Village Bank has $350 million worth of assets with a duration of 12 years and liabilities worth $301 million with a duration of six years. In the interest of hedging interest rate risk, Village Bank is contemplating a macrohedge with interest rate T-bond futures contracts now selling for 103-22 (30nds). The T-bond underlying the futures contract has a duration of nine years. If the spot and futures interest rates move together, how many futures contracts must Village Bank sell to fully hedge the balance sheet

-2591.

Explanation:

From the question, we are given that Village Bank's assets,A = $350 million, duration for the assets,DA = 12 years, Village Bank's liabilities,L = $301 million, duration for the liabilities,DL = six years and the interest rate T-bond futures contracts now selling for 103-22 (30nds) and T-bond underlying the futures contract has a duration of nine(9) years.

The numbers of futures contracts must Village Bank sell to fully hedge the balance sheet is;

= - [ DA - (L/A) DL × A].

= - [ 12 - (301/350) × 6] × 350,000,000.

= - [ 12 - (0.86 × 6] × 350,000,000.

= - [ 12 - 5.16] × 350,000,000.

= - 2394000000.

Also, T-bond underlying the futures contract duration × price of future contract.

[ price of future contract = 100000 × 102 (20/30) = 102666.66667].

= 9 × 102666.66667 = 924000.00003.

Then, the numbers of futures contracts must Village Bank sell to fully hedge the balance sheet is;

= - 2394000000 ÷ 924000.00003.

= -2590.90909082497.

= - 2591.