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Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst % of cases.
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 ...
The discounted maximum loss is the expected shortfall at level =. It is therefore a coherent risk measure . The worst-case risk measure ρ max {\displaystyle \rho _{\max }} is the most conservative (normalized) risk measure in the sense that for any risk measure ρ {\displaystyle \rho } and any portfolio X {\displaystyle X} then ρ ( X ) ≤ ρ ...
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 .
For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, that means that there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one-day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% probability).
The use of expected shortfall instead of value at risk as a measure of risk under stress; thus ensuring that banks capture tail risk events; The risk of market illiquidity; FRTB additionally sets a "higher bar" for banks to use their own, internal models for calculating capital, as opposed to the standardised approach. [2]
If the Social Security Administration had used the CPI-E to calculate the 2025 COLA, seniors would have gotten a 3% raise instead of 2.5%. That would've increased the average check by $58 per month.
The most well-known examples of risk deviation measures are: [1] Standard deviation ... is Expected shortfall. See also. Unitized risk ...