Final answer:
The mark-to-market cash flow from the futures contract after the stock market index rises from 1,800 to 1,820 is $1,000. This is calculated using the multiplier of $50 and the change in the index level.
Step-by-step explanation:
Understanding the Futures Contract
The student is seeking to calculate the mark-to-market cash flows of a futures contract on a stock market index with specific parameters given. Since the multiplier is $50, and after one month, the index has risen from 1,800 to 1,820, the mark-to-market gain would be the difference in the index levels multiplied by the multiplier. Therefore, the calculation would be (1820 - 1800) x $50 = $1,000. This would be the cash flow from the mark-to-market proceeds. A key concept to remember is that futures contracts are marked to market daily, meaning the change in value is settled between the parties at the end of each trading day.
The parity condition was also mentioned but no further calculation using this was required. Had it been necessary, the parity condition would ensure that the futures price adjusts considering the risk-free interest rate and the dividend yield on the index. However, to answer the student's question, this detail isn't needed.