CAPM and Beta

The Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM), developed by William Sharpe in 1964, is one of the most important — and most criticized — models in finance. It answers a fundamental question: if investors can diversify away idiosyncratic risk for free, what risk should be compensated with higher expected returns?

CAPM says: only market risk (also called systematic risk or undiversifiable risk) is rewarded. The expected return of any asset is:

E[R_i] = R_f + β_i × (E[R_m] − R_f)

Where:

• R_f = risk-free rate (e.g., 5.25% on 3-month T-bills)
• E[R_m] = expected market return (~10% historically for S&P 500)
• E[R_m] − R_f = equity risk premium — the extra return for taking equity risk (~5–6%)
• β_i = beta — a stock's sensitivity to market movements

Beta: Market Sensitivity

Beta measures how much a stock moves for a 1% move in the market:

β = Cov(R_i, R_m) / Var(R_m)

• β = 1.0: Moves exactly with the market. Average S&P 500 stock.
• β > 1.0: Amplified market sensitivity. Tech stocks often have β = 1.3–1.8. When the market rises 10%, the stock rises ~15%. But also falls more.
• β < 1.0: Defensive — less sensitive to market swings. Utilities, consumer staples often have β = 0.4–0.7.
• β < 0: Moves opposite the market. Gold, some volatility products. Rare for stocks.

You can estimate beta by regressing a stock's returns against market returns over 1–5 years of daily or weekly data. This is ordinary least squares (OLS) linear regression — the slope is beta, the intercept is alpha.

Alpha: The Holy Grail

In the CAPM regression:

R_i = α + β × R_m + ε

Alpha (α) is the intercept — the return unexplained by market exposure. In CAPM theory, alpha should be zero in an efficient market: all excess returns are just compensation for beta. In practice, investors hunt for positive alpha — returns above what beta predicts.

Genuine alpha is rare and hard to sustain. Most of what looks like alpha (a fund beating the S&P 500 for 3 years) is often just factor exposure (small-cap tilt, value tilt), luck, or fee-driven illusions. Academic research suggests persistent alpha exists only for a small fraction of managers, and it's hard to identify in advance.

Limitations of CAPM

CAPM makes heroic assumptions: all investors have the same beliefs, can borrow at the risk-free rate, hold diversified portfolios, and only care about mean and variance. None of these are true. Empirical tests have found that:

• Low-beta stocks have historically outperformed what CAPM predicts ("low-volatility anomaly")
• Value stocks (low price-to-book) and small-cap stocks earn higher returns than CAPM predicts — the Fama-French factors
• Momentum (stocks that went up continue going up for 3–12 months) is a persistent anomaly

These empirical failures led to multi-factor models (Fama-French 3-factor, Carhart 4-factor, Fama-French 5-factor) that extend CAPM. But CAPM remains the starting point for thinking about risk and return.

Practical Uses of Beta

• Portfolio construction: A portfolio of high-beta stocks will amplify market swings. During bull markets, great. During bear markets, devastating. Knowing your portfolio's beta lets you predict drawdowns.
• Hedging: To reduce market exposure, short futures on the S&P 500 equal to your portfolio's dollar beta.
• Cost of capital: Companies use CAPM to estimate their cost of equity for capital budgeting (should we invest in this project?)