The Sharpe ratio / Sharpe index / Sharpe measure / 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. It is defined as:
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Where, R is the asset return, Rf is the return on a benchmark asset such as the risk free rate of return, [R − Rf] is the expected value of the excess of the asset return over the benchmark return and σ is the standard deviation of the asset.
The Sharpe ratio is a risk-adjusted measure of return that is often used to evaluate the performance of an asset or a portfolio. The ratio helps to make the performance of one portfolio comparable to that of another portfolio by making an adjustment for risk. It is excess return generated for an asset or a portfolio for every one unit of risk.
For example, if stock A generates a return of 15% while stock B generates a return of 12%, it would appear that stock A is a better performer. However, if stock A, which produced the 15% return but has much larger risks than stock B (as reflected by standard deviation of stock returns or beta), it may actually be the case that stock B has a better risk-adjusted return.
To continue with the example, say that the risk free-rate is 5%, and stock A has a standard deviation (risk) of 8%, while stock B has a standard deviation of 5%. The Sharpe ratio for stock A would be 1.25 while stock B’s ratio would be 1.4, which is better than stock A. Based on these calculations, stock B was able to generate a higher return on a risk-adjusted basis. A ratio of 1 or better is considered good, 2 and better is very good, and 3 and better is considered excellent.
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Where, R is the asset return, Rf is the return on a benchmark asset such as the risk free rate of return, [R − Rf] is the expected value of the excess of the asset return over the benchmark return and σ is the standard deviation of the asset.The Sharpe ratio is a risk-adjusted measure of return that is often used to evaluate the performance of an asset or a portfolio. The ratio helps to make the performance of one portfolio comparable to that of another portfolio by making an adjustment for risk. It is excess return generated for an asset or a portfolio for every one unit of risk.
For example, if stock A generates a return of 15% while stock B generates a return of 12%, it would appear that stock A is a better performer. However, if stock A, which produced the 15% return but has much larger risks than stock B (as reflected by standard deviation of stock returns or beta), it may actually be the case that stock B has a better risk-adjusted return.
To continue with the example, say that the risk free-rate is 5%, and stock A has a standard deviation (risk) of 8%, while stock B has a standard deviation of 5%. The Sharpe ratio for stock A would be 1.25 while stock B’s ratio would be 1.4, which is better than stock A. Based on these calculations, stock B was able to generate a higher return on a risk-adjusted basis. A ratio of 1 or better is considered good, 2 and better is very good, and 3 and better is considered excellent.
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