Question

OneChicago has just introduced a single-stock futures contract on Brandex stock, a company that currently pays no dividends. Each contract calls for delivery of 2,200 shares of stock in 1 year. The T-bill rate is 6% per year.

  

a.	If Brandex stock now sells at $180 per share, what should the futures price be? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

  

Futures price

$

  

b.

If the Brandex price drops by 3%, what will be the new futures price and the change in the investor’s margin account? (Round intermediate calculations and "Futures price (new)" answer to 3 decimal places and other answer to the nearest dollar amount. Negative amount should be indicated by a minus sign. Omit the "$" sign in your response.)

  

Futures price (new)	$
Change in the investor’s margin account	$

  

c.	If the margin on the contract is $11,100, what is the percentage return on the investor’s position? (Round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign. Omit the "%" sign in your response.)

  

Percentage return on the investor’s position

%

Answer 1

Futures price = S₀ x (1 + r)^t

where, S₀ = current stock price, r = risk free rate of interest, t = time till maturity in years

a) Futures price = $180 x (1 + 0.06)¹ = $190.80

b) New share price = $180 - (3% x $180) = $174.60

New Futures price = $174.60 x (1 + 0.06)¹ = $185.076

Change in investor's margin account = (New futures price - Old futures price) x No. of shares in a contract

or, Change in investor's margin account = ($185.076 - $190.80) x 2200 = (-)$12,592.8 or (-)$12,593

c) Percentage return = Change in account / margin on the contract = (-)$12,593 / $11,100 = (-)1.1345 or (-)113.45%