# 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.

##### Source:

- CFA