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# jorion chapter 11 mapping var

#### Pflik

##### Active Member
I'm not really comfortable with this chapter (or the previous one although i should be able to cope with that on my own)

I'm looking at the various mapping methods... And i'm just a bit confused.

For example, The return var is a product of the modified duration and the yield var... how do i calculate the yield var? where does this number come from? (is it given?)

(as a side note: I'm also curious to know if we are expected to calculate the modified duration for the exam... i learned to do it for part 1 but it's very tedious work and would consume me more than 3 min)

furthermore the tracking error is stated as the deviation relative to the benchmark... however in question 5 of the reading it takes the active risk rather than the difference in volatility between benchmark and portfolio... i'm a bit confused as to why that is.

lastly we have the mapping for different products. Again, i'm a bit unsure where the var % comes from and how the correlation matrix figures into the calculation (is it for the componend var?) and if we even need to do the matrix calculation on the exam.

I'm inclined to reread these few chapters again since it's Jorion and i have a feeling it might be one of the more important chapters.

Thanks.

#### inik

##### New Member
i feel quite the same way (esp the issues quoted below).

For example, The return var is a product of the modified duration and the yield var... how do i calculate the yield var? where does this number come from? (is it given?)

(as a side note: I'm also curious to know if we are expected to calculate the modified duration for the exam... i learned to do it for part 1 but it's very tedious work and would consume me more than 3 min)

furthermore the tracking error is stated as the deviation relative to the benchmark... however in question 5 of the reading it takes the active risk rather than the difference in volatility between benchmark and portfolio... i'm a bit confused as to why that is.
on the topic of ---
lastly we have the mapping for different products. Again, i'm a bit unsure where the var % comes from and how the correlation matrix figures into the calculation (is it for the componend var?) and if we even need to do the matrix calculation on the exam.
I very much doubt that matrix calculation is going to be on the test. The questions very well test the concepts related to ops that rely on matrix math, but I don't see it as a likely question. ...from the test-taking strategy, even if it is going to be on the test, is it really worth dedicating 5+ mins to finding the exact answer (esp. considering "grading" is on a curve & often, at least some of the answers can be eliminated via mental math alone)? From what I can tell, few people are done before the time is called, which leads me to believe my effort will probably best spent working through the other, less involved questions.

Overall, though, i find that there is a measurable disconnect b/w the
• stated FRM AIMs (what they wish us to know),
• FRM-assigned readings (chapters excised from different books, w/different conventions, assumptions, and context: e.g., cont. vs. discrete compounding, etc.),
• BT practice questions (ones requiring Excel --- illustrative, but not representative), and
• what's going to be on the exam (what is actually testable w/ provided resources (time/calculator))
that makes preparing for such chapters difficult. ...This is speaking strictly from the point of view of preparing for the exam / getting the FRM certification --- I got the Jorion book and quite enjoyed working through the chapters that weren't in the assigned reading, but, that's my own initiative that has nothing to do w/passing the FRM exam...

#### afterworkguinness

##### Active Member
Hi @Pflik,
Since VaR returns =|D*| x VaR(dY) we can solve for VaR yield

VaR change in yield =VaR(dP/P)/|D*|

Where D* is modified duration

Check out this video of David's

EDIT: I forgot to include that you can calculate Yield var by doing a historic simulation on the daily yield observations of the yield curve pertaining to that bond.

On another note (on this topic), I'm a bit confused by the mapping example table (below) in the study notes for Jorian chapter 11. I can't understand how each risk factor column is aggregated.

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#### Stenmaster

##### New Member
Hi David,

My Name is stennett, and i am new to the forum. let me first congratulate you on the great work you're doing re the FRM prep material. I have a brief question as it relates to the Var mapping example 63.2 in the review video. how did you calculate the duration for year 2 and 3? Everything else is clear to me

Looking forward o your prompt response.

Stennett

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Stenmaster Thanks for liking the work. With respect to 63.2, I committed an error. What I did is assume that the 1-year and 5-year bonds are zero-coupon bonds; if they were zero-coupon bonds, under annual compounding, the modified duration of the equally weighted portfolio is the average of their durations: (1/1.04 + 5/1.04)/2 = 2.885 years. But as they are coupon-bearing bonds, that overstates the portfolio duration. See @pichetzh@gmail.com 's comment here https://www.bionicturtle.com/forum/threads/l2-t5-63-fixed-income-mapping.3617/#post-9682
... sorry for the confusion ... Thanks,

#### brian.field

##### Well-Known Member
Subscriber
@David Harper CFA FRM CIPM
What is the exam relevance of Jorion's chapter 11? The video does not provide an indication and the material seems very confusing at firstread!

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#### cash king

##### New Member
Hi Pflik,

Regarding Chapter 11 of Jorion's book, I got a reading note. It may help with respect to your question "how the correlation matrix figures into the calculation".

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#### tosuhn

##### Active Member
Hi @David Harper CFA FRM CIPM, I am hving problems trying to understand Jorion Table 11-6 on the mapping of forwards, comm forwards, FRAs, IRS and options. Cant grasp the methods and how the undiversified VaR and diversified VaR comes into play? Will calculation be required in the exam as the AIM mentioned to only "DESCRIBE" the methods.

