Arbitrage Pricing Theory

Arbitrage Pricing Theory (APT) Based on the law of one price. Two

items that are the same cannot sell at different prices

If they sell at a different price, arbitrage will take place in which arbitrageurs buy the good which is cheap and sell the one which is higher priced till all prices for the goods are equal

APT In APT, the assumption of investors

utilizing a mean-variance framework is replaced by an assumption of the process of generating security returns.

APT requires that the returns on any stock be linearly related to a set of indices.

In APT, multiple factors have an impact on the returns of an asset in contrast with CAPM model that suggests that return is related to only one factor, i.e., systematic risk

Factors that have an impact the returns of all assets may include inflation, growth in GNP, major political upheavals, or changes in interest rates

ri = ai + bi1F1 + bi2F2 + …+bikFk + ei Given these common factors, the bik

terms determine how each asset reacts to this common factor.

While all assets may be affected by growth in GNP, the impact will differ.

Which firms will be affected more by the growth in GNP?

The APT assumes that, in equilibrium, the return on a zero-investment, zero-systematic risk portfolio is zero, when the unique effects are diversified away:

E(ri) = 0 + 1bi1 + 2bi2 + … + kbik

Example of two stocks and two factor model:

Three Major Assumptions: capital markets are perfectly competitive investors always prefer more to less wealth price-generating process is a K factor model

PROBLEMS WITH APT Factors are not well specified ex ante

To implement the APT model, we need the factors that account for the differences among security returns

This is a similar problem with the CAPM, which defines the unobservable market portfolio as a single factor

Neither CAPM or APT has been proven superior Both rely on unobservable expectations