How to Calculate Sharpe Ratio From Yearly Returns

by Cynthia Hartman

The Sharpe ratio helps investors evaluate the performance of their portfolio over time as measured against another portfolio or the market. The ratio uses a simple formula, although an investor must calculate the inputs to the formula. The Sharpe ratio is easily calculated using yearly data, or other time periods such as monthly or daily information. The higher a portfolio's Sharpe ratio, the more beneficial its returns have been historically, compared to its degree of investment risk.

Calculate Your Average Return and Standard Deviation

Calculate the average portfolio return for the years under analysis. For example, say you are assessing the last five years of returns on your portfolio. Add up each year's return and divide by the number of years to get the average. For example, in percentage terms, Year 1 = 6.9, Year 2 = 8.3, Year 3 = 12.2, Year 4 = 10.7 and Year 5 = 11.2. The average is 9.86.

Begin the standard deviation calculation by subtracting each individual year's return from your average return, 9.86. This leaves you with Year 1 = 2.64, Year 2 = 1.24, Year 3 = -2.66, Year 4 = -1.16 and Year 5 = -1.66. This shows how the portfolio has deviated each year from its average return.

Calculate the square of each year's deviation. For example, Year 1 = 2.64 x 2.64 = 7.0. For years 2 through 5, you should have: Year 2 = 1.5, Year 3 = 7.1, Year 4 = 1.3, Year 5 = 2.8.

Add up all five of your annual squared deviations to reach the sum of 19.7. Divide this result by the sum of years you are analyzing, minus one. For example, 19.7 / (5-1) = 19.7 / 4 = 4.92.

Calculate the square root of the above result. For example, the square root of 4.92 is 2.22. This number translates to the annual standard deviation of your portfolio.

Calculate the Sharpe Ratio

Locate the risk free rate. The U.S. Department of the Treasury provides daily treasury security yields on its website. These returns are the closest approximation to a risk-free rate. Choose the return on a U.S. government bond with a five-year maturity. For example, we will use the current yield of .91.

Plug your earlier results into the Sharpe ratio equation. The equation is (average portfolio rate of return - risk-free rate) / portfolio standard deviation. This translates to (9.86 - .91) / 4.92 = 8.95 / 4.92 = 1.82. The Sharpe ratio for your portfolio is 1.82, based on the five years of data with which you started.

Tips

• Compare your Sharpe ratio to the same portfolio's returns at different points in time, or the Sharpe ratio of the Standard & Poor 500 Index. This provides a meaningful way to interpret the results as they change over time, and shows how your portfolio return compares to the market's overall performance.
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