Arbitrage Portfolio Theory (APT) – A Multifactor Macroeconomic Model

• Arbitrage Portfolio Theory (APT) came along after CAPM as a multifactor model to explain returns.

• APT explains returns under the construct where:

• Multiple risks with an excess return above the risk free rate of return can be priced.

• Any security or portfolio has its own beta coefficient to each of the priced risk variables in the model.

• There is a linear relationship between the security's return and the priced risk (a basic assumption of multi-variable regression).

• APT calculates the alpha value, or y-intercept of the model graph.

Comparing CAPM vs. APT

APT is less restrictive in CAPM, as:

• Asset returns can be described using a multifactor model (CAPM being a single factor model).

• Diversification eliminates the security specific risk of the individual securities in a multi-asset portfolio.

• Assets are priced such that arbitrage profit does not exist.

• The factor sensitivities of the assets in an arbitrage portfolio equal zero and the portfolios expected return is zero.

• Note: If the investor believes that the expected return on the arbitrage portfolio is not equal to zero, then a single factor or multifactor APT style model can be used to capture risk free profit.

• Step 1: Identify and purchase the undervalued asset or portfolio.

• Step 2: Finance the long position with a short sale of overvalued assets.

• Step 3: Close the long and short positions once the assets return to their APT determined equilibrium model values for zero return.

• Whenever two portfolios have the same risk but different expected returns or the same expected return, but different risks, an arbitrage opportunity may be possible.

• It is important to note a couple of key differences between CAPM and APT as these modeling techniques and their variations are extensive in financial research.