Question

A stock price is $60 today. It pays dividend of $1 after two months and $1.05 after five months. The continuously compounded interest rate is 2% per year. Transaction costs are $0.10 per stock traded, a $0.25 one-time fee for trading forward contracts, and no costs for saving or borrowing. If the six-month forward price is $61, demonstrate how to make arbitrage profits or explain why you cannot.

Answer 1

No arbitrage six month forward price

= (S₀ + C₁ + C₂)e^rT - D₁e^{r(T - t₁)} - D₂e^{r(T - t₂)}

= (60 + 0.10 + 0.25)e^{2% x 6/12} - 1e^{2%(6 - 2)/12} - 1.05e^{2%(6 - 5)/12}

= $ 58.90

But the actual six-month forward price is $61. Hence, there is an arbitrage possible. The arbitrage strategy should be:

• Buy the stock today
• Enter into a six month future contract to sell the stock @ 61
• Reinvest the periodic dividends received
• Use the stock bought to deliver against the forward contract at the end of six months to close the position.

The arbitrage profit will be = Forward price - No arbitrage forward price = 61 - 58.90 = $ 2.10 per share

answered by: anonymous