The formula assumes investors are willing to forego part of the return for reduced volatility.

By Morningstar Canada | 16/10/17

**Question: **I often see references to "risk-adjusted returns" on Morningstar.ca. What does this mean?

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**Answer: **Think of risk-adjusted returns as a way to level the playing field by taking into account the volatility of a fund's performance. They help investors compare funds that take on lots of risk -- and therefore may experience outsized gains or losses -- with funds that take on less risk and have more stable returns, while acknowledging that investors tend to prefer the latter.

Most investors focus primarily on a fund's total return over a given period, but how the fund delivers those returns matters as well. Say that two funds both returned 20% last year, but one took a relatively smooth path while the other took investors on a roller coaster ride. For most investors, the smoother performance is preferable because a fund that is less volatile is easier to own than one that is more volatile. After all, a fund that experiences steep gains and steep losses is more likely to see investors bail out when the going gets rough -- possibly locking in losses in the process and, thus, missing out on any rebound that might occur. And even if investors in a volatile fund don't sell out at the worst possible time, they might still endure some sleepless nights.

That's where risk-adjusted returns come in. There are several ways to calculate risk-adjusted returns, but the general idea is to show how a fund's performance relates to the degree of risk it takes on. Morningstar's risk-adjusted return approach is based on something called "expected utility theory," which assumes that the typical investor is risk-averse and willing to give up part of the return on an investment for greater certainty about that return. Risk-adjusted returns are the underpinning for the Morningstar Rating for funds (otherwise known as the star rating). Other metrics, such as the Sharpe ratio, also attempt to depict risk-adjusted returns.

**What's in the formula? **

The risk-adjustment formula used by Morningstar is rather technical but is based on a fund's performance above and beyond what an investor would have gained by investing in a risk-free asset -- in this case, the three-month Government of Canada Treasury bill. In essence, the return on this risk-free investment is subtracted from the fund's actual return in calculating its risk-adjusted performance.

The formula is calibrated to assume a certain degree of willingness on the investor's part to sacrifice some return in order to lower investment risk. For example, an investor might view a moderately risky fund that generates a 9% return and a low-risk fund that generates a 6% return as being of equal value because of the difference in volatility. In that case, the investor is willing to give up 3% in return in order to remove the risk. By converting all returns to their riskless equivalents, Morningstar can compare one fund to another on a risk-adjusted basis. This equalizes the playing field for funds in the same category that have different exposures to risk factors.

**Same, but different**

While similar to standard deviation, which measures the volatility of fund returns over a given period, the Morningstar risk-adjustment method is different in that it places greater emphasis on downside movements. That's because investors tend to be more concerned about heavy losses than heavy gains, so funds that experience fewer heavy losses tend to look better using our methodology than they would by simply using standard deviation.

Morningstar Risk-Adjusted Returns are particularly important because they form the basis for one of our most popular metrics: the Morningstar Rating. Funds are rated from 1 star (worst performance) to 5 stars (best performance), based on their risk-adjusted returns over the trailing three-, five- and 10-year periods relative to other funds in their category, as described here.

**Related metrics**

Another fund metric, the Morningstar Return, uses a calculation similar to Morningstar Risk-Adjusted Return but without the emphasis on downside movements. Both metrics also are used to calculate a fund's Morningstar Risk rating, which is determined by subtracting the Morningstar Risk-Adjusted Return from the Morningstar Return, thus isolating the fund's level of risk. Results are then compared with those of other funds in the category to determine a relative rating.

Another variation on risk-adjusted returns is the Sharpe ratio, which uses the relationship between a fund's standard deviation and its excess return above the risk-free rate to determine how effectively it performs relative to the level of risk it takes. (Sharpe ratio and other volatility measures can be found under the Risk/Ratings tab on the fund pages.) However, Sharpe ratio tends to be less useful when returns are negative, a circumstance that the Morningstar Risk-Adjusted Return metric is designed to account for.

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