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

#### Karim_B

##### Active Member
Thanks @Nicole Seaman

Hi @David Harper CFA FRM
This one isn't an error per se, but when you eventually revisit R39-P2-T5-Tuckman Study Notes it would be helpful if you could number the formulae since the explanation refers to a bunch of formula numbers which are hard to follow since the fomulae themselves aren't numbered.

Screenshot example from page 26 on the CMT swap:

Thanks
Karim

#### Karim_B

##### Active Member
Hi @David Harper CFA FRM
R39-P2-T5 Tuckman Study Notes chapter 8 page 39 I think we're missing the E for E[r] in the Jensen's inequality formula.

Screenshot:

Thanks
Karim

#### David Harper CFA FRM

##### David Harper CFA FRM (test)
Staff member
@Karim_B Yes, an error for sure. Thank you, again, Karim!

#### Karim_B

##### Active Member
Thanks @David Harper CFA FRM
It looks like a couple of the learning objectives in R39-P2-T5 Tuckman Chapter 9 Study Notes aren't explicitly covered although they appear in the list in the study note itself.

I'll use the wording of GARP's 2018 learning objectives since it's slightly different in the study notes:

A) Standard deviation of the rate change

This appears in both:
1. Calculate the short-term rate change and standard deviation of the rate change using a model with normally distributed rates and no drift.
2. Calculate the Vasicek Model rate change, standard deviation of the rate change, expected rate in T years, and half-life.
For A.1 on pages 53 & 54 of the study notes I just see rate change calculations.

Similarly for A.2 on page 58 I see calcs for the other 3 items, but not std dev.

From your Tuckman screenshot in the post below it looks like the formula is:
https://www.bionicturtle.com/forum/...th-and-without-drift-tuckman.6683/#post-45631

Standard deviation of the change in rate = Sigma*SQRT(dt)

Screenshot:

B) Describe the effectiveness of the Vasicek Model
This one is missing.

Could you please confirm whether the formula for point A is correct and add an explanation for point B?

Thanks!
Karim

#### bhoyare.nilesh

##### New Member
P2.T5.303. Simulations with short-term interest rate models: 303.3 Typo

Hello,

Its regarding Answer for 303.3 which is given as Option A. But in explanation its mentioned as "In regard to (A), (B), and (C), each is TRUE" and respective explanation is given for each option mentioned. Whereas it should be mentioned as "In regard to (B), (C), and (D), each is TRUE" & similar changes need to be done in explanation as well. Further, small typo in explanation needs to be rectified as "interest" (Changing the distribution of nterest rates is one solution.)

Please correct me if I am wrong or missed something in explanation.

#### bhoyare.nilesh

##### New Member
P2.T5.404. Lessons on value at risk (VaR) implementation: Typo

Hello,

I assumed their is a type in P2.T5.404 answer. Correct answer is B (404.1. B. False: "Scaling of short-horizon VaR to a longer time horizon with the commonly used square-root of-time scaling rule has been found to be an inaccurate approximation in many studies.) And rest of the options are true which are A, C & D. Whereas its erroneously mentioned as (A), (B), and (D), each is TRUE.

Please correct me if I am wrong or missed something in explanation.

#### David Harper CFA FRM

##### David Harper CFA FRM (test)
Staff member
Hi @Karim_B (belated, sorry). Yes, thank you. Where σ is the annual basis point volatility, in general the standard deviation of the rate change applies the square root rule with σ*sqrt(dt) or σ*sqrt(Δt). I will task us to ensure these phrases are explicitly addressed in the revisions.

@bhoyare.nilesh Yes, thank you, you are correct on both. It looks like these changes have not been updated yet in the PDFs. (cc @Nicole Seaman : the sources have already been corrected):

#### Nicole Seaman

Staff member
Subscriber
P2.T5.404. Lessons on value at risk (VaR) implementation: Typo

Hello,

I assumed their is a type in P2.T5.404 answer. Correct answer is B (404.1. B. False: "Scaling of short-horizon VaR to a longer time horizon with the commonly used square-root of-time scaling rule has been found to be an inaccurate approximation in many studies.) And rest of the options are true which are A, C & D. Whereas its erroneously mentioned as (A), (B), and (D), each is TRUE.

Please correct me if I am wrong or missed something in explanation.
Hi @Karim_B (belated, sorry). Yes, thank you. Where σ is the annual basis point volatility, in general the standard deviation of the rate change applies the square root rule with σ*sqrt(dt) or σ*sqrt(Δt). I will task us to ensure these phrases are explicitly addressed in the revisions.

@bhoyare.nilesh Yes, thank you, you are correct on both. It looks like these changes have not been updated yet in the PDFs. (cc @Nicole Seaman : the sources have already been corrected):
@bhoyare.nilesh

I just wanted to make sure that you know this thread is only for errors that are found in the Study Notes. The practice questions each have their own forum thread, which David pointed out above. Any errors or questions regarding the practice questions should be posted in their corresponding forum thread, which is located on the answer pages in the PDF.

Thank you,

Nicole

#### Nicole Seaman

Staff member
Subscriber
Hi @David Harper CFA FRM @Nicole Seaman
In the Market Risk focus review video 2 it refers to the original incorrect solution to question 63.2 which was fixed here:

Screenshot from P2_FR2.PDF:
View attachment 1593

View attachment 1594

Thanks
Karim
@Karim_B

We will be updating the focus review videos this year, so we will make sure that any mistakes are corrected in the new videos.

Thank you,

Nicole

#### Karim_B

##### Active Member
@Karim_B

We will be updating the focus review videos this year, so we will make sure that any mistakes are corrected in the new videos.

