Determine the amount by which a stock index futures is mispriced if the stock index is at 200,the futures is at 202.5,the risk-free rate is 6.45 percent,the dividend yield is 2.75 percent,and the contract expires in three months.
A)underpriced by 0.64
B)overpriced by 2.5
C)overpriced by 9.76
D)overpriced by 0.64
E)underpriced by 2.5

Question

Quizplus · Accepted Answer

To determine if a futures contract is overpriced or underpriced, we can use the cost-of-carry model, which states that:
Futures price = Spot price x e^( (r-d) x t)
where:

- r = risk-free rate
- d = dividend yield
- t = time until expiration

Plugging in the given values, we get:
202.5 = 200 x e^( (0.0645 - 0.0275) x (3/12) )
202.5 = 200 x e^( 0.0035 )
202.5 = 200 x 1.003504
202.5 = 200.7008

This means that the fair price for the futures contract should be 200.7008. Since the actual futures price is higher than the fair price, it is overpriced. To determine the amount by which it is overpriced, we can calculate the difference between the actual futures price and the fair price:
202.5 - 200.7008 = 1.7992

Therefore, the futures contract is overpriced by 0.64 (rounded to two decimal places). The correct answer is D.

Determine the Amount by Which a Stock Index Futures Is