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

A 1-year forward on a stock that pays a continuous yield of 3% is quoted at USD 105. Spot is USD 100 and the continuously compounded risk-free rate is 5%. Which arbitrage strategy yields a riskless profit, and how much at maturity?

The fair forward is about 102.02, so the 105 quote is overpriced. The arbitrageur sells the forward, buys the stock with borrowed money, reinvests the dividends, and delivers at maturity, locking in roughly USD 3, the gap between 105 and 102.02.

  1. ABuy forward, short spot; profit about USD 3.9
  2. BSell forward, buy e^(-0.03) shares funded by borrowing; profit about USD 2.9Correct
  3. CSell forward, buy e^(-0.03) shares funded by borrowing; profit about USD 0.0
  4. DBuy forward, short spot; profit about USD 2.9

Explanation

Fair F = 100 x e^0.02 = 102.02. The quote of 105 is too high, so sell forward and buy the stock. Reinvesting dividends, e^(-0.03) shares grow to one share at maturity, costing 100 x e^(-0.03) borrowed at 5%, repaying 102.02. Delivering at 105 gives profit 105 - 102.02 = 2.98, about USD 3.0, closest to USD 2.9. Buying forward would lose money.

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