**Quantitative Methods: Basic Concepts**

**Reading 7. Statistical Concepts and Market Returns**

**Learning Outcome Statements**

i. calculate and interpret the coefficient of variation and the Sharpe ratio;

*CFA Curriculum, 2020, Volume 1*

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### Subject 8. The Sharpe Measure of Risk-Adjusted Performance

**Sharpe Measure**is a more precise return-risk measure than standard deviation. It recognizes the existence of a risk-free return, a return for virtually zero standard deviation. It measures the reward to total volatility trade-off.

It is defined as:

- r
_{p}= the mean return to a portfolio - r
_{f}= the mean return to a risk-free asset - (r
_{p}- r_{f}) = the extra reward that investors receive for the added risk taken, called the**excess return**on portfolio p - σ
_{p}= the standard deviation of the portfolio returns

Note that the numerator of the Sharpe measure recognizes the existence of a risk-free return. Portfolios with large Sharpe ratios are preferred to those with smaller ratios because we assume that investors prefer return and dislike risk. The Sharpe ratio is also called the

**reward-to-variability ratio**.

*Example*

The mean monthly return on T-bills (the risk-free rate) is 0.25%. The mean monthly return on the S&P 500 is 1.30% with a standard deviation of 7.30%. Calculate the Sharpe measure for the S&P 500 and interpret the results.

Sharpe measure = (1.30 - 0.25)/7.30 = 0.144

Interpretation: The S&P 500 earned 0.144% of excess return per unit of risk, where risk is measured by standard deviation.

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**User Contributed Comments**
5

You need to log in first to add your comment. ###### jehangir

Sharpes measure is more suerior to sd and measures excess return per unit of risk which is measured by standard deviation

###### loisliu88

except when Sharpe ratio is negative, it doesn't work

###### mohsindi

How come it recognize Risk free return ? the formula deducts the Rf from rp

###### choas69

it recognize the existence of risk free thus excluding it out of the formula to compute only the returns associated with risk, the bigger the results the more the better the assist.

Why the S&P 500 earned 0.144% of excess return in the example? Why not 14.4%?