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

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The average duration of the loans is 10 years.The average duration of the deposits is 3 years.  Consumer loans $50 million Deposits $235 million  Commercial Loans $200 million Equity $15 million  Total Assets $250 million Total Liabilities & Equity $250 million \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. , Δ\Delta R/(1 + R) = 0.01,the implied rate on the deliverable bonds in the futures market increases by 1.1 percent,i.e. , Δ\Delta Rf/(1 + Rf) = 0.011?

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Definitions:

Rate of Return

The increase or decrease in the value of an investment during a set timeframe, represented as a percentage of the investment's starting price.

Indifference Curves

Graphical representations used in microeconomics to illustrate different combinations of two goods that provide the same level of utility or satisfaction to a consumer.

Standard Deviation

A statistical measure of the dispersion or variability of a set of numbers, indicating how spread out the numbers are from the mean.

Expected Return

The weighted average of all possible returns from an investment, where each return is weighted by its probability of occurring.

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