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

Village Bank must calculate the number of T-bond futures contracts to sell in order to hedge its balance sheet using the formula that equates the duration-weighted positions of assets and liabilities, though specific numbers need additional data.

Step-by-step explanation:

The student question pertains to the calculation of the number of futures contracts needed for a bank to hedge its balance sheet against interest rate risk. Village Bank needs to establish how to offset the disparity in duration of assets and liabilities using T-bond futures contracts. Using the formula (DA - DL) x (A / P) x (1 / Df), where DA is the duration of assets, DL is the duration of liabilities, A is the value of the assets, P is the price of one futures contract, and Df is the duration of the futures contract, the bank can calculate the necessary number of contracts to sell. Since specifics like the contract size and current price of the T-bonds in dollars are not provided, the exact number of contracts cannot be determined. However, the approach to hedging is by using a macro hedge that equates the duration-weighted positions of assets and liabilities, adjusted for the duration of the futures contract.

Answer 2

2129 futures contracts to be sold

Step-by-step 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 )