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. Calculate the return on a cash investment in the S&P 500 stock index if the ending index value is 1170 over the same time period.
A)1.87%
B)-0.68%
C)-14.90%
D)10.36%
E)None of the above

Question

Quizplus · Accepted Answer

The initial margin required by the broker is 10%. This means that if the index moves against our position by more than 10%, we will get a margin call and need to deposit additional funds to maintain our position. 
The value of the contract is 250 times the index value, so the initial margin requirement is:
0.10 x (250 x 1187.70) = $29,694.50
If the ending index value is 1170, the loss on the futures contract is:
1187.70 - 1170 = 17.70
The value of the futures contract at expiration is:
250 x 1170 = $292,500
So the return on investment is:
(292,500 - 29,694.50) / 29,694.50 = 8.84
But this is the return on margin, not on the cash investment in the S&P 500 stock index. 
To compute the return on the cash invested in the S&P index, we need to consider the value of the stock index at the beginning and at the end of the period, and the dividends paid during the period. 
Assuming no dividends, the return on the cash investment is:
(1170 / 1178) - 1 = -0.00678
So the cash investment lost 0.678% over the period. 
But we still need to adjust for the fact that we only had to put up 10% of the value of the futures contract as initial margin, and financed the rest with borrowed funds. 
The notional value of the contract was:
250 x 1187.70 = $296,925
So the cash investment was only 10% of this, or:
0.10 x 296,925 = $29,692.50
The loss on the cash investment was then:
$29,692.50 x 0.00678 = $201.34
The return on the cash investment was then:
(-$201.34 / $29,692.50) x 100% = -0.678%
which is choice B.

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