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

A non-dividend-paying stock trades at USD 100 and the continuously compounded risk-free rate is 5%. A dealer quotes a one-year forward price of USD 108. Which strategy captures a riskless profit, and how large is it at maturity?

Sell the overpriced forward, borrow USD 100 and buy the stock. At maturity deliver the stock for 108 and repay 105.13, locking in USD 2.87. Buying the forward would be the wrong direction, and ignoring the financing cost overstates the profit.

  1. ABuy the forward, short the stock and lend the proceeds, for a profit of USD 2.87
  2. BSell the forward, borrow USD 100 and buy the stock, for a profit of USD 2.87Correct
  3. CSell the forward, borrow USD 100 and buy the stock, for a profit of USD 3.00
  4. DSell the forward, borrow USD 100 and buy the stock, for a profit of USD 8.00

Explanation

The fair forward price is 100e^0.05 = 105.13, so the quote of 108 is too high. Sell the forward, buy the stock with borrowed money, and deliver the stock for 108. Repaying the loan costs 105.13, leaving 2.87. USD 8.00 ignores financing cost and USD 3.00 uses simple interest.

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