How does Arbitrage Pricing Theory differ from CAPM, and how do you apply a multifactor model?

APT and CAPM are both asset pricing models, but they're built on fundamentally different foundations. Let's compare them carefully.

CAPM Foundation:

• Built on mean-variance optimization and market equilibrium
• Every investor holds the market portfolio
• Single risk factor: the market return
• Strong assumptions about investor behavior

APT Foundation:

• Built on the law of one price (no arbitrage)
• Does NOT require all investors to hold the market portfolio
• Multiple systematic risk factors
• Fewer assumptions about investor behavior

The APT Model:

E(Ri) = Rf + b1 x RP1 + b2 x RP2 + ... + bk x RPk

Where bi = sensitivity (factor loading) of asset i to factor k, and RPk = risk premium for factor k.

How to Choose Factors:

APT doesn't specify which factors to use — that's both its strength (flexibility) and weakness (ambiguity). Common approaches:

1. Macroeconomic factors (Chen, Roll, Ross): GDP growth surprise, inflation surprise, term structure changes, credit spread changes, industrial production
2. Statistical factors (principal components): derived from return data without economic interpretation
3. Fundamental factors: P/E ratio, size, book-to-market

Worked Example:

Crestwood Capital uses a 3-factor APT model:

Risk-free rate = 4.0%

E(Ri) = 4.0% + 3.60% + (-1.20%) + 1.00% = 7.40%

The Arbitrage Argument:

If an asset's actual expected return differs from what the APT model implies, an arbitrage opportunity exists. Investors can construct a factor-mimicking portfolio with the same factor exposures but different expected return, creating a risk-free profit. This trading pressure pushes prices until the arbitrage vanishes.

Key Difference in Testability:

CAPM is testable (you know the factor — the market), but the market portfolio is unobservable (Roll's critique). APT doesn't specify factors, so it's untestable unless you commit to a specific factor set.

Exam tip: CFA Level II frequently asks you to calculate expected returns using a multifactor model and then determine if an asset is overvalued or undervalued relative to the model's prediction. If E(R) from APT is 7.40% but the asset's forecast return is 9.0%, the asset is undervalued (alpha = +1.60%).

Deepen your understanding of factor models in our CFA Level II portfolio management course on AcadiFi.