The multiplier for a futures contract on the stock-market index is $250. The mat
ID: 2761512 • 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 600, and the risk-free interest rate is 0.3% per month. The dividend yield on the index is 0.2% per month. Suppose that after one month, the stock index is at 605.
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.
Holding-period return _____%
Explanation / Answer
CALCULATION OF FUTURE PRICE ACCORDING TO MARK TO MARKET APPROACH
FUTURE PRICE = STOCK MARKET VALUE*MONTH END INDEX/ MONTH START INDEX { (RISKFREE RATE-DIVIDEND RATE)/12}
= $250*605/600{(.036-.024)/12}= $252.08
so cash flow will be $252.08-$250 = $2.08
and part b one month holding return will be
$20000/$250= 80 future contracts
cash flow = $2.08 PER CONTRACT
TOTAL CASH FLOW ON ALL 80 FUTURE CONTRACTS = $2.08*80=$166.4
% RETURN = $166.4/20000*100=.832%
ANNULAIZED RETURN = .832%*12=9.984%