Memorizing facts about distributions

[wrongsaidfred]

Hi David,

I noticed that in a few of your questions you included the formulas for the cdf that pertains to that question. Will the exam do the same or do we need to memorize the cdf and/or pdf for all of the distributions we learned about? If there are any that we should memorize, what would those be?

Also, quite a few questions that you ask involve formulas or figures concerning the skewness and kurtosis of other distributions. Are these formulas that we need to devote to memory?

Thank you,

Mike

 

[David Harper CFA FRM]

Hi Mike,

It's a good question, it comes up every year. A few things:

* The FRM exam does NOT require you to have memorized all the pdf/CDF distributional functions; to attempt to do so, for most candidates, would be a misuse of valuable study time.
* GARP FRM AIMs, in their endearing charm have always biased in favor of "asking for more in the AIMs" than they will query in the exam. This is true of the distributions.
* I am currently working on updated formula sheets, I am including guidance on this topic ... so the formula sheets will NOT include many of the pdf/CDF functions (if i view them as very low probability)
* My (our) questions often are more difficult--they routinely go deeper--than exam questions. You can refer to the associated AIM to see what GARP is saying you should know. The reason (e.g.) that i will include a worked/calculated kurtosis is not because i think you will be asked to calculate kurtosis. It's because to work an quantitative example tends to give a much more concrete understanding; for example, "copula" is hard to understand via the qualitative definition. To work quantitative examples gives a much richer view of qualitatively expressed concepts.

With those caveats/qualifiers/hedges, here is what i think matters for the exam (i.e., here is what i think could really be tested. But I assume you know that i cannot really know for certain?), IN ORDER OF IMPORTANCE:

* The only functions I would memorize are the two discrete distributions: binomial and Poisson (both have been historically popular on test). In my opinion, it's conceivable these are the only pdf functions you would see on the test! The rest will be qualitative/properties
* Normal (of course you will see "normal"): neither the pdf/CDF, just the two popular quantiles: one-tailed 1.645 @ 95%, one-tailed 2.33 @ 99%. If you want to be careful, also know two-tailed 1.96 @ 95% and 2.58 @ 99%.
* Sampling distributions: student's t (properties not pdf/CDF); I can never predict about the chi-square and F distribution, safe to be familiar (properties not pdf/CDF)
* Exponential: I would memorize pdf/CDF because they aren't hard and because CDF exponential is the formula for cumulative PD (kills two birds)
* EVT: Level 1 highly unlikely. Level 2: they are on the table, can't predict
* about SKEW and KURTOSIS, I perceive these are always "threatened" but owing to their difficulty in calculating, I don't think they've really appeared as calculations. I think a skew question would have to be very simple and so too a kurtosis.

I hope that helps, more in the forthcoming formula sheets, thanks, David

 

[wrongsaidfred]

Thank you, thank you, thank you!!!!

 

[wrongsaidfred]

This may be a dumb question, but for the binomial and the Poisson, all we know are the probability mass distributions. We do not have anything concerning the cdf. Is this correct?

Also, when I asked about kurtosis, I was talking about the formulas such as excess kurtosis=6/(v-4) and kurtosis for a uniform = 1.8.

Thanks again,
Mike

 

[David Harper CFA FRM]

Hi Mike,

Yes, correct re: binomial & Poisson. The test has asked CDF questions (<=) of both but they require you to add up P(X=0) + P(X=1) + P(X=2) at most

Re kurtosis, the real problem is that you are asking me for predictive precision i don't have; e.g., here is an AIM:
"Define, calculate, and interpret the skewness, and kurtosis of a distribution."

See the problem? GARP has given themselves the latitude to, yes, query the kurtosis of distributions ... every year i am constantly pushing back on AIMs like this (both levels have many many AIMs with very low likelihood of getting on the exam; lately i seem to send an email every week trying to get them booted -- this is a key reason the FRM is perceived to be so difficult IMO), because WILL they ask you for quantitative skew/kurtosis (either sample, as my first or variable, as yours)? It is unlikely to very unlikely

thanks, David

 

[David Harper CFA FRM]

Mike,

I just noticed that GARP, on their facebook page, has the following Q&A (emphasis is mine):

Question: "Do we get a formula sheet for the exam?"
Answer:

"If a question requires information from a specific distribution table, that information will be provided.

With respect to “Quantitative Analysis” topics outlined in the 2011 Study Guide, candidates are not expected to memorize formulas of distributions, but should understand when it is appropriate to use a particular type of distribution. The two approved calculators are capable of performing any required present value and future value calculations.

Best regards,
GARP FRM
August 29 at 10:26am "

... softer than i've seen before. Given they've appeared before, I would still memorize the binomial and Poisson pdfs. Thanks, David

 

[Aleksander Hansen]

I don't believe the person postin that is the same as the ones writing the exams.
Do yourself a big favor and know the distributions well. I bet there will be some questions where you have to know them. Might not be the core of the question but it will be there.

GARP seem to be fans of having people memorize a lot of formulas, so I don't know why they would draw the line at distributions.

