On 4 January 2021, a financial institution (FI) has the following balance sheet (rates = 9 per cent)

Assets			Liabilities/equity
A	200m	DA = 8 years	L	150m	DL = 5 years
			E	50m

The FI manager thinks rates will increase by 0.8 per cent (DR) in the next three months. 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 15 years and the T-bonds are selling at a price $112,200 for each $100,000 face value. T-bond futures rates, currently 7 per cent, are expected to increase by 1 per cent (DR) 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 115 and an option premium of 1.57 per cent. The spot price on the T-bond underlying the option is 138 per cent. 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 1.2 per cent (DR) from 7.5 per cent in the next three months.

If by 4 April 2021, balance sheet rates increase by 1 per cent (DR), futures rates by 1.25 per cent (DR) and T-bond rates underlying the option contract by 1.4 per cent (DR).

1. What is the leverage adjusted duration gap? (0.5 mark)

2. What does a positive/negative leverage adjusted duration gap mean? (1 mark)

3. What is the actual change on equity value on 4 April 2021? (1 mark)

4. How many futures will the FI manager buy to hedge the position? (3 marks)

5. On 4 April 2021, what is the total gain/loss on the futures? (3 marks)