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# Errors Found in Study Materials P2.T5. Market Risk

#### Naveen Kanth

##### New Member
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Hi in R38 P2 T5 , Reading material , page 38 in spearman's Rank correlation , example has been taken from GARP reading, it would be better if table 8.1 (In GARP reading it is completely given ) and then next step of order the return set pairs is shown . ( ranked return of X).

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
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Hi in R38 P2 T5 , Reading material , page 38 in spearman's Rank correlation , example has been taken from GARP reading, it would be better if table 8.1 (In GARP reading it is completely given ) and then next step of order the return set pairs is shown . ( ranked return of X).
Thank you @Naveen Kanth but I don't quite understand. @Nicole Seaman when you get a chance, can you seek clarification on this feedback item? Thanks!

#### RushilChulani

##### New Member
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AIM: Describe the peaks-over-threshold (POT) approach.
Compute VaR and expected shortfall using the POT approach, given various parameter values.

Questions:

87.1 If X is a random i.i.d loss with distribution function F(x), and (u) is a threshold value of X, what function defines the peaks-over-threshold (POT) approach?
a. F(x) = P{ X <= x | X > u}
b. F(x) = P{ X <= x | X = u}
c. F(x) = P{ X - u <= x | X > u}
d. F(x) = P{ X - u <= x | X = u}

87.2 Assume the following GP parameters under POT approach to extreme values: scale (beta) = 0.9, shape/tail index (xi) = 0.15, threshold (u) = 4.0%, and the percentage of observations above the threshold (Nu/n) = 10.0%. What are, respectively, the 99.5% and 99.9% value at risk (VaR)? (note: variation on Dowd's Example 7.5)
a. 3.95% (99.5%) and 5.24% (99.9%)
b. 4.15% and 6.24%
c. 7.40% and 9.97%
d. 9.03% and 11.31%

87.3 Using the same assumptions and same POT approach (generalized Pareto distribution), what are, respectively, the 99.5% and 99.9% expected shortfall (ES)?
a. 7.40% (99.5%) and 9.97% (99.9%)
b. 9.06% and 12.08%
c. 10.22% and 14.65%
d. 12.62% and 16.68%

87.1 C. F(x) = P{ X - u <= x | X > u}
Conditional on X exceeding the threshold (X>u), what is the probability that the loss in excess of the threshold (X-u) is less than or equal to x (i.e., CDF).
… note that F(x) is the parent distribution.

87.2 C. (7.404 @ 99.5% and 9.972 @ 99.9%)

87.3 B. (9.06 @ 99.5% and 12.08 @ 99.9%) @David Harper CFA FRM @Nicole Seaman I had a confusion with the study notes associated with this question. I believe equation 7.18 on page 5 of the associated Study notes is wrong. It misses the condition that "X - u <= x". Please correct me if I am wrong. Thank you!

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @RushilChulani Yes, you are correct (cc @Nicole Seaman) , there is a typo. Apologies. Thank you. On page 5 on the study note, it currently reads "Fu(x) = Pr{X - µ ≤ | X > µ } ... " which omits the x, as it should read ""Fu(x) = Pr{X - µ ≤ x | X > µ } ... ". We will fix this. Thank you!

#### aangermeyer

##### Member
Hi @David Harper CFA FRM ,

I might have discovered a typo in Tuckman chapter 8, study notes p. 42.

• Current calculation approach of one-year forward discount facor at node 1,1: 50%*[(1/1.1840) + (1/1.1040)]/1.10 = 0.766371
• How it should be at node 1,1: 50%*[(1/1.1840) + (1/1.1040)]/1.142 = 0.766371

• Current calculation approach of one-year forward discount facor at node 1,0: 50%*[(1/1.1040) + (1/1.0240)]/1.10 = 0.886233
• How it should be at node 1,0: 50%*[(1/1.1040) + (1/1.0240)]/1.062 = 0.886233
Can you backcheck and confirm?

Thanks and best,

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @aangermeyer Yes, you are absolutely correct. Thank you for identifying these typos (cc @Nicole Seaman ). The solutions of 0.766371 and 0.886233 do reflect the denominators /1.142 and /1.062 but the text is incorrect. Really appreciate your attention to detail here. Thank you!

#### evelyn.peng

##### Member
Subscriber
Hi,
I tried to search the forum to see if this was previously discussed but couldn't find anything specific. Apologies if this is already discussed.
The learning spreadsheet for Dowd Ch3 and Ch4 does not seem to contain any of the examples used in the Study Notes/Learning Video. For instance, page 17 of the Study Note references return data for Apple, Applied Materials and HP Inc. for 21 days. I'm trying to follow the bootstrap method by replicating David's steps but I cannot find where this data is stored in the learning spreadsheet.
Thanks,
Evelyn #### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @evelyn.peng That's a good point, that XLS apparently has not been updated to match the Study Notes. I've tasked myself to do that, but I can't do it immediately. I will do it ASAP and notify you here after I have updated the XLS. Thanks,

(in the meantime for Evelyn: working XLS to go here: tbd)

#### Detective

##### Active Member
Subscriber
Minor points:

R39-P2-T5-Tuckman
(1) p.39  