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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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APT and the four-factor model for the cost of equity · The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models