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# CourseErrors Found in 2021 Study Materials P1.T4. Valuation & Risk Models

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Please use this new thread to let David and I know about any errors, missing/broken links, etc. that you find in the 2021 materials that are published in the study planner under P1.T4. Valuation & Risk Models. 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. This thread is for any other materials (notes, spreadsheets, videos, etc.) where you might find errors.

Information needed for us to correct errors:

• Page number
• Error

#### bollengc

##### Member
Subscriber
hello Nicole, David,

on T4-VRM-10-Ch10-Int-Rates-v3.1, page 8, the 2nd formula might be missing the first just after the equal sign

current formula:

I would be expecting sthg like:

thanks,
Camille

#### bollengc

##### Member
Subscriber
hello Nicole, David,

On T4-VRM-4-Ch4-Credit-Ratings-v3:

page 14:

formula should be Conditional PD = Unconditional PD (t)/Cumulative survival proba (t-1)

page 21: in the paragraph about credit scoring:
while credit rating uses a combination of qualitative and qualitative factors -> qualitative and quantitative

thanks,
Camille

#### RSchwarzer

##### New Member
Subscriber
Hi Dave,
Hi Nicole,

could you check the study notes on P1_T4-VRM-Ch6-Credit Risk, page 12.

I think there is a minor issue within the formula in the first example. Instead of multiplying the PD with the recovery rate, it should be the loss rate to calculate the expected loss (see screenshot). However, the calculation itself is correct. Like I said: just a minor issue.

Cheers
Roland

#### bollengc

##### Member
Subscriber
hello Nicole, David,

on T4-VRM-14-Ch14-Bin-Trees-v2.1, page 17, there is an additional u on the right side of the equation that should not be there.

and on the next line, the Delta on the right side should be removed as well

and same for following line

This error FIXED in PDF As discussed here:
exercise 812.2 + solution might request a small update (to replace the d used for proba of down mvt by q)

thanks,
Camille

Last edited by a moderator:

#### bollengc

##### Member
Subscriber
hi Nicole, David,

on T4-VRM-15-Ch15-Black-Scholes-v2

page 4

We are considering a period return (and not log return here, no?)
wouldn't it be more logical as well to have std dev = sigma*sqrt( ) instead of sigma*sqrt(T) as we are considering a small time interval ?

thanks
Camille

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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Camille (@bollengc) Yes, indeed, agreed. Thank you!

#### bollengc

##### Member
Subscriber
hi Nicole and David,

on T4-VRM-16-Ch16-Greeks-v2

page 19: there are typos on puts delta. It should be N(d1) - 1 (1 outside of parenthesis)
so for the 2nd occurrence, it should be 1- N(d1)

thanks
Camille

#### bollengc

##### Member
Subscriber
hi Nicole, David,

in T4-VRM-1-Ch1-FR-Measures-v3

page 18:

(mentioning 2 times ES(X) instead of ES(X) and ES(Y))

page 19:

same kind of typo

exercise 31.2 not corrected per:

(but the note on page 22 makes it clear they are both general risk measures)

And more general comment, it looks like the Learning Objectives for 2021 do not contain general risk measures and spectral risk measures anymore.

thanks
Camille

#### bollengc

##### Member
Subscriber
hi Nicole, David,

on T4-VRM-3-Ch3-Volatility-v3.1, there are some paragraphs that are mixed up:
page 17:
and the content below is about GARCH and EWMA

Thanks,
Camille

#### bollengc

##### Member
Subscriber
hi Nicole, David,

on T4-VRM-6-Ch6-Credit-Risk-v3
page 12

it should be either PD*LR or PD*(1-RR) as per the numerical example.

+ a few error! Bookmark not defined:
page 12

page 13:

page 13:
typo in the numerical example:

page 15:

either remove the square sign or change standard deviation into variance

page 16:
portfolio variance defined as: (no error)

but std dev of % loss should be sqrt(ptf variance)/sum(Li) (the formula misses the sqrt)

p25:

the standard deviation will be increased by 1% to 1.1*1.01

thanks,
Camille

#### bollengc

##### Member
Subscriber
hi Nicole, David,

On T4-VRM-7-Ch7-Op-Risk-v3

page 13:

might be good to add parenthesis around (Lambda*T)^n so that there is no confusion on what is set to the power n. (both lambda and T, not T alone)

thanks,
Camille

#### reiss1

##### New Member
Subscriber
Hello all,

On Ch1 notes p.20, I am a bit confused with the statement: "The VaR violates the subadditivity: VaR(A + B) ≥ VaR(A) = VaR(B)"

My understanding of subadditivity is that since VaR(A) + VaR(B) ≥ VaR(A + B) does not hold, since 0 + 0 ≥ 100 is false, is proof by contradiction. I am confused as to what "VaR(A + B) ≥ VaR(A) = VaR(B)" represents especially since it seems to hold in this example: 100 ≥ 0 = 0.

Reiss

#### lushukai

##### Active Member
Subscriber
Hi @reiss1 ,

The subadditivity property, as you mentioned, is f(A+B) <= f(A) + f(B) (one example of this is the VaR instance). The paragraph is trying to say that VaR is not coherent measure due to its lack of subadditivity. The screenshot proves this by quoting:

VaR(A+B) > VaR(A) = VaR(B)

Another way of quoting this is VaR(A+B) > VaR(A) + VaR(B), as VaR(A) = VaR(B) = 0. As this is proof of violation of subadditivity, we can see that VaR is not a coherent risk measure.

Hope this helps!

Last edited:

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Thank you @lushukai ... but @reiss1 it is a typo, apologies, I will fix it. There are actually two problems:
1. First, the example needs to specify the confidence level for the VaR. Given each bond has a PD of 4.0% (with LGD = 100%), then 99.0% VaR (A) = \$100 and 95.0% VaR(A) = 0. So this example assumes a 95.0% VaR.
2. Second, it should read "The VaR violates subadditivity because VaR(A+B) ≥ VaR(A) + VaR(B) because 100 > 0 + 0"
Thanks,

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