Question

The multiplier for a futures contract on a stock market index is $70. The maturity of the contract is 1 year, the current level of the index is 1,840, and the risk-free interest rate is 0.8% per month. The dividend yield on the index is 0.3% per month. Suppose that after 1 month, the stock index is at 1,860. 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 $5,400. (Round your answer to 2 decimal places.) Holding period return

Answer 1

a). F0 = Current Index Value * [1 + r - dividend yield]ⁿ

= 1,840 * [1 + 0.008 - 0.003]¹² = 1,840 * 1.0617 = 1,953.49

In one month;

Future Price = Index Value in one month * [1 + r - dividend yield]ⁿ

= 1,860 * [1 + 0.008 - 0.003]¹¹ = 1,860 * 1.0564 = 1,964.90

Change in Futures Price = F1 - F0 = 1,964.90 - 1,953.49 = 11.41

Cash Flow = Change in Futures Price * Multiplier = 11.41 * $70 = $798.64

b). HPR = Cash Flow / Initial Investment = $798.64 / $5,400 = 0.1479, or 14.79%