# Hedging Interest Rate Risk wit

Hedging Interest Rate Risk with Futures: A financial institution has \$100m in

assets and \$90m in liabilities. Further, assume that the average duration on the asset

side 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 forecast

of 1% increase in interest rates over the next six months, what is the interest rate

risk 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 contract

size is 100,000 and the duration of the deliverable bond is 4.25 years. How many

futures contracts will be needed? Should the manager buy or sell these contracts?

Assume no basis risk.

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# Hedging Interest Rate Risk wit

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?

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# Hedging Interest Rate Risk Wit

Hedging Interest Rate Risk With Futures Versus Options Versus Swaps On January 4, 2015, an FI has the following balance sheet (rates  =  8 percent): The FI manager thinks rates will increase by 0.55 percent in the next three months. If this happens, the equity value will change by: The FI manager will hedge this interest rate risk with either futures contracts, option contracts, or swap contracts. If the FI uses futures, it will select June T-bonds to hedge. The duration on the T-bonds underlying the contract is 14.5 years, and the T-bond futures are selling at a price of \$110.53125 per \$100, or \$110,531.25. T-bond futures rates, currently 5 percent, are expected to increase by 0.75 percent over the next three months. If the FI uses options, it will buy puts on 15-year T-bonds futures with a June maturity, an exercise price of 109, and an option premium of 36 64 percent.

The spot price on the T-bond underlying the option is \$115.78125 per \$100 of face value. The duration on the T-bonds underlying the options is 14.5 years, and the delta of the put options is  0.85. Managers expect these T-bond rates to increase by 0.7 percent from 5.25 percent in the next three months. If the FI uses swaps, a swap agent offers a swap involving D Fixed   =   8 years (based on the 15-year Treasury bond rate) and D Floating   = 1 year (based on Treasury bills).

If by April 4, 2015, balance sheet rates increase by 0.5 percent, futures rates by 0.7 percent, and T-bond rates underlying the option contracts by 0.66 percent, calculate the on- and off-balancesheet cash flows to the FI when using futures contracts, option contracts, and swap contracts as its hedge instrument.

If by April 4, 2015, balance sheet rates actually fall by 0.25 percent, futures rates fall by 0.35 percent, and T-bond rates underlying the option contract fall by 0.34 percent, calculate the on- and off balance-sheet cash flows to the FI when using futures contracts, option contracts, and swap contracts as its hedge instrument.

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# Hedging Interest Rate Risk Wit

Hedging Interest Rate Risk With Futures Versus Options On January 4, 2015, an FI has the following balance sheet (rates  =  10 percent): The FI manager thinks rates will increase by 0.75 percent in the next three months. If this happens, the equity value will change by: The FI manager will hedge this interest rate risk with either futures contracts or option contracts. If the FI uses futures, it will select June T-bonds to hedge. The duration on the T-bonds underlying the contract is 14.5 years, and the T-bonds are selling at a price of \$114.34375 per \$100 or \$114,343.75. T-bond futures rates, currently 9 percent, are expected to increase by 1.25 percent over the next three months.

If the FI uses options, it will buy puts on 15-year T-bonds with a June maturity, an exercise price of 113, and an option premium of 136 64 percent. The spot price on the T-bond underlying the option is \$135.71875 per \$100. The duration on the T-bonds underlying the options is 14.5 years, and the delta of the put options is – 0.75. Managers expect these T-bond rates to increase by 1.24 percent from 7.875 percent in the next three months.

If by April 4, 2015, balance sheet rates increase by 0.8 percent, futures rates by 1.4 percent, and T-bond rates underlying the option contract by 1.30 percent, would the FI have been better off using the futures contract or the option contract as its hedge instrument? If by April 4, 2015, balance sheet rates actually fall by 0.75 percent, futures rates fall by 1.05 percent, and T-bond rates underlying the option contract fall by 1.24 percent, would the FI have been better off using the futures contract or the option contract as its hedge instrument?

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