Morningstar Risk
An assessment of the variations in a fund's monthly returns in comparison to similar funds, with an emphasis on downward variation. The greater the variation, the larger the risk score. If two funds have the exact same return, the one with greater variations in its return is given the larger risk score. In each Morningstar Category, the 10% of funds with the lowest measured risk are described as Low Risk, the next 22.5% Below Average, the middle 35% Average, the next 22.5% Above Average, and the top 10% High. Morningstar Risk is measured for up to three time periods (three-, five-, and 10-years). These separate measures are then weighted and averaged to produce an overall measure for the fund. Funds with less than three years of performance history are not rated.

Morningstar Return
Morningstar return is an assessment of the fund's excess return over a risk-free rate (the return of the 90-day Treasury bill) in comparison to similar funds, with an emphasis on downward variation. Therefore, if two funds have precisely the same return, the one with greater variations in its return is given the larger risk score. In each Morningstar Category, the top 10% of funds earn a High Morningstar Return, the next 22.5% Above Average, the middle 35% Average, the next 22.5% Below Average, and the bottom 10% Low. Morningstar Return is measured for up to three time periods (three-, five-, and 10-years). These separate measures are then weighted and averaged to produce an overall measure for the fund. Funds with less than three years of performance history are not rated.

In any case, the greater the standard deviation, the greater the fund's volatility. For example, an investor can compare two funds with the same average annual return of 10%, but with different standard deviations. The first fund has a standard deviation of 2.0, which means that 67% of the time its returns for the past 36 months have been between 8% and 12%. On the other hand, assume that the second fund has a standard deviation of 10.0 for the same period. This higher deviation indicates that 67% of the time this fund experienced returns between 0% and 20%. With the second fund, an investor might expect greater volatility.

Mean
The mean represents the annualized average monthly return from which the standard deviation is calculated. The mean will not be exactly the same as the annualized trailing, three-year return figure for the same year. (Technically, the mean is an annualized arithmetic average while the total return figure is an annualized geometric average.)

Sharpe Ratio
Our Sharpe ratio is based on a risk-adjusted measure developed by Nobel Laureate William Sharpe. It is calculated using standard deviation and excess return to determine reward per unit of risk. First, the average monthly return of the 90-day Treasury bill (over a 36-month period) is subtracted from the fund's average monthly return. The difference in total return represents the fund's excess return beyond that of the 90-day Treasury bill, a risk-free investment. An arithmetic annualized excess return is then calculated by multiplying this monthly return by 12. To show a relationship between excess return and risk, this number is then divided by the standard deviation of the fund's annualized excess returns. The higher the Sharpe ratio, the better the fund's historical risk-adjusted performance.

Bear Market Decile Rank
This statistic enables investors to gauge a fund's performance during a bear market. As a standard measure, Morningstar compares all equity funds against the S&P 500 index and all fixed-income funds against the Lehman Brothers Aggregate Index . We add together a fund's performance during each bear-market month over the past five years to reach a cumulative bear-market return. Based on these returns, equity funds are compared with other equity funds and bond funds are compared with other bond funds. They are then assigned a decile ranking where the 10% of funds with the worst performance receive a ranking of 10, and the 10% of funds with the best performance receive a ranking of 1. Because Morningstar employs the trailing five-year time period for this statistic, only funds with five years of history are given a bear-market decile ranking.

R-Squared vs. Standard Index
R-squared ranges from 0 to 100 and reflects the percentage of a fund's movements that are explained by movements in its benchmark index. An R-squared of 100 means that all movements of a fund are completely explained by movements in the index. Thus, index funds that invest only in S&P 500 stocks will have an R-squared very close to 100. Conversely, a low R-squared indicates that very few of the fund's movements are explained by movements in its benchmark index. An R-squared measure of 35, for example, means that only 35% of the fund's movements can be explained by movements in its benchmark index. Therefore, R-squared can be used to ascertain the significance of a particular beta or alpha. Generally, a higher R-squared will indicate a more useful beta figure. If the R-squared is lower, then the beta is less relevant to the fund's performance.

Beta vs. Standard Index
Beta, a component of Modern Portfolio Theory statistics, is a measure of a fund's sensitivity to market movements. It measures the relationship between a fund's excess return over T-bills and the excess return of the benchmark index. Equity funds are compared with the S&P 500 index; bond funds are compared with the Lehman Brothers Aggregate Bond index. Morningstar calculates beta using the same regression equation as the one used for alpha, which regresses excess return for the fund against excess return for the index. This approach differs slightly from other methodologies that rely on a regression of raw returns.

