At the inception of a six-month forward contract on a stock index, the value of the index was $1,150, the interest rate was 4.4 percent, and the continuous dividend was 1.8 percent. Three months later, the value of the index is $1,075. Which of the following statements is TRUE? The value of the: short position is $47.56. long position is $47.56. long position is $82.41. long position is -$82.41.
Value Long = Contract Value at Time t - (Contract Value locked at inception * discount factor)
Value Short = - Value Long
hence
Value of contract at inception = S exp (0.044 - 0.018) * 0.5 = 1,150 * 1.013085 = 1,165
Value of contract at time t = S exp (0.044 - 0.018) * 0.25 = 1,075 * 1.006521 = 1,082
Value of Long position = (1,082 - 1,165) * discount factor. Thus - 83 \* exp <sup>- (0.044 - 0.018) * 0.25</sup> = **-** 82.4.
Value of short position is then $ 82.4 since this is a zero sum game.
None of the answers is correct. I’ve found one possible source for the question and their explanation has a typo. I hope it’s ok to post the link (http://forum.theanalystspace.com/viewthread.php?action=printable&tid=553831)
Flashback’s example also has a mistake in the calculation of the discount factor for the value of the long position it should be exp(-0.044*0.25), the dividend yield should not be included. (Flashback’s answer is actually -82.46)
The answer is thus: -82.14
You can use the formula from the readings:
Value of long forward = S_0 * exp(-qT) - K * exp(-rT). Equation 8.7 on page 148 of Financial Markets and Products (or chapter 5 of Hull’s OF&OD)
This is equivalent to:
Value of long forward = exp(-rT) * [S\_0 \* exp((r-q)T) - K].
Doesn’t matter. Due to enhanced elimination of dummy choices, you still have at least 50 % chance to circle right solution. I mean none of answers is correct is never the solution in GARP Mocks. Maybe I’m wrong, will know shortly.
True, an answer should always be selected but that was not my point.
I simply provided the correct methodology for solving that question and pointed out an error.