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FRM Part I · FRM Exam Part I · Pricing Financial Forwards and Futures

A 1-year forward on a non-dividend-paying stock with spot price USD 50 is quoted at USD 55. The continuously compounded risk-free rate is 8%. (e^0.08 = 1.083287) Which arbitrage strategy is appropriate, and what is the approximate profit at maturity per share?

The forward is overpriced versus its fair value of about USD 54.16, so sell the forward, borrow USD 50 and buy the stock. At maturity, delivering the stock earns USD 55 against a loan repayment of USD 54.16, locking in about USD 0.84.

  1. ABuy the forward, short the stock and invest proceeds; profit about USD 0.84
  2. BSell the forward, borrow USD 50 and buy the stock; profit about USD 0.84Correct
  3. CSell the forward, borrow USD 50 and buy the stock; profit about USD 5.00
  4. DBuy the forward, short the stock and invest proceeds; profit about USD 5.00

Explanation

Fair forward = 50 × 1.083287 = 54.164. The quoted USD 55 is too high, so sell the forward, buy the stock with borrowed money, and deliver. At maturity receive 55 and repay 54.164, so profit = 0.836, about USD 0.84. USD 5.00 ignores the financing cost.

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