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FRM Part I · FRM Exam Part I · Introduction to Derivatives

A stock trades at USD 40. The one-year forward price is USD 43. The continuously compounded risk-free rate is 5% per year and the stock pays no dividends. Which strategy exploits the mispricing, and what is the approximate arbitrage profit at maturity per share? (e^0.05 = 1.05127)

The forward at USD 43 exceeds the no-arbitrage price of about USD 42.05 (40 x e^0.05). The arbitrageur borrows to buy the stock and shorts the forward, delivering at maturity, locking in roughly USD 0.95 per share after repaying the loan.

  1. ABuy the stock with borrowed money and short the forward; profit about USD 0.95Correct
  2. BShort the stock and buy the forward; profit about USD 0.95
  3. CBuy the stock with borrowed money and short the forward; profit about USD 3.00
  4. DShort the stock and buy the forward; profit about USD 3.00

Explanation

Fair forward = 40 x 1.05127 = USD 42.05. The actual forward of 43 is too high, so sell the forward and buy the stock financed by borrowing. At maturity, receive 43 and repay 42.05, profit USD 0.95. The USD 3.00 ignores financing cost.

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