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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.
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), which is a robust version of CVaR. [41]
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.
The authors start by proposing an auxiliary function (), where is a vector of portfolio returns, that is defined by: = {+ [(,)] +} They call this the conditional drawdown-at-risk (CDaR); this is a nod to conditional value-at-risk (CVaR), which may also be optimized using linear programming. There are two limiting cases to be aware of:
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.
Expected shortfall (ES; also called conditional value at risk (CVaR), average value at risk (AVaR), expected tail loss (ETL)) Tail value at risk; Statistical dispersion; Discounted maximum loss; Indifference price; Measures Dual-beta. Downside beta; Upside beta; Upside potential ratio; Upside risk; Downside risk; Sortino ratio; Omega ratio ...
That is, if portfolio always has better values than portfolio under almost all scenarios then the risk of should be less than the risk of . [2] E.g. If is an in the money call option (or otherwise) on a stock, and is also an in the money call option with a lower strike price.
Therefore, by definition, bPOE is equal to one minus the confidence level at which the Conditional Value at Risk (CVaR) is equal to . bPOE is similar to the probability of exceedance of the threshold x {\displaystyle x} , but the tail is defined by its mean rather than the lowest point x {\displaystyle x} of the tail.