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# Errors Found in Study Materials P1.T4. Valuation & Risk Models (OLD thread)

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#### Sixcarbs

##### Active Member
Subscriber
Hi David,

I hope this is the right place for this. There is an error in the video on Hull Chapter 15. You say things correctly but the slide you are pointing at is incorrect.

It is in Hull's example 15.3

Slide says:

.17-(.2/2) = .15

.2 is the volatility, should be variance (.2)^2. Answer .15 is correct.

.17-[(.2)^2]/2= .15

Then below it slide says:

Standard deviation,
sqrt(.2/3)= 0.1155

Should be .2/sqrt(3)= 0.1155

Also, in Study notes, Hull Chapter 13, Binomial Trees. Page 6.

"The risk-neutral probability (= 0.6523) is found first."

I think it should be .5503, which it is in the spreadsheet below. I looked high and low for a way to come up with .6523 and could not calculate it or find a place for it.

I hope this helps.

Sixcarbs

#### tattoo

##### Member
Hi david.
In page 6 of R27-P1-T4, it says "The risk-neutral probability p= 0.6523". However, according to

and

I came up with the result of p is 0.5503 which is consistent with the result of the spreadsheet showed below.

So where does "p= 0.6523" come from?
In addition, does the symbol "<" in the picture above(< probability of up jump) mean "less than"? If so, why is p less than probability of up jump? Many thanks.

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#### samuelfu9999

##### New Member
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Hi David,

For 818.1 of the Practice Questions of R27 (P.93), the d1 of rate of
change of the option price with respect to the futures price should be ln[F(0)/K] + σ^2*T/2 )/ [σ*sqrt(T)].

For 818.3, it is missing in the pdf.

#### tattoo

##### Member
Hi david, in page 12 of R27-P1-T4, Hull's example 13.11:
the result from my side is like this

The figures in red are different with yours. But I cannot figure out why. Could you have a check? Thanks.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@tattoo (cc: @Nicole Seaman )

1. You and @Sixcarbs are correct, thank you! There is a typo in the R27 Study Note, page 6, in the 3rd paragraph, instead of "(p = 0.6523)" it should read "(p = 0.5503)" to match the exhibit, as follows:
"The risk-neutral probability (p = 0.5503) is found first. The option prices at the final nodes are calculated as payoffs from the option. At the topmost node of time period two (T=0.5), the option value () is 3.2 (stock price of 24.2 minus strike price of 21). In the middle and lowermost nodes, the option is out of the money and so its value is zero (for and )."

2. In your binomial, it looks like you are discounting with exp[-(r-q)]; e.g., your 101.1160 = [(0.5126 * 189.3362) + (0.4874 * 10.000)] * exp[-(5.0% - 2.0%)*0.25] but you want [(0.5126 * 189.3362) + (0.4874 * 10.000)] * exp(-5.0%*0.25) = 100.6614; i.e., this is just a discounting function, you don't subtract the dividend yield here.

@samuelfu9999 Yes, totally agree thank you! (@Nicole Seaman it looks like 818.3 is missing ....)

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#### Nicole Seaman

Staff member
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Hi David,

For 818.3, it is missing in the pdf.
Hello @samuelfu9999

Thank you for pointing out that 818.3 is missing. I've fixed it in the PDF and will upload the corrected version to the study planner. In the future, when you find any errors in the practice questions, please comment directly in the PQ forum thread, as this thread is just for study note and video errors. The PQ forum threads are on the answer pages in the PDF documents.

@David Harper CFA FRM

Can you also let me know if samuelfu9999 is correct about 818.1? There is some discussion about this in the original thread, but I want to make sure I'm understanding it correctly before I change anything.

For 818.1 of the Practice Questions of R27 (P.93), the d1 of rate of
change of the option price with respect to the futures price should be ln[F(0)/K] + σ^2*T/2 )/ [σ*sqrt(T)].

Thank you,

Nicole

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#### tattoo

##### Member
Hello David, in page 6 of R28-P1-T4: regarding the calculation of PV of 1 year bond

#### pbhalava

##### New Member
Hi @pbhalava Yes, the use of L/P versus P/L should not change the VaR. In the pasted example above, the 95.0% 10-day absolute VaR = [-9.0%*(10/250) + 20.0%*sqrt(10/250)*1.645] * $100.00 =$6.22 regardless of L/P or P/L; in P/L, µ = 9.0% and in L/P, µ = -9.0% is the only input difference.

But as the text explains, the comparison above is between absolute VaR versus relative VaR: the relative VaR is 20.0%*sqrt(10/250)*1.645 * $100.00 =$6.58, which is greater (than absolute VaR) by exactly the drift because it omits the drift (and the relative VaR is just scaled volatility so it really doesn't care about L/P versus P/L). Relative VaR is the worst expected loss relative to the expected future value, and the expected future value is 9%*(10/250)*100 = \$0.36 higher because that is the (positive) expected drift over the next ten days. The absolute VaR is less by the drift because it is the worst expected loss relative to today's position, so it's "giving credit" to the VaR for positive drift. The absolute VaR is the return-adjusted risk measure, is how I like to think about it; the relative VaR doesn't credit the drift (the return). So I don't see an error in the above, let me know if you still do? Thanks,

Thank you for the explanation. I thought, the values coming in the green highlighted portion should be the same as calculated in the paragraph above. But yes, I got the gist of it.

#### Elizabeth_Babalola

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

This was found on page 18, Chapter 1 of Topic 4- VRM study notes.

It seem more like a typo to me and should instead be: ES$\alpha$(X) + ES$\alpha$(Y).

Kindly reconfirm.

Thanks.

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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Elizabeth_Babalola Yes, you are correct, it should be: ES(X) + ES(Y) ≥ ES(X + Y). Thank you for spotting these typos! @Nicole Seaman I have saved correct version (in ROOT) to T4-VRM-1-Ch1-FR-Measures-v3.01 (but this can await next batch; i.e., let's without publish until we have more to edit)

#### Elizabeth_Babalola

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

There seems to be some errors on page 32; Chapter 3 of the VRM note:

The return is 2% i.e 0.02 not 20% (0.2) as used in the calculations; kindly review.

Thanks.

Update: Fixed in v1.3

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#### Elizabeth_Babalola

##### Member
Also on page 9 of Topic 4 (same VRM). Taking a look at the below calculations, i am assuming that a negative sign was omitted the unconditional default probability formula.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Elizabeth_Babalola Yes, you are correct about both mistakes. Thank you for your attention to detail. We will fix on revision. In regard to page 32 of VRM-3, the red circled (see below) 0.2s should be 0.020, just as you suggest. And in regard to page 9 of VRM-4, yes the negative sign was mistakenly omitted. Thank you again.

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