9.4 Arbitrage, Pricing, and No-Arbitrage Intuition

Arbitrage as a pricing anchor

Arbitrage is the ability to earn a riskless profit with no net investment, after transaction costs and practical constraints. In competitive markets, obvious arbitrage opportunities tend to be short lived because traders buy the underpriced position, sell the overpriced position, and push prices back toward fair value.

CFA Level I uses arbitrage as intuition more than as a trading manual. The point is that two strategies with the same future payoff should have the same current cost. If they cost different amounts, investors can buy the cheaper package and sell the more expensive package.

Derivative pricing often comes from replication. If a derivative payoff can be replicated with the underlying asset and borrowing or lending, the derivative value should equal the cost of that replicating portfolio. This logic is called no-arbitrage pricing.

Forward pricing intuition

For an asset with no income, storage cost, or convenience yield, the forward price should reflect the spot price grown at the risk-free financing rate to the delivery date. If the forward price is too high, an arbitrageur can buy the asset now, finance the purchase, and sell it forward. This is a cash-and-carry trade.

If the forward price is too low, an arbitrageur can short the asset, invest the proceeds, and buy it forward. This is a reverse cash-and-carry trade. Practical limits can affect execution, but the Level I intuition is clear: the forward price is tied to spot price and carrying cost.

For income-producing assets, expected income lowers the forward price because the owner of the asset receives benefits before delivery. Dividends on a stock index or coupons on a bond reduce the net carry cost. For commodities, storage and insurance costs raise the forward price, while convenience yield can lower it.

Value versus price

The forward price is the delivery price that makes a new contract fair at initiation. The value of an existing forward is what the contract is worth after market conditions change. A contract entered at a delivery price of 100 may have positive value to the long if the current fair forward price rises to 106.

This distinction also applies more broadly. An option premium is the price paid to enter the option. The option value later changes with the underlying, volatility, time, rates, and income. A swap fixed rate is set so the swap has near-zero value at initiation, then the swap's value changes as rates move.

Put-call parity intuition

For European options on the same underlying with the same exercise price and expiration, put-call parity links calls, puts, the underlying, and a risk-free bond. The exact formula may vary with dividends, but the intuition is stable: a protective put and a fiduciary call can be designed to create equivalent payoffs.

A protective put is stock plus a put. A fiduciary call is a call plus a risk-free bond that will pay the exercise price at expiration. If the payoffs are the same, the current costs should be the same. If they differ, an arbitrage relation is violated.

Structured aid: no-arbitrage decision tree

1. Identify two strategies that produce the same future payoff.
2. Compare their current costs.
3. If one costs less, buy the cheaper strategy.
4. Sell the more expensive strategy.
5. Lock in the cost difference, subject to transaction costs and execution risk.
6. Expect arbitrage pressure to push prices toward equality.

Exam focus

Do not treat arbitrage as simply a good trade idea. Arbitrage requires matched future payoffs and minimal risk, not just a belief that a price will rise. A risky expected profit is speculation, not arbitrage.

When a forward price looks too high, think cash and carry: buy the underlying, finance it, and sell the forward. When a forward price looks too low, think reverse cash and carry: short the underlying, invest proceeds, and buy the forward. Then adjust intuition for income, storage, and convenience benefits.