## Sharpe ratio

##### Published: Feb 2010

The Sharpe ratio was developed by William Forsyth Sharpe in 1966 and subsequently revised by its creator in 1994. It is the most commonly used measure of risk-adjusted performance. The calculation takes into account the rate of return on a portfolio in relation to its volatility and provides a measure of how far the returns on a portfolio are due to wise investment decisions as opposed to excess levels of risk. It does this by determining the reward per unit of risk.

The Sharpe ratio is also a useful tool for investors seeking to determine whether the excess return generated on a higher-risk asset adequately compensates for the increased level of exposure to risk. The risk-adjustment feature of the Sharpe ratio enables direct comparison of the performance of two portfolios, regardless of their volatility.

### How is it calculated?

The Sharpe ratio takes the difference in return between the portfolio in question and a risk-free investment. This gives the excess return. In order to account for the level of risk involved, the excess return is divided by the standard deviation of the return on the portfolio:

$$\mathrm{S}=\frac{R_p-R_f}{δ_p}$$

• Return on portfolio, Rp.
• Return on a risk-free investment, Rf. This must be measured over the same period as the return on the portfolio.
• Excess return, Rp – Rf. This is the additional return achieved from the increased volatility of higher-risk assets.
• Portfolio volatility, δp . This is the standard deviation of the return on the portfolio. The greater the standard deviation, the greater the risk/volatility of the portfolio.

The Sharpe ratio can be used to analyse historical returns and also to predict expected returns. When comparing two portfolios against the same benchmark risk-free rate of return, the portfolio with the highest Sharpe ratio will offer the greatest return per unit of risk. A portfolio with a negative Sharpe ratio would be considered an unwise investment since it will be expected to show a lower return per unit of risk than a risk-free asset. The Sharpe ratio of a portfolio is also affected by diversification as this minimises the risk of the investment, thus decreasing the standard deviation.

#### Example

Investment manager A generates a return of 12%, whilst investment manager B generates a return of 9%. This would indicate that A’s investment portfolio performed better than B’s. Assuming that the risk-free rate of return is 2.5%, and that the standard deviations of each portfolio are 6% and 4% respectively:

##### A
$$\mathrm{S}=\frac{12\:-\:2.5}{6}=\mathrm{1\:.58}$$
##### B

$$\mathrm{S}=\frac{9\:-\:2.5}{4}=\mathrm{1\:.\:63}$$
This shows that, despite investing in lower-risk assets than investment manager A, investment manager B succeeded in generating a better rate of risk-adjusted return.

#### Points to consider

The Sharpe ratio is most successful for calculating the risk-adjusted return on liquid investments with normally distributed returns. Any anomalies in the distribution of portfolio returns will restrict the effectiveness of the standard deviation as a measure of risk. For this reason the Sharpe ratio is not usually an appropriate measure of risk-adjusted return for hedge funds. Also, hedge funds that are illiquid appear to be less volatile, which would thus positively affect their Sharpe ratio. Since the Sharpe ratio contains no measure of illiquidity it sometimes provides a misleading measure of risk-adjusted return.

It is important that treasurers understand the Sharpe ratio, as it provides a guide as to the optimum level of risk exposure for generating the best returns, and can help to keep investments in line with company policy on the appropriate balance of risk and reward.