Arbitrage is a risk-free profit from simultaneous trades in two equivalent positions priced differently. If asset A and portfolio B produce identical future cash flows, they must trade at the same price today. Otherwise you buy the cheap one, sell the expensive one, and pocket the gap.
KEY: The Law of One Price says assets with identical payoffs must have identical prices today. Derivative pricing is its application.
Textbook formulas assume frictionless markets: free shorting and unlimited borrowing at the risk-free rate.
Replication builds a portfolio of spot plus risk-free financing that reproduces a derivative's payoff at expiration. Because both packages deliver the same future cash flow, the Law of One Price forces equal prices today.
For a forward on a non-income asset, buy the underlying at S₀ and finance with borrowing at r for time T. At expiration you own the asset and owe S₀ × (1 + r)^T. That loan balance is the forward price.
Common mistakes
- Using expected future spot as the forward price. Forward pricing uses only carry inputs and the risk-free rate. Trap: discounting E(S_T) at r to derive F₀(T). F₀(T) comes from arbitrage replication, not from expectations.
- Adding income instead of subtracting it. Dividends, coupons, and convenience yields are cash collected by the holder while waiting. They REDUCE F. Trap: a stock pays a $3 dividend and the candidate adds $3 to the forward.
- Forgetting to compound storage. Year-end storage is added at face value. Upfront storage must be future-valued at r. Trap: treating prepaid storage like end-period storage and underpricing F.
Bottom line
- Arbitrage forces the forward price to equal the cost of buying and carrying the underlying. Direction views never enter.
- Replication builds the derivative payoff from spot plus financing. The portfolio's cost IS the no-arbitrage price.
- F₀(T) = S₀ × (1 + r)^T + FV(storage) − FV(income), using the risk-free rate r, never the expected return.
- Forward price ≠ expected future spot. Forward uses carry only; expected spot includes a risk premium.
Exam shortcut
For forward pricing: "Spot, grow at r, add storage, subtract income." For contango vs. backwardation: "Contango = Carry costs win; Backwardation = Benefits win." For the spot-versus-expected trap: forward prices ignore risk premia; expected future spots contain them. If a question quotes an expected return on the underlying, ignore it and use the risk-free rate.
The full lesson (about 1,498 words, 10 min read) adds 2 worked examples, all 5 common mistakes, a self-check, free in the app.
Learning objectives
- arbitrage replication and cost of carry
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