Low Quality Benchmark - Style Component

[archived_user]

From Wiley: Which of the following would most likely indicate a low quality benchmark?
1. Active return and style components are highly correlated
2. The volatility of active return is lower than the market’s volatility
3. Turnover within the benchmark portfolio is relatively low
#1 is the answer. Explanation is “The active return component should be uncorrelated with the style component, but the style component should be highly correlated with the market return.”
Why would the style component be highly correlated with the market return? I thought the point of selecting a benchmark was that it was different than the market. And the active component is based on the style of the benchmark, so wouldn’t they be highly correlated?
Very confused, any help appreciated

 

[archived_user]

FYI all of this is from “”5.6 Tests of Benchmark Quality” – 2014 - “Reading 34 ■ Evaluating Portfolio Performance”
1. “Potential systematic bias can also be identified through a set of correlation statistics. Consider the correlation between A = (P – B) and S = (B – M). The contention is that a manager’s ability to identify attractive and unattractive investment opportunities should be uncorrelated with whether the manager’s style is in or out of favor relative to the overall market. Accordingly, a good benchmark will display a correlation between A and S that is not statistically different from zero.”

(so high correlation between those would indicate a low quality benchmark).
2. “Similarly, let us define the difference between the account and the market index as E = (P – M). When a manager’s style (S) is in favor (out of favor) relative to the market, we expect both the benchmark and the account to outperform (underperform) the market. Therefore, a good benchmark will have a statistically significant positive correlation coefficient between S and E.”

3. “Tracking Error We define tracking error as the volatility of A or (P – B). A good benchmark should reduce the “noise” in the performance evaluation process. Thus, the volatility (standard deviation) of an account’s returns relative to a good benchmark should be less than the volatility of the account’s returns versus a market index or other alternative benchmarks. Such a result indicates that the benchmark is capturing important aspects of the manager’s investment style.”