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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.
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 .
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 ...
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 ...
Financial risk modeling is the use of formal mathematical and econometric techniques to measure, monitor and control the market risk, credit risk, and operational risk on a firm's balance sheet, on a bank's accounting ledger of tradeable financial assets, or of a fund manager's portfolio value; see Financial risk management.
The scope here - ie in non-financial firms [12] - is thus broadened [9] [67] [68] (re banking) to overlap enterprise risk management, and financial risk management then addresses risks to the firm's overall strategic objectives, incorporating various (all) financial aspects [69] of the exposures and opportunities arising from business decisions ...
Tail conditional expectation; Value at risk; Convex risk measure Entropic risk measure; Coherent risk measure. Discounted maximum loss; Expected shortfall; Superhedging price; Spectral risk measure; Deviation risk measure. Standard deviation or Variance; Mid-range Interdecile range; Interquartile range
A core technique continues to be value at risk - applying both the parametric and "Historical" approaches, as well as Conditional value at risk and Extreme value theory - while this is supplemented with various forms of stress test, expected shortfall methodologies, economic capital analysis, direct analysis of the positions at the desk level ...