10. Measuring and explaining futures price movements

a. Assume that you purchased an S&P 500 futures contract in September 2023, with the first settlement date beyond November 2023. Also assume that you sold an S&P 500 futures contract with this same settlement date at the end of November 2023. Given that this contract has a value of the futures price times $250, determine the difference between the dollar value of the contract you sold and the dollar amount of the contract that you purchased.

b. Assume that you invested an initial margin of 20 percent of the amount that you would owe to purchase the S&P 500 index at the settlement date. Measure your return from taking a position in the S&P 500 index futures as follows. Take the difference determined in the previous question (which represents the dollar amount of the gain on the futures position), and divide it by the amount you originally invested (the amount you originally invested is 20 percent of the dollar value of the futures contract that you purchased).

c. The return that you just derived in the previous question is not annualized. To annualize your return, multiply it by (12/m), where m is the number of months for September, October, and November.

d. Explain why your return on your S&P 500 index futures position was low or high over the given timeframe.

e. Assume that you purchased a Treasury bond futures contract at the beginning of September 2023 with the first settlement date beyond the end of November 2023. Also assume that you sold this same type of futures contract at the end of November 2023. Recall that Treasury bond futures contracts are priced relative to a $100,000 face value, and the fractions are in thirty-seconds. What was the dollar value of the futures contract at the beginning of September 2023 when you purchased it?

f. What was the dollar value of the Treasury bond futures contract at the end of November 2023 when you sold it?

g. What was the difference between the dollar value of the Treasury bond futures contract when you sold it and the value when you purchased it?

h. Assume that you invested an initial margin of 20 percent of the amount that you would owe to purchase the Treasury bonds at the settlement date. Your investment is equal to 20 percent of the dollar value of the Treasury bond futures contract as of the time you purchased the futures. Determine the return on your futures position, which is the difference you derived in the previous question as a percentage of your investment.

i. The return that you just derived in the previous question is not annualized. To annualize your return, multiply your return times (12/m), where m is the number of months for September, October, and November 2023.

j. Explain why the return on your Treasury bond futures position was low or high.