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.
APT vs CAPM explained simply
Arbitrage Pricing Theory (APT) explains expected return with several risk factors, each with its own beta and premium: E(R) = R_f + β₁ × RP₁ + β₂ × RP₂ + … CAPM is the special case with one factor, the market. In the example, 3% + 0.8 × 4% + 0.5 × 2% gives 7.2%.
What this APT lesson covers
- 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
APT formula, explained
- 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
How to calculate expected return with APT step by step (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%
APT vs CAPM
| APT | CAPM | |
|---|---|---|
| Number of risk factors | Several (you choose them) | One: the market |
| Betas | One per factor | One |
| Main strength | More flexible and realistic | Simple and widely used |
| Main weakness | Theory doesn't say which factors to use | One factor may miss real risks |
Who picks the factors in APT? David's take
APT gives 7.2% here from two factors, GDP growth and inflation. The maths is easy. The hard part is choosing which factors matter and whether you're measuring them right, and the theory doesn't tell you that. Smart people can reason perfectly with the variables they're given and still be poor at choosing which variables matter. With APT, choosing the variables is the whole job.
From David's concept: High IQ, Wrong Variables. This is David's opinion, alongside the standard textbook answer above.
Harder APT questions
What happens if the inflation premium rises from 2% to 3%?
Expected return = 3% + 0.8 × 4% + 0.5 × 3% = 7.7%. Each factor's beta tells you how sensitive the stock is to that factor's premium.
Why is it called 'arbitrage' pricing theory?
Because if a stock's price implied a return different from what its factor exposures justify, investors could build a riskless arbitrage between portfolios with the same exposures. Prices adjust until that opportunity disappears.
Common APT 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.