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In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure. Deviation risk measures generalize the concept of standard deviation .
The standard deviation is a deviation risk measure. To avoid any confusion, note that deviation risk measures, such as variance and standard deviation are sometimes called risk measures in different fields.
That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. [1] [2] Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. [1] A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
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 ...
The MPT is a mean-variance theory, and it compares the expected (mean) return of a portfolio with the standard deviation of the same portfolio. The image shows expected return on the vertical axis, and the standard deviation on the horizontal axis (volatility). Volatility is described by standard deviation and it serves as a measure of risk. [7]
One measure of the statistical risk of a continuous variable, such as the return on an investment, is simply the estimated variance of the variable, or equivalently the square root of the variance, called the standard deviation. Another measure in finance, one which views upside risk as unimportant compared to downside risk, is the downside beta.
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 .