Type I and Type II errors in manager selection

CFA Level III Portfolio Management
#1

Hi folks,

This is what Schweser is summarizing as Type I and Type II errors
image

Then, this is what Schweser says with respect to mean-reverting markets:
“If markets are mean-reverting, then Type I errors may occur when firing a poor
performer, only to have performance improve subsequently” This really confuses me because aren’t Type I errors linked to hiring/retaining a manager?

Schweser also says this: “Type II errors occur in mean-reverting markets when strong
managers are fired or not hired (e.g., they subsequently underperform when the market
goes down)”. Can someone explain this?

Thanks!

#2

keep it simple,

  1. a type I error is rejecting the null incorrectly or false positive.
  2. here, you have the Null as manager is bad [perhaps H0: manager outperformance is <= 0; HA: outperformance > 0 ]
    to get a Type I; you’d have to reject saying a manager was bad and then they actually turn out to be bad.
    What they describe is: a manager was bad and they turn out to be good.
    If a manager was bad you’d accept the null and this would actually turn out to be wrong. this is a type II error / a false negative.
    you can see in the table the two scenarios I lay out in words are neatly summarized in the matrix as Type I and Type II so its not clear from the part you post here why the apparent contradiction.
#3

Thanks @Dan_Thorn

  1. The null is when the manager has no value add. Hence, if we reject the null (incorrectly), we are saying that we thought that the manager could value add (when in fact he could not). Hence, we would have retained/hired him initially. So why is the text talking about firing the manager?

  2. Is it correct to think of it this way - when the markets are down (due to mean reversion), it appears that the managers are not value adding. Hence, the null (of no value add) is accepted, although these are actually managers who can value add. Is this correct?

Thanks so much