Question

5.

Village Bank has $210 million worth of assets with a duration of 14 years and liabilities worth $168 million with a duration of four 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 102-20 (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? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to the nearest whole number.) Number of contracts

Answer 1

Solution:

The number of future contracts, $N_{F}$ is calculated as follows:-

$N_{F} = \frac{(D_{A}-kD_{L})A}{D_{F}\times P_{F}}$

$N_{F} = \frac{(14- (168/210)(4))210,000,000}{9\times 102,667}$

2454.55 ~ 2455 contracts