Hope to hear from you soon
Regards,
Sun

#### ami44

##### Active Member
Subscriber
Hi Tosuhn,

GARP seems to change the table numbering to fit their chapter numbers. So I will just assume your table 11-6 is my table 5-6 in the core readings (Risk and correlations for Forward contract risk factors).

The Forward contract will be mapped on the following 3 risk factors:
EUR Spot FX Rate
EUR Bill i.e. One year EUR interest rate
USD Bill i.e. One year USD interest rate

Table 5-6 now shows the market data that are necessary for the calculation. For each riskfactor (row header) we get the current market value, a VaR and the correlation between the risk factors.
For Example the market rate for an EUR Bill is currently 2.281% . The VaR is 0.1396% which means with 95% probability the VaR will not fall about more than 0.1396% of the current value.
Also the rate for the EUR Bill is correlated with the USD Bill rate with corr. coefficient -0.0583.

Table 5-7 illustrates the necessary calculations.
First the sensitivity (delta) of the forward contract for each risk factor is cslculated. This sensitivity is given by the present value of the cashflows and is shown in column "PV of flows , x".
This sensitivity is then multiplicated with the VaR of this risk factor to get the VaR of the Forward Contract Value specific to this factor ("individual VaR, |x|V).
Example: holding the risk factors EUR Spot and EUR Bill constant and looking only at the variation of the USD Bill, the Value of the Forward Contract will not decrease more than 0.267USD with 95% probability.

The sum of these individual VaRs for each risk factor is the undiversified VaR. If we would have no correlations between the risk factors, it would be the true VaR.

To account for the existing correlations between the risk factors we have to multiply the covariance matrix and the undiversified VaR like it is described in the document posted by cash king and we get the diversified VaR.
The column "Component VaR" is a in between step in this calculation. Be aware, we need the covariance matrix, but the correlation matrix is given in table 5-6. The conversion formula is also im the document.

I hope that helped you a little bit with the understanding, if something is not clear please ask.
If or what part of this might be asked in the exam is of course beyond my lnowledge.

#### tosuhn

##### Active Member
Hi @ami44 thanks for taking time to reply to my query. It is slightly clearer to me now. But I am still not getting how we are going to apply these mapping methods for the exam as it seems kinda tedious hehe
any thoughts on this?

regards,
sun

#### ami44

##### Active Member
Subscriber
I can imagine, that we get a table like the ones mentioned before with the mapping already done. The task would be for example to calculate undiversified VaR.
Or maybe we have to do the mapping on risk factors for a bond portfolio.
I believe doing the mapping for other products or calculations with the covariance matrice will be to complex for the test.
But that is only my feeling, I dont lnow anything of course.

#### ami44

##### Active Member
Subscriber
I wrote:
The sum of these individual VaRs for each risk factor is the undiversified VaR. If we would have no correlations between the risk factors, it would be the true VaR.
Actually now I think it must read:
If we would have perfect correlations between the risk factors, it would be the true VaR.

Perfect correlation is the worst case.

#### NNath

##### Active Member
Hi @David Harper CFA FRM, quick question, on how you are calculating the Portfolio's average duration in the below screen.

How about [(5 years /( 1 + 0.06)) + (1 year / ( 1 + 0.04) )] / 2 = 2.839 but your getting 2.73

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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @NNath

This is Jorion 11-2. They are coupon bonds, so the duration of the 5-year bond is less than 5 years. It looks like Mac duration of 5-year 6% annual pay par bond (ie., yield = 6%) is 4.465 years, such that average(4.65, 1) = 2.73 years. Thanks,

#### Stuti

##### Member
What do we mean by this statement - "A greater number of general risk factors should create less residual risk"?

#### brian.field

##### Well-Known Member
Subscriber
kind of like the error term in a regression...the more independent variables you have, i.e., the more risk factors, the less you are leaving to the error term, or to the residual term, presumably.

#### Stuti

##### Member
kind of like the error term in a regression...the more independent variables you have, i.e., the more risk factors, the less you are leaving to the error term, or to the residual term, presumably.
Thanks! Got it!

#### vivek7

##### New Member
I have a question related to Questions 3 and 4 on page 25 of Jorion Chapter6&11 notes. Question 3 is on Principal Mapping and 4 on Cash Flow mapping. I updated the excel sheet provided for the answer of question 4 and updated the parameters as follows - prob - 95%, all cashflows zero except year 3 which is 200 and spot rate flat at 4%. As you can probably see I am trying to solve question 3 here. Answer that I get from excel is 8.18 while the answer given for question 3 is 9.5. Calculations in excel and in explanation provided for question 3 are consistent until the time we arrive at returns VAR (which is 4.75%) however when calculating \$ amount the calcs are different. One is 200*4.75% other is much more involved. Shouldn't the 2 calculations match in this case? See modified excel file attached.

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#### mh2452

##### New Member
Sorry if it has been asked before.
Where would I find the excel sheet associated to Jorion, Chapter 11.
I cannot seem to find it along with the video...

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