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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.
In financial mathematics, tail value at risk (TVaR), also known as tail conditional expectation (TCE) or conditional tail expectation (CTE), is a risk measure associated with the more general value at risk. It quantifies the expected value of the loss given that an event outside a given probability level has occurred.
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 .
However, it can be bounded by coherent risk measures like Conditional Value-at-Risk (CVaR) or entropic value at risk (EVaR). CVaR is defined by average of VaR values for confidence levels between 0 and α. However VaR, unlike CVaR, has the property of being a robust statistic. A related class of risk measures is the 'Range Value at Risk' (RVaR ...
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]
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.
Many risk measures have hitherto been proposed, each having certain characteristics. 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.
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.