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

Answer: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