Question

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

• Annualized, continuously compounded risk-free interest rate for 2-month period: r = 2.61%.
• Annualized, continuously compounded risk-free interest rate for 4-month period: r = 6.8%.
• Current spot price of Apple stock: $578 per share.
• Dividend per share of $0.74 in 2 months.
• Contract expiration: T = 4 months.
• Futures price on Apple single-stock futures: $600 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 and zero net cash flows in two months.

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 = $578

I is the present value of dividends =0.74*e^(-0.0261*2/12) =$0.736788

r is the risk free rate till matuity = 6.8%

t is the time till maturity in years = 4/12

So, F =(578-0.736788)*e^(0.068*4/12) = $590.4973

As the Futures price is different from the Theoretical price calculated above, there is an arbitrage opportunity. (Futures is costlier and has to be sold)

Steps of Arbitrage

1. Borrow $577.2632 for 4 months and $$0.7368 for 2 months to get $578. Purchase one share today. (No initial net cash flow)

2. Simultaneously today, Sell the 4 month Futures at $600

3. After 2 months, get $0.74 as dividend and repay the 2 month loan (no cash flow)

4. After 4 months ,get $600 by selling the share in the Futures and repay the loan amount equal to   $590.4973.  Get remaining $9.5027 as Arbitrage profit.

Net profit per share is $9.50 when the Futures contract expires (Enter 9.50 as answer)