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?

Short answer

Answer

a. $127.20

b. $3816.00

c.-31.8%

Step-by-step solution

Given information

Based on the input template:

Spot Price (S0) = $120

Risk-free rate (rf) = 6%

Future price (F0) = ?

Calculation of future price ‘a’

Futures price F0 = S0(1 + rf)

= $120 (1 + .06)

= $127.20

Calculation of future price ‘b’

The stock price after the fall(S0) = $120 (1 - .03)

=$116.40

The futures price after the fall = S0(1 + rf)

=$116.40 x 1.06

= $123.384

The loss to investor = ($127.20 - $123.384) x 1000

=$3,816.00

Calculation of percentage return ‘c’

Percentage return (loss) = Loss / Margin

= -$3,816 /$12,000

= -31.80%