Where does arbitrage pricing theory collide?

Arbitrage pricing theory holds that an asset's expected return is a linear function of its exposures to several systematic risk factors, each factor carrying its own risk premium. Ross derived it in 1976 from a single idea: in a market with many assets, prices must settle so that no investor can build a portfolio that earns a sure profit with no risk and no cost. Because that no-arbitrage condition does the work, APT does not need the strong assumptions about investor preferences or a single market portfolio that the capital asset pricing model relies on, and it allows many factors rather than one. Ross's paper is titled The arbitrage theory of capital asset pricing. The factors themselves are left open, which is both the model's flexibility and its main weakness, since it does not say what they are or how many there should be.[1]

Unit

An asset's expected return, as a linear function of factor exposures

Recovery means

Not applicable

Measured by

Estimated by regressing asset returns on factor returns to recover factor loadings and their premia

No arbitrage is the principle that a market in equilibrium offers no way to make a certain gain for nothing: no portfolio can be assembled that costs nothing today, never loses, and still pays off with positive probability. This idea is the shared foundation under APT, the Black and Scholes 1973 option formula, and much of modern pricing, because a price that admitted arbitrage would be competed away. Harrison and Kreps made it precise in 1979, showing that the absence of arbitrage is equivalent to the existence of a probability measure under which discounted prices are martingales, a result now called the fundamental theorem of asset pricing. Delbaen and Schachermayer later proved a general version of that theorem for continuous-time markets. Here the referent is a mathematical condition on prices, not a trading strategy that anyone actually runs.[2][3][4]

Unit

A condition on prices: no zero-cost portfolio yields a sure gain

Recovery means

Not applicable

Measured by

Checked mathematically by whether an equivalent martingale measure exists for the price process

In textbook theory arbitrage is riskless and self-correcting, but Shleifer and Vishny argued in 1997 that real arbitrage is carried out by specialists using other people's money, and is neither riskless nor unlimited. When a mispricing widens before it closes, an arbitrageur can face losses and investor withdrawals exactly when the opportunity is greatest, and may be forced to unwind at the worst time. So the forces that are supposed to erase mispricings can be weakest when prices are furthest from value, which helps explain why some anomalies persist. This is the same word as the idealized arbitrage that APT and no-arbitrage pricing assume away, but the referent is a costly, risky activity with agency and capital constraints. Their paper is titled The limits of arbitrage.[5]

Unit

A real trade to exploit mispricing, bearing risk and capital limits

Recovery means

Not applicable

Measured by

Studied through arbitrageur returns, fund flows, and the persistence of pricing anomalies