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# FRM 2007 PII q74 - Repo, bond and max exposure

#### fullofquestions

##### New Member
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.

INCORRECT: A
To get the 99% confidence interval, this answer incorrectly multiplies the volatility of the swap value
by 2.0; the volatility of the swap value should be multiplied by 2.33.
INCORRECT: C
This answer incorrectly sets the duration to 10.
INCORRECT: D
This answer results from forgetting to take the square root of the horizon length.

One thing:
1. Sounds like the duration calculation was a breeze. At the moment, I cannot figure out how they solved and got the answer Duration = 7.