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FRM Part I · FRM Exam Part I · Trading Strategies

A one-year box spread on strikes 80 and 100 pays a certain 20 at expiry. The continuously compounded risk-free rate is 5% (e^-0.05 = 0.9512). Its components, a bull call spread and a bear put spread, are currently priced at a combined net cost of 18.50. What arbitrage is available and what is the profit in present value terms?

Buy the box spread, since it costs 18.50 but is worth 19.02 (20 discounted at 5%). Financing the purchase by borrowing against the certain 20 payoff locks in a present-value profit of 0.52 with no risk.

  1. ASell the box and invest the proceeds; PV profit 0.48
  2. BBuy the box and borrow against the certain 20 payoff; PV profit 0.52Correct
  3. CBuy the box, financing at the risk-free rate; PV profit 1.50
  4. DSell the box; PV profit 1.50

Explanation

Fair value is 20 × 0.9512 = 19.02. The box costs only 18.50, so it is cheap. Buy it and borrow 19.02 against the certain 20; profit = 19.02 - 18.50 = 0.52 today. Selling would lock in a loss. The 1.50 uses undiscounted data.

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