The multiplier for a futures contract on a stock market index is $50. The maturity of the contract is 1 year, the current level of the index is 1,800, and the risk-free interest rate is 0.5% per month. The dividend yield on the index is 0.2% per month. Suppose that after 1 month, the stock index is at 1,820. a. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly

Cash Flow mark to market proceeds = $754.45

Explanation:

given :

stock market index = $50

current stock index= 1800

risk free interest rate= 0.5%

dividend yield=0.2%

Contract=1 year=12 month

Solution

The Current Index value after 12 months ie for future price = Current Stock Index * (1 + Risk Free - Dividend Yield)^12

Current Index value after 12 months = 1800 * (1 + 0.50% - 0.20%)^12

Current Index value after 12 months = 1865.88

Also, Future Index value after 1 month = Future Stock Index * (1 + Risk Free - Dividend Yield)^12-1

Future Index value after 1 month= 1820 * (1 + 0.50% - 0.20%)^11

Future Index value after 1 month = 1880.97

Therefore, Cash Flow mark to market proceeds = (Future Index Future Value - Current Index Future value) * Multiplier  which when variables are imputed gives us

Cash Flow mark to market proceeds = (1880.97 - 1865.88) * 50

Cash Flow mark to market proceeds = $754.45

$754.5

Explanation:

Given that

S0 = 1800

Interest rate = 5% = 0.05

Dividend yield = 2% = 0.02

Recall that

The initial futures price is:

F0 = S0 (1 + rf - d)

Thus,

= 1800 x (1 + .005 - .002)12

= 1865.88

Again,

In one month, the futures price will be:

F0 = 1820x (1 + .005 - .002)11 = 1880.97

The increase in the futures price is 15.09, that is 1880.97 - 1865.88, so the cash flow will be:

15.0 x $ 50

= $754.5