Many investors choose which mutual funds to buy based on the highest historical returns they can find in a given category of funds. However, what do you do if two mutual funds have the exact same performance? This question will be answered in a moment, but first we need to develop a process to help us make these decisions.

Broadly, your investment choices can be boiled down to two measures: your risk tolerance and your required return. Therefore, rather than just investing in a mutual fund based on performance, you also must consider the risk of the fund. Therefore, to answer our questions, we will employ a measure of risk-adjusted returns known as the Sharpe Ratio, which tells us how much excess return the fund manager achieves relative to the riskiness of the fund. In developing this ratio (and formula), we will need to know both the excess return and the volatility of the fund.

## Excess Return

In the most common Sharpe Ratio framework, we calculate the excess return as the total return on the fund minus the risk-free rate, or Treasury yield. The excess return is important because we know that a riskless security, such as a Treasury bill, has no variability. Therefore, we specifically want to capture the amount of return that the mutual fund is generating *in excess* of the risk-free rate, which represents the portion of the return that is at risk.

We can denote the average annual return of the fund as Rmf. For example, let’s say a mutual fund returns an average of 10% each year for the past ten years. In this case, the Rmf = 10%. In practice, analysts use either the short-term (3 month) Treasury yield or they choose a Treasury yield that matches the duration of the investment (say 10-year Treasury bond). We will denote the risk-free yield as Rf and assume it is 3%: Rf =3%. Therefore our excess return: (Rmf_{ }– Rf) = (10%-3%) = 7%.

## Volatility

When calculating the Sharpe Ratio, variability is defined as the investment’s standard deviation of returns using the same time period chosen when calculating average annual returns. We can denote the standard deviation as Smf; therefore, if the standard deviation is 15%: Smf= 15%.

## Putting It All Together

Now that we have all three components, let’s apply them to see how we can choose the better mutual fund manager. Both managers earn 10%; at first glance they appear to be the same. However, Manager 1 achieves this return with a standard deviation of 15%, while Manager 2 only has a standard deviation of 10%.

Our formula is: Sharpe= (Rmf – Rf)/Smf. Consider that Rf = 3%. For Manager 1, the formula is (10%-3%)/15% = 7%/15% = 0.47, which is similar to the long-term average Sharpe ratio of the entire market. However, for Manager 2, the formula is (10%-3%)/10% = 7%/10% = 0.7, which is noticeably better.

By using the Sharpe Ratio, we were able to prove that while both mutual fund managers had the same performance, the second manager and mutual fund was better because he was able to achieve the same return with less risk. Now that you know how to calculate this simple, yet powerful formula, you will be able to make better investment decisions that balance both risk and return.