Updated for the 2026-2027 CFA® Level I curriculum.
Derivatives are priced using logic, not guesswork. If you can build a portfolio that produces the exact same future payoff as a derivative, that portfolio and the derivative must trade at the same price today. This idea, called no-arbitrage pricing, is the foundation for every derivative pricing model tested at Level I. After this note, you should be able to explain why mispriced derivatives create arbitrage opportunities and how replication pins down a derivative's fair price.
Quick Answer
Arbitrage is a risk-free profit earned when identical future payoffs trade at different current prices. Replication means building a portfolio of other assets that produces the same future payoff as a derivative. Because two positions with identical future payoffs must have the same value today (the law of one price), traders price derivatives by pricing the replicating portfolio. If the derivative's market price differs from the replicating portfolio's cost, an arbitrage trade is available.
Key Takeaways About Arbitrage and Replication in Derivatives Pricing
Arbitrage is a riskless profit with no net investment, earned by exploiting a price difference between two positions with identical future payoffs.
Replication means creating a portfolio from other instruments (like the underlying asset and borrowing or lending) that matches a derivative's future payoff exactly.
The law of one price states that identical future cash flows must have the same value today, regardless of how they are created.
No-arbitrage pricing sets a derivative's fair price equal to the cost of its replicating portfolio.
If a derivative is mispriced relative to its replicating portfolio, traders buy the cheap side and sell the expensive side to lock in a riskless gain.
Replication matches payoffs, not legal form. The replicating instruments do not need to resemble the derivative itself.
A common error is comparing cash flows without adjusting for timing, which produces a false arbitrage signal.
What You Need to Know for CFA Level I
Define arbitrage and identify why it requires no net investment and no risk.
Explain no-arbitrage pricing and why it anchors derivative valuation.
State the law of one price and apply it to two positions with matching payoffs.
Describe a replicating portfolio and explain how it is built from the underlying asset and financing.
Explain why identical future payoffs must carry the same current value.
Identify the arbitrage trade available when a derivative is mispriced relative to its replicating portfolio.
What Is Arbitrage?
Arbitrage is the simultaneous purchase and sale of equivalent assets to capture a price difference, with no net investment and no risk. Two things separate arbitrage from ordinary trading. First, the trader risks nothing, since any cash paid out on one side is funded by cash received on the other. Second, the profit is certain, not expected. If a trade depends on a forecast, a probability, or a favorable market move, it is speculation, not arbitrage.
Arbitrage matters for pricing because it explains why prices cannot drift too far from fair value. If a mispricing appears, arbitrage traders act on it immediately, and their trading pushes prices back toward the no-arbitrage level. Level I does not ask you to find arbitrage opportunities in real markets. It asks you to use the no-arbitrage argument to derive or verify a derivative's price.
No-Arbitrage Pricing
No-arbitrage pricing is the principle that a derivative's price must equal the cost of a portfolio that replicates its payoff. If it did not, an arbitrage trade would exist, and traders would exploit it until the mispricing disappeared.
This is different from pricing based on a forecast of where the underlying asset will end up. No-arbitrage pricing does not require any view on whether a stock will go up or down. It only requires that two positions with matching future payoffs trade at the same price today. That is why this approach dominates derivative pricing at every CFA level.
What Is Replication?
Replication means constructing a portfolio, usually from the underlying asset plus borrowing or lending, that produces the same future payoff as a derivative. The replicating portfolio does not need to look like the derivative. It only needs to behave like it at every future date and in every future state of the world.
For example, a long forward contract on a stock can be replicated by borrowing money today, buying the stock with the borrowed funds, and repaying the loan at expiration. The forward contract and this borrow-and-buy strategy are not the same instrument. They produce the same payoff, which is what matters for pricing.
Law of One Price
The law of one price states that two assets or portfolios with identical future cash flows must have the same value today. If they did not, a trader could buy the cheaper one, sell the more expensive one, and collect the price difference risk-free.
This is the logical backbone of no-arbitrage pricing. Once you confirm that a derivative and a replicating portfolio produce identical payoffs, the law of one price forces their current prices to match.
Concept | Meaning |
|---|---|
Price | What you pay or receive to enter a position today |
Value | What a position is economically worth today, based on its future payoffs |
Payoff | The cash flow a position delivers at a specific future date |
Profit | Payoff minus the cost of establishing and financing the position |
Keep these terms separate. A derivative's price should equal its value under no-arbitrage pricing, but its payoff and profit are different figures calculated at different points in time.
