Q.25 of 2010 Practice Exam (Hedging)

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Hi David,

The following is the Q.25 of the GARP Practice Exam 2010.

Nicholas is responsible for the asset and liability management of JerseyBeech Bank, a small retail bank with USD 300 million in interest-bearing assets that yield approximately 70 bp above LIBOR. The duration of the interest-bearing assets is 2.5 years. Due to the recent financial turmoil, the bank seeks to reduce potential negative impacts on earnings from adverse moves in interest rates. Thus, the bank decides to hedge 50% of its interest rate exposures using Treasury bond futures. Nicholas decides to use September T-bond futures that trade at 106-22 and will mature in three months; the cheapest-to-deliver bond associated with this contract is a 7-year, 10% coupon, with a current duration of 5 years. At the maturity of the futures contract, the duration of the bank’s interest rate sensitive assets will not change; however, the duration of the cheapest-to-deliver bond will fall to 4.9.

How many contracts should Nicholas buy or sell?

a. Buy 703 contracts.
b. Sell 703 contracts.
c. Buy 717 contracts.
d. Sell 717 contracts.


Answer: d


Explanation: N = Exposure to hedge * Duration of assets to be hedged
Price of futures contract * Duration of futures contract = 150 mil * 2.5 = 375 mil = 375

717 contracts 106 22/32 * 0.1 mil * 4.9 106.6875 * 0.1 mil * 4.9 0.52276875

Since he is long in the asset, he should sell 717 contracts. The answer with 703 contracts comes from not using the duration at
the maturity of the futures contract.



Could you please explain how to derive the value "717" as I dont understand from the explanation given above.


Thanks.

 

[David Harper CFA FRM]

Hi nidzrulz,

Here is the explanation we give in the paid member's area
(http://forum.bionicturtle.com/viewthread/2514/). I hope this is helpful! David

The number of contracts required is given by (Hull 6.5):
N = (Portfolio Value * Portfolio duration @ hedge maturity) / (Futures contract price * Duration of CTD underlying the interest rate futures contract)

As Treasury futures prices are quoted with a face value of $100,000, the price 106-22 = 106 22/32 * $100,000 = $106,687.50; and
N = ($300 MM portfolio * 50% hedge * 2.5 portfolio duration) / ($106,687.5 future* 4.9 CTD duration) = 717.33.
So, short ~ 717 contracts. (Since he is long in the asset, he should sell 717 contracts. The answer with 703 contracts comes from not using the duration at the maturity of the futures contract.)

Please note that the hedge is simply ensuring that the DOLLAR DURATIONS match:
Dollar duration of underlying = $150 MM * 2.5 = $375 MM
Dollar duration of hedge = $106, 687.5 * 4.9 * 717 contracts = $375 MM
… is the same thing as matching DV01/PV01/PVBP (the DV01 = DD/10,000 = $37,500)
So we want equal dollar durations (i.e., portfolio versus hedge) such that P * Dp = F* Df * N, and so solve for N:
N = (P * Dp)/(F * Df)

 

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Hey Thanks David....