Definition of Arbitrage Pricing Theory

Arbitrage pricing theory is a financial model that incorporates multiple factors containing systematic risk represented by a beta that is then used to estimate returns on security when securities are mispriced. The situation of arbitrage exists when the market is not 100% efficient and some securities are mispriced so the opportunity of having profit exists (arbitrage). In this situation, a regression model is run to find out a linear relationship between multiple systematic risk factors and expected return on a security. The mathematical expression of arbitrage pricing theory is

E(r_i)=E(r_f) + Beta x [E(R_m)−E(R_f)]

The above expression will calculate the expected return on asset-based on factor ‘i’.