Picture yourself at a fancy party. There is a group of high-powered professionals is in the corner guffawing and comparing the performance of their investment managers. Strange, unfamiliar terms drift through the air: Sharpe ratio, alpha, r-squared, down-market capture ratio ... You hear the term "batting average" and think you can join in, but it's quickly apparent they aren't talking baseball.

There are many statistical factors that professional analysts use to assess an investment manager. They may seem confusing at first, but many of these factors can be used by non-professionals to determine the value of their own investment managers. To make calculations easier, several of these statistical measures are available in commercial software packages such as Wilshire, Zephyr, or PSN Informa. In this article, we'll go through the key statistics you need to know to assess your own managers performance.

Alpha is a measure of investment performance adjusted for the risk taken. It indicates the portion of a manager's return that can attributed to the manager's skill rather than the movement of the overall market. A positive alpha implies that a manager has added value over and above the performance of the market; conversely, a negative alpha would indicate that the manager has reduced value by underperforming the market. (To learn more, read Adding Alpha Without Adding Risk.)

Beta measures the manager's systematic risk. It compares the return volatility of the manager to the volatility of returns for a comparable market index. The index has a beta of 1 by definition. A beta of 1.20 would imply a volatility level 20% higher than the overall market, and a beta of 0.80 would indicate volatility 20% lower than the market. (For more insight, read Beta: Gauging Price Fluctuations and Beta: Know The Risk.)

R-squared measures how closely the manager's returns match the returns of the market index against which it is compared. Derived from regression analysis, it essentially indicates alpha and beta's reliability in explaining the manager's return and risk. An R-squared of 90% indicates the manager correlates with the style or benchmark index by a factor 90% over time. An R-squared of 40% would indicate very little correlation with the chosen benchmark and, therefore, alpha and beta might be considered statistically insignificant. (To learn more on alpha, beta, R-squared and others, see Understanding Volatility Measurements.)

Standard Deviation
The standard deviation is a gauge of the variance, or dispersion, of the manager's return over its average or mean. Statistically, it is the square root of the variance. Because it measures total variation of the return, standard deviation is a measure of total risk, unlike beta, which measures only market risk.

Tracking Error
The tracking error, conceptually, is the inverse of R-squared. It is a measure of how closely the manager tracks the index returns. Statistically, it is the annualized standard deviation of the difference between the manager's return and the benchmark return. (For further insight, see Is tracking error a significant measure for determining ex-post risk?)

Sharpe Ratio
The Sharpe ratio measures the manager's excess return over the risk-free rate of return (normally the cash return), divided by the standard deviation. It is a statistical measure that incorporates return and risk into a single number. (To learn more on this important measure, see Understanding The Sharpe Ratio.)

Up-Market Capture Ratio
The up-market capture ratio is a measure of a manager's performance in up markets relative to the index during the same period. A ratio value of 115 indicates that the manager has outperformed the market index by 15% in periods when the index has risen.

Down-Market Capture Ratio
This ratio is the direct opposite of the up-market capture ratio, gauging performance of the manager relative to the index in down markets. A ratio value of 80 would indicate the manager has declined only 80% as much as the declining overall market, indicating relative outperformance.

Batting Average
The batting average measures the manager's ability to meet or beat the market consistently. It is calculated by diving the number of quarters (or months) in which the manager beats or matches the index by the total number of quarters (or months) in the period. A manager who outperforms the market one-half of the time will have a statistical batting average of 50. The longer the time period analyzed, the more statistically significant the measure becomes.

Putting It All Together

Example Analysis
Investment Manager XYZ
(Three Years Ending December 31, 2006)
Alpha Beta R-Squared Track Error St. Dev Sharpe UpCap DCap BA
Manager 5.0% 1.15 88% 10% 16% 1.2 120 110 80
Index 0.0% 1.00 100% 0% 12% 1.1 100 100 100

It's two weeks later, and you're at another party, but this time you've come prepared with the above statistics. Here's what you can say about your manager. The advisor generated solid excess, non-systematic returns over the past three years, but at a somewhat higher systematic risk level, as indicated by the higher beta. This pulled down the Sharpe ratio somewhat, although it is still higher than the index Sharpe ratio. Your manager doesn't hug the index, as indicated by the R-squared correlation coefficient of 88% and the fairly wide track error of 10%. The manager might have explained this by stating that making bets away from the index (insofar as sector/industry weights, holdings, etc.), is what allows him or her to generate the excess returns over time.

The level of the R-squared coefficient confirms the statistical significance of alpha and beta. The capture ratios indicate positive relative performance in up markets, but clear underperformance in down markets. The batting average indicates the manager's ability to outdistance the overall market roughly 80% of the time.


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