. R {\displaystyle R} must have the following properties: [ 3 ]
The entropic value at risk (EVaR) is a coherent risk measure introduced by Ahmadi-Javid, [1] [2] which is an upper bound for the value at risk (VaR) and the conditional value at risk (CVaR), obtained from the Chernoff inequality.
The Marginal VaR of a position with respect to a portfolio can be thought of as the amount of risk that the position is adding to the portfolio. It can be formally defined as the difference between the VaR of the total portfolio and the VaR of the portfolio without the position.
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For (ii) on value at risk, or "VaR", an estimate of how much the investment or area in question might lose with a given probability in a set time period, with the bank holding "economic"-or “risk capital” correspondingly; common parameters are 99% and 95% worst-case losses - i.e. 1% and 5% - and one day and two week horizons. [28]