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. 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 5.0%, 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 -3% and 13%. With the second fund, an investor might expect greater volatility.
Mean Total Return
The mean represents the annualized average monthly return from which the standard deviation is calculated. The mean will be the same as the annualized trailing, three-year return figure for the same time period.
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. For stock funds, a bear market is defined as all months in the past five years that the S&P 500 lost more than 3%; for bond funds, it's all months in the past five years in which the Lehman Brothers Aggregate Bond index lost more than 1%. 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 against other equity funds and bond funds are compared against 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
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
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
to the S&P 500 index; bond funds are compared to 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--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 500
may remain low.
Alpha
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. 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 of 90-day Treasury Bill
©
Copyright 2009 Morningstar, Inc. All rights reserved.