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 2,400 shares of stock in 1 year. The T-bill rate is 4% per year. a. If Brandex stock now sells at $110 per share, what should the futures price be?
Answered on
The futures price for a single-stock futures contract is determined using the cost of carry model, which considers the current stock price, the risk-free rate, dividends (if any), and the time to expiration.
In this case, since Brandex stock pays no dividends, the cost of carry model simplifies to:
Futures Price = Spot Price×e x e (r×T)
Where:
Spot Price = Current price of Brandex stock = $110
r = Risk-free rate = 4% per year or 0.04
T = Time to expiration in years = 1 year
Plugging in the values:
Futures Price = 110 × e(0.04×1)
Futures Price=110 × e0.04
Futures Price = 110 x 1.0408
Futures Price = 114.488
Rounded to two decimal places, the futures price for the single-stock futures contract on Brandex stock should be approximately $114.49.