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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

A non-dividend-paying stock is priced at USD 50. A 1-year forward on it is quoted at USD 54. The continuously compounded risk-free rate is 6%. What arbitrage profit, valued at the forward's maturity, can be locked in per share?

The profit is USD 0.91 per share. The fair forward price is 50 × e^0.06 = 53.09, so the USD 54 quote is too high. Selling the forward, borrowing to buy the stock and delivering it at maturity locks in 54 minus 53.09.

  1. AUSD 0.91 profit, by selling the forward, borrowing USD 50 and buying the stockCorrect
  2. BUSD 1.00 profit, by selling the forward, borrowing USD 50 and buying the stock
  3. CUSD 4.00 profit, by selling the forward, borrowing USD 50 and buying the stock
  4. DUSD 0.91 profit, by buying the forward, short selling the stock and investing the proceeds

Explanation

The fair forward price is 50 × e^0.06 = 50 × 1.061837 = 53.09. The quote of 54 is too high. Sell the forward, borrow 50 and buy the stock. At maturity, deliver the stock and receive 54, then repay 53.09, leaving 0.91. USD 1.00 uses simple interest and USD 4.00 ignores financing costs. The last option takes the wrong side of the trade.

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