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forward contract calculation

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.

FREE – Over 2 hours of calculations videos for Part I and Part II from Christian Cooper – Essential Exam Prep

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  - (0.044 - 0.018) * 0.25 = - $ 82.4.

Value of short position is then $ 82.4 since this is a zero sum game.

I do not ask for the trust nor give it to you.

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.

I do not ask for the trust nor give it to you.

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.