Maximum potential exposure (Sample FRM 2007 question )

[turtle2]

David,
This is a question from Sample FRM 2007 exam. Can you please explain why is the answer B ? I can not get this answer with the data provided,

Hong Kong Shanghi Bank has entered into a repurchase agreement with a client where the client will sell a 10-year US treasury bond to the bank and repurchase it in 10 days. The bond has a notional value of USD 10m, trades at par with the yield volatility for a 10-year US treasury 0.074%. The swap’s maximum potential exposure at a 99% confidence level is closest to:

a. USD 320,000
b. USD 380,000
c. USD 550,000
d. USD 1,200,000
CORRECT ANS: B

Thanks
turtle2

 

[David Harper CFA FRM]

Hi turtle2,

I happen to know that GARP used to incorrectly expect the candidate to assume that a 10-year Treasury has a (modified) duration of 7.0; this is, of course, very incorrect as duration varies with coupon. But knowing they used to employ that error, it appears to want:

0.074% daily vol * SQRT(10) [i.e., scale over 10 days] * 2.33 deviate * 7 mod duration * 10,000,000=381,667

... note the question should say 0.074% is daily volatility and should make explicit assumption of normal distribution of yield. Actually, as these are yields, should clarify normal i.i.d. to make way for the scaling over 10 days.

but you are correct: technically it cannot be solved without duration assumption

Hope that helps, David

 

[turtle2]

David,
If modified duration is 7 for 10 yr bond, then 10/7= 1.43 = (1+y/2). This implies a value of y=0.43*2= 0.86. Is this a valid assumption for 10 yr bond yield ? I would argue that 320,000 is a better answer. You need an unrealistic yield assumption of 86% for 381,000 (answer).

Thanks.

Turtle2

 

[David Harper CFA FRM]

Turtle2,

Right, but your assume Macaulay duration = 10; if this were a 10 year C-STRIP (zero coupon), then yours make sense and implied yield is unrealistic. However, we can assume a coupon, such that the Mac Duration could be 6.x to 9.x. So, we've got two unknowns: Mac Duration /(1+y/2) = 7.0. There are an dozens solutions, one for each coupon rate.

David

 

[turtle2]

David,
Right, it depends on Mac Duration. Do we need to know how to calculate Mac Duration in exam given, T=10 and C= some value, using a closed form formula ? Can you please add the closed formula for Mac Duration in Market Formula Sheet for L2 ?. Should we assume modified durarion of 7 if something like this shows up in exam ? Any advise.

Thanks.

Turtle2

 

[David Harper CFA FRM]

Turtle2,

Technically, closed form Mac duration is not assigned and should not be quizzed (and they never have). Good idea to add to formula sheet but frankly, given our obligations until the exam, I don't think i update T5 formula sheet before the next exam (will need to wait for next version).

Of course, you can expect them to assume a zero coupon bond such that (eg) a 10 year zero has Mac duration = 10 and Mod duration = 10/(1+y/k).

Re: "Should we assume modified duration of 7" ... No, that is a bad historical habit (IMO) and i have made this error very clear to them (and will include again, on my next update to them, tomorrow). It should not appear, and it leads to bad thinking; e.g., we are assigned Tuckman who shows duration varies with coupon and yield, so much better to understand why we cannot assume mod duration = 7.0 without more information

David