Question

One Chicago has just introduced a new single stock futures contract on the stock of Brandex, a company that currently pays no dividends. Each contract calls for delivery of 1,000 shares of stock in one year. The T-bill rate is 6% per year.
a. If Brandex stock now sells at $120 per share, what should the futures price be?



b. If the Brandex stock price drops by 3%, what will be the change in the futures price and the change in the investor’s margin account?



c. If the margin on the contract is $12,000, what is the percentage return on the investor’s position?

Answer 1

Answer:

A: $127.2

B: $123.384, $3.816 per share and $3,816 per contract

C: 9.43%

Explanation:

A: Futures price

F° = S° (1 + rₙ) = $120 x 1.06

= $127.20

B: Change in Future Price and Investor Margin account:

New Spot = $120 (1 – 0.03)

= $120 x 0.97

= $116.40

New Futures = $116.40 (1.06)

= $123.384

The long investor loses = $127.20 - $123.384

= $3.816 per share

or $3.816 (1,000) = $3,816 per contract

C: Percentage return on the investor’s position:

Percentage return = $12,000 / $127,200

= 9.43%