The multiplier for a futures contract on a stock market index is $$75.$ The maturity of the contract is one year, the

current level of the index is $$4,500,$ and the risk$-$free interest rate is $0\mathrm{.}5\%$ per month. The dividend yield on the index

is $0\mathrm{.}3\%$ per month. Suppose that after one month, the stock index is at $4,550.$

Required:

a$.$ Find the cash flow from the mark$-$to$-$market proceeds on the contract. Assume that the parity condition always

holds exactly.

b$.$ Find the holding$-$period return if the initial margin on the contract is $$10,500.$