Given a stock index with a value of $1,125, an anticipated dividend of $33, and a risk-free rate of 4%, what should be the value of one futures contract on the index?
A) $1137.00
B) $1070.00
C) $993.40
D) $995.09
E) $1000.00

Question

Quizplus · Accepted Answer

The value of a futures contract on a stock index can be calculated using the formula: Futures Price = Spot Price * e^(r - q)T, where r is the risk-free rate, q is the dividend yield, and T is the time to maturity. Since no specific time to maturity is given, we'll assume it's one year for simplicity. The dividend yield (q) can be calculated as the dividend divided by the spot price, which is $33 / $1125 = 0.0293 or 2.93%. Using the formula with r = 4% or 0.04, q = 2.93% or 0.0293, and T = 1, we get: Futures Price = $1125 * e^(0.04 - 0.0293) = $1125 * e^(0.0107) ≈ $1125 * 1.01075 ≈ $1137.00.

Given a Stock Index with a Value of $1,125, an Anticipated