Question

The multiplier for a futures contract on a stock market index is $250. The maturity of the contract is three months, and the current level of the index is 3,350. The risk-free interest rate is 0.4% per month. The dividend yield on the index is 0.1% per month. Suppose that after one month, the stock index is at 3,280.

1. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly.

2. Find the one-month holding-period return if the initial margin on the contract is $15,500.

next full steps, thx!!!

Answer 1

Solution:

Spot Price = 3,350

F = Spot price * (1+r−q) ^t

Interest rate per month = 0.4%

Dividend yield per month = 0.1%

F = 3350 * ( 1+ 0.4%-0.1%)^3 = $3380.24

Part A )

Stock index after one month = 3280

Now 2 month will be remained in the maturity of the contract hence

Future price = 3280 * (( 1+ 0.4%-0.1%)^2 = 3299.71

Cash flow  = 3299.71 - 3380.24 = -80.53

Total cash flow = -80.53 * 250 = -20,132.8

Part B )

1- month holding period return = Cash flow / Initial margin= -20132.8 / 15500 = -129.89%