How to Calculate Sharpe Ratio
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
Instructions
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Average Return and Standard Deviation
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1
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
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2
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.
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3
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
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4
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
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5
Find the sum of each year's squared deviation.
For example: 77.44 + 38.44 + 33.64 + 125.44 + 7.84 = 282.8
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6
Divide the sum by the number of years minus one.
For example: 282.8 / 4 = 70.7
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7
Calculate the square root of this number.
For example: 8.408
This the annual standard deviation of the portfolio.
Sharpe Ratio
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8
Place your three numbers into the Sharpe Ratio equation.
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9
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
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10
Divide by the standard deviation.
For example: 0.3575 / 8.408 = 0.04252 (approximate)
This is your Sharpe Ratio.
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1
References
- Photo Credit Comstock/Comstock/Getty Images
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Comments
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QUESTION ONE: A company has identified two pricing strategies for a new product. The first strategy is to set a selling price of £170 which will entail annual fixed costs of £22 million. The second strategy has a much higher sales price per unit of £190 and entails much higher annual fixed costs of £27 million. The variable cost per unit is estimated to be £35 whether strategy one or two is adopted. The following probability distribution has been agreed with the managers after consultation is considered to be the same for both of the above selling prices. The forecast probability distribution is as follows: Estimated demand (units) Probability. 150,000 0.1 160,000 0.4 180,000 0.3 200,000 0.1 210,000 0.1 The estimated standard deviation of sales is 18,547 units. REQUIRED: (a) For both pricing strategies, calculate the probability of: (i) obtaining the break-even point (profit equals zero);. (ii) obtaining a profit greater than £1.5 million;. (iii) Obtaining a profit greater than £4 million. (12 marks) (b) Assuming that management decided to aim for a target profit of £4 million, discuss whether your results from your calculations to (a) above assist management in choosing between the two proposed pricing strategies. (8 marks) (c) Comment on the assumptions implicit in the above financial data and the reliability, for decision-making purposes, of the calculations you have made. (5 marks) (Total marks: 25).
