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P2.T5.714. When is VaR mapping useful? (Jorion, Ch 11)

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Hi @David Harper CFA FRM regarding 714.2 i am confused with GARP 2018

Computing VaR on a portfolio containing a very large number of positions can be simplified by mapping these positions to a smaller number of elementary risk factors. Which of the following mapping technique for the given positions is the most appropriate?
A.USD/EUR forward contracts are mapped to the USD/EUR spot exchange rate.
B.Each position in a corporate bond portfolio is mapped to the bond with the closest maturity among a set of government bonds.
C.Zero-coupon government bonds are mapped to government bonds paying regular coupons.
D.A position in the stock market index is mapped to a position in a stock within that index.

As per the same logic of 714.2 why answer is not b also please explain option a why is it correct. Sorry if it is unrelated to the thread

David Harper CFA FRM

David Harper CFA FRM
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Hi @Shadma This is a question that GARP had to revise from its original version in 2015. The relevant discussion is here at https://www.bionicturtle.com/forum/threads/garp-2015-p2-13.10332/

Choice GARP 2018 P2.30.B is incorrect for the same reason that my 714.2.D is true: the corporate bond cannot map only to government bonds because they are presumed to be virtually risk-free; mapping to them is only addressing the market risk (interest rate risk). Additionally, corporate bonds contain credit risk, hence the need for additional mappings. I hope that's helpful!

P.S. You might find this thread helpful, I thought my answer was pretty good (if i do say so myself! :rolleyes:), to this question https://www.bionicturtle.com/forum/threads/fixed-income-mapping.6449/post-61818 i.e.,
Hi @Nikita Gusev I think that's a great question, by which I mean to suggest that I don't necessarily perceive there is a single correct answer. But I think the theory (in the FRM at least) is that mapping is essentially the exercise of simplifying an intractably complex reality by defining a portfolio (or position etc) in terms of its sensitivity to a limited number of primitive risk factors, or put another way, by expressing its value as a simple(r) function of some small set of primatives.

I was just earlier answering a question about option delta/bond duration, as they are both first partial derivatives. I would like to remind that when we estimate an option's price change by multiplying a worst expected stock price change by delta, we are "mapping" the option value (as the exposure) to the stock price change (as the underlying factor): ~Δc = ∂c/∂S * ΔS. But, if somebody else wants to be more accurate by adding a sensitivity to volatility, with ~Δc = ∂c/∂S * ΔS + ∂c/∂σ * Δσ, it's not like one of is right or wrong!

So, philosophically, knowing that we cannot (and do not want to) map to all possible risk factors, we would like to map to a limited number of primitive risk factors that, in the ideal, are somewhat "reusable" (ie., common to our various exposure and positions). Further, and in that vein, we probably want to parse out visibly different risks, in this case: we probably want to parse out interest rate risk (market risk) from credit risk (as measured by credit spread). So for me personally, the best answer to your question is risk factors that capture only market risk, and therefore my vote would go to what Fabozzi calls "default-free theoretical spot rates;" aka, risk-free zero rates, typically captured in practice with US Treasury zeros. In general, you do want to map to zeros. And then credit spreads would be separate risk factors. (And i do recall there is some earlier GARP question where the answer wants you to parse the credit spreads from the risk-free interest rate shifts).

I hope that's helpful!
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