An FI has a $$100$ million portfolio of six$-$year Eurodollar bonds that have an $8$ percent coupon. The bonds are trading at par and have a duration of five years. The FI wishes to hedge the portfolio with T$-$bond options that have a delta of $-0\mathrm{.}625.$ The underlying longterm Treasury bonds for the option have a duration of $10\mathrm{.}1$ years and trade at a market value of $$96,157$ per $$100,000$ of par value. Each put option has a premium of $$3\mathrm{.}25$ per $$100$ of face value.

a$.$ How many bond put options are necessary to hedge the bond portfolio?

b$.$ If interest rates increase $100$ basis points, what is the expected gain or loss on the put option hedge?

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c$.$ What is the expected change in market value on the bond portfolio?

d$.$ What is the total cost of placing the hedge?

e$.$ Diagram the payoff possibilities.

f$.$ How far must interest rates move before the payoff on the hedge will exactly offset the cost of placing the hedge?

g$.$ How far must interest rates move before the gain on the bond portfolio will exactly offset the cost of placing the hedge?

h$.$ Summarize the gain, loss, and cost conditions of the hedge on the bond portfolio in terms of changes in interest rates