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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
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,

#### Library_books

##### New Member
Subscriber
Hi,
In chapter 6: Credit Risk and Capital Modeling
Pg 25:
Increase of 1% exposure to loan 2 or 3 is calculated as 1.997904 - 1.997078 = 0.006924
It should be 1.997904 - 1.990980 = 0.006924

#### Garbanzo

##### Member
Subscriber
T4CH1 Measures of risk, Study Notes, page 11:
The positive/negative descriptions are flipped, the first shown is actually negative (mean<median<mode), second is positive (mode<median<mean)

edit: now I see that it is actually correct, I got confused by the unusually shifted mode. usually if the mode is to the right of 0 skew 0 mean, the distribution is negatively skewed. but the mass under the curve shows it indeed is a positive skew (#1) and negative skew (#2)

#### Garbanzo

##### Member
Subscriber
T4CH6 Credit risk and capital modeling, Study notes p16 bottom formula:

numerator should be a square root

#### Garbanzo

##### Member
Subscriber
T4CH6 Credit risk and capital modeling, Study notes p22 bottom substitution:

N(0.2784) should be N(-0.2784)

#### Garbanzo

##### Member
Subscriber
T4CH9 Pricing Conventions, Discounting, and Arbitrage. Study notes, page 7 (and 8 same table):

I think the bond maturities should be 1, 1.5 and 2.0.

Last edited:

#### Garbanzo

##### Member
Subscriber
T4CH11 Bond Yields and Return Calculations. Study notes, page 12:

there's a typo in the first table, should be -982.00

Page 16: they start at half-year not one year

Page 20: the price actually depreciated by 0.004 (pulled down to par because coupon is higher than yield), which was more than compensated by the 1.000 coupon

Last edited:

#### Garbanzo

##### Member
Subscriber
T4CH12 Applying Duration, Convexity, and DV01. Study notes page 3:

should be
(1 + yield/m)

Page 24:
should be -DV01 * 10,000

Last edited:

#### Garbanzo

##### Member
Subscriber
T4CH13 Modeling and Hedging Non-Parallel Term Structure Shifts. Study notes page 9

not sure how a zero coupon bond is a C-STRIP (?), did you mean P-STRIP?

Last edited:

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Garbanzo That's the final stripped coupon (yes, Tuckman does refer to C-STRIP here). So if it's a 30-year Treasury, you'd have one P-STRIP plus 60 C-strips where the "last" is a 30-year C-strip. Thank you for all of your posts/corrections/etc, I just haven't had time to carefully process. Just wanted to quickly respond to your latest. Thanks,

#### Garbanzo

##### Member
Subscriber
Thanks @David

T4CH14 Binomial Trees. Study Notes, page 5:

That yellow should be a 10.00 strike.

Page 11:

u formula is missing "0.2" (sigma)

Last edited:

#### Garbanzo

##### Member
Subscriber
T4CH15 The Black-Scholes-Merton Model. Study notes page 19:

w = N/(N+M) * c

Page 12:
aren't we assuming lognormal prices -> normal returns?

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