The multiplier for a futures contract on the stock-market index is $250. The mat
ID: 2759256 • Letter: T
Question
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 900, and the risk-free interest rate is 0.5% per month. The dividend yield on the index is 0.2% per month. Suppose that after one month, the stock index is at 905.
Please Show All Steps, Thank you!
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 $20,000. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Holding-period return=?? (Percentage)
Explanation / Answer
Solution:
a) Calculation of cash flow from the mark-to-market proceeds on the contract:
The initial futures price is: Fo = 900 x (1 + .005-.002)12
= 900 * 1.0366
= 932.94
In one month, the maturity of the contract will be only 11 months, so the futures price will be F0 = 905 x (1 + .005-.002) 11
= 905 * 1.0355
= 935.32
The increase in the futures price is 2.3775, so the cash flow will be 2.3775 x 250 = 594.375
= 594.38
b) Calculation of one-month holding-period return if the initial margin on the contract is $20,000:
The rate of return is = 594.38/ 20,000
= 0.029719
= 2.97%