CAPM and the Security Market Line

The CAPM equation

In equilibrium, every investor holds the market portfolio. So the risk that matters for any single asset $i$ is its contribution to the market portfolio’s risk — its covariance with the market.

That intuition produces the Capital Asset Pricing Model:

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

Three pieces:

• $R_f$ — risk-free rate (Treasury yield matching the horizon).
• $E[R_m] - R_f$ — market risk premium. Compensation per unit of market risk. Historically ~5-7% for US equities.
• $\beta_i$ — beta of asset $i$. How much asset $i$ moves when the market moves.

A beta of 1.0 means the asset moves one-for-one with the market. A beta of 0 means the asset is uncorrelated with the market (risk-free in the systematic sense). A beta of 2.0 means the asset is twice as volatile as the market in the systematic dimension.

Where beta comes from

Formally:

$$\beta_i = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)}.$$

In practice: run a regression of asset $i$‘s excess return ($R_i - R_f$) on the market’s excess return ($R_m - R_f$). The slope coefficient is beta. Use weekly or monthly data over 3-5 years. Most data providers (Bloomberg, FactSet, Yahoo Finance) publish estimated betas for any traded security.

Typical industry betas (US equities):

Industry	Typical β
Utilities	0.4-0.7
Consumer staples	0.5-0.8
Healthcare	0.8-1.0
Industrials	1.0-1.2
Financials	1.0-1.3
Technology	1.2-1.5
Highly leveraged / cyclical	1.5-2.5

The Security Market Line (SML)

CAPM plotted in $(\beta, E[R])$ space is a straight line — the SML:

• Y-intercept: $R_f$.
• Slope: market risk premium $E[R_m] - R_f$.

Every fairly-priced asset sits on the SML.

Risk-free rate Rf: 4.00%Market risk premium: 6.0%

Slope of SML = MRP = 6.0%

Asset	β	Observed	CAPM E[R]	α
Treasury 10Y	0.05	4.5%	4.3%	+0.2%
Utility ETF	0.55	7.5%	7.3%	+0.2%
S&P 500	1.00	10.5%	10.0%	+0.5%
Tech ETF	1.30	15.0%	11.8%	+3.2%
Levered HF	1.80	14.0%	14.8%	-0.8%

Points above the SML have positive α (mispriced cheap / outperforming). Below the line ⇒ negative α. In a CAPM-efficient market, α = 0 for every asset on average.

The scatter plot in the viz shows several example assets with observed returns plotted against their betas. Three patterns:

• Treasuries (β ≈ 0): observed return near $R_f$, on the line.
• S&P 500 ETF (β = 1): observed return equal to $R_f +$ market premium, on the line.
• Levered hedge fund (β = 1.8): observed return below the line, meaning negative alpha. The high-beta strategy hasn’t been earning its risk premium.

Alpha: the deviation from CAPM

For any asset $i$, alpha is the difference between observed return and CAPM’s prediction:

$$\alpha_i = R_i - \big[R_f + \beta_i (R_m - R_f)\big].$$

• $\alpha > 0$: asset outperformed what CAPM predicts (above the SML). Either a skillful active manager, or a mispriced asset, or CAPM is missing a risk factor.
• $\alpha < 0$: underperformed. Same three possibilities in reverse.
• $\alpha = 0$: exactly on the SML. CAPM-fair pricing.

Active managers exist to deliver positive alpha. The empirical record is sobering: most don’t, after fees.

What CAPM gets right

CAPM is conceptually clean, requires few inputs, and gives intuitive results. The risk-free rate is observable; the market risk premium and beta are estimable from data. For most introductory and undergraduate work — including this course — CAPM is the workhorse model for cost of equity.

What CAPM gets wrong

Decades of empirical work have shown that asset returns aren’t fully explained by beta. Three robust patterns CAPM doesn’t predict:

1. Size effect: small-cap stocks earn higher returns than CAPM says they should.
2. Value effect: stocks with high book-to-market ratios (value stocks) earn higher returns than growth stocks at similar beta.
3. Momentum: past winners keep winning over 3-12 month horizons.

These motivated factor models that add more risk dimensions (Fama-French three-factor, five-factor, momentum). We cover those in the last lesson of this unit.

Practical procedure: cost of equity via CAPM

To estimate the cost of equity for a firm or project:

1. $R_f$: yield on a Treasury matching the horizon of cash flows. For a 5-10 year DCF, use the 10-year Treasury yield. (~4.2% in mid-2026.)

2. Market risk premium: typically 5-6% for the US, based on the long-run historical excess return of stocks over T-bills. Survey-based estimates range 4-7%; pick a reasonable middle.

3. Beta: pull from a data provider, or estimate via regression on 60 months of returns. For a private firm, use the average beta of public comparables (after unlevering and re-levering for capital structure — covered in Unit 5).

4. Plug in: $R_f + \beta \times \text{MRP}$.

Example. A tech firm with beta 1.4, $R_f = 4.2\%$, market premium 6%:

$$r_E = 0.042 + 1.4 \times 0.06 = 0.042 + 0.084 = 12.6\%.$$

This is the rate you’d use to discount the firm’s equity cash flows in a DCF.