Tree Row Bank has assets of $150 million, liabilities $135 million, and equity o

Question

Tree Row Bank has assets of $150 million, liabilities $135 million, and equity of $15 million. The asset duration is 6 years and the duration of the liabilities is 4 years. Market interest rates are 10%. Tree Row Bank wishes to hedge the balance sheet with Treasury bond futures contracts, which currently have a price quote of $95 per $100 face value for the benchmark 20 year, 8% coupon bond underlying the contract, a market yield of 8.5295% and a duration of 10.3725 years.  

How many contracts are necessary to fully hedge the bank?

Verify that the change in the futures position will offset the change in the cash balance sheet position for a change in market interest rates of plus 100 basis point and minus 50 basis points.

Explanation / Answer

a.) For initiating a hedge, the bank is required to sell the futures as increase in interest rates will impact the futures in an inverse manner.

k = Liabilities/Assets = 135/150 =0.90

Number of Contracts required to Hedge = -(DAssets - kDLiab) x Assets / (DBond x PBond)

                                                         = -(6 - 0.90 x 4) x 150,000,000 / (10.3725 x 95,000)

                                                         = -365.33 contracts

                                                         = -365 contracts (as conttracts can be bought in whole number)

b.) Interest Rate increase = 100 basis points

Change in the cash balance = Expected E

                                         = -DGAP x [R/(1 + R)] x A

                                         = -2.4 x (0.01/1.10) x 150m

                                         = -$3,272,727.27

Change in bond price = -10.3725 x (0.01/1.085295) x $95,000 = -$9,079.41

Value change in 365 contracts = $9,079.41 x -365 = $3,313,986.25

Gain in future contracts = $3,313,986.25

Net gain =-$3,272,727.27 + 3,313,986.25 = $ 41,258.98

c.) Interest Rates Decrease = 50 basis points

Cash balance change = Expected E

                                = -DGAP x [R/(1 + R)] x A

                                = -2.4 x (-0.005/1.10) x $150m

                                = $1,636,363.6

Bond price change = -10.37255 x (-0.005/1.085295) x $95,000 = $4,539.71

Change in 365 contracts = $4,539.71 x -365 = -$1,656,993.13

Loss in Future contracts = $1,656,993.13

Total Loss = $1,636,363.6 -1,656,993.13 = $20,629.49

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