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

The spot price of a non-dividend-paying stock is 50. The one-year forward price is quoted at 55. The continuously compounded risk-free rate is 8% per year, and e^0.08 = 1.0833. Which arbitrage strategy is available, and what is the approximate profit at maturity per share?

Borrow 50 to buy the stock and sell the forward at 55. The fair forward is 54.17, so repaying the loan costs 54.17 and delivery yields 55, locking in about 0.83 per share risk-free.

  1. ABuy the stock by borrowing 50 and sell the forward; profit about 0.83Correct
  2. BSell the stock short and buy the forward; profit about 0.83
  3. CBuy the stock by borrowing 50 and sell the forward; profit about 5.00
  4. DNo arbitrage exists because the forward exceeds the spot price

Explanation

Fair forward price is 50 x 1.0833 = 54.17. The quoted 55 is too high, so sell the forward, buy the stock with borrowed money, and deliver the stock at 55 while repaying 54.17, earning 0.83. The 5.00 option ignores the cost of financing.

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