How to compute the CAPM Capital Asset Pricing Model: the Sharpe-Lintner-Mossin formula (1964) E(R_i) = R_f + beta_i * (E(R_m) - R_f) determines expected return of asset i as function of risk-free rate R_f, expected market return E(R_m), and asset beta (sensitivity to market fluctuations). Equity risk premium ERP = E(R_m) - R_f represents premium required for assuming market risk. SML (Security Market Line) is graphical representation of linear beta-return relationship. Fundamental model for stock pricing, cost of capital calculation (WACC), DCF valuations, performance attribution. Central tool of Modern Portfolio Theory (MPT) Markowitz 1952 + CAPM 1964.

CAPM formula and components

Fundamental equation: E(R_i) = R_f + beta_i * [E(R_m) - R_f]. Example: R_f = 4.5% (10y Treasury), E(R_m) = 10% (S&P 500 long-term), beta = 1.2 (medium-high risk stock). E(R_i) = 4.5% + 1.2 * (10% - 4.5%) = 4.5% + 6.6% = 11.1%. Investor demands 11.1% to hold the asset.

Beta: systematic risk measure: beta_i = Cov(R_i, R_m) / Var(R_m). beta = 1 stock moves with market. beta 1 cyclical (tech, financial, consumer discretionary). Negative beta: rare (gold, some hedge funds). Computed via OLS regression of historical returns (2-5 years monthly). Bloomberg adjusted beta: 0.67*beta_raw + 0.33 (Blume 1971 mean reversion).

Jensen's alpha: alpha = R_i_realized - E(R_i)_CAPM. Measures outperformance not explained by model. alpha > 0 manager skill or undervalued stock; alpha < 0 underperformance. T-statistic test for significance on sample of 60+ monthly observations. Fama-French (1992) showed CAPM alpha is often absorbed by SMB (size) and HML (value) factors.

Theoretical lines: SML (Security Market Line) plots E(R_i) vs beta_i, intercept R_f, slope ERP. All CAPM-efficient stocks lie on SML; those above are undervalued (alpha+), below overvalued. CML (Capital Market Line) plots E(R) vs sigma for portfolios (not single stocks), slope is market Sharpe ratio.

Model assumptions: rational mean-variance investors, efficient markets, ability to borrow/lend at R_f, no transaction costs, no taxes, homogeneous expectations. Critiques: simplifying assumptions violated in practice (Roll 1977 testability critique), CAPM often fails empirically (low-beta puzzle, value/size effects). Extensions: Fama-French 3-factor (1992), 5-factor (2015), Carhart 4-factor (1997 momentum).

History and context

Harry Markowitz (1952, J. of Finance) introduced Modern Portfolio Theory with "Portfolio Selection" paper, proposing mean-variance optimization. William F. Sharpe (1964, J. of Finance) developed CAPM in "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk", independently from John Lintner (1965, Review of Economics and Statistics) and Jan Mossin (1966, Econometrica). Sharpe and Markowitz won Nobel Prize in Economics 1990 (with Merton Miller). The model was rapidly adopted by financial industry as theoretical benchmark. Eugene Fama (Nobel 2013) and Kenneth French extended the model with three-factor (1992, 1993) adding SMB (small-minus-big size) and HML (high-minus-low book-to-market value), explaining CAPM anomalies. Mark Carhart (1997) added momentum, forming 4-factor model. Fama-French 5-factor (2015) includes profitability and investment. Today financial industry practice: Bloomberg Terminal, FactSet, Refinitiv calculate beta automatically. CFA Institute (Chartered Financial Analyst) includes CAPM in Level I/II/III curriculum. Federal Reserve, SEC, FINRA use CAPM for stress tests, private equity valuation, regulated capital costs (energy FERC, telecom FCC).

Typical sector betas table (developed markets)

• Utilities (regulated power, water): beta 0.3-0.6 (e.g., NextEra 0.5)
• Consumer staples (food, tobacco): beta 0.4-0.7 (Procter&Gamble 0.6)
• Healthcare (pharma): beta 0.5-0.8 (Pfizer 0.7)
• Telecom: beta 0.5-0.9 (Verizon 0.6)
• Energy (oil&gas): beta 1.0-1.5 (ExxonMobil 1.1)
• Industrial (manufacturing): beta 1.0-1.3 (Caterpillar 1.3)
• Materials (chemicals, mining): beta 1.2-1.5 (Dow 1.3)
• Financials (banks, insurance): beta 1.2-1.8 (JPMorgan 1.2)
• Consumer discretionary (auto, luxury): beta 1.2-1.8 (Tesla 2.0)
• Tech (IT, software): beta 1.3-2.0 (NVIDIA 1.8 Q1-2026)
• Real Estate (REITs): beta 0.8-1.2 (Simon Property 1.1)
• Biotech early-stage: beta 1.5-2.5 (high dispersion)
• Risk-free US Treasury 10y: 4.45% (Federal Reserve Q1 2026)
• ERP US (Damodaran 2025): 4.6% mature implied

Worked numerical examples

Example 1 - NextEra Energy defensive utility. R_f = 4.45% (10y Treasury Federal Reserve Q1 2026), E(R_m) S&P500 = 9.5% (1928-2024 historical), beta_NEE = 0.5 (Bloomberg adjusted). E(R) = 4.45% + 0.5*(9.5% - 4.45%) = 4.45% + 2.525% = 6.98%. NEE expected 6.98%/year. 5y historical dividend yield 3% + capital gain 5% = ~8%, modest alpha +1.02%. SEC EDGAR Schedule 13F compliance.

