CFA Level IDerivativesHard
A portfolio manager wants to replicate the payoff of a fiduciary call (a long call plus a risk-free bond paying the strike price at expiration) using only stock and put options. Which combination correctly replicates this payoff?
- AShort stock and short put
- BShort stock and long put
- CLong stock and long put
- DLong stock and short put
Show answer & explanationAnswer & explanation
Correct answer: C. Long stock and long put
Put-call parity states that a fiduciary call (c + PV(X)) has the same payoff as a protective put (S0 + p). Therefore, holding long stock combined with a long put replicates the fiduciary call's payoff exactly.
Why the other options are wrong
- A. This combination has no basis in the put-call parity relationship and produces an unrelated payoff.
- B. Shorting the stock reverses the payoff direction and does not match the fiduciary call.
- D. Shorting the put removes downside protection, producing a different payoff profile.
Fiduciary Call and Protective Put Equivalence
Put-call parity shows that a fiduciary call (long call + risk-free bond) and a protective put (long stock + long put) produce identical payoffs at expiration.
- Fiduciary call = c + PV(X)
- Protective put = S0 + p
- Both strategies have the same payoff, hence the same price by no-arbitrage
Memory trick: Fiduciary call and protective put are twins — same payoff, different wrapper.