Arbitrage Pricing Theory

The Arbitrage Pricing Theory (APT) of Ross (1977) is also used in finance to determine the return of different securities. The APT states that, in equilibrium, no arbitrage opportunity can exist and, also, that the expected return of an asset is the linear combination of multiple random factors (Wilmott 2007). These factors can be various macro-economic factors or market indices. In this model, each factor has a specific beta coefficient:

αi is a constant denoting security i; βij is the sensitivity of security i to factor j; Fj is the systematic factor; while ei is the security's unsystematic risk, with zero mean.

A central notion of the APT is the factorportfolio. A factorportfolio is a well-diversified portfolio which reacts to only one of the factors, so it has zero beta for all other factors, and a beta of 1 to that specified factor. Assuming the existence of the factorportfolios, it can be shown using the arbitrage argument that any well-diversified portfolio...