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# Errors Found in Study Materials P2.T5. Market Risk (OLD thread)

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#### Nicole Seaman

##### Director of FRM Operations
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Please use this thread to let David and I know about any errors, missing/broken links, etc. that you find in the materials that are published in the study planner under P2.T5. Market Risk. This will keep our forum much more organized. We appreciate your cooperation!

PLEASE NOTE: Our Practice Question sets already have links to their specific forum threads where you can post about any errors that you find. The new forum threads are for any other materials (notes, spreadsheets, videos,etc.) where you might find errors.

Information needed for us to correct errors:

• Page number
• Error

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#### Annushka

##### New Member
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Hi @Nicole Manley,
I think Tuckman, page 41 has got a sign error in the tree. The last time point lowest term: I think it should be r0 + 2 Lambda dt - 2 sigma squareroot dt (consistent to Model 1, page 40).

#### Sima

##### New Member
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(Page 25, Reading 40) : Describe the impact of embedded options ...
Shouldn't be there an interest-rate tree? as mentioned in the text: " The illustrated interest-rate tree below..."

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#### Sima

##### New Member
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Notes: Truckman, Chapter 8, Page 32: In the Jensen's Inequality Formula, on the right hand side of the equation there is an "E" for expected missing

#### Deepak Chitnis

##### Active Member
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Hi @David Harper CFA FRM and @Nicole Manley R39.p2.t5. Meissner study notes page no. 21 contains some typo I think.
Formula must be=cor(XY)*SQRT{(P(X)*(1-PX)*P(Y)*(1-PY)}+PXPY
+PXPY must be outside of SQRT.
On same notes page no.42 how did you get kendall T -60 I think it should be +60.

again on same notes page no.39 Variance of x should be variance of X=E(X^2)-E(X)^2.

Nothing important just some typos I think. Probably wont matter at this stage I think. But just for your note. Sorry for trouble.
Thank you

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#### rxbx

##### New Member
Hi @David Harper CFA FRM and @Nicole Manley.
There are inconsistencies in the Meissner study notes regarding Kendall's tau (page 42). I believe the definition of a pair being being neither concordant nor discordant is incorrect: it should be "xt = yt or xt*=yt*"
Thus the calculation in the example is not consistent with what appears in the Garp book: the Kendall tau should be -0,2 as per the Garp book (the 2009 observation leads to 4 pairs being neither concordant nor discordant). Can you please have a look?
Thank you

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#### rxbx

##### New Member
@Nicole Manley @David Harper CFA FRM
I have re-read the notes and found out that the calculation in the Study Note page 42 is correct but what misled me was the inconsistency in the definition of concordant and discordant pairs vs neither concordant nor discordant pairs. So I believe the definition of concordant and discordant pairs should be amended in the Study Notes as below:
"A concordant pair is defined as any pair of observations where xt > xt* and yt > yt* or xt < xt* and yt < yt*, where t ≠ t ."
"A discordant data pair is where xt > xt* and yt < yt* or xt > xt* and yt < yt*, where t ≠ t* ."
The definition of neither concordant nor discordant pairs would then be consistent.

#### David Harper CFA FRM

##### David Harper CFA FRM
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Hi @Deepak Chitnis and @rxbx

Just with respect to the Kendall's tau, please see my note here (which includes a confirmation from the book's author, Meissner) https://www.bionicturtle.com/forum/...lls-tau-and-concordant-discordant-pairs.8209/

The Meissner text contains an error (confirmed) such that the text of our study note on page 42 inherits the mistake however my calculations and illustrated exhibit are correct such that the Kendall's tau for the given exhibit is -0.60 not -0.20.

Specifically,
• @rxbx is correct that the text (in both the book and notes) should be "A concordant pair is defined as any pair of observations where x(t) > x*(t) and y(t) > y*(t) or x(t) < x*(t) and y(t) < y*(t), where t ≠ t, and a discordant data pair is where x(t) > x*(t) and y(t) < y*(t) or x(t) > x*(t) and y(t) < y*(t), where t ≠ t* ."
• The x(t) vs x*(t) notation makes this more confusing than it needs to be; I prefer to think of it visually, see https://www.bionicturtle.com/forum/threads/concordant-and-discordant-values.9453/#post-41335
Awesome @QuantMan2318 ! ... except please notice that Meissner's text contains a mistake, see https://www.bionicturtle.com/forum/threads/kendalls-t-which-is-correct.9447/
.... his example contains 2 concordant pairs and eight (8) discordant pairs; e.g., (1,4)(3,3) is discordant.

