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ravishankar80

New Member
Hi David,

List of questions where "I don't get it" is growing as exam approaches :down: .( A bit disappointed about the Flash Quiz because there are no reliable set of questions to practice on which cover all the AIMS and since you are best teacher I have come across your questions would have really helped practice better .)
Anyway will attempt some of your 2007 questions. I did not understand this question in 2007 FRM practice exam .It's from Hull and i am supposed to know it and i don't .I understand it is a Var calculation and the square root rule has been used but why duration?

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: B
The approximate duration for a 10 year bond is 7.0. The volatility of the swap value over
10 years is calculated as follows:
σ(V) = [market_value * duration * yield volatility *(10)0.5]
= 10,000,000 * 7.0 * 0.00074 * 3.16 = 163,806.
To get the 99% confidence interval, we multiply σ(V) by 2.33, which gives approximately
$380,000.

Reference: John Hull, Options, Futures, and Other Derivatives, 6th ed. Chapter 7.

Regards
Ravi
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi Ravi,

("A bit disappointed about the Flash Quiz..." I agree and apologize. I didn't meet that goal, that i set. Thanks for stating your disappointment so nicely)

This is another flawed question.

First, we don't say the approximate duration of a bond is 7.0 precisely because, per the assigned Tuckman, duration varies with yield. The bond here is par, so we do know coupon = yield. Given that, this highest duration here is 9+ for a lower yield/lower coupon bond and could go down to 6 or less for high yield/high coupon. Ceteris paribus, higher yield implies lower duration.

Second, Hull Chapter 6 does not cover this (yield volatility). Technically, yield volatilty isn't under any assignment in FRM 2008

Okay, but given that,

The daily yield volatility is scaled by SQRT[10] to a a 10-day yield volatility, then to 99% confidence with 2.33. So what you have here is:

price * duration * worst expected yield change

it is just like
change in price = price * duration * 1%

but instead it is a worst expected change in price. If you divide each side by price/market value:
% change in market value = duration * worst expected % change in yield

Hope that helps,
David
 

skcd

New Member
I dont get this at all! I mean how do we know the duration is 7 anyway? The bond is at par can be assumed but there is no yield or coupon info. Is there a way to back out yield from yield vol? Am i missing something?
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
skcd -

you are correct, it's a bad question. Given priced at par, we can infer coupon = yield; but duration may vary from ~6 (higher yield) ~9+ (lower yield). Can't infer from yield volatility - David
 
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