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115 CFA
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115.020.20.08 Reading 7 - 8. The Sharpe Measure of Risk-Adjusted Performance

# 8. The Sharpe Measure of Risk-Adjusted Performance

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

What is the Sharpe measure of risk-adjusted performance?
It is a return risk measure that is more precise than standard deviation which measures the reward to total volatility trade-off.

What is the mathematical formula for the Sharpe Measure?
$$\frac{r_p - r_f}{\sigma_p}$$
- 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 for the added risk taken, called the excess return
- \sigma_p = the standard deviation of the portfolio returns

What is another term for the Sharpe Measure?
It is also called the reward-to-variability ratio

Do investors prefer to see a larger Sharpe Ratio or a smaller one? Why?
Portfolios with large Sharpe ratios are preferred to those with smaller ratios because we assume that investors prefer return and dislike risk.

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