The Sharpe ratio is a well-known and well-reputed measure of risk-adjusted return on an investment or portfolio. It was 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 can be accentuated by investments that don’t have a normal distribution of returns.
- Normally, a higher Sharpe ratio indicates good investment performance, given the risk.
- A Sharpe ratio of less than one is considered less than good.

#### Calculating the Sharpe Ratio

Since William Sharpe’s creation of the Sharpe ratio in 1966,1 it has been one of the most referenced risk-return measures used in finance. 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).2

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.

#### Sharpe Ratio Formula Example

Assume a mutual fund has an expected return over time of 25%. A risk-free rate of return is 2.70%. The standard deviation is 20%. Under these circumstances, the Sharpe ratio calculation is:

25 – 2.70/20 = 1.11

A Sharpe ratio greater than one but less than two indicates acceptable performance compared to the performance of the risk-free investment.

#### Interpreting the Sharpe Ratio

So, what is considered a good Sharpe ratio? What would indicate 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.

Certain factors can affect the Sharpe ratio. For instance, adding assets to a portfolio to better diversify it can increase the ratio. Investing in stocks with higher risk-adjusted returns can power the ratio upward. Investments with an abnormal distribution of returns can result in a flawed high ratio.

#### 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.

#### What Does a Sharpe Ratio of Less Than One Mean?

A Sharpe ratio of less than one is considered unacceptable or bad. The risk your portfolio encounters isn’t being offset well enough by its return. The higher the Sharpe ratio, the better.

#### Can You Use the Sharpe Ratio to Evaluate a Single Investment?

Yes, you can. In fact, the Sharpe ratio is useful as a way to compare investments. It is also often used by institutional investors managing large portfolios for many investors in an effort to maximize returns without taking on excessive risk.

#### What Does the Sharpe Ratio Indicate?

It can indicate how well an investment in equities performs when compared to the return offered by an essentially risk-free investment over the long-term. It can give help improve your investment decision-making as you take steps to improve portfolio performance.

To find out about our Quantitative trading strategies, get in touch with us at info@quantara.com.au.

*Article reproduced courtesy of Investopedia*