This chapter explored the relationship between arbitrage, hedging, the Law of One Price, the Law of One Expected Return, and the structure of asset prices. The same thing is expected to sell for the same price. This is the Law of One Price. Securities are the same if they produce the same outcomes, which encompass both their expected returns and risk. Similarly, equivalent combinations of assets providing the same outcomes should sell for the same prices. Thus, the criteria for sameness or equivalence among financial securities involve the comparability of expected returns and risk. If the same thing sells for different prices, the Law of One Price is violated, and the price disparity can be exploited if transactions costs are not prohibitive. Thus, the Law of One Price imposes structure on asset prices through the discipline of the profit motive. Similarly, equivalent securities and portfolios must have the same expected return. This is the Law of One Expected Return.
If the Law of One Price defines the resting place for an asset’s price, arbitrage is the action that draws prices to that resting place. Arbitrage is defined as the process of earning a riskless profit by taking advantage of different prices or expected returns for the same asset, whether priced alone or in equivalent combinations of assets.
True arbitrage must be riskless. The ability to hedge is a necessary condition for arbitrage because it can eliminate risk. Thus, a hedging transaction is intended to reduce or eliminate the risk of a primary security or portfolio position. An investor consequently establishes a secondary position that is designed to counterbalance some or all of the risk associated with another investment position.
This chapter identified the conditions associated with the presence of an arbitrage opportunity. An arbitrage opportunity exists when an investor can put up no cash and yet still expect a positive payoff in the future and when an investor receives an initial net inflow but can still expect a positive or zero payoff in the future. An arbitrage opportunity is also present when the value of a portfolio of assets is not equal to the sum of the prices of the underlying securities composing that portfolio.
The absence of arbitrage opportunities is consistent with equilibrium prices. Thus, arbitrage-free prices are expected to be the norm in efficient financial markets. The act of arbitraging mispriced assets should return prices to appropriate values. Arbitrage consequently reinforces the Law of One Price or the Law of One Expected Return and imposes order on asset prices.