I was thinking about this visually. If (X,Y) is the first pair represented by the intersection, then concordant pairs fall into the green regions and discordant fall into the red regions, relatively speaking:
• Given this, with respect to @Deepak Chitnis 's table above (which is Meissner's example and the same in our study notes), Meissner's text is incorrect and our study note is correct: The Kendall's Tau is -0.60 because there are two concordant pairs, eight discordant pairs and zero pairs are neither. The mistake is due to the notational mistake cited by @rxbx. Consider the following pair: [(2,5), (3,3)]. Meissner's text mistakenly assigns this "neither" because x[2009] = y[2009]; i.e., 3 = 3. But this pair is discordant because 2 < 3 yet 5 > 3; or visually, if (2,5) represents the center of the grid, then in relative proximity (3,3) falls in the lower-right. Or conversely, if (3,3) is the center of the grid, then (2,5) in relative proximity falls in the upper-right. Both are discordant (concordance between pairs is necessarily symmetric: if (2,5) is discordant to (3,3) because 2<3 yet 5>3, it is also true that (3,3) is discordant to (2,5) because 3>2 yet 3<5).

#### Kaiser

##### Member
Hi,

Not sure if this typo has been flagged already:

p21, The formula shows :

When the formula seems to be

Rgds,

#### Kaiser

##### Member
Hi,

Note sure if this has been flagged already.:

p28: we have the table:

But p35, the answer to the question 2 says:

"2) In which state of the economy is equity correlation volatility high?

Generally in bad economic times. However, in our study, the correlation volatility was only slightly lower in normal economic periods (83.40%) than in a recession (80.48%). Correlation volatility was lowest in expansionary periods (71.17%)
"

It seems that:

"However, in our study, the correlation volatility was only slightly higher in normal economic periods (83.40%) than in a recession (80.48%)."

is more appropriate ?

Rgds,

#### Kaiser

##### Member
Hi,

p39. Typo in the formula, the square root for X has to account for E(X)^2

typo:

Rgds,

#### Kaiser

##### Member
Hi,

p42 of the notes:

In the example Nc = 2 and Nd = 8, so the numerator should be (2-8) .

While the result is correct the numerator is incorrect:

Should be Kendall T = (2-8) / (5(5-1)/2) = -0.6

Rgds,

#### Kaiser

##### Member
Btw, just realized that the Kendall T can also be expressed as T = (C-D) / (C+D)

#### Kaiser

##### Member
Minor Typo:

The theory is elegant and has the advantage of reducing multidimensional pairwise default correlations--by assuming shared exposure to a common market factor--into a simple but powerful mathematical model. But due to the Global Financial Crisis (CFC)

Should be (GFC)

Rgds,

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
@Kaiser

When posting errors that you find in the notes, please make sure to list the exact reading number or name of the reading and the page number in each post so we know which specific document to look at. This thread is for the entire T5 Market Risk topic so listing the reading makes it easier for us to keep things organized.

Thank you,

Nicole

#### Kaiser

##### Member
Hi,

Typo in the graph page 41:

should be:

Rgds,

#### Kaiser

##### Member
Sorry, pasted the wrong image, should be read as:

Hi,

Page 47

not

Rgds,

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Hi,

Typo in the graph page 41:

View attachment 758

should be:

View attachment 759

Rgds,
@Kaiser

Note that I moved the threads that you created to this thread, which is specifically for errors found in the study notes. Also, as stated previously, when posting errors that you find in the notes, please make sure to list the exact reading number or name of the reading and the page number in each post so we know which specific document to look at. This thread is for the entire T5 Market Risk topic so listing the reading makes it easier for us to quickly fix errors and keep things organized.

Thank you,

Nicole

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