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Managing Risk on Balance Sheet

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An FI has DA= 2.45 years and kDL= 0.97 years. The FI has total assets equal to $375 million. The FI wishes to effectively reduce the duration gap to one year by hedging with T-Bond futures that have a market value of $115,000 and a DFut= 8 years. How many contracts are needed and should the FI buy or sell them? (D = Duration)

How do I know whether i should buy or sell them?


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If Duration of Assets is > Duration of Liabilities, you have a positive Duration GAP. Thus, to reduce the gap you always need to sell the contracts.
I found formula in Schweser FRM material
N = - P×DP F×DF
a bit confusing.

I rather use this one:

No of contracts = (yield beta) ((MdT - MdP) / MdF) ) ( Vp / FP (Multiplier))

where MDT is a target duration and MDP is an actual duration. Assuming no multiplier in your example or is already embedded into FUT Value and assuming a yield beta of 1 if not stated differently,
we should reduce a duration for a gap amount, 2,45 - 0,97 = 1,48.

Thus, we simply imply, MDT as 0 and MDP as 1,48

No of Contracts = (0 - 1,48) / 8 x ( $ 375 M / $ 115.000) = - 0.185 x 3.260,8696 = - 603 contracts need to be sold.

That's how I'd solve for this. Correct me if I'm wrong.
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