Thank you,

Nicole
Thanks @Nicole Seaman
I also thought I'd post it since we're in the last weeks before exam day and more people might be using the review videos. I spent some time scratching my head as to how the answer was reached until I realized it wasn't correct

Best
Karim

#### JulioFRM

##### Member
Subscriber
Maybe in Dowd, Measuring Market Risk, Chapters 3 & 4 Study notes page 8, for positive homogeneity it says p(v*x)=v*p(x) But afterwards it says p(v*x)=v*p(y). Y should be X?

#### David Harper CFA FRM

##### David Harper CFA FRM (test)
Staff member
@JulioFRM Yes, thank you! I edited this but missed that. Indeed, the second occurrence should read For λ > 0, ρ(X) = λρ(X) ... as positive homogeneity only invokes one variable. Thank you!

#### David Harper CFA FRM

##### David Harper CFA FRM (test)
Staff member
@jaivipin what's the mistake? e.g. model 1: dr = σdw appears to be correct. oh, I do see on page 11, there is a typo. Please let me know if this isn't what you mean?

#### jaivipin

##### Active Member
Subscriber
I thought instead of + it should have been -, the one you pointed.

Thanks

#### Ashok_Kothavle

##### Member
Subscriber
Dear Mr David

I guess there is one very trivial error in the study notes on Jorion Chapter 6 : Page 3, last para. You have mentioned

A good (aka, accurate) model will produce approximately the number of expected
exceptions. For example,
over 250 days, a good (aka, accurate) 95.0% VaR model
will produce approximately 5.0% * 500 days = 25 exceptions. Over 100 days, a good
99.0% VaR model is expected to produce only 1.0% * 100 = 1 exception.

Since you are dealing with 250 days, the no of exceptions will be 5.0% * 250 = 12.5 and not 25. Hence, either you need to change the no of exceptions from 25 to 12 or change the number of business days to 500 from 250 as mentioned.

Do understand, it is very trivial error though.

However, will appreciate to get your valuable word / insight on the following:

As you mentioned, Model validation tools include:

(1) Backtesting

(2) Stress testing

(3) Independent review and oversight.

Backtesting, by the inherent process it follows, is a natural and obvious candidate for the model validation tool.

But, how stress testing is considered as validation tool. The VaR models are as I understand static and the output depends on the input we provide. For the outstanding exposure positions, whether we provide the models regular rates or stressed rates of the related risk factors, model just runs the process and gives some output (in this case, the stressed VaR value). So the VaR models as such aren’t Artificial Intelligent compliant to realize these are stressed values. Hence, I had used the word static. So basically. what I meant is like "garbage in, garbage out". What we provide, we get according results.

Will be grateful if you can explain and enlighten with your wise words about how stress testing being used as validation tool.

Regards

Ashok

#### Nicole Seaman

Staff member
Subscriber
Dear Mr David

I guess there is one very trivial error in the study notes on Jorion Chapter 6 : Page 3, last para. You have mentioned

A good (aka, accurate) model will produce approximately the number of expected
exceptions. For example,
over 250 days, a good (aka, accurate) 95.0% VaR model
will produce approximately 5.0% * 500 days =
25 exceptions. Over 100 days, a good
99.0% VaR model is expected to produce only 1.0% * 100 = 1 exception.

Since you are dealing with 250 days, the no of exceptions will be 5.0% * 250 = 12.5 and not 25. Hence, either you need to change the no of exceptions from 25 to 12 or change the number of business days to 500 from 250 as mentioned.

Do understand, it is very trivial error though.

However, will appreciate to get your valuable word / insight on the following:

As you mentioned, Model validation tools include:

(1) Backtesting

(2) Stress testing

(3) Independent review and oversight.

Backtesting, by the inherent process it follows, is a natural and obvious candidate for the model validation tool.

But, how stress testing is considered as validation tool. The VaR models are as I understand static and the output depends on the input we provide. For the outstanding exposure positions, whether we provide the models regular rates or stressed rates of the related risk factors, model just runs the process and gives some output (in this case, the stressed VaR value). So the VaR models as such aren’t Artificial Intelligent compliant to realize these are stressed values. Hence, I had used the word static. So basically. what I meant is like "garbage in, garbage out". What we provide, we get according results.

Will be grateful if you can explain and enlighten with your wise words about how stress testing being used as validation tool.

Regards

Ashok
Hello @Ashok_Kothavle

Please note that I moved your question here to this thread, which is specifically for errors found in any of the Topic 5 study notes. There is a study note error thread for each topic. You can find the links here: https://www.bionicturtle.com/forum/threads/errors-found-in-study-planner-materials.8764/.

Thank you,

Nicole

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

In the screenshot below, capture from your notes from "The Evolution of Short Rates and the Shape of the Term Structure", while calculating discount rate of 0.766371 you have discounted year 2 rates of 18.4 and 10.2 with 10% should it be 14.2% instead of 10% as in the upstate situation we are assuming rate to be 14.2 in year 1

#### David Harper CFA FRM

##### David Harper CFA FRM (test)
Staff member
Hi @Jaskarn Yes, you are correct! Sorry, it's my mistake (apologies!). The solutions are are correct (as this matches Tuckman's tree in Chapter 8, as we can see from the underlying XLS here https://www.dropbox.com/s/ykjc72t7bdjlodm/012319-tuckman-tree-error.xlsx?dl=0) but the interim calculation has a mistake. Further, the second bullet repeats the same mistake, these bullets should read:
• One year forward, at node [1,1] the two-year discount factor = 50%*[(1/1.1840) + (1/1.1040)]/1.1420 = 0.766371
• One year forward, at node [1,0] the two-year discount factor = 50%*[(1/1.1040) + (1/1.0240)]/1.0620 = 0.886233

Thank you for noticing! (cc @Nicole Seaman I think we can wait on these until batch revision ....)