CFA Level I · CFA Level I Exam · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
Two portfolios of securities will produce identical payoffs in every future state of the world. Under the law of one price and no arbitrage, the two portfolios most likely:
The two portfolios will most likely have the same price today. The law of one price states that identical future payoffs in all states must have identical current prices. Otherwise, buying the cheaper and selling the dearer would lock in a riskless profit.
- Ahave the same price todayCorrect
- Bhave the same standard deviation of returns only
- Chave prices that differ by the risk-free rate
Explanation
The law of one price says assets with identical future cash flows must sell for the same price. If they differed, an investor could buy the cheaper and sell the expensive one for a risk-free profit. A price difference equal to the risk-free rate would still leave an arbitrage.
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