S&P

$500$

$$Index futures: Beginning of term $

$4$

$,$

$465(09/12/2023)$

$,$

$$End of term $

$4$

$,$

$518(11/14/2023)$

$.$

$$ a

$.$

$$Assume that you purchased an S&P

$500$

$$futures contract at the beginning of the school term, with the first settlement date being beyond the end of the school term. Also assume that you sold an S&P

$500$

$$futures contract with this same settlement date at the end of the school term. 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 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 part

$($

a

$)($

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 part

$($

b

$)$

$$is not annualized. To annualize your return, multiply it by

$12/$

m

$,$

$$where m is the number of months in your school term.

d

$.$

$$Apply the concepts discussed in Chapter

$13$

$$to explain why your return on your S&P

$500$

$$index futures position was low or high over the school term.