Question

Consider a single-stock futures contract on Exxon-Mobil stock. Consider the following scenario:

• Annualized, continuously compounded risk-free interest rate for 3-month period: r = 3.99%.
• Annualized, continuously compounded risk-free interest rate for 5-month period: r = 6.55%.
• Current spot price of Exxon Mobil stock: $157 per share.
• Dividend per share of $0.87 in 3 months.
• Contract expiration: T = 5 months.
• Futures price on Exxon Mobil single-stock futures: $150 per share.

An arbitrage opportunity exists. What is the net profit per share when the futures contract expires? Use a strategy that has zero net cash flows today.

Do not round values at intermediate steps in your calculations. Enter your answer in dollars and cents, but omit the $ symbol and commas. For example, enter $1,234.56 as 1234.56 as your answer.

Answer 1

The Theoretical Futures price F = (S-I) * e^(rt)

where S is the Spot price = 157

I is the present value of dividends =0.87*e^(-0.0399*3/12) =$0.861365

r is the risk free rate till matuity = 6.55%

t is the time till maturity in years = 5/12

So, F =(157-0.861365)*e^(0.0655*5/12) = $160.46

As the Futures price is different from the Theoretical price calculated above, there is an arbitrage opportunity

Steps of Arbitrage

1. Short Sell the stock at $157 today (by undertaking that the dividends will be paid to the lender of the stock in time and borrowing for 5 months) and invest $0.861365 for 3 months and $156.1386 for 5 months. (Total initial cashflow is zero)

2. Simultaneously today, buy the 5 month Futures at $150

3. After 3 months, $0.861365 to mature to become $0.87 and return it to the lender

4. After 5 months ,$156.1386 to mature $160.4586, use $150 to buy the share from the Futures and return to the Lender,. Get remaining $10.4586 as Arbitrage profit.

Net profit per share is $10.46 when the Futures contract expires (Enter 10.46 as answer)