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Problem 1 Assume the T-bill maturity and futures delivery are on the same day. Ignore transactions...

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                 1,905.00          1,911.00          1,901.00            1,907.70

S&P 500 closed at $1,910.00 on the same day.

  1. Find the discount factor using the T-bill data. Please use the “Bid” yield for the calculation.
  1. 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-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
  1. Considering that each S&P 500 futures contract is for 250 units of the index, what is your total arbitrage profit per 1000 contracts?

Solutions

Expert Solution

a.

Calculation of discount factor by using the Treasury-bill data:

Formula to calculate the discount factor:

Substituting Equation (1) with $100 for FV, $98.82 (100-1.18) for PP and 90 days for M to calculate the value of discount factor.

Hence, the value of discount factor is 0.295%.

Where,

FV is face value of bond

PP is price of bond

M is the date to maturity

b.

Completing the table:

Hence, profit per unit is $4.

c.

Calculation of Total Arbitrage Profit:

Formula to calculate total arbitrage profit:

Substituting Equation (2) with $4 for profit per unit, 250 for total units in contract and 1000 for total contracts to calculate the value of total arbitrage profit.

Hence, the value of total arbitrage profit is $1,000,000.

jeff jeffy answered 3 months ago
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