Risk Analysis
Alpha
A measure of the difference between a separate account’s actual returns and its expected performance, given its level of risk as measured by beta. A positive alpha figure indicates the separate account has performed better than its beta would predict. In contrast, a negative alpha indicates the separate account’s underperformance, given the expectations established by the separate account’s beta. All MPT statistics (alpha, beta, and R-squared) are based on a least-squared regression of the separate account’s return over Treasury bills (called excess return) and the excess returns of the separate account’s benchmark index.
Alpha can be used to directly measure the value added or subtracted by a separate account’s manager. Alpha depends on two factors: 1) the assumption that market risk, as measured by beta, is the only risk measure necessary and 2) the strength of the linear relationship between the separate account and the index, as it has been measured by R-squared.
Beta
A measure of a separate account’s sensitivity to market movements. The beta of the market is 1.00 by definition. Morningstar calculates beta by comparing a separate account’s excess return over Treasury bills to the market's excess return over Treasury bills, so a beta of 1.10 shows that the separate account has performed 10% better than its benchmark 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 separate account’s excess return is expected to perform 15% worse than the market’s excess return during up markets and 15% better during down markets.
Beta can be a useful tool when at least some of a separate account’s performance history can be explained by the market as a whole. Beta is particularly appropriate when used to measure the risk of a combined portfolio of separate accounts.
R-Squared
Reflects the percentage of a separate account’s movements that can be explained by movements in its benchmark index. An R-squared of 100 indicates that all movements of a separate account can be explained by movements in the index. Thus, index separate accounts 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 separate account’s movements can be explained by movements in its benchmark index. An R-squared measure of 35, for example, means that only 35% of the separate account’s movements can be explained by movements in the benchmark index.
R-squared can be used to ascertain the significance of a particular beta. Generally, a higher R-squared will indicate a more reliable beta figure. If the R-squared is lower, then the beta is less relevant to the separate account’s performance.
Standard Deviation
A statistical measurement of dispersion about an average, which, for a separate account, depicts how widely the returns varied over a certain period of time. Investors use the standard deviation of historical performance to try to predict the range of returns that are most likely for a given separate account. When a separate account has a high standard deviation, the predicted range of performance is wide, implying greater volatility.
Standard deviation is most appropriate for measuring risk if it is for a fund that is an investor’s only holding. The figure can not be combined for more than one fund because the standard deviation for a portfolio of multiple separate accounts is a function of not only the individual standard deviations, but also of the degree of correlation among the separate accounts' returns.
If a separate account’s returns follow a normal distribution, then approximately 68 percent of the time they will fall within one standard deviation of the mean return for the fund, and 95 percent of the time within two standard deviations. For example, for a separate account with a mean annual return of 10 percent and a standard deviation of 2 percent, you would expect the return to be between 8 and 12 percent about 68 percent of the time, and between 6 and 14 percent about 95 percent of the time.
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.
Up and Down Quarters
This information reflects the number of positive and negative quarters for the separate account.