Question

Suppose the current stock price is $45.34 and the continuously compounded intrest rate is 5% The stock pays a dividend of $1.20 in three months. You observe a 9-month forward contract with forward price $47.56. Is there an arbitrage opportunity on the forward contract? If so describe the strategy to realize a profit and find the arbitrage profit. Answer: $1.7178 W1

Answer 1

As rate is continuously compounding we will use > e = exponential value = 2.718281828

.

Present value of dividend = Dividend x e^(-5% x 3/12)

PV of dividend = 1.20 x 2.718281828^(-5% x 3/12) = $1.185093361

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Now,

Forward price calculated = (Stock price - PV of Dividend) x e^(5% x 9/12)

= (45.34 - 1.185093361) x 2.718281828^(5% x 9/12)

= $45.8421538

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Given Forward price = $47.56 ; hence, forward is selling at higher rate than calculated forward.

Arbitrage opportunity = Given price - Forward price calculated

Arbitrage opportunity = $47.56 - $45.8421538

Arbitrage opportunity = $1.7178

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Strategy: sell forward contract