How to Calculate Sharpe Ratio

••• Comstock/Comstock/Getty Images

The Sharpe Ratio, created in 1966 by Nobel laureate William F. Sharpe, is an equation to calculate risk-adjusted performance of a stock portfolio. The ratio determines whether a portfolio's profit can be attributed to correct thinking or high risk. The higher the ratio, the better the portfolio has performed after being adjusted for risk. While a certain portfolio may generate a great profit, that profit may be the result of huge and potentially dangerous risk. The exact calculation for the ratio requires subtracting the rate of a risk-free investment from the expected portfolio return, divided by the portfolio's standard deviation:

(rate of portfolio return - risk free rate) / portfolio standard deviation

Average Return and Standard Deviation

    List the annual returns of your portfolio. If your portfolio is five years old, begin from the first year. For example:

    2005: 12 percent 2006: -3 percent 2007: 9 percent 2008: -8 percent 2009: 6 percent

    Calculate the average of portfolio returns by adding up each return percentage and dividing by the number of years.

    For example: 12 + -3 + 9 + -8 + 6 = 3.2

    This is your portfolio's average return.

    Subtract each year's individual return from average portfolio return. For example:

    2005: 3.2 - 12 = -8.8 2006: 3.2 - -3 = 6.2 2007: 3.2 - 9 = -5.8 2008: 3.2 - -8 = 11.2 2009: 3.2 - 6 = -2.8

    Square the individual deviations.

    For example: 2005: -8.8 x -8.8 = 77.44 2006: 6.2 x 6.2 = 38.44 2007: -5.8 x -5.8 = 33.64 2008: 11.2 x 11.2 = 125.44 2009: -2.8 x -2.8 = 7.84

    Find the sum of each year's squared deviation.

    For example: 77.44 + 38.44 + 33.64 + 125.44 + 7.84 = 282.8

    Divide the sum by the number of years minus one.

    For example: 282.8 / 4 = 70.7

    Calculate the square root of this number.

    For example: 8.408

    This the annual standard deviation of the portfolio.

Sharpe Ratio

    Place your three numbers into the Sharpe Ratio equation.

    Subtract the rate of risk-free return from the rate of return for the portfolio.

    For example: (Using the previous numbers and the rate of return on a five-year US government bond) 3.2 - 1.43 = 0.3575

    Divide by the standard deviation.

    For example: 0.3575 / 8.408 = 0.04252 (approximate)

    This is your Sharpe Ratio.

References

About the Author

Jess Kroll has been writing since 2005. He has contributed to "Hawaii Independent," "Honolulu Weekly" and "News Drops," as well as numerous websites. His prose, poetry and essays have been published in numerous journals and literary magazines. Kroll holds a Master of Fine Arts in writing from the University of San Francisco.

Photo Credits

  • Comstock/Comstock/Getty Images

Dont Go!

We Have More Great Sciencing Articles!