Question

Suppose the current price on a stock is $50, the stock has an annual dividend of $1.80. The risk-free rate is 3.75%. If a futures contract on this stock is available with a 3-month maturity, what should its price be? If the future price in the market is 50.75, how can you structure an arbitrage position?

Answer 1

The price of the futures contract can be calculated using the cost of carry formula. If the future price in the market is higher than the calculated price, an arbitrage position can be structured.

Step-by-step explanation:

To calculate the price of the futures contract, we can use the concept of the cost of carry. The cost of carry is the difference between the risk-free rate and the dividends paid by the stock. In this case, the cost of carry would be 3.75% - 1.80% = 1.95%. The price of the futures contract would then be:

Price of futures contract = Current stock price * (1 + Cost of carry) ^ (Time to maturity in years)

Given that the current stock price is $50 and the time to maturity is 3 months (or 0.25 years), the price of the futures contract would be:

Price of futures contract = $50 * (1 + 1.95%) ^ 0.25

Now, if the future price in the market is $50.75, you can structure an arbitrage position by buying the stock at $50 and simultaneously selling the futures contract at $50.75. This would result in an immediate profit of $0.75 per share.