How Replication Establishes a Derivative Price
To price a derivative using replication, follow three steps.
Identify the derivative's payoff at expiration.
Build a portfolio from the underlying asset and financing (borrowing or lending) that produces the identical payoff.
Set the derivative's current price equal to the cost of building that portfolio today.
If the derivative's market price differs from the replicating portfolio's cost, the mispriced side gets sold and the underpriced side gets bought, funded by the sale. The trade requires no net cash outlay and produces a riskless profit at expiration.
The table below shows the logic behind a forward contract's replicating portfolio.
Time | Strategy A: Long Forward | Strategy B: Borrow and Buy Stock |
|---|---|---|
Today | Enter forward contract, no cash exchanged | Borrow present value of forward price, buy one share |
At expiration | Pay forward price, receive one share | Repay loan, already own one share |
Both strategies end at expiration with ownership of one share, having effectively paid the forward price. Since the payoffs match, the two strategies must cost the same today. That equality is what pins down the fair forward price.
Simple Arbitrage Example
Setup. A stock trades today at $40. The one-year risk-free rate is 5%. A one-year forward contract on the stock is quoted in the market at $44.
Step 1: Find the no-arbitrage forward price.
Step 2: Compare to the market price.
The market forward price of $44 is $2 above fair value. The forward is overpriced relative to the replicating portfolio.
Step 3: Build the arbitrage trade.
Sell the forward contract. Borrow $40 today and buy one share of the stock.
Step 4: Settle at expiration.
Deliver the share into the forward contract and receive $44. Repay the loan of $40 × 1.05 = $42.
$2 per share, earned with no net investment and no price risk
The forward price was set above the cost of carrying the stock through borrowing. Traders would immediately sell the overpriced forward and buy stock with borrowed money, capturing a certain $2 profit until the forward price falls back to $42.
Common Exam Traps
Treating arbitrage as ordinary speculation
Arbitrage requires no net investment and no risk. If a trade depends on a market forecast or carries any exposure to price movement, it is speculation, not arbitrage.
Assuming replication means identical instruments
A replicating portfolio does not need to resemble the derivative in legal form. It only needs to produce the same future payoff.
Ignoring timing when comparing cash flows
Cash flows at different dates cannot be compared directly. Always bring them to the same point in time before checking for a price difference.
Using expected return instead of matched cash flows
No-arbitrage pricing compares actual matched payoffs, not probability-weighted expected outcomes. A derivative's fair price does not depend on how likely a future price move is.
Practice Questions
A share trades today at $60. The one-year risk-free rate is 4%. A one-year forward contract on the share is quoted in the market at $65. Which action describes the correct arbitrage strategy and the resulting riskless profit per share?
Buy the forward contract and lend $60 today, earning a profit of $1.60
Sell the forward contract, borrow $60 to buy the stock today, earning a profit of $2.60
Buy the stock and buy the forward contract, earning a profit of $5.00
Correct Answer: B
The fair forward price is $60 × 1.04 = $62.40. The market forward price of $65 is $2.60 too high. Since the forward is overpriced, sell it and replicate the offsetting long stock position by borrowing $60 and buying one share. At expiration, deliver the share into the forward for $65 and repay the loan of $62.40. Profit equals $65 − $62.40 = $2.60 per share, with no net investment today.
Option A: Buying the already overpriced forward locks in a loss, not a profit, and the dollar figure does not match the correct calculation.
Option C: Buying both the stock and the forward doubles exposure to the underlying and does not produce a riskless, self-financing position. It is not an arbitrage trade.
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FAQs About Arbitrage and Replication in Derivatives Pricing
Is arbitrage completely risk-free?
In the idealized no-arbitrage models tested at Level I, yes. Real markets add transaction costs, execution timing, and short-selling constraints that can reduce or eliminate a theoretical arbitrage profit.
How is arbitrage different from speculation?
Arbitrage requires no net investment and produces a certain profit from matched cash flows. Speculation risks capital on a directional view about future prices.
Why does replication matter if I am not building trades myself?
Replication is the tool used to derive fair derivative prices. Understanding it lets you verify or calculate a no-arbitrage price on exam questions without memorizing separate formulas for every contract type.