The average duration of the loans is 10 years.The average duration of the deposits is 3 years. $$\begin{array} { | l | r | l | r | }
\hline \text { Consumer loans } & \$ 50 \text { million } & \text { Deposits } & \$ 235 \text { million } \
\hline \text { Commercial Loans } & \$ 200 \text { million } & \text { Equity } & \$ 15 \text { million } \
\hline \text { Total Assets } & \$ 250 \text { million } & \text { Total Liabilities \& Equity } & \$ 250 \text { million } \
\hline
\end{array}$$ What is the number of T-Bill futures contracts necessary to hedge the balance sheet if the duration of the deliverable T-bills is 0.25 years and the current price of the futures contract is $98 per $100 face value?
A)6,212 contracts.
B)6,805 contracts.
C)6,900 contracts.
D)7,112 contracts.
E)7,327 contracts.

Question

The average duration of the loans is 10 years.The average duration of the deposits is 3 years. $$\begin{array} { | l | r | l | r | } 
\hline \text { Consumer loans } & \$ 50 \text { million } & \text { Deposits } & \$ 235 \text { million } \
\hline \text { Commercial Loans } & \$ 200 \text { million } & \text { Equity } & \$ 15 \text { million } \
\hline \text { Total Assets } & \$ 250 \text { million } & \text { Total Liabilities \& Equity } & \$ 250 \text { million } \
\hline
\end{array}$$ What is the number of T-Bill futures contracts necessary to hedge the balance sheet if the duration of the deliverable T-bills is 0.25 years and the current price of the futures contract is $98 per $100 face value?
A)6,212 contracts.
B)6,805 contracts.
C)6,900 contracts.
D)7,112 contracts.
E)7,327 contracts.

Quizplus · Accepted Answer

The duration gap is calculated as (10 years * $250 million - 3 years * $235 million) / $250 million = 6.58 years. The hedge ratio is 6.58 / 0.25 = 26.32. The dollar duration of the assets is $250 million * 6.58 = $1,645 million. The dollar duration of the futures is $100 * 0.25 = $25. The number of contracts needed is $1,645 million / $25 = 65,800 contracts. Adjusting for the futures price, 65,800 * (98/100) = 7,327 contracts.

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