By definition, the beta of the benchmark (in this case, an index) is 1.00. Accordingly, a fund with a 1.10 beta has performed 10% better than its benchmark index--after deducting the T-bill rate--than the index in up markets and 10% worse in down markets, assuming all other factors remain constant. Conversely, a beta of 0.85 indicates that the fund has performed 15% worse than the index in up markets and 15% better in down markets. A low beta does not imply that the fund has a low level of volatility, though; rather, a low beta means only that the funds market-related risk is low. A specialty fund that invests primarily in gold, for example, will often have a low beta (and a low R-squared), relative to the S&P 500 index, as its performance is tied more closely to the price of gold and gold-mining stocks than to the overall stock market. Thus, though the specialty fund might fluctuate wildly because of rapid changes in gold prices, its beta relative to the S&P may remain low.

Alpha vs. Standard Index
Alpha measures the difference between a fund's actual returns and its expected performance, given its level of risk (as measured by beta). A positive alpha figure indicates the fund has performed better than its beta would predict. In contrast, a negative alpha indicates a fund has underperformed, given the expectations established by the fund's beta. Some investors see alpha as a measurement of the value added or subtracted by a fund's manager. There are limitations to alpha's ability to accurately depict a manager's added or subtracted value. In some cases, a negative alpha can result from the expenses that are present in the fund figures but are not present in the figures of the comparison index. Alpha is dependent on the accuracy of beta: If the investor accepts beta as a conclusive definition of risk, a positive alpha would be a conclusive indicator of good fund performance. Of course, the value of beta is dependent on another statistic, known as R-squared. (Alpha, beta, and R-squared statistics are all provided on Morningstar.com.)

For Alpha vs. the Standard Index, Morningstar performs its calculations using the S&P 500 as the benchmark index for equity funds and the Lehman Brothers Aggregate as the benchmark index for bond funds. Morningstar deducts the current return of the 90-day T-bill from the total return of both the fund and the benchmark index. The difference is called the fund's excess return. The exact mathematical definition of alpha that Morningstar uses is listed below.

Alpha = Excess Return - ((Beta x (Benchmark - Treasury))
Benchmark = Total Return of Benchmark Index
Treasury = Return on Three-month Treasury Bill

R-Squared vs. Best-fit Index
R-squared ranges from 0 to 100 and reflects the percentage of a fund's movements that are explained by movements in its benchmark index.
An R-squared of 100 means that all movements of a fund are completely explained by movements in the index. In this instance, the benchmark index is the best-fit index. To obtain the best-fit index, Morningstar regresses the fund's monthly excess returns against monthly excess returns of several well-known market indexes. Best fit signifies the index that provides the highest R-squared.

Beta vs. Best-fit Index
Beta, a component of Modern Portfolio Theory statistics, is a measure of a fund's sensitivity to market movements. It measures the relationship between a fund's excess return over T-bills and the excess return of the best-fit index. For Beta vs. the Best-Fit Index, Morningstar first determines the fund's best-fit index. Morningstar regresses the fund's monthly excess returns against monthly excess returns of several well-known market indexes. Best fit signifies the index that provided the highest R-squared when the fund was regressed against it.

Alpha vs. Best Fit Index
Alpha measures the difference between a fund's actual returns and its expected performance, given its level of risk (as measured by beta).
A positive alpha figure indicates the fund has performed better than its beta would predict. In contrast, a negative alpha indicates a fund has underperformed, given the expectations established by the fund's beta. Some investors see alpha as a measurement of the value added or subtracted by a fund's manager. There are limitations to alpha's ability to accurately depict a manager's added or subtracted value. In some cases, a negative alpha can result from the expenses that are present in the fund figures but are not present in the figures of the comparison index. Alpha is dependent on the accuracy of beta: If the investor accepts beta as a conclusive definition of risk, a positive alpha would be a conclusive indicator of good fund performance. Of course, the value of beta is dependent on another statistic, known as R-squared. (Alpha, beta, and R-squared statistics are all provided on Morningstar.com.)

For Alpha vs. the Best-Fit Index, Morningstar first determines the fund's best-fit index. Morningstar regresses the fund's monthly excess returns against monthly excess returns of several well-known market indexes. Best fit signifies the index that provided the highest R-squared when the fund was regressed against it. After determining the best-fit index, Morningstar deducts the current return of the 90-day T-bill from the total return of both the fund and the best-fit index. The difference is called the fund's excess return. The exact mathematical definition of alpha that Morningstar uses is listed below.