How to Calculate Sharpe Ratio

How to Calculate Sharpe Ratio How to Calculate Sharpe Ratio Sharpe ratio is generally used for taking smart investment decisions based on the comparison of returns and expected risk. This ratio was named after its developer Nobel laureate William F. Sharpe. The Sharpe ratio is calculated by subtracting the risk-free rate – such as that of the 10-year U.S. Treasury bond – from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns.

The Sharpe ratio formula is:
(Portfolio Return Rate- Risk Free Rate) / Standard Deviation of the Portfolio

The ratio helps in deciding whether the returns on a particular portfolio are yield based on smart investment decisions or a result of taking excessive risk. Always an investment is considered good if it yields higher returns than its peers without taking any additional or excessive risk. So the investment can be evaluated easily by using the Sharpe ratio. The risk-adjusted performance is considered better, if the investment has got a higher Sharpe ratio. So the risk-adjusted performance gets better as the Sharpe ratio of an investment rises. The Sharpe ratio can also be negative which will indicate that a risk-less asset is performing better than the security being analyzed.

Instructions

Calculating Average Return

List down your annual portfolio returns in a chronological manner by starting with the first year. For example, if you have started the investment in 2005 before 6 years, then start with 2005 and follow it with 2006, 2007, 2008, 2009, and 2010.
Calculate your portfolio’s average returns by adding up the individual percentage returns for each year and divide it by number of years. For example, if you have percentage returns of 9, 7, 6, 4, 6, 10 respectively for 2005, 2006, 2007, 2008, 2009, and 2010. The average return r portfolio will be, (9+7+6+4+ 6+10)/6= 7. This is the average return you will use for calculating the Sharpe ration.

Calculating Standard Deviation

Now deduct the individual return for each year from the average return calculated by you. For example, deduct the individual return of 9 for 2005 from the average return of 7. So for 2004 the amount is 7-9=-2. So after deducting the values will be -2, 0, 1, 3, 1, -3 respectively for 2005, 2006, 2007, 2008, 2009, and 2010.
Calculate the square the individual deviations. In the example the square of deviation for 2005 will be (-2)*(-2) =4. Similarly the square of the deviations will be, 4, 0, 1, 9, 1, and 9 respectively for 2005, 2006, 2007, 2008, 2009, and 2010.
Sum these individual deviations. The sum will be (4+0+1+9+1+9)= 24
Divide the total of individual deviations calculated by you with a figure of number of years minus one. So in the example, divide 24 by (6-1) =5 which will come to 4.8.
Calculate the square root of the number calculated by you after dividing the total of individual deviations by number of years minus one. The square root of 4.8 will be 2.1908. This calculated square root will be used as annual standard deviation of the portfolio while calculating Sharpe ratio.

Calculating Sharpe Ratio

Now you have got the numbers required to calculate the Sharpe ratio. So put these numbers as per the Sharpe ratio equation.
Now you have to subtract the rate of risk-free return from the rate of return for the portfolio. For example if the rate of return on a six-year US government bond is 1.23, deduct 1.23 from the average portfolio of 7. So the figure will be 7-1.23= 5.77.
Calculate the Sharpe ration by dividing the subtracted figure by the standard deviation. So in the example, the Sharpe ratio will be 5.77/2.1908= 2.6337.