TYPE 1 and TYPE 2 ERROR (Crticial thinking on lower bound) UnderPerformance

CFA Level III
#1

Hi guys,

Trying to check on the folloiwng understanding

Type 1 error occurs because you set your confidence level too low which means your confidence band is too low

(Based on Page 177 Diagram 17)

This means that it is easier to breach the upper edge of the confidence band…And you reject Ho far too often(which means keep managers with zero value added)

Let decipher a scenario where the manager underperform.

A manager consistently breach the lower bound of the confidence band…indicates it is peforming badly.The firm fire the manager. After further investigation it shows that the manager is running into bad luck and not really an under performer.

So what type of error is that? Type 2 or Type 1?

#2

2

#3

Type 1: Keep underperformers too long

Type 2: Fire good managers

-> Type 2

#4

Can i offer another perspective?

Type 1 error can occur if confidence level is low and the band is narrow as a result. The band is easily exceeded…This led to reject of Ho and keep the manager…

If band is narrow(type 1 error), another thing can happen…the manager will exceed the lower bound easily …and this seems to concude he is a underperformer …so why cant this be a result of type 1 error?

#5

you mean to say if the band had been bigger - the guy may have “squeezed” thro as a “ok” performer?

#6

Sorry if i did not make any sense,

I am trying to comprehend.

if the band is bigger…the manager is still within the supposingly variance band…which means the manager although add negative VALUE added return but it is considered under the norm of investing due to variance.

So in this case it seems that because type 1 error has caused confidence band to be too narrow and causes the manager to be fired as it violatesand exceed the supposed norm(of a narrow band)