307.1. C. S = 4.1, K = 18.1
Let X = 0 with prob 95.0% and X = 1 with prob 5.0%, such that mean (X) = 0.050:
3rd central moment = (1-0.05)^3*5% + (0-0.05)^3*95% = 0.04275, such that skew = 0.04275/(5%*95%)^(3/2) = 4.1295 (or -4.1295)
4th central moment = (1-0.05)^4*5% + (0-0.05)^4*95% = 0.04073, such that kurtosis = 0.04073/(5%*95%)^2= 18.053
i.e., excess kurtosis = 18.053 - 3.0 = 15.053
@David Harper CFA FRMHI @yadav.anil 0.05 is the mean, so the 0.05 is correct. Instead, there should not be a 0.95 in the 4th moment per the correction in the source at https://www.bionicturtle.com/forum/threads/p1-t2-307-skew-and-kurtosis-miller.6825/
i.e., correct is:
cc @Nicole Seaman the pdf isn't updated to match the corrections in the thread, fyi
Hello @truongngoR16.P1.T2 (page 36): the first sentence in the section "Explain tail dependence" is unreadable due to formatting error.
Thank you for the response. I guess it's the problem with Adobe Acrobat Reader as I saw quite a few errors like that. I will try as you advised.Hello @truongngo
I just downloaded the R16 Hull reading from the study planner, and there are no formatting errors on the document. Generally, when a member is having issues with formatting it is due to the PDF software that they are using to view the document. We recommend using the free Foxit PDF reader to view documents, which can be downloaded here: https://www.foxitsoftware.com/pdf-reader/.
Hi @FlorenceCC As part of my youtube series, it happens to be that I recorded a video reviewing this problem (Miller Chapter 6 Sample #2), see below.
This sample question is perhaps not "exam-level" quality due to the slightly loose wording. I would not say it's wrong (is just my opinion) because I think it's right to infer that the second question is asking for the posterior (conditional) probability given the "evidence" of three years of beating the market:
... but, at the same time, to qualify as exam-level a good question should be precise and explicit. As somebody who write questions constantly, I agree with the spirit of your point: I would definitely want to edit that second question, because a good question does not hang people up in semantic interpretation like this question very well could. I hope you like my video about this question, thanks!
Hi @vaisman (cc @Nicole Seaman ) Apologies, but the upper matrix on page 101 is a mistake and should not be there (you are correct, it's a mistaken copy from the previous sample problem). For sample problem #2, we should be showing only the following matrix (notice that I have colored in YELLOW the three assumptions given: these are all we need to populate the entire matrix!):
And then I notice a second problem, I don't know how this happened but the problem statement omits the following emphasized sentence: "Stars are rare. Of a given pool of managers, only 16% turn out to be stars. A new manager was added to your portfolio three years ago. Since then, the new manager has beaten the market every year." Hence the cubed probability: the probability that a star manager beats the market on any given year is 75%, such that the probability she/he will do that for three consecutive years is 75%^3. In this way, the Bayes theorem applied is P(S | 3B) = P(3B | S)*P(S) / P(3B). Sorry for the confusions, thanks!