Hedging Interest Rate Risk with Futures:A financial institution has$100m inassets and$90m in liabilities. Further, assume that the average duration on the assetside is 34 years and the same for liability side is 12.75 years.

(a) If the interest rate on the assets as well as the liabilities is 8% and there is a forecastof 1% increase in interest rates over the next six months, what is the interest raterisk exposure of the financial institution?

(b) Suppose the FI wants to hedge this interest rate risk with T-bond futures contracts.The current futures price quote is 125 per 100 of face value. The minimum contractsize is 100,000 and the duration of the deliverable bond is 4.25 years. How manyfutures contracts will be needed? Should the manager buy or sell these contracts?Assume no basis risk.2

(c) Verify that selling T-bond futures contracts will indeed hedge the FI against asudden increase in interest rates from 8 to 9%, a 1% interest rate shock.

(d) How would your answer for part (b) change if the relationship of the price sensitivityof futures contracts to the price sensitivity of underlying bonds were such that br= 1.15?