Consider a financial institution (FI) with the following balance sheet structure: Assets 1.000.000, 10-year deep discount bond and Liabilities 700,000, 6- year discount bond and equity 300,000 .The current level of interest rates is 5% and analysts have forecasted an increase in interest rates by 100bp 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, 0.8 and 1.8? 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 institutions overall IRR exposure.