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First City Bank (FCB) has $600 million of total assets, composed of $200 million in fixed rate loans which are priced at 6% and $400 million in variable rate loans floating at 200 basis points (this is 2%) over prime. Assume the prime rate is currently 3.25%. FCBs liabilities are composed of $150 million in fixed rate CDs at a rate of 3%, and $350 million variable rate jumbo CDs which pay 125 basis points (1.25%) less than prime. FCBs fixed expenses are $10 million annually, and assume no taxes on income

Working with their investment team, they have selected 26 week (6 month) T-Bill futures contracts as a potential instrument to hedge their interest rate risk. Each futures contract is for $1 million face value of T-Bills. The investment team also estimates that the correlation between changes in prime rate and T-Bill rates is 0.75, meaning that cash positions change only 75% as much as futures positions when rates change (beta is 0.75). Assume the maturity of the cash assets is 1 month.

1. How could the bank hedge their current position over the next year using the 6 month T bill futures? Specifically, answer these questions: would it buy or sell contracts (explain your answer), and how many contracts are needed to perfectly hedge the position based on the investment committees estimate of the relation between the change in the prime rate and change in futures contracts?

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