Understanding M*’s Mutual Fund Risk Measures: Alpha, Beta, and R-squared

[This is the third segment of Understanding M* series (first part Understanding M*'s Star Rating, second part Understanding M*'s Total Return and Investor Return)].

Morningstar is the my primary website for mutual fund research. When I look for a mutual fund investment (mostly actively managed funds), not only I am concerned with a fund’s past performance and costs, but its risk factors as well. Before getting into the details, let’s first see how risk is defined in finance.

According to Investopedia, risk is

The chance that an investment’s actual return will be different than expected. This includes the possibility of losing some or all of the original investment. It is usually measured by calculating the standard deviation of the historical returns or average returns of a specific investment. A fundamental idea in finance is the relationship between risk and return. The greater the amount of risk that an investor is willing to take on, the greater the potential return. The reason for this is that investors need to be compensated for taking on additional risk.

For each fund, Morningstar offers two sets of data to help investors get a sense of the risk of owning a particular fund (enter a fund symbol to get a quote, then click “Risk Measures”):

Volatility Measurements:

• Mean
• Standard Deviation
• Sharpe Ratio
• Bear Market Decile Rank

Modern Portfolio Theory Statistics:

• R-Squared
• Beta
• Alpha

In this part, I will mainly discuss mean, standard deviation, beta, R-squared, and alpha and how to use these measurements to assess an investment’s risk.

What they are

Simply speaking, mean is the mathematical average of a set of data. If, for example, a stock XYZ’s annual return in the past three years are 10%, 5% and 15%, respectively, then the arithmetic mean of the stock’s return is 10%, the average 10%, 5% and 15%. Once the mean is known, we can calculate stock XYZ’s standard deviation , which measures the dispersion of the stock’s annual returns (i.e., 10%, 5% and 15%) from the mean expected return (10%). Therefore, the further away an equity’s annual return from the mean, the higher the standard deviation. In finance, standard deviation is used to gauge an equity’s volatility, whether the equity is a stock or a mutual fund.

During the recent market sell-off, the majority of stocks followed the movement of the general market and turned lower, the only difference among stocks is the extent of the downturn as compared to the benchmark. The risk that a stock tends to go along with the general market is captured by beta, also known as systematic risk (or market risk), which measure how an individual stock or fund reacts to the general market fluctuations. By definition, a benchmark (or index) has a beta of 1.00 and the beta of an equity is relative to this value. If the movement of a stock or fund can be completely explained by the movements of the general market, then this stock or fund will have a R-squared of 100. According to Morningstar, R-squared, represented by a percentage number ranging from 0 to 100, characterizes an equity’s movement against a benchmark. A R-squared that equals to 100 means all the equity’s movements are in-line with the benchmark.

With the Greek letter beta, investors can have an sense of how sensitive an equity is in relation to the broad market. If investors decide to take on a higher risk by investing in a volatile equity that carries a larger beta, then in theory, they should be rewarded with a higher than average return. The difference between the realized return and the average expected return is measured by another Greek letter alpha. A positive alpha indicates that the equity exceeds its expectations (Seeking Alpha?) against the respective benchmark.

How they work

Now we know what the risk measurements are, let’s see how we can use them to assess the risk/reward of an investment.

To illustrate, I use two funds, Dodge & Cox Stock Fund (DODGX) and CGM Focus Fund (CGMFX), that I own to show how they are measured up against each other in each category. Using S&P 500 index as the benchmark, the performance and risk data of the two funds are shown in the following table (obtained from Morningstar.com, trailing 3-year data through February 28, 2007):

• Mean: The mean represents the annualized average monthly return. Therefore, a higher mean suggests a higher return the fund has delivered. In this case, CGMFX has a superior average return of 19.46.
• Standard deviation (STD): Though CGMFX has a higher average return, this fund is by no means less volatile, which is indicated by its much higher STD (20.32) than DODGX’s 7.46.
• R-squared: If we recall that R-squared measures a fund’s movement against the benchmark and a value close to 100 means the fund follows the benchmark very closely. Also, R-squared can help investor assess the usefulness of a fund’s beta or alpha statistics. A higher R-squared means the fund’s beta is more trustworthy. In this case, CGMFX’s 19 R-squared value says that only 19% of its movements can be explained by the fluctuations of S&P 500 index, an ill-fitted benchmark for CGMFX (indeed, Morningstar points that the best fit index for CGMFX is the Goldman Sachs Natural Resources index, which will give the fund a R-squared value of 80). On the other hand, DODGX’s 86 R-squared value indicates the fund is well represented by S&P 500 and its beta value can be trusted.
• Beta: Now we know S&P 500 is not a good benchmark for CGMFX, its beta value, though higher, is not particularly helpful in assessing the fund’s risk in comparison to the benchmark. Generally, beta measures a fund’s risk associated with the market and a low beta only means that the funds market-related risk is low. For DODGX, a beta value of 0.98 tells us that the fund has performed 2% worse than S&P 500 index (beta equals to 1.00) in up markets and 2% better in down markets.
• Alpha: With a R-square value that we can trust, beta can be used to predict the fund’s expected return and alpha is the yardstick for the difference between a fund’s actual return and the predication. A large, positive alpha then means a fund has performed better than what its beta would predict. For DODGX, its alpha of 4.16 means the fund has outperformed the benchmark (S&P 500 index) by 4.16% (according to Morningstar data, DODGX has indeed outperformed S&P 500 by 4.41% in the 3-year annualized total return category).

Conclusions

When evaluating an investment (mutual fund in particular), there are many obvious factors we should consider: returns, risks, expenses, and turn-over ratio, etc. Among them, the risk factor, when used properly, can help us gauge what we can expect from the investment, though past performance does not necessarily indicate future results.

If you enjoyed reading this post, please consider subscribing to my full RSS feed (What's RSS feed?). Or you can also choose to have free daily updates delivered right to your inbox.

• Ready to buy stocks/ETFs with zero commission? Check out the Zecco review and try Zecco Trading to get 10 free trades/month.
• Seeking higher returns for your cash? Take a look at the latest interest rates from leading online banks and find out where to get the most for your money.