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Expected shortfall is considered a more useful risk measure than VaR because it is a coherent spectral measure of financial portfolio risk. It is calculated for a given quantile -level q {\displaystyle q} and is defined to be the mean loss of portfolio value given that a loss is occurring at or below the q {\displaystyle q} -quantile.
Under some formulations, it is only equivalent to expected shortfall when the underlying distribution function is continuous at (), the value at risk of level . [2] Under some other settings, TVaR is the conditional expectation of loss above a given value, whereas the expected shortfall is the product of this value with the probability of ...
The average value at risk (sometimes called expected shortfall or conditional value-at-risk or ) is a coherent risk measure, even though it is derived from Value at Risk which is not. The domain can be extended for more general Orlitz Hearts from the more typical Lp spaces .
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.
(ii) For Value at Risk, the traditional parametric and "Historical" approaches, are now supplemented [32] [27] with the more sophisticated Conditional value at risk / expected shortfall, Tail value at risk, and Extreme value theory.
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions , such as banks and insurance companies, acceptable to the regulator .
Standard deviation and expected shortfall are subadditive, while VaR is not. Subadditivity is required in connection with aggregation of risks across desks, business units, accounts, or subsidiary companies.
The most popular tail risk measures include conditional value-at-risk (CVaR) and value-at-risk (VaR). These measures are used both in finance and insurance industries, which tend to be highly volatile, as well as in highly reliable, safety-critical uncertain environments with heavy-tailed underlying probability distributions. [7]