Capital Asset Pricing Model (CAPM)
Overview
CAPM (Sharpe, 1964; Lintner, 1965) establishes a linear relationship between systematic risk and expected return. The model states that the expected return on any asset equals the risk-free rate plus a premium for bearing market risk, scaled by the asset's beta.
When to Use
- Estimating required rate of return for equity valuation
- Calculating cost of equity in WACC
- Comparing asset risk via beta
- Evaluating portfolio performance against the Security Market Line (SML)
When NOT to Use
- When the asset has significant exposure to size, value, or other factors beyond market risk
- For illiquid or non-traded assets where beta estimation is unreliable
- When market portfolio proxy is questionable (Roll's critique)
Assumptions
IRON LAW: CAPM only prices SYSTEMATIC risk — diversifiable (unsystematic)
risk earns NO premium. An asset's expected return depends solely on its
beta with the market portfolio.Key assumptions:
- Investors are mean-variance optimizers with homogeneous expectations
- A risk-free asset exists for unlimited borrowing and lending
- Markets are frictionless — no taxes, transaction costs, or short-selling constraints
- All assets are infinitely divisible and publicly traded
Methodology
Step 1 — Identify Inputs
- Risk-free rate (Rf): government bond yield matching investment horizon
- Market return E(Rm): historical average or forward-looking estimate
- Beta: regression of asset returns against market returns
Step 2 — Compute Expected Return
E(Ri) = Rf + Bi x (E(Rm) - Rf). See references/derivation.md for the derivation from mean-variance optimization.
Step 3 — Plot on Security Market Line
Assets above the SML are undervalued (positive alpha); below are overvalued (negative alpha).
Step 4 — Interpret and Decide
- Beta > 1: amplifies market moves, higher risk-higher expected return
- Beta < 1: dampens market moves, lower risk-lower expected return
- Beta = 0: returns equal the risk-free rate
Output Format
⚠️ Decimal vs percent: When passing values to or from the bundled script, all rates (risk_free,market_return,beta_contribution,expected_return,alpha) are decimals —0.05means 5%, NOT5.0. The narrative report below renders them as percentages for humans, but never mix the two in the same JSON object.
## CAPM Analysis: [Asset / Portfolio]
### Inputs
| Parameter | Value | Source |
|-----------|-------|--------|
| Risk-free rate (Rf) | x% | [source] |
| Market return E(Rm) | x% | [source] |
| Beta | x.xx | [estimation method] |
### Expected Return
- E(Ri) = Rf + B x (E(Rm) - Rf) = x%
### SML Assessment
- Alpha = Actual return - Expected return = x%
- Interpretation: [undervalued / overvalued / fairly priced]
### Limitations in This Context
- [Note any assumption violations]Gotchas
- Beta is backward-looking; future beta may differ from historical estimates
- Choice of market proxy matters enormously (Roll's critique, 1977)
- CAPM assumes a single risk factor; empirical evidence supports multi-factor models
- Risk-free rate selection (T-bill vs T-bond) affects results significantly
- Beta estimation is sensitive to return frequency (daily vs monthly) and sample period
- CAPM fails to explain the low-beta anomaly (low-beta stocks outperform predictions)
Scripts
| Script | Description | Usage |
|---|---|---|
scripts/capm.py | Compute CAPM expected return and alpha | python scripts/capm.py --help |
Run python scripts/capm.py --verify to execute built-in sanity tests.
References
- Sharpe, W. (1964). Capital asset prices. *Journal of Finance*, 19(3), 425-442.
- Lintner, J. (1965). The valuation of risk assets. *Review of Economics and Statistics*, 47(1), 13-37.
- Roll, R. (1977). A critique of the asset pricing theory's tests. *Journal of Financial Economics*, 4(2), 129-176.