Morningstar Risk
The Morningstar Risk statistic evaluates the fund's downside volatility relative to that of other funds in its broad investment class (domestic stock, international stock, taxable bond, or municipal bond). Morningstar uses a proprietary risk measure that operates differently from traditional risk measures, such as beta and standard deviation, which see both greater- and less-than-expected returns as added volatility. Morningstar believes that most investors' greatest fear is losing money--defined as underperforming the risk-free rate of return an investor can earn from the 90-day Treasury bill--so our risk measure focuses only on that downside risk. To calculate the risk score, we plot monthly fund returns in relation to T-bill returns. We add up the amounts by which the fund trails the T-bill return each month and divide that total by the period's total number of months. This number, the average monthly underperformance statistic, is then compared with those of other funds in the same broad investment class to assign our risk scores. The resulting risk score expresses how risky the fund is relative to the average fund in its class. The average risk score for the category is set equal to 1.00; a Morningstar Risk score of 1.35 for a taxable-bond fund means that the fund has been 35% riskier than the average taxable-bond fund for the period considered. Note that Morningstar does not rate any fund that has less than three years of performance data.

Morningstar Return
The Morningstar Return figure rates a fund's performance relative to other funds in its broad investment class (domestic stock, international stock, taxable bond, or municipal bond). After adjusting for maximum front-end loads, applicable deferred loads, and applicable redemption fees, Morningstar calculates the excess return for each fund, defined as the fund's load-adjusted return minus the return of the 90-day T-bill over the same period. The use of excess instead of raw returns reflects our belief that mutual funds should be rated highly for only those returns earned beyond those of a T-bill, which is essentially a risk-free investment. The excess returns are then compared with the higher of the average excess return of the fund's broad investment class or the 90-day T-bill return. This last adjustment prevents distortions caused by having low or negative average excess returns in the equation's denominator, as might occur during a protracted down market. The equation is: (Return on Fund* - T-bill)/Higher of (Category Return* - T-bill) or T-bill

* Fund returns are adjusted for loads. Class average is based on load-adjusted returns. The resulting Morningstar Return figure is listed relative to the average excess return of the investment class or the T-bill, whichever is higher. A footnote indicates when the T-bill comparison is used. If the Morningstar Return figure is compared to the broad investment class, 1.00 represents the class average. Thus, a figure of 1.10 means that the fund outperformed the class average by 10 percent, while 0.90 means that the fund underperformed by 10 percent. For T-bill comparisons, the same concept is true, but 1.00 occurs when a fund's load-adjusted excess return equals the T-bill. Therefore, a score of 0.90 with a T-bill footnote indicates that the fund's excess return has been 10% lower than the T-bill. In periods of low returns, a fund's raw returns could hypothetically underperform T-bill returns, in which case the figure would be a negative number, such as minus 0.35, meaning that fund's raw returns were 35% less than those of the T-bill.

Category Rating
Like the star rating, the Morningstar category rating is a quantitative measure of risk-adjusted returns. This three-year rating shows how well a fund has balanced risk and return relative to other funds in the same Morningstar category. The rating uses the same methodology as the star rating. Unlike the star rating, however, the category rating does not reflect any front- or back-end loads. Other expenses, such as 12b-1 fees, are included. As with the star rating, 5 is the best rating and 1 is the worst.

Category Return
A statistic that compares a fund's excess return over the risk-free rate (as measured by the return on Treasury bills) to the average excess return for the Morningstar category. With the return on Treasury bills set as the benchmark, the bottom 10% of funds in each Morningstar category earn a Low category return, 22.5% Below Average, 35% Average, 22.5% Above Average, and 10% High. If the average excess return of the category is below the return of the T-bill, the return of T-bill alone is used as the benchmark. Unlike the familiar Morningstar Return statistic, loads are not accounted for in category return. Category return is calculated only for a three-year period.

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 monthly return of 5%, but with different standard deviations. The first fund has a standard deviation of 2.0, which means that its range of returns for the past 36 months has typically remained between 1% and 9%. On the other hand, assume that the second fund has a standard deviation of 4.0 for the same period. This higher deviation indicates that this fund has experienced returns fluctuating between minus 3% and 13%. 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.