 

[David Harper CFA FRM]

Aleks - thanks, that's a good "realistic" correction. While I parroted GARP's official line, your suggestion is consistent with my experience; i.e., given that exam questions aren't sourced necessarily according to a literal syllabus, it makes sense they may occasionally assume distributional knowledge. Thanks,

 

[Aleksander Hansen]

Indeed, FRM P1 in May had a question requiring Bayes' formulae and from what I can gather it GARP did not include this in ther syllabus or AIMs. Personally, I think there should be more Bayesian statistics on the exams, considering how important it is in applications; such as mixing your a priori distribution with the market implied distribution, with flexible probabilities for deriving the posterior distribution. A powerful tool, indeed.

 

[Aleksander Hansen]

Just as an FYI:
If you're looking at Tuckman's new edition on, e.g. Amazon, do note that the chapters have changed. What used to be chapter 6&7 has been merged into one arguably better chapter (chapter 5) which does a very good job with duration, convexity & Co. Chapter 7 is now what used to be chapter 9 (used to be = what is currently on GARPs reading list.)

The new chapter 6 is very useful (hedging using regression) but is not required for the exam. I think it will/should be included in the 2013 reading list as it is the most practical chapter, and if you do any sort of hedging related activity you need to know it.

[dont have the book right in front of me but I think that was the new format.]

Tuckman also says that chapters 7-10 or so are essentially unchanged. Completely wrong. Think what he meant to say that the contents of those chapters have not changed, but they were previously numbered as 10-15 (just an example) as the content is entirely different (chapters don't map one-to-one)

 

[Aleksander Hansen]

FYI
If you're using Bruce Tuckman's new edition be wary of a typo in the term structure chapter.
I emailed Tuckman and he was quick to reply:

From: Bruce Tuckman [[email protected]]
Sent: Friday, June 22, 2012 12:11 AM
To: Hansen, Aleksander
Subject: RE: Typo in new (3rd) edition of Fixed Income Securities: Tools for Today's Markets

Thank very much, Aleks. [...] this error and it will be corrected in the second printing.
[...]
I’m glad you are enjoying the 3rd edition.

BT

From: Hansen, Aleksander
Sent: Thursday, June 21, 2012 9:22 PM
To: Bruce Tuckman [[email protected]]
Subject: Typo in new (3rd) edition of Fixed Income Securities: Tools for Today's Markets

Chapter: The science of term structure models
Page: 208
Paragraph: 3

The probability used in the sentence starting, “Hence, the date 1 up-state price is $1000/(1+0.5/2) = $973.23,”
Should be 0.55, such that it would read: […]$1000/(1+0.55/2) = $973.23
[...]

........................
*Some information was redacted for privacy reasons

 

[Mark W]

Hi David,

Taking the above into consideration and given that most students probably err on the side of caution I think a 'crib/cheat sheet' for the distributions would be very helpful. I've got in mind (as I've just made one myeself) a one page sheet with about 10-12 distributions down the short side (landscape!) and the various properties across the top, such as:

Mean
Variance
Skew (+ve/-ve)
Kurtosis/Tails (e.g heavy, light, flexible)
# parameters
Discrete/Continuous
Support/Non-negative
Usage
Other (e.g reduces to, approaches...)

Then on the back I've got the PDF/CDFs of the most common ones and a few other salient/commonly tested facts. I know it's too late for P1 now, but I think it would be a useful one-stop reference point in the future vs. going to the notes/wikipedia/a question you did last week to find the answer out.

Now I'll confess that the reason I did this is because I saw that Kaplan had done it for one of the CFA exams but relating to all formulas (they provide a big foldable, laminated and very glossy sheet) on a huge page! Whilst I'm not a fan of this for a whole topic (I like your PDF approach, gives me room to annotate and is a lot more expository) I think it's potentially useful for things like properties of distributions which lend themselves to rote learning somewhat.

I always try to draw a distinction between what I call 'L&C' (learn and churn) stuff and the stuff that actually requires understanding. The L&C stuff works its way in over time/with Q practice and if necessary can be chucked in the short term memory bank in the days before. The understanding stuff is where you really earn your corn and takes most of the time.

Thus I've classified the properties of distributions in the L&C camp and was looking for an easy way to tackle in an hour or so....

As Sherlock Holmes famously said:

“I consider that a man's brain originally is like a little empty attic, and you have to stock it with such furniture as you choose. A fool takes in all the lumber of every sort that he comes across, so that the knowledge which might be useful to him gets crowded out, or at best is jumbled up with a lot of other things, so that he has a difficulty in laying his hands upon it. Now the skillful workman is very careful indeed as to what he takes into his brain-attic. He will have nothing but the tools which may help him in doing his work, but of these he has a large assortment, and all in the most perfect order. It is a mistake to think that that little room has elastic walls and can distend to any extent. Depend upon it there comes a time when for every addition of knowledge you forget something that you knew before. It is of the highest importance, therefore, not to have useless facts elbowing out the useful ones.”

- A Study in Scarlet

I'm also doing an option strategy one, but that's a separate thing...

Many thanks,

Mark

P.S. I know the key formulas PDF has some information on, but it's not comprehensive.