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CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity

An analyst finds that a protective put (stock plus put) costs less than a fiduciary call (call plus risk-free bond) with the same strike and expiration. Which action would most likely produce an arbitrage profit?

Buy the cheaper protective put and sell the more expensive fiduciary call. The two have identical expiration payoffs, so the positions offset at expiration while the price difference is kept as a riskless profit at the start.

  1. ABuy the fiduciary call and sell the protective put
  2. BBuy the protective put and sell the fiduciary callCorrect
  3. CBuy both portfolios and hold to expiration

Explanation

Both portfolios have identical payoffs at expiration, max(S,X). Buy the cheaper one (protective put) and sell the more expensive one (fiduciary call). The net payoff at expiration is zero while the initial inflow is positive. Buying both or reversing the trade locks in a loss or no gain.

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