How to Calculate Sharpe Ratio From Yearly Returns

Higher yearly returns can boost an investment's Sharpe ratio.

Higher yearly returns can boost an investment's Sharpe ratio.

When you invest in anything other than a U.S. Treasury bill or other risk-free asset, there’s a chance you might lose money. The Sharpe ratio is a metric that measures how well an investment or portfolio compensates you for taking on this extra risk. If you know an investment’s yearly returns for at least two years, you can calculate its Sharpe ratio. A yearly return is the percentage profit an investment generates in a year. In general, a higher ratio is better, but the ratio has the most meaning when you are comparing two or more investments.

Add the investment’s yearly returns. Divide your result by the number of years of returns to determine the average yearly return. For example, assume an investment had yearly returns of 15 percent, 20 percent and 4 percent for the past three years. Add these to get 39 percent. Divide 39 percent by 3 to get a 13 percent average return.

Subtract the average return from each yearly return. In this example, subtract 13 percent from 15 percent to get 2 percent. The other two results are 7 percent and -9 percent.

Square each Step 2 result. In this example, multiply 2 percent, or 0.02, by 0.02 to get 0.0004. The other results are 0.0049 and 0.0081.

Add your Step 3 results. In this example, add the results to get 0.0134.

Subtract 1 from the number of years of returns you have. Divide your Step 4 result by this result. In this example, subtract 1 from 3 to get 2. Divide 0.0134 by 2 to get 0.0067.

Calculate the square root of your Step 5 result to determine the investment’s standard deviation, a statistic that measures risk. In this example, calculate the square root of 0.0067 to get a standard deviation of 0.0819.

Visit the Daily Treasury Yield Curve Rates page of the U.S. Department of the Treasury website. Select a year that corresponds to one of your yearly returns in the “Select Time Period” box. Click “Go,” and identify the one-month Treasury bill yield on the first day of that year. Do this for each year of returns you have. In this example, assume the one-month Treasury bill had yields of 2 percent, 2.25 percent and 1.9 percent in each of the three years.

Add each yield. Divide your result by the number of years to calculate the average risk-free return. In this example, add 2 percent, 2.25 percent and 1.9 percent to get 6.15 percent. Divide 6.15 percent by 3 to get an average risk-free return of 2.05 percent.

Subtract your Step 8 result from the investment’s average yearly return. In this example, subtract 2.05 percent, or 0.0205, from 0.13 to get 0.1095.

Divide your Step 9 result by the investment’s standard deviation to calculate the Sharpe ratio. Concluding the example, divide 0.1095 by 0.0819 to get a Sharpe ratio of 1.34. Say another investment has a Sharpe ratio of 0.89. The one with the 1.34 ratio generates stronger returns for its given level of risk.

 

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