Example 2 - Tesla luxury cyclical. R_f = 4.45%, E(R_m) = 9.5%, beta_TSLA = 2.0. E(R) = 4.45% + 2.0*5.05% = 4.45% + 10.1% = 14.55%. High required return covers cyclical risk. Historical 5y return ~30%/year post-IPO momentum. Strong positive Jensen alpha but Fama-French 3-factor may explain via momentum + growth tilts. NASDAQ100 top constituent.

Example 3 - JPMorgan Chase banking sector. R_f = 4.45%, E(R_m) = 9.5%, beta_JPM = 1.2. E(R) = 4.45% + 1.2*5.05% = 4.45% + 6.06% = 10.51%. US banks sensitive to Fed rate curves: historical beta fluctuates 1.0-1.8 with monetary regime. Federal Reserve DFAST stress test 2024-2026 incorporates these returns for capital assessment.

Example 4 - corporate WACC ExxonMobil for DCF valuation. XOM capital structure 25% debt + 75% equity. After-tax cost of debt kd = 5%*(1-0.21 federal tax)= 3.95%. Cost of equity ke via CAPM: R_f=4.45%, ERP=5.05%, unlevered beta 0.9 -> levered 1.05 with D/E 0.33. ke = 4.45% + 1.05*5.05% = 9.75%. WACC = 0.25*3.95% + 0.75*9.75% = 0.99% + 7.31% = 8.30%. Discount rate for FCFF DCF. SEC Form 10-K disclosure.

Example 5 - regulated utility FERC rate of return. FERC Order 569 sets allowed return on equity for natural gas pipelines: rate of return regulated. Unlevered beta sector 0.4-0.5 (asset-intensive, low risk regulated revenue). R_f Treasury 10y 5y average = 3.5%. ERP regulated = 5.5%. WACC real post-tax = 6.0% (Order 569-A 2020). Williams Companies, Kinder Morgan apply for pipeline tariff pricing.

Limits and considerations

1. Historical beta unstable: use minimum 60 monthly observations (5 years) or optimal 24 months (Blume adj).
2. Single-factor: ignores SMB, HML, momentum (Fama-French 3-5 factor better predictors).
3. Roll critique 1977: market portfolio not observable (S&P500 and Russell 3000 are imperfect proxies).
4. Low-beta puzzle: low-beta stocks historically outperform CAPM (Frazzini-Pedersen 2014).
5. R_f choice: 1y (T-Bill) for short-term, 10y (Treasury) for long DCF matching, German Bund for true zero-risk.
6. ERP choice: historical (1928-2024 ~5.05% US) vs implied (forward Damodaran 2025: 4.6%).
7. Liquidity: illiquid stocks underestimate beta (price staleness), Dimson adjustment.
8. Alternative models: Fama-French, APT (Ross 1976), CCAPM (Breeden 1979), Black-Litterman.
9. ESG factor: BlackRock 2024 incorporates sustainability as additional factor.
10. Emerging markets: additional country risk premium Damodaran methodology.

Common errors

1. Mixing nominal R_f with real return (deflate with expected inflation).
2. Beta computed on total returns vs excess returns: subtle but important difference.
3. Confusing CAPM with WACC: CAPM gives equity cost, WACC = equity+debt combination.
4. Using unlevered beta for equity (wrong): need Hamada (1972) relevering for capital structure.
5. Extrapolating historical beta beyond 5 years: business cycles change sensitivity.
6. Confusing statistical with economic alpha: 1% alpha may be insignificant (wide CI).
7. Computing ERP only on market history: emerging requires additional country premium (Damodaran).
8. Applying CAPM to illiquid stocks without corrections (biased beta).
9. Ignoring risk-free curve: for 30y cash flow use 30y rate, not 10y.
10. Using CAPM for derivative valuation (option pricing requires Black-Scholes-Merton).

Practical applications

1. Equity research: DCF target price Goldman Sachs, Morgan Stanley, JPMorgan.
2. Corporate WACC: PwC, Deloitte, EY transaction services.
3. Regulatory rate setting: FERC energy, FCC telecom, surface transportation board.
4. Asset management: BlackRock, Vanguard, State Street performance attribution.
5. Pension funds: CalPERS, NY State Common, ABP benchmark with CAPM.
6. Stress tests: Federal Reserve DFAST, European Banking Authority EBA 2024-2026.
7. M&A valuation: Goldman Sachs, Morgan Stanley fairness opinions.
8. Insurance: AIG, MetLife capital risk calculation.
9. CFA curriculum: Level I-II-III asset valuation, portfolio management.
10. Academic research: Wharton, Booth Chicago, MIT Sloan finance.

Support

Questions: info@calcoi.com. Educational tool for asset pricing. For professional applications consult Sharpe 1964 J Finance, Markowitz 1952 J Finance, Fama-French 1992-2015 J Financial Economics, Damodaran "Investment Valuation" 4th ed (Wiley 2024), Hull "Options Futures Other Derivatives" 11th ed (Pearson 2021).

Updated July 2026