Based on economic forecasts, it is most likely that interest rates will rise in the next six months. A summary of your banks position is as follows:

Total assets: $150 million

Duration gap: 2.20 years

Primary holdings of concern: $7 million in 6% Canada bonds selling at par that will mature in 5 years

$12 million in stocks with an average beta of 0.90

Your assignment after the first study session is to set up a micro hedge for the Canada bonds that will help the bank offset the adverse effect of interest-rate increases on the bonds being held and to set up a macro hedge that will minimize any negative effect on the market value of net worth when interest rates rise. You gather information from the most recent financial press regarding Canada bond contracts with a maturity of about one year. Historical relationships between Canada bond futures contracts and Canada bonds indicate that the change in the value of the hedged asset relative to the futures contract would be about 1.3 and that interest rates on the hedged asset change on average for a given change in the interest rate on the futures contract by about 0.90. A 1% increase in interest rates results in a decline in value for Canada bonds of 8% of par.

question:

If the bank cannot find a set of futures contracts with the same duration as the bank (2.20 years) but has found enough contracts with a duration of 4.40 years, a. How much of this contract would the bank sell? b. For a 1% increase in interest rates, what would be the percentage change in the price of the futures contract? c. What would be the decline in the market value of the banks net worth without the futures contract in place? d. What would be the change in the market value of the banks net worth with the futures contract in place?