The multiplier for a futures contract on the stockmarket ind

The multiplier for a futures contract on the stock-market index is $250. The maturity of the contract is one year, the current level of the index is 800, and the risk-free interest rate is 0.5% per month. The dividend yield on the index is 0.3% per month. Suppose that after one month, the stock index is at 820.

a. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Cash flow            $

b. Find the one-month holding-period return if the initial margin on the contract is $10,000. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Holding-period return             %

Solution

a). The initial futures price is:
F0 = 800 × (1 + 0.005 - 0.003)¹² = 800 x 1.024 = 819.41
In one month, the futures price will be:
F0 = 820(1 + 0.005- 0.003)¹¹ = 820 x 1.022 = 838.22
The increase in the futures price is 18.81, so the cash flow will be:
18.81 × 250 =$4,702.87

b). The holding period return is: $4,702.87/$10,000 = 0.4703 or 47.03%