Problem 1

Assume the T-bill maturity and futures delivery are on the same day. Ignore transactions costs.

Treasury Bill

Maturity DTM Bid Asked

Mar 90 1.18 1.17

Index Futures

S&P 500 Index (CME)

Open High Low Settle

Mar 2,905.00 2,911.00 2,901.00 2,907.70

S&P 500 closed at $2,910.00 on the same day.

1. Find the discount factor using the T-bill data. Please use the Bid yield for the calculation.

2. Suppose that if you buy one unit of S&P 500 index today, you will be entitled to a 1.5% dividend yield on the delivery day. Consider the following zero-net-investment strategy: buy S&P 500 index spot, borrow at the risk-free rate, and short the S&P 500 futures. Make sure your positions add up to zero at t=0. Show the cash flows from all your positions in the following table, per unit.

Position	Cash Flow, t=0	Cash Flow, Maturity
Buy S&P 500
Borrow
Short Futures
TOTAL CASH FLOW	0

3. Considering that each S&P 500 futures contract is for 250 units of the index, what is your total arbitrage profit per 1000 contracts?