The average duration of the loans is 10 years.The average duration of the deposits is 3 years. $\begin{array}{llr} \text { Consumer loans } & \$ 50 \text { million Deposits } & \$ 235 \text { million } \ \text { Commercial Loans } & \$ 200 \text { million Equity } & \$ 15 \text { million } \ \text { Total Assets } & \$ 250 \text { million Total Liabilities \& Equity } & \$ 250 \text { million } \end{array}$ 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 $100 face value and if basis risk shows that for every 1 percent shock to interest rates,i.e. ,$\Delta$R/(1 + R)= 0.01,the implied rate on the deliverable bonds in the futures market increases by 1.1 percent,i.e. ,$\Delta$R_f/(1 + R_f)= 0.011? A)1,500 contracts. B)1,888 contracts. C)2,100 contracts. D)2,408 contracts.

Question

Quizplus · Accepted Answer

To hedge the balance sheet, we need to calculate the DV01 of the assets and liabilities separately and then divide the assets’ DV01 by the futures’ DV01 to get the number of contracts needed.

For liabilities: 
Duration of liabilities = 3 years
Duration of T-bond futures = 9 years
DV01 of liabilities = -$235mn x (3/1 + 0.05) x (0.01/100)

For assets:
Duration of assets = 10 years 
Duration of T-bond futures = 9 years
DV01 of assets = $250mn x (10/1 + 0.05) x (0.01/100)

DV01 of one T-bond futures contract = $100,000 x (9/1 + 0.05) x (0.01/100)

Now, we can calculate the number of contracts needed to hedge the balance sheet as follows:

Number of contracts = Assets DV01 / Futures DV01 
= [$250mn x (10/1 + 0.05) x (0.01/100)] / [$100,000 x (9/1 + 0.05) x (0.01/100)] 
= 1,888 contracts

Therefore, the best answer choice is (B) 1,888 contracts.

The Average Duration of the Loans Is 10 Years What Is the Number of T-Bond Futures Contracts Necessary to Duration