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
It is defined as:
- rp = the mean return to a portfolio
- rf = the mean return to a risk-free asset
- (rp - rf) = the extra reward that investors receive for the added risk taken, called the excess return on portfolio p
- σp = 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.
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.
User Contributed Comments 5You need to log in first to add your comment.
Sharpes measure is more suerior to sd and measures excess return per unit of risk which is measured by standard deviation
except when Sharpe ratio is negative, it doesn't work
How come it recognize Risk free return ? the formula deducts the Rf from rp
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%?