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

The futures price for the Brandex stock should be approximately $127.51 per share, calculated using the cost of carry model. If the stock price drops by 3%, this does not directly translate to the futures price, which is based on the original terms of the contract. The percentage return on the investor's margin account depends on the change in the futures price and the details of the futures contract.

Step-by-step explanation:

Calculation of Futures Price and Investor's Margin Account

To calculate the futures price for a single stock futures contract, we use the cost of carry model. Given that Brandex stock presently sells at $120 per share and considering a T-bill rate of 6% per year, the futures price (F) can be computed as:

F = S *
`e^((r * t))`

Where:
S = Current stock price = $120
r = Risk-free interest rate (T-bill rate) = 6% or 0.06
t = Time in years = 1

Therefore, the futures price F is:
F = 120 *
`e^((0.06 * 1))` = $120 *
`e^(0.06)` ≈ $127.51 per share

If the Brandex stock price drops by 3%, the new stock price is 120 * (1 - 0.03) = $116.40 per share. However, the change in the futures price would still be predicted using the initial risk-free rate and the future contract term, not necessarily the stock's percent change in price at any given moment.

Regarding the investor's margin account, any profit or loss resulting from the change in the underlying stock price would affect the margin account balance. The initial margin is $12,000, and the percent change in the investor's margin account will depend on the specifics of the contract.

Percentage Return on Investor's Position

The percentage return on the investor's margin position can be calculated by the formula:

Percentage Return = (Change in the Margin Account / Initial Margin) * 100%

Without a specific change in margin, we cannot determine the exact percentage return.

Answer 2

A: $127.2

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

C: 9.43%

Step-by-step 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%