Suppose that all of a firm’s managers are outperforming the benchmark, some by a little, some by a lot. If the confidence intervals for a quality control charts in portfolio management were widened, what would the most likely effect be?
A. Type I error would become more likely and Type II error would become more likely.
B. Type I error would become less likely and Type II error would become more likely.
C. Type I error would become more likely and Type II error would become less likely.
My Question:
Here I did not understand the confidence interval for a quality control charts in portfolio management were widened playing to identify Type -I and Type _ manager, Could you please clear my doubt?
Explanation is given below from the source:
Type I error is retaining a poorly performing manager. If the confidence intervals are widened and a poor manager is barely outperforming the benchmark, it is less likely that they will have statistically significant excess returns. We are thus more likely to fire them and hence less likely to commit Type I error. At the same time, we may be firing good managers who are outperforming the benchmark but yet do not have statistically significant excess returns. We are thus more likely to commit Type II error as Type II error is firing a superior manager.
So, that confidence interval for quality control charts have widened essentially means that because the market is so broad based and robust right now that everyone is able to beat the benchmark easily and not much superior skill difference is being seen overall.