a$)$ Consider a financial institution $($FI$)$ with the following balance sheet structure.

Assets $10-$year deep discount bond $1,000,000$

Equity $300,000$

Liabilities $6-$year deep discount bond $700,000$

The current level of interest rates is $5\%$ and analysts have forecasted an increase in interest rates

by $100$bp over the next $12$ months. The duration of a deliverable bond in the futures market is $7$

years, while the price per contract is $95,000.$ Assuming that the management has decided to use

the futures market to hedge its interest rate risk exposure, answer the following:

i$.$ Calculate the IRR exposure of equity.

ii$.$ What is the optimum number of futures contracts that the FI should consider, assuming

that the basis risk adjustment factor $($b$)$ is $1,0\mathrm{.}8$ and $1\mathrm{.}8?$ Explain the effect of b$.$

iii. Calculate the hedge ratio in each of the above cases and explain its meaning. How can

one calculate the hedge ratio

iv$.$ Assuming b $=1,$ calculate the IRR exposure of the off$-$balance sheet position

v$.$ Assuming b $=1,$ calculate the institution$$s overall IRR exposure

b$)$ Under what balance sheet structure do FIs sell or buy interest rate futures? Explain.

c$)$ Under what interest rate environment and balance sheet structure do FI use caps and floors to

hedge their interest rate risk exposure

d$)$ Consider a $8\%$ cap and a $3\%$ floor with premium $0\mathrm{.}5\%$ and maturity one year. Construct a

strategy to hedge a $$2$m IRR exposure while minimizing the cost of hedging. What is this strategy

called?

e$)$ If interest rates by the end of the year rise to $10\%$ what is the net payoff? What if rates fall to $2\%?$

Draw the strategy net payoff graph for the full range of IR values.