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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.
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.
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 ...
The 5% Value at Risk of a hypothetical profit-and-loss probability density function. Value at risk (VaR) is a measure of the risk of loss of investment/capital. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day.
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.
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.
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:
Conditional value at risk is a distortion risk measure with associated distortion function () = {<. [2] [3] The negative expectation is a distortion risk measure with associated distortion function g ( x ) = x {\displaystyle g(x)=x} .