A Bank with Total Assets of $271 Million and Equity

question 108

Multiple Choice

A bank with total assets of $271 million and equity of $31 million has a leverage adjusted duration gap of +0.21 years. Use the following quotation from the Wall Street Journal to construct an at-the-money futures option hedge of the bank's duration gap position. $$\begin{array}{l}\text { TREASURY BILLS (IMM) -\$1 million; 91-day (\$25.28 ea.) }\\\begin{array} { | c | c | c | } \hline \text { Strike Price } & \text { Calls-Settle } & \text { Puts-Settle } \\\hline 96.00 & 28 \text { basis points } & 63 \text { basis points } \\\hline 96.25 & 19 \text { basis points } & 78 \text { basis points } \\\hline 96.50 & 12 \text { basis points } & 96 \text { basis points } \\\hline\end{array}\end{array}$$ If 91-day Treasury bill rates increase from 3.75 percent to 4.75 percent, what will be the profit/loss per contract on the bank's futures option hedge?

• A)A loss of $556.10 per put option contract.
• B)A profit of $556.10 per put option contract.
• C)A loss of $1,971.84 per call option contract.
• D)A profit of $1,971.84 per call option contract.
• E)A profit of $2,528 per put option contract.

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Definitions:

Standard Deviation

A statistical measure of the dispersion of a set of data points from their mean, widely used in finance to quantify the variability of returns.

Required Return

The minimum expected return an investor demands for investing in a particular asset, considering the risk involved.

Correlation Coefficients

Statistical measures that indicate the extent to which two variables fluctuate together.

Risk-Free Rate

The rate of return on an investment with no risk of financial loss, often represented by the yield on government securities.