The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models

A portfolio manager needs a required return for a single stock to discount its cash flows. Three workhorse models compete: the capital asset pricing model (CAPM), with one theoretical factor; the market model, with one empirical factor; and multi-factor models (arbitrage pricing theory (APT) and its descendants). Knowing which tool answers which question is the exam's core test.

CAPM says one thing: in equilibrium, an asset's expected return equals the risk-free rate plus a premium for the systematic (non-diversifiable) risk it adds to a fully diversified portfolio. That risk is measured by beta.

$$E(R_i) = R_f + \beta_i \, [E(R_m) - R_f]$$

Here, $i$ identifies the asset and $m$ the market portfolio. $R_i$ and $R_m$ are their returns, and $E(\cdot)$ denotes an expected value. $R_f$ is the risk-free rate, and $\beta_i$ is the asset's beta, its sensitivity to market returns. $E(R_m) - R_f$ is the market risk premium.

Beta is the scaling factor the CAPM applies to the market risk premium when it estimates a required return on equity.

Common mistakes

• Confusing CAPM with the market model. CAPM is an equilibrium theory predicting expected returns with no alpha. The market model is an empirical regression of realized returns with a free alpha intercept. Trap: using NorthStar's market model estimate of 11.40%, which carries a historical alpha, as its required return instead of the CAPM's 10.0%.
• Multiplying beta by the market return instead of the premium. CAPM scales the equity risk premium $E(R_m) - R_f$, not the whole market return. Trap: computing $R_f + \beta E(R_m)$ instead of $R_f + \beta[E(R_m) - R_f]$, which overstates the required return by $\beta R_f$. For NorthStar, $4.0\% + 1.20 \times 9.0\% = 14.8\%$ instead of 10.0%.
• Using the volatility ratio as beta. Beta is $\rho \, \sigma_i / \sigma_m$, not $\sigma_i / \sigma_m$. Trap: NorthStar's 30% / 15% gives 2.00 and a required return of 14.0%, because it drops the 0.60 correlation and prices firm-specific noise.

Bottom line

• CAPM: $E(R_i) = R_f + \beta_i [E(R_m) - R_f]$. Equilibrium, one factor (market risk), assumes diversified investors, prices only systematic risk.
• Market model: $R_i = \alpha_i + \beta_i R_m + \epsilon_i$, so $E(R_i) = \hat{\alpha}_i + \hat{\beta}_i E(R_m)$. It matches CAPM only when the intercept equals $R_f(1 - \beta_i)$; for a required return, keep its beta and use CAPM.
• Beta = Cov / Var = $\rho_{i,m}\,\sigma_i/\sigma_m$, estimated as the slope of the market model regression. Beta > 1 means more systematic risk than the market.
• APT: multi-factor, no-arbitrage. The theory does not specify the factors, the analyst chooses them empirically (macro or fundamental).

Exam shortcut

For CAPM vs. market model: "CAPM forecasts (no alpha); market model fits (with alpha)." When a question gives a correlation and two standard deviations, compute beta as $\rho \, \sigma_i / \sigma_m$ first; the plain volatility ratio is a planted answer. For APT, remember the theory gives you the equation but never the factors, the analyst picks. For Carhart, memorize MSV-M: Market, Size, Value, Momentum.

The full lesson (about 3,338 words, 22 min read) adds 3 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• CAPM market model and factor models

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