# Schweser mistake? reading 10 page 249

In the professors note they say

We build a 95% confidence interval around the expected return

If teh desired return falls in the 2.5% lower tail of the distribution the client can be 95% confident that the minimum will not be violated

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if you are in the lowest 2.5 tail, does not that leave at least 97.5% of the values greater than you. basiclly the goal will be met at least 97.5% of the time and up to 99.9999% of the time, depending on how much into the tail the desired return is…

i think page 196 in CFAI volume 2 agrees with what i said ?

if you have a 95% confidence interval around the mean - you have 2.5% in the lower tail.

this is different from VAR stuff … where you are looking at 95% confidence and arriving at a minimum threshold.

exactly, you have 2.5 in the lower tail, and 97.5 above that value…

With a two tailed test if you have 2.5% in the lower tail you are only 95% confident.

Well one of the 2 is incorrect since CFAI on page 196 sais it is 2.5% probability of failing…

Also this is a one tail test, I putting 2.5% in the left tail and looking at what is above it, the fact that I looked up this value using the 95% does not make it a 2 tail test…

anyway, so CFAi is wrrong ?

No, but the difference in your H(0) does.

your first H(0) is return = x --> two tailed test

your next H(0) is losses exceed x —> one tailed test

Schweser is right. If you feel Schweser is wrong, go read the book.

I am reading Schweser Level I material and when the put 5% in one tail, they say they are 95% confident!

So how is it here that we are putting 2.5% in the tail and saying we are 95% confident ? And how is it that CFAI is not saying the same thing as Schweser…

two tailed vs. 1 tailed - you seem to have forgotten that aspect of it completely.

when you have two tails - it is 2.5% in each tail.

for a 95% two tailed test - you take the factor as 1.96

vs. 1.645 for a 1-tailed 95% CI.

What is beta?

Just kidding.

Okay, this is a one tailed test because we are worried about getting returns bellow our minimum return, we do not care about the other tail.

Even though Schweser represented it as a confidence interval leaving 2.5% in each tail

and like you said CP, for a 1 tailed 95% we use 1.645 and not 2 (1.96 rounded).

now since we used 2, this would corrispond to 97.5% one tail test.

Your original statement says : “We build a 95% confidence interval around the expected return”

when you build a confidence interval “around” something it is a two tailed test period. it doesn’t matter if you just “look” at one tail, the test is still structured as two.