__Arbitrage Pricing Theory:__The arbitrage pricing theory (APT) is a multifactor mathematical model used to describe the relation between the risk and expected return of securities in financial markets. It computes the expected return on a security based on the security’s sensitivity to movements in macroeconomic factors. The resultant expected return can then be used to price the security.

The arbitrage pricing theory is based on three assumptions. First, that a factor model can be used to describe the relation between the risk and return of a security. Second, idiosyncratic risk can be diversified away. Third, efficient financial markets do not allow for persisting arbitrage opportunities.

The arbitrage pricing theory calculates the expected return for a security based on the security’s sensitivity to movements in multiple macroeconomic factors. Whereas the standard capital asset pricing model (CAPM) is a single factor model, incorporating the systematic and firm specific risk related to the overall market return, the arbitrage pricing theory is a multifactor model.

The arbitrage pricing theory can be set up to consider several risk factors, such as the business cycle, interest rates, inflation rates, and energy prices. The model distinguishes between systematic risk and firm-specific risk and incorporates both types of risk into the model for each given factor.

The formula includes a variable for each factor, and then a factor beta for each factor, representing the security’s sensitivity to movements in that factor. Because it includes more factors, the arbitrage pricing theory can be considered more nuanced, if not more accurate, than the capital asset pricing model.

A two-factor version of the arbitrage pricing theory would look like this:

**r = E(r) + B**

_{1}F_{1}+ B_{2}F_{2}+ er = return on the security

E(r) = expected return on the security

F

_{1}= the first factor

B

_{1}= the security’s sensitivity to movements in the first factor

F

_{2}= the second factor

B

_{2}= the security’s sensitivity to movements in the second factor

e = the idiosyncratic component of the security’s return