Question

Village Bank has $310 million worth of assets with a duration of 12 years and liabilities worth $248 million with a duration of five 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 104-20 (30nds). The T-bond underlying the futures contract has a duration of eight years. If the spot and futures interest rates move together, how many futures contracts must Village Bank sell to fully hedge the balance sheet? (

Answer 1

Answer:

2129  futures contracts to be sold

Explanation:

Asset worth = $310 million

Asset duration = 12 years

liabilities = $248 million

Liabilities duration = 5 years

T-bond futures contracts = 104-20 (30nds)

% of assets = 310 / 248 =

Determine how many futures contracts Village Bank will sell to fully hedge the balance

Number of Contracts = -[Assets * (Asset Duration – (Liabilities Duration * % of Assets) / (Duration * Contract Value)]

 = - [ 310 * ( 12 - ( 5 * (310/248)) / ( 8 * ( 104 + ( 20/30)) ]

= - [ 310 * ( 12 -  6.25 ) / ( 8 * 104.6667 ) ]

= - [ 310 * 5.75 / 837.3336 ]

= - 2.12878 * 1000

= 2128.78 ≈  2129 ( number of futures contracts to be sold )