CAPM — risk and return in one equation

The economic story

The Capital Asset Pricing Model (Sharpe 1964, Lintner 1965, Mossin 1966 — sometimes called Sharpe-Lintner CAPM) gives the simplest "right answer" for what a stock's expected return should be:

$E[r_i] = r_f + \beta_i \cdot (E[r_m] - r_f)$

Components:

• $E[r_i]$ — expected return on asset $i$
• $r_f$ — risk-free rate (e.g., 1-year Treasury yield)
• $E[r_m] - r_f$ — market risk premium (the equity premium)
• $\beta_i$ — asset's sensitivity to market

The logic: you should be compensated only for risk you can't diversify away.

If you hold a well-diversified portfolio, each stock's idiosyncratic risk (Apple-specific news) cancels out. Only the market risk (the part correlated with everything else) remains. So in equilibrium, the market only pays a risk premium for the un-diversifiable part — which is beta.

Why this is beautiful (and why it's wrong)

Beautiful because it gives a clean prediction:

• A stock's expected return depends only on its beta.
• Two stocks with the same beta should have the same expected return, regardless of any other property (industry, size, valuation).
• High-beta stocks should outperform low-beta stocks by the market risk premium times the beta gap.

Wrong in practice:

• Empirically, low-beta stocks actually outperform what CAPM predicts (the "low-beta anomaly," Frazzini & Pedersen 2014).
• High-beta stocks underperform predictions.
• Stocks with the same beta but different sizes (small vs. large cap) have systematically different returns — pure CAPM says this shouldn't happen.

Fama and French (1992) put a fork in single-factor CAPM by showing that size and book-to-market explain cross-sectional returns better than beta alone. This is the launching point for multi-factor models (next several lessons in D2).

But CAPM is still the right baseline — every more-sophisticated model is a correction to it.

How to use CAPM in practice

Three practical applications:

1. Hurdle rate for evaluating a stock

What return is reasonable to expect from a stock?

$E[r] = r_f + \beta \cdot \text{MRP}$

With $r_f = 4\%$, MRP = 6%, $\beta = 1.2$: expected return $= 4\% + 1.2 \cdot 6\% = 11.2\%$.

If you believe the stock will return more than this, it's underpriced (positive alpha). If less, overpriced.

2. Required return for capital budgeting

Companies use CAPM to set the discount rate for project NPV calculations:

$\text{NPV} = \sum_t \frac{\text{cash flow}_t}{(1 + r_\text{CAPM})^t}$

Higher business risk (higher $\beta$) means higher required return means lower NPV for the same cash flows.

3. Decomposing strategy returns

For a strategy returns $r_s$ regressed on market: $r_s = \alpha + \beta r_m + \varepsilon$.

• $\alpha > 0$ with $|\beta|$ reasonable: real edge (subject to all our hypothesis-testing caveats).
• $\alpha \approx 0$, $\beta = 1$: you're effectively holding the market.
• $\alpha < 0$, $\beta > 1$: you're paying for leveraged market exposure (worse than buying SPY on margin).

The market risk premium — how big is it really?

The historical equity risk premium (US, 1928–present): roughly 5–6% per year. Globally and over longer windows: 3–5%.

This is the biggest single edge available to long-term investors. Compound 5% per year for 30 years and you have ~4.3× your money in real terms.

Forward-looking estimates (Damodaran, Asness, others) suggest the future MRP might be lower (3–4%) than historical (5–6%) due to high current valuations. Reasonable people disagree by 2–3 percentage points. The right answer is "use a range and stress-test."

Why CAPM isn't enough

Fama-French (1992) showed that:

1. Size effect — small caps earned more than CAPM predicted in the historical data FF studied (though this premium has weakened substantially since publication).
2. Value effect — high book-to-market ("value") stocks earn ~5% per year more than CAPM predicts.

This led to the Fama-French 3-Factor model: market + size (SMB) + value (HML). Later extended to 5 factors (adding profitability and investment quality). We'll meet each in subsequent lessons.

The pattern is: CAPM is a useful baseline. Real-world expected returns are explained by multiple factors. The whole field of "factor investing" / "smart beta" is built on this.

The most important practical takeaway

Always benchmark a strategy's return against the CAPM prediction, not against zero. Example: with $r_f = 4\%$ and a 12% market return (MRP = 8%), a strategy earning 15% per year with $\beta = 1.5$ has CAPM-required return $4\% + 1.5 \cdot 8\% = 16\%$ — its alpha is −1% despite the impressive-looking headline. It's just leveraging beta inefficiently. Most retail strategies fall into this trap.

We'll see this rigorously in D4 (backtesting methodology) when we discuss benchmark choice.

Try it

Turn the CAPM equation into code:

Predict before the next lesson

Tomorrow we'll look at regression diagnostics — when does OLS lie to you? Predict:

• If two of your predictors are perfectly correlated, what happens to their estimated coefficients?
• What does a "fat-tailed" residual distribution imply about hypothesis tests on the regression?