The multiplier for a futures contract on a certain stock mar

The multiplier for a futures contract on a certain stock market index is $250. The maturity of the contract is one year, the current level of the index is 1,000, and the risk-free interest rate is 0.2% per month. The dividend yield on the index is 0.3% per month. Suppose that after one month, the stock index is at 1,018.

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 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 future price is:

F₀ = S₀(1+r_f -d)ⁿ

= 1000(1+0.002-0.003)¹²

= 1000(0.999)¹²

= 988

In one month,the futures price will be:

F₀ = 1018(1+0.002-0.003)¹¹

= 1018(0.999)¹¹

= 1006.85

Increase in future price = 18.85 (1006.85 - 988)

Cash flow = 18.85 * $250

= $4712.5

Cash flow = $4,712.5

b.

Holding period return = Cash flow / Initial margin

= $4,712.5 / $10,000

= 0.47125

= 47.125%

Holding period return = 47.125%