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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.
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-variance approach where the risk of a portfolio is measured by the variance of the ...
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 ...
Along the scenario approach, it is also possible to pursue a risk-return trade-off. [7] [8] Moreover, a full-fledged method can be used to apply this approach to control. [9] First constraints are sampled and then the user starts removing some of the constraints in succession. This can be done in different ways, even according to greedy algorithms.
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.
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 it occurring. [3] The former definition may not be a coherent risk measure in general, however it is coherent if the underlying distribution is continuous. [4]
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In financial mathematics and economics, a distortion risk measure is a type of risk measure which is related to the cumulative distribution function of the return of a financial portfolio. Mathematical definition