Sharpe Ratio

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The **Sharpe ratio** or **Sharpe index** or **Sharpe measure** or **reward-to-variability ratio** is a measure of the excess return (or risk premium) per unit of risk in an investment asset or a trading strategy, named after William Forsyth Sharpe. Since its revision by the original author in 1994, it is defined as:

where <math>R</math> is the asset return, <math>R_f</math> is the return on a benchmark asset, such as the risk free rate of return, <math>E</math> is the expected value of the excess of the asset return over the benchmark return, and <math></math> is the standard deviation of the excess of the asset return. (This is often confused with the excess return over the benchmark return; the Sharpe ratio utilizes the asset standard deviation whereas the information ratio utilizes standard deviation of excess return over the benchmark, i.e. the tracking error, as the denominator.) Note, if <math>R_f</math> is a constant risk free return throughout the period,

The Sharpe ratio is used to characterize how well the return of an asset compensates the investor for the risk taken, the higher the Sharpe ratio number the better. When comparing two assets each with the expected return <math>E</math> against the same benchmark with return <math>R_f</math>, the asset with the higher Sharpe ratio gives more return for the same risk....

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- <math>S = frac = frac,</math>

where <math>R</math> is the asset return, <math>R_f</math> is the return on a benchmark asset, such as the risk free rate of return, <math>E</math> is the expected value of the excess of the asset return over the benchmark return, and <math></math> is the standard deviation of the excess of the asset return. (This is often confused with the excess return over the benchmark return; the Sharpe ratio utilizes the asset standard deviation whereas the information ratio utilizes standard deviation of excess return over the benchmark, i.e. the tracking error, as the denominator.) Note, if <math>R_f</math> is a constant risk free return throughout the period,

- <math>sqrt=sqrt.</math>

The Sharpe ratio is used to characterize how well the return of an asset compensates the investor for the risk taken, the higher the Sharpe ratio number the better. When comparing two assets each with the expected return <math>E</math> against the same benchmark with return <math>R_f</math>, the asset with the higher Sharpe ratio gives more return for the same risk....

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