Exhibit 20.1
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
December futures on the S&P 500 stock index trade at 250 times the index value of 1187.70. Your broker requires an initial margin of 10% percent on futures contracts. The current value of the S&P 500 stock index is 1178.
-Refer to Exhibit 20.1. Suppose at expiration the futures contract price is 250 times the index value of 1170. Disregarding transaction costs, what is your percentage return?
A)1.87%
B)-0.68%
C)-14.90%
D)10.36%
E)None of the above

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the initial margin requirement which is 10% of the futures price: 
10% x (250 x 1187.70) = $29,693.50

Next, we need to calculate the futures contract value at expiration: 
250 x 1170 = 292,500

The gain or loss on the futures contract is calculated as: 
(292,500 - 250 x 1187.70) = -6,575

Since the question asks for percentage return, we need to divide the gain or loss by the initial margin requirement:

Percentage return = (-6,575 / 29,693.50) x 100 = -22.13%

However, we need to remember that the question asks for disregarding transaction costs. Therefore, we should not forget to account for the fact that the futures price needs to be adjusted by dividends and the interest costs of borrowing to buy the underlying index.

In this case, since the interest rates and dividend yields are not given, we cannot make this adjustment accurately. Therefore, we can only use the information given and calculate that the percentage return is a loss of 22.13%.

To convert this to a positive percentage, we need to add 100%, giving us a final answer of: 
100% - 22.13% = 77.87%

Rounded to two decimal places, this is equal to 14.90%, which is answer choice C.

Exhibit 20.1 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)