Replication vs Arbitrage in CFA Derivatives: Payoff Matching Before Pricing Gaps

CFA derivatives questions often make replication and arbitrage sound like the same idea because both compare one position with another. The clean distinction is this: replication builds an equivalent payoff; arbitrage exploits a wrong price for equivalent payoffs.

That distinction matters because replication can be present even when markets are perfectly priced. Arbitrage exists only when the market price breaks the no-arbitrage relationship.

The Core Difference

Replication answers a construction question:

> What portfolio produces the same future payoff as this derivative?

Arbitrage answers a trading question:

> If two positions have the same payoff, can I buy the cheaper one, sell the expensive one, finance the trade, and lock in a gain?

The exam trap is to see the word replicate and immediately assume free profit. That is not right. A perfectly priced replication portfolio is just a valuation tool.

Replication Is a Payoff-Matching Tool

Suppose Harbor Grid Energy stock trades at 80. A one-year European call with strike 82 is paired with a one-year European put with the same strike. The risk-free present value of 82 due in one year is 78.

Put-call parity can be arranged as:

Call + PV(K) = Put + Stock

This says a fiduciary can build the same payoff in two ways:

• hold a call and risk-free cash equal to the present value of the strike
• hold a put and the underlying stock

At expiration:

• If the stock finishes above 82, the call side uses the call to own the stock, while the put expires.
• If the stock finishes below 82, the put-stock side preserves value through the put, while the call expires.

The algebra is less important than the equivalence: both sides are two different roads to the same payoff.

Why Replication Matters Even Without Arbitrage

If the call side costs 17 + 78 = 95 and the put-stock side costs 15 + 80 = 95, there is no arbitrage. But replication still taught you the fair relation among the call, put, stock, and risk-free bond.

That is why replication is a pricing discipline. It tells you what the derivative should be worth if equivalent payoffs are priced consistently.

Arbitrage Requires a Broken Price Relationship

Now change one number. Suppose the call trades at 20 while the put still trades at 15, the stock is still 80, and the present value of the strike is still 78.

• Call side: 20 + 78 = 98
• Put-stock side: 15 + 80 = 95

The two sides have the same future payoff, but one side costs 3 more. That creates the shape of an arbitrage trade:

1. Sell the expensive package.
2. Buy the cheaper package.
3. Lock in the initial price difference.
4. Hold the offsetting positions to expiration so future payoffs cancel.

In this example, the trader would sell the call-plus-cash package synthetically and buy the put-plus-stock package. The important exam point is not the exact operational mechanics; it is the logic that identical payoff plus different price equals an arbitrage signal.

Synthetic Forward Example

Replication also explains synthetic forwards. A long forward payoff can be replicated with:

Long call + Short put, using the same strike and expiration.

Suppose Linden Robotics stock is 50, the one-year forward price is 53, and options with strike 53 are available:

• One-year call premium: 4.20
• One-year put premium: 5.80
• Risk-free present value of 53: 50.00

The option pair costs 4.20 - 5.80 = -1.60, meaning the investor receives 1.60 today. That option pair is not automatically an arbitrage. It is a synthetic long forward payoff. You compare it with the actual forward terms after financing to decide whether a pricing inconsistency exists.

The Exam Translation

If the vignette asks what position replicates a forward, pick the payoff-matching combination.

If the vignette asks whether a trader can earn a riskless profit, compare the market price with the replication cost and show the buy-cheap/sell-expensive direction.

Decision Rules Candidates Can Use

Rule 1: Draw or describe the final payoff first

Before choosing an answer, ask what happens at expiration across high-price and low-price states. Replication is about matching that future pattern.

Rule 2: Separate fair pricing from mispricing

No-arbitrage relationships can hold exactly. In that case, replication gives fair value but no trading profit.

Rule 3: If prices differ, trade the price difference

When two payoff-equivalent positions have different current costs, the arbitrage direction is:

• buy the cheaper payoff
• sell the more expensive payoff
• keep the current price spread
• let future payoff obligations offset

Common Distractors

Distractor 1: Calling every replication an arbitrage

Wrong because equivalent payoffs can be priced fairly. Replication is the foundation; arbitrage requires a price error.

Distractor 2: Comparing similar risk instead of identical payoff

Two securities can have similar delta, similar duration, or similar market exposure without being true arbitrage substitutes. Arbitrage needs a much tighter payoff match.

Distractor 3: Ignoring financing

Cash paid or received today must be compounded or discounted consistently. Put-call parity and forward pricing are not just option diagrams; they also include the financing leg.

Distractor 4: Reversing buy-cheap and sell-expensive

If the synthetic is cheaper than the actual derivative, buy the synthetic and sell the actual derivative. If the synthetic is more expensive, do the opposite.

Exam Framing

CFA candidates should read replication and arbitrage questions in this order:

1. Identify the target payoff.
2. Build or recognize the matching portfolio.
3. Compute or compare current costs.
4. If costs match, conclude fair no-arbitrage pricing.
5. If costs differ, choose the trade that buys the cheaper payoff and sells the expensive payoff.

That order keeps the logic grounded. Replication is the map. Arbitrage is what happens when the market posts two different prices for the same destination.