The Sharpe ratio is a well-known and well-reputed measure of risk-adjusted return on an investment or portfolio, developed by the economist William Sharpe. The Sharpe ratio can be used to evaluate the total performance of an aggregate investment portfolio or the performance of an individual stock.

The Sharpe ratio indicates how well an equity investment performs in comparison to the rate of return on a risk-free investment, such as U.S. government treasury bonds or bills. There is some disagreement as to whether the rate of return on the shortest maturity treasury bill should be used in the calculation or whether the risk-free instrument chosen should more closely match the length of time that an investor expects to hold the equity investments.

### Key Takeaways

- The Sharpe ratio indicates how well an equity investment performs in comparison to the rate of return on a risk-free investment, such as U.S. government treasury bonds or bills.
- To calculate the Sharpe ratio, you first calculate the expected return on an investment portfolio or individual stock and then subtract the risk-free rate of return.
- The main problem with the Sharpe ratio is that it is accentuated by investments that don't have a normal distribution of returns.

## Calculating the Sharpe Ratio

Since William Sharpe's creation of the Sharpe ratio in 1966, it has been one of the most referenced risk-return measures used in finance, and much of this popularity is attributed to its simplicity. The ratio's credibility was bolstered further when Professor Sharpe won a Nobel Memorial Prize in Economic Sciences in 1990 for his work on the capital asset pricing model (CAPM).

To calculate the Sharpe ratio, you first calculate the expected return on an investment portfolio or individual stock and then subtract the risk-free rate of return. Then, you divide that figure by the standard deviation of the portfolio or investment. The Sharpe ratio can be recalculated at the end of the year to examine the actual return rather than the expected return.

So what is considered a good Sharpe ratio that indicates a high degree of expected return for a relatively low amount of risk?

- Usually, any Sharpe ratio greater than 1.0 is considered acceptable to good by investors.
- A ratio higher than 2.0 is rated as very good.
- A ratio of 3.0 or higher is considered excellent.
- A ratio under 1.0 is considered sub-optimal.

## The Formula for the Sharpe Ratio Is

$\begin{aligned}&\text{Sharpe Ratio}\ =\ \frac{R_p-R_f}{\sigma_p}\\&\textbf{where:}\\&R_p=\text{the expected return on the asset or portfolio}\\&R_f=\text{the risk-free rate of return}\\&\sigma_p=\text{the standard deviation of returns (the risk) of}\\&\qquad\ \,\text{the asset or portfolio}\end{aligned}$

## Limitations of the Sharpe Ratio

The main problem with the Sharpe ratio is that it is accentuated by investments that don't have a normal distribution of returns. Asset prices are bounded to the downside by zero but have theoretically unlimited upside potential, making their returns right-skewed or log-normal, which is a violation of the assumptions built into the Sharpe ratio that asset returns are normally distributed.

A good example of this can also be found with the distribution of returns earned by hedge funds. Many of them use dynamic trading strategies and options that give way to skewness and kurtosis in their distribution of returns. Many hedge fund strategies produce small positive returns with the occasional large negative return. For instance, a simple strategy of selling deep out-of-the-money options tends to collect small premiums and pay out nothing until the "big one" hits. Until a big loss takes place, this strategy would (erroneously) show a very high and favorable Sharpe ratio.