Calculating the Fair Price of Futures Contract

Lucas is a portfolio manager considering entering into a futures contract for crude oil to hedge against a fluctuation in prices. Currently, the spot price of crude oil is $80 per barrel, and it is expected that in 6 months, the price will either rise to $90 or fall to $70. The risk-free rate is 5% per annum. Lucas is looking at a futures contract that expires in 6 months. He wants to determine what the fair price of the futures contract should be based on the current spot price and the risk-free rate.

To calculate the fair price of the futures contract, Lucas applies the formula: F = S * e^(rt), where F is the futures price, S is the spot price, r is the risk-free rate, and t is the time to expiration in years.