Lesson 6 of 6 · All lessons in this module
  1. Return-generating models, the market model and betaVideo lesson
  2. The CAPM: assumptions, the SML and its limitsVideo lesson
  3. Estimating beta for the cost of equity
  4. Industry betas: unlevering and relevering
  5. The market risk premium and the country risk premium
  6. APT and the four-factor model for the cost of equity

This lesson is part of the 2027 curriculum. You are following the 2026 curriculum, where it is not taught in this form. Switch if you are sitting the exam under the 2027 curriculum.

Lesson 6 of 6 · 14 min

APT and the four-factor model for the cost of equity

Multi-factor models price several sources of systematic risk, so a stock's cost of equity is the risk-free rate plus the sum of each factor beta times that factor's premium, which can be well above or below the CAPM figure.

In short

  • APT: E(ri)=rf+βi,1E(f1)+⋯+βi,kE(fk)E(r_i) = r_f + \beta_{i,1}E(f_1) + \dots + \beta_{i,k}E(f_k). It does not name the factors or their number, and the market need not be one of them.
  • Factors can be built from stock market data, macroeconomic data and company accounting data. Research has found hundreds; many are likely data mining, and most believe a few factors capture the relevant systematic risks.
  • Four-factor model: market, SMB (small minus big), HML (high minus low book-to-market: value minus growth), UMD (up minus down: winners minus losers). SMB, HML and UMD are zero-investment long-short portfolios.
  • The average stock has a market beta of 1 and zero betas on the other factors; negative size, value and momentum betas are common.
  • Annualise monthly premiums (× 12) before use. A stock's market beta in a multi-factor model is unlikely to equal its single-factor beta, and the omitted exposures can push the CAPM figure up or down.

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