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The "expected shortfall at q% level" is the expected return on the portfolio in the worst % of cases. ES is an alternative to value at risk that is more sensitive to the shape of the tail of the loss distribution. Expected shortfall is also called conditional value at risk (CVaR), [1] average value at risk (AVaR), expected tail loss (ETL), and ...
The ex-post Sharpe ratio uses the same equation as the one above but with realized returns of the asset and benchmark rather than expected returns; see the second example below. The information ratio is a generalization of the Sharpe ratio that uses as benchmark some other, typically risky index rather than using risk-free returns.
Under the assumption of normality of returns, an active risk of x per cent would mean that approximately 2/3 of the portfolio's active returns (one standard deviation from the mean) can be expected to fall between +x and -x per cent of the mean excess return and about 95% of the portfolio's active returns (two standard deviations from the mean) can be expected to fall between +2x and -2x per ...
As a simple example to demonstrate the non-coherence of value-at-risk consider looking at the VaR of a portfolio at 95% confidence over the next year of two default-able zero coupon bonds that mature in 1 years time denominated in our numeraire currency. Assume the following: The current yield on the two bonds is 0%
In finance, Jensen's alpha [1] (or Jensen's Performance Index, ex-post alpha) is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. It is a version of the standard alpha based on a theoretical performance instead of a market index .
Risk premium is the product of the market price of risk and the quantity of risk, and the risk is the standard deviation of the portfolio. The CML equation is : R P = I RF + (R M – I RF)σ P /σ M. where, R P = expected return of portfolio I RF = risk-free rate of interest R M = return on the market portfolio σ M = standard deviation of the ...
A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. [1] It is used widely in finance and economics, the general definition being the expected risky return less the risk-free return, as demonstrated by the formula below. [2]
If Portfolio A has an expected return of 10% and standard deviation of 15%, while portfolio B has a mean return of 8% and a standard deviation of 5%, and the investor is willing to invest in a portfolio that maximizes the probability of a return no lower than 0%: SFRatio(A) = 10 − 0 / 15 = 0.67, SFRatio(B) = 8 − 0 / 5 = 1.6