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Course 205
Gauging Risk and Return Together, Part 1


Up until now, we've focused on yardsticks that tell you either how good or how volatile a fund's returns have been. But there are also measures that treat performance and risk together: risk-adjusted performance measures. We'll cover two of the more common yardsticks, alpha and the Sharpe ratio, in this lesson. You can find both of these figures on the Morningstar fund report.

Alpha Defined

In a nutshell, alpha is the difference between a fund's expected returns based on its beta and its actual returns. Alpha is sometimes interpreted as the value that a portfolio manager adds, above and beyond a relevant index's risk/reward profile. If a fund returns more than what you'd expect given its beta, it has a positive alpha. If a fund returns less than its beta predicts, it has a negative alpha.

As you'll recall from our earlier lesson on risk, beta tells you how much you can expect a fund's returns to move up or down given a gain or loss of its benchmark. For example, if the ABC Fund has a beta of 1.1 in comparison with the S&P 500 and the S&P 500 returns 30% for the year, you would expect ABC Fund to return 33%. (30% x 1.1 = 33%.) Since mutual funds don't necessarily produce the returns predicted by their betas, alpha can be helpful to investors.

To calculate a fund's alpha, first subtract the return of the 90-day Treasury bill, for whatever time period you want to measure, from the fund's raw return. What does a government bond have to do with all this? The T-bill serves as a proxy for a risk-free investment and we're assuming that the return of a mutual fund should, at the very least, exceed that of a risk-free investment. This figure gives you the fund's excess return over the risk-free, guaranteed investment. From that, subtract the fund's expected excess return based on its beta. What's left over is the alpha.

Because a fund's return and its risk both contribute to its alpha, two funds with the same returns could have different alphas. Further, if a fund has a high beta, it's quite possible for it to have a negative alpha. That's because the higher a fund's risk level (beta), the greater the returns it must generate in order to produce a high alpha. Just as a teacher would expect his or her students in an advanced class to work at a higher level than those in a less-advanced class, investors expect more return from their higher-risk investments.

How to Use Alpha

It seems to follow, then, that you would want to find high-alpha funds. After all, these are funds that are delivering returns higher than they should be, given the amount of risk they assume.

But alpha has its quirks. First, it's dependent on the legitimacy of the fund's beta measurement. After all, it measures performance relative to beta. So, for example, if a fund's beta isn't meaningful because its R-squared is too low (below 75), its alpha isn't valid, either.

Second, alpha fails to distinguish between underperformance caused by incompetence and underperformance caused by fees. For example, because managers of index funds don't select stocks, they don't add or subtract much value. Thus, in theory, index funds should carry alphas of zero. Yet many index funds have negative alphas. Here, alpha usually reflects the drag of the fund's expenses.

Finally, it's impossible to judge whether alpha reflects managerial skill or just plain old luck. Is that high-alpha manager a genius, or did he just stumble upon a few hot stocks? If it's the latter, a positive alpha today may turn into a negative alpha tomorrow.

The Sharpe Ratio Defined

The Sharpe ratio uses standard deviation to measure a fund's risk-adjusted returns. The higher a fund's Sharpe ratio, the better a fund's returns have been relative to the risk it has taken on. Because it uses standard deviation, the Sharpe ratio can be used to compare risk-adjusted returns across all fund categories.

Developed by its namesake, Nobel Laureate William Sharpe, this measure quantifies a fund's return in excess of our proxy for a risk-free, guaranteed investment (the 90-day Treasury bill) relative to its standard deviation. To calculate a fund's Sharpe ratio, first subtract the return of the 90-day Treasury bill from the fund's returns, then divide that figure by the fund's standard deviation. If a fund produced a return of 25% with a standard deviation of 10 and the T-bill returned 5%, the fund's Sharpe ratio would be 2.0: (25-5)/10.

The higher a fund's Sharpe ratio, the better its returns have been relative to the amount of investment risk it has taken. For example, both State Street Global Research SSGRX and Morgan Stanley Inst. European Real Estate MSUAX have enjoyed heady three-year returns of 23.9% through August 2004. But Morgan Stanley sports a Sharpe ratio of 1.09 versus State Street's 0.74, indicating that Morgan Stanley took on less risk to achieve the same return.

The higher a fund's standard deviation, the higher the fund's returns need to be to earn a high Sharpe ratio. Conversely, funds with lower standard deviations can sport a higher Sharpe ratio if they have consistently decent returns. Keep in mind that even though a higher Sharpe ratio indicates a better historical risk-adjusted performance, this doesn't necessarily translate to a lower-volatility fund. A higher Sharpe ratio just means that the fund's risk/return relationship is more proportional or optimal..

How to Use the Sharpe Ratio

The Sharpe ratio has a real advantage over alpha. Remember that standard deviation measures the volatility of a fund's return in absolute terms, not relative to an index. So whereas a fund's R-squared must be high for alpha to be meaningful, Sharpe ratios are meaningful all the time.

Moreover, it's easier to compare funds of all types using the standard-deviation-based Sharpe ratio than with beta-based alpha. Unlike beta—which is usually calculated using different benchmarks for stock and bond funds—standard deviation is calculated the exact same way for any type of fund, be it stock or bond. We can therefore use the Sharpe ratio to compare the risk-adjusted returns of stock funds with those of bond funds.

As with alpha, the main drawback of the Sharpe ratio is that it is expressed as a raw number. Of course, the higher the Sharpe ratio the better. But given no other information, you can't tell whether a Sharpe ratio of 1.5 is good or bad. Only when you compare one fund's Sharpe ratio with that of another fund (or group of funds) do you get a feel for its risk-adjusted return relative to other funds.

Quiz 205
There is only one correct answer to each question.

1 A fund with a negative alpha:
a. Has returned more than you'd expect, given its beta.
b. Has returned less than you'd expect, given its beta.
c. Has returned less than you'd expect, given its standard deviation.
2 Funds A, B, and C each return 15%, while the S&P 500 returns 10%. Relative to the S&P 500, which fund has the highest alpha?
a. Fund A, which has a beta of 1.0.
b. Fund B, which has a beta of 1.7.
c. Fund C, which has a beta of 0.8.
3 Which measurement is most useful to investors?
a. An alpha of 1.3 for a fund with a beta of 1.1 and an R-squared of 50.
b. An alpha of -0.5 for a fund with a beta of 0.9 and an R-squared of 70.
c. A Sharpe ratio of 1.7 for a fund with a standard deviation of 12%.
4 If a fund returned 30% with a standard deviation of 15%, and the 90-day Treasury bill returned 3%, what's the fund's Sharpe ratio?
a. 1.8.
b. 2.0.
c. 2.2.
5 The higher a fund's Sharpe ratio:
a. The greater its risk.
b. The greater its returns.
c. The greater its returns given the amount of risk it's taking on.
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