The average duration of the loans is 10 years. The average duration of the deposits is 3 years. What is the number of T-bond futures contracts necessary to hedge the balance sheet if the duration of the deliverable bonds is 9 years and the current price of the futures contract is $96 per $100 face value and if basis risk shows that for every 1 percent shock to interest rates, i.e., ΔR/(1 + R) = 0.01, the implied rate on the deliverable bonds in the futures market increases by 1.1 percent, i.e., ΔR_f/(1 + R_f) = 0.011?

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Quizplus · Accepted Answer

Step 1: Calculate the duration gap of the balance sheet: Duration Gap = (Duration of Loans × Amount of Loans) - (Duration of Deposits × Amount of Deposits) Duration Gap = (10 × $100,000,000) - (3 × $80,000,000) Duration Gap = $900,000,000 Step 2: Calculate the number of futures contracts required to hedge the duration gap: Number of Contracts = Duration Gap / (Duration of Deliverable Bonds × $100,000) Number of Contracts = $900,000,000 / (9 × $100,000) Number of Contracts = 1,000 Step 3: Adjust for basis risk: Basis Point Value (BPV) of T-bond futures contract = $100,000 × 0.01 = $1,000 ΔR_f / (1 + R_f) = 0.011 ΔR_f = 0.011 + 0.011 × R_f ΔR_f = 0.0121 × R_f Basis risk adjustment factor = BPV of futures contract / (BPV of deliverable bonds × ΔR_f) Basis risk adjustment factor = $1000 / ($100,000 × 0.011 × 9) = 0.985 Adjusted number of contracts = Number of contracts / basis risk adjustment factor Adjusted number of contracts = 1,000 / 0.985 = 1,014.213 Step 4: Round up to the nearest integer: Number of contracts required = 1,015 Therefore, the answer is choice B (1,888 contracts is not the correct answer as it is not even close to the answer obtained through the calculation).

The Average Duration of the Loans Is 10 Years