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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.
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 ...
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 .
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.
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.
Market risk: Variable annuities are subject to market fluctuations, and the value can go up or down based on the performance of the underlying investments, potentially even resulting in a loss of ...
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...
How variable rate caps work. In many cases, lenders set caps on variable-rate products. This was designed to protect consumer borrowers from the kind of runaway interest the country saw during the ...