Mean 3 Year, 5 Year, 10 Year
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.)
Standard Deviation 3 Year, 5 Year, 10 Year
Standard deviation is a statistical measure of the range of a fund's performance. When a fund has a high standard deviation, its range of performance has been very wide, indicating that there is a greater potential for volatility. The standard deviation figure provided here is an annualized statistic based on 36 monthly returns. By definition, approximately 68% of the time, the total returns of any given fund are expected to differ from its mean total return by no more than plus or minus the standard deviation figure. Ninety-five percent of the time, a fund's total returns should be within a range of plus or minus two times the standard deviation from its mean. These ranges assume that a fund's returns fall in a typical bell-shaped distribution.
Sharpe Ratio 3 Year, 5 Year, 10 Year
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.
Alpha 3 Year, 5 Year, 10 Year
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.
Beta 3 Year, 5 Year, 10 Year
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 Barclays 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.
R2 (R-Squared) 3 Year, 5 Year, 10 Year
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.
©2023 Morningstar. All Rights Reserved.
