Why you should care about risk-adjusted returns

Moving from the portfolio level to the individual fund level: There are metrics you can use to determine whether a particular mutual fund has rewarded investors for taking on a given level of risk. Suppose you have two mutual funds--an intermediate-term bond fund, and a large-cap Canadian equity fund. The bond fund earned a 5% annualized return over the trailing 10-year period, and the large-cap fund has gained 7% annualized. But the intermediate-bond fund's standard deviation was 3.33, while the large-cap fund's standard deviation was 14.99.

Standard deviation is a measure of how spread out the data are. In a normal distribution, 68% of the data will fall within one standard deviation of the mean; 95% will fall within two standard deviations; 99.7% within three, etc. At Morningstar, we collect all monthly total returns for the appropriate time period, and then all of the monthly standard deviations are annualized. For the large-cap equity fund, the mean return was 7%, and in more than 68% of cases, the returns were within one standard deviation (14.99) -- meaning that they fell between -8% and 22%. That's a big range. When you see a higher standard deviation, you can imagine a shorter, fatter bell curve with thicker tails.

The bond fund, on the other hand, had a standard deviation of 3.33. In this case, you can imagine a higher, narrower bell curve with skinnier tails. Sixty-eight percent of the time, this fund's returns fell within one standard deviation of the mean return of 5% -- in other words, 5% plus or minus 3.33 -- for a range of 1.67% to 8.33%.

Sharpe and Sortino ratios

On a total return basis, the large-cap blend fund outperformed the bond fund. But what about when risk is taken into account? There are several ways to calculate risk-adjusted returns; perhaps the most widely known method is the Sharpe ratio. This is calculated by taking an asset's return minus a risk-free rate, which is the return you could get from investing in a virtually risk-free asset such as a three-month T-bill (we'll use 1.8% in our example) and dividing by the standard deviation. The idea is to come up with a measure of return per unit of risk taken; the higher the resulting number the better the risk-adjusted return. Let's compute the Sharpe ratios for the two investments here:

Large-cap Canadian equity fund: (7% - 1.8%) / 14.99 = 0.35
Intermediate-term bond fund: (5% - 1.8%) / 3.33 = 0.96

When viewing the performance through the Sharpe ratio lens, it's really no contest; you get a much better return per unit of risk with the bond fund.

The Sharpe has a few drawbacks. For one, it treats upside and downside volatility as equally "risky," but in the world of investing, investors are more concerned with downside volatility than upside volatility.

That's where the Sortino ratio comes in. The calculation is set up very similarly to the Sharpe ratio -- investment return minus risk-free rate in the numerator -- but instead of using standard deviation in the denominator, it uses only the standard deviation of returns below the mean. Just like the Sharpe ratio, the higher the Sortino ratio the better, because that means that the investment is earning a higher return for each unit of downside risk it's taking on.

To find the Sharpe and Sortino ratios for funds on Morningstar.ca, click on the "Risk/Rating" tab on a fund's quote page and look under "Volatility Measures."

Morningstar's risk-adjusted return metrics

The risk-adjustment formula used by Morningstar is similar to both the Sharpe and Sortino ratios, with the return of the risk-free investment subtracted from the fund's actual return. The denominator used in the Morningstar Risk-Adjusted Return calculation is more similar to the Sortino ratio's, placing greater emphasis on downside movements. Morningstar’s Risk-Adjusted Return is based on "expected utility theory," which assumes that investors are generally more concerned about heavy losses than big gains. They are willing to give up a portion of the expected return on an investment for greater certainty about that return. Funds that experience fewer heavy losses tend to look better using the Morningstar Risk-Adjusted Return methodology than they would by simply using standard deviation.

The Morningstar Risk-Adjusted Return forms the basis for one of our most popular metrics, the Morningstar Rating for funds, which is most commonly known as the star rating. To determine funds' star ratings, we sort all funds in the category by three-, five- and 10-year Morningstar Risk-Adjusted Return percentage rank in descending order. Funds are rated from 1 star (worst performance) to 5 stars (best performance). Click here for the full methodology document.

The star rating is a tool you can use to quickly and easily identify mutual funds that have performed better on a risk-adjusted basis than other funds that invest in a similar way (its category peers). These funds might be worthy of further research.

To find a fund's Morningstar Risk-Adjusted Returns and star ratings on Morningstar.ca, click on the "Risk/Rating " tab on a fund's quote page and look under the heading "Morningstar Risk & Rating Statistics."

(Morningstar Risk is the difference between a fund's return and its Morningstar Risk-Adjusted Return.)