APT 1: Arbitrage Pricing Theory vs. CAPM
Arbitrage Pricing Theory (APT) explains a stock's expected return using several risk factors instead of just one. CAPM uses only the market. APT lets you add factors like inflation or economic growth, each with its own beta and risk premium.
What you will learn
- The core idea behind Arbitrage Pricing Theory
- How the APT formula extends CAPM to several factors
- What factor betas and factor risk premiums are
- Key differences in assumptions between APT and CAPM
- How to calculate an expected return with a two-factor APT model
The formulas
- R_f
- risk-free rate
- βₖ
- the asset's sensitivity to factor k
- RPₖ
- risk premium for factor k
- R_m − R_f
- market risk premium
Worked example
Risk-free rate 3%. A stock has a beta of 0.8 to a GDP-growth factor (premium 4%) and 0.5 to an inflation factor (premium 2%). What is its expected return under APT?
- GDP factor: 0.8 × 4% = 3.2%
- Inflation factor: 0.5 × 2% = 1.0%
- Add the risk-free rate: 3% + 3.2% + 1.0% = 7.2%
Answer: Expected return = 7.2%
Common questions
What is the difference between APT and CAPM?
CAPM uses a single risk factor, the market, and one beta. APT allows several macroeconomic or statistical factors, each with its own beta and premium. APT also needs fewer assumptions: it relies on no-arbitrage pricing rather than the idea that everyone holds the market portfolio.
What is the formula for arbitrage pricing theory?
Expected return equals the risk-free rate plus the sum of each factor beta times that factor's risk premium: E(R) = R_f + β₁RP₁ + β₂RP₂ + … + βₖRPₖ. The factors and premiums are chosen or estimated by the analyst.
Is CAPM a special case of APT?
In effect, yes. If the only factor in an APT model is the market, with a premium equal to the market risk premium, the APT formula becomes the CAPM formula. That is why APT is often described as a generalization of CAPM.
What are the weaknesses of APT?
APT does not tell you which factors to use or how many. Analysts must pick factors and estimate their premiums, and different choices can give different answers. CAPM is simpler to apply, which is one reason it is still more common in practice.