Problem 1 (10 Marks) Today is 1 June. The spot interest rate for 90-day bank bil

Question

Problem 1 (10 Marks) Today is 1 June. The spot interest rate for 90-day bank bills is quoted at 5.25% pa. The 3-month futures price for 90-day bank bills is 95.25. The standard contract size for bank bill futures is a face value of $1 million. The settlement price is computed as the present value of that S1 million using the bpak bickahate days 365 a. Your company expects a cash shortfall in 90 days. Specifically, you expect to need to borrow around $1 million. If you want to hedge the cost of borrowing, would you buy or sell bank bill futures? (1 mark) b. Assume you take one futures contract according to your answer in (a). On maturity of the futures contract the spot rate (which equals the futures rate) trade, compute the gain or loss on the futures contract. Briefly explain how the futures transaction has hedged your underlying (7 marks) c. position. (2 marks)

Explanation / Answer

a) The way bond/bill futures work is that since the underlying is a bond and with the increase in rate, results in decrease in underlying bond value and the one who is long on bond futures incurs loss and vice versa. The scenaris in question where there is a need to borrow in future, the risk is of increase in interest rate. To mitigate this risk, requires one to short the bond futures.

b) Assuming if only one bond futures was sold and three months lates the spot rate has risen to 6.25%. To calcualte the gain for short position, below are the steps:

3-months futures price for 90-day band bilss is 95.25 (or 100-95.25 = 4.75% discount p.a.)

spot rate = 6.25%

Difference between spot and futures rate = 6.25-4.75 = 1.5%

for the bond futures, given 1 mil usd principal for 90 days, change in one tick (1 basis point) results in 25 usd change in gains

here change is of 1.25% or 125 basis point, so total gains for short position = 125*25 = 3125 usd

c) For the short position, increase in spot rate increased the outflow for borrowing however same increased outflow was offset by the gains from short position in futures as calculated in part b

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