Morningstar Mutual Fund Risk Measures: Alpha, Beta, and Rsquared
By Sun
A large portion of our taxable investments are held in 10 mutual funds (check out my 2010 Year in Review for a list of mutual funds we currently own and asset allocation at the end of 2010). Though it has been a long time since I made any change to our mutual fund investments, I still keep an idea on any new funds, funds closed before now reopened, etc. Not that I really need any overhaul of our holdings, but to see what are out there.
When I check out a mutual fund, the tool that I use most often is Morningstar because, comparing with other mutual fund research websites, Morningstar offers more tools to help me know about a fund’s fundamentals as well as the past performance. In addition to the fund returns, which usually play a big role in my fund selection process (even though I know past returns don’t guarantee future performance), I also pay attention to the fund’s risk. And Morningstar has a set of measures to let me understand better a fund’s risk characters before making a decision.
What Is Risk
Before getting into the of Morningstar risk measures, let’s first take a look a the general definition of risk in investment. 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, Volatility Measurements and Modern Portfolio Theory Statistics, to help investors get a sense of the risk of owning a particular fund. For Volatility Measurements, you can use the following data to gauge a fund’s volatility compared to the broad market:
 Mean
 Standard Deviation
 Sharpe Ratio
 Bear Market Decile Rank
And for Modern Portfolio Theory Statistics, you will see these data provided by Morningstar:
 RSquared
 Beta
 Alpha
In the following, I will explain mean, standard deviation, beta, Rsquared, and alpha and how to use them to assess risk involved in investing a mutual fund.
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Mean, Standard Deviation, Beta, Rsquared, and Alpha
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.
Since the recession more than three years ago, 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 Rsquared of 100. According to Morningstar, Rsquared, represented by a percentage number ranging from 0 to 100, characterizes an equity’s movement against a benchmark. A Rsquared that equals to 100 means all the equity’s movements are inline 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 against the respective benchmark.
How Risk Measures 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 3year data through January 31, 2011):
Funds  2008 Return  2009 Return  2010 Return  Mean  STD  Rsquared  Beta  Alpha 
DODGX  43.31  31.27  13.49  0.06  26.41  97.13  1.19  1.95 
CGMFX  48.18  10.42  16.94  0.45  33.32  62.15  1.20  8.10 
 Mean: The mean represents the annualized average monthly return. Therefore, a higher mean suggests a higher return the fund has delivered. In this case, DODGX performed a little better in the past three years with a mean of 0.06.
 Standard deviation (STD): In this case, both funds have a quite high STD comparing to the S&P 500, which has a mean of 0.20 and STD 21.91. A higher STD of CGMFX indicates that the fund is more volatile than the DODGX.
 Rsquared: If we recall that Rsquared measures a fund’s movement against the benchmark and a value close to 100 means the fund follows the benchmark very closely. Also, Rsquared can help investor assess the usefulness of a fund’s beta or alpha statistics. A higher Rsquared means the fund’s beta is more trustworthy. In this case, CGMFX’s 62.15 Rsquared value says that only 62.15% of its movements can be explained by the fluctuations of S&P 500 index. This means that S&P 500 may not be a good benchmark to measure CGMFX. On the other hand, DODGX’s 97.13 Rsquared value indicates the fund is well represented by S&P 500 and its beta value can thus be trusted.
 Beta: Now we know S&P 500 may not be a good benchmark for CGMFX, its beta value, though higher than that of DODGX, 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 marketrelated risk is low. For both DODGX and CGFMX, which have almost identical betas, they tend to swing 20% more than the benchmark in the same direction.
 Alpha: With a Rsquare 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 1.95 means the fund has underperformed the benchmark (S&P 500 index) by 1.95%, better than CGMFX’s 8.10 alpha.
Conclusions
When evaluating an investment (mutual fund in particular), there are many obvious factors we should consider: returns, risks, expenses, and turnover 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.
Photo credit: jay kid
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I have a little thought…
If we calculate the standard deviation of a mutual fund by Nav…we have the risk of these price distribution.
But we are trying to evaluate the risk of portfolio.
If we calculare the risk of the portfolio, taking care about correlation, we have a different rate of volatility.
Wich one is the real risk?
Are we simplifying the calculate assumin the Nav price keep inside the correlation among stocks?
Thanks for your help!
Dino