Assume the T-bill maturity and futures delivery are on the same day. Ignore tran
ID: 2817911 • Letter: A
Question
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 1,905.00 1,911.00 1,901.00 1,907.70
S&P 500closed at $1,910.00on the same day.
a)Find the discount factor using the T-bill data. Please use the “Bid” yield for the calculation.
b)Suppose that if you buy one unit of S&P 500 index today, you will be entitled to a $10.00 dividend on the delivery day. Consider the following zero-net-investmentstrategy: 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
c)Considering that each S&P 500 futures contract is for 250 units of the index, what is your total arbitrage profit per 1000 contracts?
Position
Cash Flow, t=0
Cash Flow, Maturity
Buy S&P 500
Borrow
Short Futures
TOTAL CASH FLOW
0
Explanation / Answer
1 90 Months T-Bill- DF calculation Maturity Value 100 Bid Yield 1.17 PP 98.83 Annual Yield 1.18385% 90 Month Yield 0.2960% 2 Position Cashflow,t-0 Cashflow Maturity Details Buy S&P 500 -1910.00 0.00 Borrow 1910.00 -1905.65 1910 * 100.2960/100-10 Short Futures 0.00 1907.70 Cashflow 0.00 2.05 3 Profit Per Index Unit (a) 2.05 Total units in contract (b) 250 Total Contracts (c) 1000 Total Arbitrage Profit a*b*c 512,500.00