Capital Asset Pricing Model
The Capital Asset Pricing Model (CAPM) is an equilibrium asset pricing framework that describes the expected return of an asset as a linear function of its systematic risk (beta) relative to the market portfolio, establishing the Security Market Line as the fundamental risk-return trade-off.
Key takeaways
- CAPM: E(R_i) = R_f + β_i × (E(R_m) − R_f), where β_i measures the asset's co-movement with the market portfolio.
- Beta above 1.0 implies the asset is more volatile than the market; beta below 1.0 implies lower systematic risk.
- CAPM assumes investors hold the mean-variance efficient market portfolio; all idiosyncratic risk is diversifiable and therefore unpriced.
- Jensen's alpha measures the excess return above CAPM-implied return; a positive alpha suggests outperformance after adjusting for systematic risk.
- Empirical tests reveal significant CAPM anomalies, including the size effect, value effect, and low-volatility anomaly, motivating multi-factor models.
Explanation
Developed independently by William Sharpe (1964), John Lintner (1965), and Jan Mossin (1966), CAPM builds on Harry Markowitz's mean-variance framework to derive equilibrium asset prices. The key insight is that in a competitive market where all investors hold mean-variance efficient portfolios, the only risk that commands a premium is systematic (market) risk — risk that cannot be eliminated through diversification. Idiosyncratic (specific) risk is diversifiable and therefore unpriced.
The CAPM equation is: E(R_i) = R_f + β_i × ERP, where R_f is the risk-free rate, β_i = Cov(R_i, R_m) / Var(R_m) is the asset's market beta, and ERP = E(R_m) − R_f is the equity risk premium. All assets plot on the Security Market Line (SML), a straight line from the risk-free rate through the market portfolio in expected return-beta space. Assets above the SML are underpriced (positive alpha); assets below are overpriced (negative alpha).
The model relies on stringent assumptions: investors are rational mean-variance optimizers with homogeneous expectations, markets are frictionless with no taxes or transaction costs, investors can borrow and lend at the risk-free rate, and a single-period investment horizon. These assumptions are clearly violated in practice, which explains much of the model's empirical failure. However, CAPM remains the most widely used pricing model in corporate finance for estimating the cost of equity capital.
Empirical tests of CAPM, including the seminal Fama-French (1992) study, revealed that the cross-sectional relationship between beta and average returns is much flatter than CAPM predicts. Small-cap stocks earn returns above CAPM predictions (size premium), and high book-to-market (value) stocks earn excess returns (value premium), suggesting systematic risk factors beyond the market beta. These findings motivated the Fama-French three-factor model and subsequently the Carhart four-factor model.
Despite its limitations, CAPM provides indispensable conceptual tools: the risk-free rate as the minimum return for time value of money, the ERP as compensation for bearing market risk, and beta as a measure of systematic exposure. In practice, unlevered beta is used to estimate the cost of equity for discounted cash flow valuations, with relevered beta applied to match the actual capital structure. The weighted average cost of capital (WACC) integrates the CAPM-derived cost of equity with the cost of debt.
Formula
E(R_i) = R_f + β_i × (E(R_m) − R_f); β_i = Cov(R_i, R_m) / Var(R_m)
Example
An analyst is valuing an industrial manufacturer with an equity beta of 1.3, using a risk-free rate of 4.5% (10-year Treasury yield) and an equity risk premium of 5.5%. CAPM implies a cost of equity of: 4.5% + 1.3 × 5.5% = 11.65%. If the company's actual return over the past year was 14.2%, Jensen's alpha equals 14.2% − 11.65% = 2.55%, suggesting the manager generated 255 basis points of risk-adjusted excess return. This alpha is then subjected to statistical significance testing to determine whether it is attributable to skill or luck.
Related terms
Alpha Basis Beta Cap Capital Structure Carhart Four Factor Model Cost Of Debt Cost Of Equity Discounted Cash Flow Diversification Dynamic Asset Allocation Equity