Introduction
} Arbitrage pricing theory (APT) is an alternative to the capital asset pricing model (CAPM) for explaining returns of assets or portfolios.
} It was developed by economist Stephen Ross in the 1970s. The arbitrage pricing theory is a lot more difficult to apply in practice because it requires a lot of data and complex statistical analysis.
What Is APT?
APT is a multi-factor technical model based on the relationship between a financial asset's expected return and its risk. The model is designed to capture the sensitivity of the asset's returns to changes in certain macroeconomic variables. Investors and financial analysts can use these results to price securities.
Three Underlying Assumptions of APT
} Asset returns are explained by systematic factors.
} Investors can build a portfolio of assets where specific risk is eliminated through diversification.
} No arbitrage opportunity exists among well-diversified portfolios. If any arbitrage opportunities do exist, they will be exploited away by investors. (This how the theory got its name.)
Formula of Expected Return of a diversified portfolio as per APT
} For a well-diversified portfolio, a basic formula describing arbitrage pricing theory can be written as the following:
} E(Rp)=Rf+β1*RP1+β2* RP2+…+βn*RPn
where:
} E(Rp)=Expected return
} Rf=Risk-free return
} βn= β is the sensitivity of the asset or portfolio in relation to the specified factor
} fn= RP is the risk premium of the specified factor.
Factors affecting expected return
} Unlike in the capital asset pricing model, the arbitrage pricing theory does not specify the factors. However, according to the research of Stephen Ross and Richard Roll, the most important factors are the following:
} Change in inflation
} Change in the level of industrial production
} Shifts in risk premiums
} Change in the shape of the term structure of interest rates
KEY TAKEAWAYS
} The CAPM lets investors quantify the expected return on investment given the risk, risk-free rate of return, expected market return, and the beta of an asset or portfolio.
} The arbitrage pricing theory is an alternative to the CAPM that uses fewer assumptions and can be harder to implement than the CAPM.
} While both are useful, many investors prefer to use the CAPM, a one-factor model, over the more complicated APT, which requires users to quantify multiple factors.
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