Consider a 6 month futures contract on the Samp;P 500. Assume the stocks underlying the index provide a 2.85% dividend yield per annum.

1.    Consider a 6 month futures contract on the S&P 500. Assume the stocks underlying the index provide a 2.85% dividend yield per annum. The index is currently priced at 2420 and the continuously compounded annual risk-free rate is 3.5%.

A.   What would be the arbitrage free price of the Future contract? That is what is F0(T)?

B.   It is now 90 days into the contract. Interest rates have moved up slightly to 3.75% and the dividend yield is still 2.85.  The current price of the index is 2439. Determine the price of the Futures contract and the profit in dollar terms, assuming you bought the contract at the price calculated in part A.

C.   At expiration the index is at 2459. Interest rates are down to 3% and the yield on the S&P 500 has increased to 3.2% per annum. What is the price of the contract and calculate total dollar profit.

2.    An asset is selling for $250. A Futures contract with the asset as underlying, expires in 8 months (assume 365 day year). Interest rates are 5% per annum and the future value of cost of carry has been calculated to be $5.35 and is net any convenience yield earned over the time period.

A.   Calculate the arbitrage free futures price.

B.   A month has passed; the contract expires in 7 months. The asset sells for $239, and net cost of carry is $4.00. Interest rates are stable at 5% Calculate price and profit or loss over the one month period of time.

C.   At expiration the cash market is showing a price of $229. Interest rates are 5%, contracts with 6 months till expiration, are showing cost of carry of $6.16. Calculate price and profit from the futures contract.

3.    Index arbitrage is a strategy used by various institutional investors to profit from mispricing in the futures market. The trading has to be done quickly, and is typically implemented using computers. Hence, Index arbitrage is also referred to as "Program Trading".

In the context of the following two equations, explain Index Arbitrage, what conditions must exist and how profits are earned through the strategy. To be awarded the most points, a numerical example should be devised that supports your answer.

Define and explain Index Arbitrage:

a.   

b.    

Use S0 = 1500, ST = 1500, r = 0.05, q = 0, T =1, and F = 1550 for scenario a, and F = 1600 for scenario b.1.    Consider a 6 month futures contract on the S&P 500. Assume the stocks underlying the index provide a 2.85% dividend yield per annum. The index is currently priced at 2420 and the continuously compounded annual risk-free rate is 3.5%.

A.   What would be the arbitrage free price of the Future contract? That is what is F0(T)?

B.   It is now 90 days into the contract. Interest rates have moved up slightly to 3.75% and the dividend yield is still 2.85.  The current price of the index is 2439. Determine the price of the Futures contract and the profit in dollar terms, assuming you bought the contract at the price calculated in part A.

C.   At expiration the index is at 2459. Interest rates are down to 3% and the yield on the S&P 500 has increased to 3.2% per annum. What is the price of the contract and calculate total dollar profit.

2.    An asset is selling for $250. A Futures contract with the asset as underlying, expires in 8 months (assume 365 day year). Interest rates are 5% per annum and the future value of cost of carry has been calculated to be $5.35 and is net any convenience yield earned over the time period.

A.   Calculate the arbitrage free futures price.

B.   A month has passed; the contract expires in 7 months. The asset sells for $239, and net cost of carry is $4.00. Interest rates are stable at 5% Calculate price and profit or loss over the one month period of time.

C.   At expiration the cash market is showing a price of $229. Interest rates are 5%, contracts with 6 months till expiration, are showing cost of carry of $6.16. Calculate price and profit from the futures contract.

3.    Index arbitrage is a strategy used by various institutional investors to profit from mispricing in the futures market. The trading has to be done quickly, and is typically implemented using computers. Hence, Index arbitrage is also referred to as "Program Trading".

In the context of the following two equations, explain Index Arbitrage, what conditions must exist and how profits are earned through the strategy. To be awarded the most points, a numerical example should be devised that supports your answer.

Define and explain Index Arbitrage:

a.   

b.    

Use S0 = 1500, ST = 1500, r = 0.05, q = 0, T =1, and F = 1550 for scenario a, and F = 1600 for scenario b.