Alpha, beta, and R-squared are components of Modern Portfolio Theory (MPT), which is a standard financial and academic method for assessing the risk of a fund, relative to a benchmark. A mutual fund's alpha and beta are calculated in relation to a market index. Each fund is linked to an appropriate index based on its investment category.
• Alpha: A measure of selection risk (also known as residual risk) of a mutual fund in relation to the market. A positive alpha is the extra return awarded to the investor for taking a risk, instead of accepting the market return. For example, an alpha of 0.4 means the fund outperformed the market-based return estimate by 0.4%. An alpha of -0.6 means a fund's monthly return was 0.6% less than would have been predicted from the change in the market alone.
• Beta: The measure of any fund's or stock's risk in relation to the market. A beta of 0.7 means the fund's total return is likely to move up or down 70% of the market change; 1.3 means total return is likely to move up or down 30% more than the market. Beta is referred to as an index of the systematic risk due to general market conditions that cannot be diversified away.
• R-Squared: 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.
Conversely, a low R-squared indicates that very few of the fund's movements are explained by movements in its benchmark index. Thus, R-squared can be used to determine the significance of a particular beta or alpha (the higher the R-squared, the more significant alpha and beta).
• Standard Deviation: Standard deviation is a statistical measure of the range of a fund's performance, and is reported as an annual number. 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.
(Approximately 68.3% of the time (2 of 3 occurrences), 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. About 95.4% of the time (19 of 20 occurrences), a fund's total returns should be within a range of plus or minus two times the standard deviation from its mean.)
• Sharpe Ratio: A measure of a fund's excess return relative to the total variability of the fund's holdings. The higher the Sharpe ratio, the better the fund's historical risk-adjusted performance.
• Treynor Ratio: A measure of the excess return per unit of risk, where excess return is defined as the difference between the portfolio's return and the risk-free rate of return over the same evaluation period and where the unit of risk is the portfolio's beta.
The fund's performance is examined for the past 36 months. Any months in which the portfolio's returns were less than those of the 90-day Treasury bill are flagged.
Morningstar then adds up the amounts by which the fund trailed the T-bill return and divides the figure by 36, to generate an average monthly underperformance.
Morningstar does the same for the rating group as a whole, and divides the fund's underperformance by the group's underperformance to arrive at a Morningstar Risk score.
To assign ratings, Morningstar subtracts each fund's Morningstar Risk score from its Morningstar Return score. The funds in each rating group are then ranked by this raw number, from highest to lowest. The top 10% of funds receive 5 stars, the next 22.5% receive 4 stars, the middle 35% receive 3 stars, the next 22.5% receive 2 stars, and the bottom 10% receive 1 star. (There is no "zero" star rating—funds with less than 36 months of return data are simply not rated.)
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