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GARP.FRM.PQ.P1Normal distribution vs distribution of risky assets

nag_san

New Member
Does anyone know if this is a part 1 or part 2 objective ? Compare the normal distribution with the typical distribution of returns of risky financial assets such as equities

There was a sample question from GARP through email as below but not sure I've seen this objective in PART 1 books. if this is indeed for part 1 can someone please explain how the correct answer being C?

nag_san

New Member
After further research Looks like it's part of book 4 chapter 1. Now just need to know the explanation for choice being C Please

nag_san

New Member
After further reading it seems that any model that follows normal distribution cannot overestimate by construction but can only underestimate because given that normal distribution predicts that 4, 5, 6 STD deviation moves should hardly ever happen. Therefore logically 7% ie 6 std deviation moves would be underestimated by the model as it follows the normal distribution. Please advise if this is correct understanding. Any further comments/explanations are welcome.

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi @nag_san The value of 7.2% is not meaningful; e.g., we could replace 7.2% with any value above 3*1.2% = 3.6% or 4*1.2% = 4.8% because any value above 3.6% would be +3 standard deviations. The question depends only on the fact that we assume actual returns have heavier tails than normally distributed returns. If we assume that returns follow the normal distribution, but in reality the actual returns have heavier tails, then our model will underestimate the frequency of large declines (because large declines are in the loss tail). This whole question is merely testing the idea that actual returns tend to exhibit leptokurtosis (ie., kurtosis > 3, or returns with a heavier-than-normal tail). If that explanation satisfies, I will tell you my honest opinion: I think it's a pretty weak question.

This question naively relies on an empirical observation that is generally true as if it were universally true, but could be untrue for any particular sample (a fact of which the question is fully aware given the use of non-absolute "will likely underestimate"). I would like to further observe that the question is not even specifying equity returns: we are told it's a hedge fund and the issue is asset returns. Well, that's a lot of different asset classes. At best, this is the sort of question that an FRM candidate should be able to answer very quickly. Think: actual equity return have a heavy tails! It's a weak, semi-disposable but non-difficult question that surrounds a super simple premise with extra annotations (specific values that are not especially meaningful). I guess I would call this is a "lazy" question. I certainly would not over-think it. I hope that's helpful,

Hamam

Member
Subscriber
Hey,
If anyone can help out on the below question that was recently sent by GARP for preparation for the part 1 exam coming up it will be much appreciated.

Question:
1. An analyst in model risk validation at a hedge fund is reviewing a model that assumes daily changes in the S&P 500 Index are normally distributed. The analyst is aware that although asset returns are often approximated using a normal distribution, actual returns can differ from this distribution. If the standard deviation of the daily change in the S&P 500 Index observed from 20 years of historical data is 1.2%, which of the following is correct?

answer: C.The model will likely underestimate the number of trading days in which the S&P 500 Index will decline by more than 7.2.

I understand the answer in the sense that the model will underestimate the number of trading days because it’s calculated under the assumption of normality. However, I just can’t seem to work out how they specifically mentioned that it will decline by more than 7.2.

nag_san

New Member
Thanks @David Harper CFA FRM. Yes after reading it a couple of times, I realized I had spent too much time clinging onto the numbers thinking it might mean something glaring. It'd have been simple not to overthink as you correctly point out.

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
@Hamam I moved your question to this post. Notice @nag_san 's comment, and I totally agree with the implication: the question is sort of teasing you to ascertain the values but the values are not themselves meaningful. The more I think about it, the more I dislike this question: the choices feature values of 4.8%, 6.0% and 7.2% and 0.1% as if the values have a special meaning. The reader is likely to try and waste time figuring out how 7.2% is calculated and why it's different than 6.0%. But that's mission impossible.

Nevermind that choice (D) is arguably problematic: for daily changes, rounding to zero is common such that we might plausibly expect zero to be the mean and approximately accurate under a normal approximation (!). The more I look at it, the more I think the question is simply not good because it's too lazy. Just my opinion.

Hamam

Member
Subscriber
Actually now it makes much more sense in my head. I probably spent way more time than necessary trying to figure out how they computed 7.2.
Anyways thanks for your support.

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
@Hamam Yes, helpful point of view. That's exactly why this is not a good question: most of us will read it and immediately (and very naturally) waste time trying to figure out why there is a choice between 4.8%, 6.0%, 7.2% and 0.1% and where they came from. Giving choices with numeric alternative values begs such a reaction. Yet they are arbitrary. Not a good question.

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