What are the key differences between CAPM and APT, and when would you use one over the other?

CAPM and APT are both equilibrium asset pricing models, but they differ fundamentally in their assumptions, number of risk factors, and practical applications.

CAPM (Capital Asset Pricing Model)

E(Rᵢ) = Rf + βᵢ × [E(Rm) - Rf]

• Single factor: Market portfolio is the only systematic risk factor
• Assumptions: Mean-variance optimization, homogeneous expectations, no taxes, unlimited borrowing at Rf
• Beta measures sensitivity to the market factor only

APT (Arbitrage Pricing Theory)

E(Rᵢ) = Rf + β₁λ₁ + β₂λ₂ + ... + βₖλₖ

• Multiple factors: Returns are driven by K systematic factors
• Assumptions: No arbitrage, factor structure in returns (much weaker assumptions than CAPM)
• Betas measure sensitivity to each factor; lambdas (λ) are factor risk premia

Key Differences

Practical Example

Glenfield Asset Management uses both models for its equity portfolio:

• CAPM: Estimates the cost of equity for Morrow Technologies as 2.5% + 1.3 × 6.0% = 10.3%
• APT (3-factor): Uses market, size, and value factors:

E(R) = 2.5% + 1.1 × 5.5% + 0.6 × 2.8% + 0.4 × 3.2% = 11.01%

The APT produces a different estimate because it captures risk dimensions (size, value) that CAPM lumps into a single beta.

When to Use Each

• CAPM: Cost of equity estimation, simple performance attribution, when you need a single-number required return
• APT: Portfolio risk decomposition, when you believe multiple factors drive returns, when CAPM beta doesn't fully explain return variation

Roll's Critique: A fundamental problem with CAPM is that the true market portfolio (all assets globally) is unobservable. Any proxy (like the S&P 500) may lead to incorrect inferences about beta and the risk premium. APT avoids this problem because it doesn't require specifying the market portfolio.

For the FRM exam, know the theoretical differences, be able to calculate expected returns under both models, and understand Roll's critique. Check our FRM practice materials for worked problems.