Question

The current price for a stock index is 1350 and there are stock index futures contracts on the index with exactly three and six months to expiration. The three months contract trades in the market with a current price of 1340 while the six month contract has a value of 1333. The current risk free continuously compounded interest rate is 3 per cent per year for both the three and six month maturities and the dividend yield on the index is 5.2 per cent per year, also continuously compounded. What is the raw, theoretical and value basis on the index futures? What is the appropriate spread to set up to exploit any mispricing between the three and the six months futures contracts based on a view that the underlying stock market will continue to rise? Briefly explain why the spread you set up should make money as the futures move towards expiration.

Answer 1

The raw basis of the index futures is the difference between the current price of the stock index and the current price of the futures contract. The theoretical basis takes into account the risk-free interest rate and dividend yield. The appropriate spread to set up would involve buying the contract at a lower price and selling the contract at a higher price.

Step-by-step explanation:

The raw basis on the index futures is the difference between the current price of the stock index and the current price of the futures contract. In this case, the raw basis for the three-month contract is 1350 - 1340 = 10, and for the six-month contract is 1350 - 1333 = 17. The theoretical basis of the index futures is the difference between the current price of the stock index and the fair value of the futures contract, which takes into account the risk-free interest rate and dividend yield. To calculate the theoretical basis, we use the formula: (S - F) * e^[(r - q) * t], where S is the current price of the stock index, F is the fair value of the futures contract, r is the risk-free interest rate, q is the dividend yield, and t is the time to expiration in years.

The value basis on the index futures is the difference between the current price of the futures contract and the fair value of the futures contract. To calculate the value basis, we subtract the fair value of the futures contract from the current price of the futures contract. In this case, the value basis for the three-month contract is 1340 - F3, and for the six-month contract is 1333 - F6. To exploit any mispricing between the three and six-month futures contracts based on a view that the underlying stock market will continue to rise, you would set up a spread trade. A spread trade involves buying the contract with the lower price and selling the contract with the higher price, anticipating that the difference will narrow as the futures move towards expiration. By setting up this spread, you can make money if the difference between the two contracts decreases over time, resulting in a profit when you close the spread trade.