📈 CAPM — Capital Asset Pricing Model

Definition: CAPM describes the relationship between systematic risk (beta) and expected return for assets. It is used to price risky securities and compute the cost of equity in WACC.

Developed by: William Sharpe (Nobel Prize 1990), John Lintner, Jan Mossin Key courses: Wharton FNCE 611, Booth BUSF 35000, HBS Finance I

📐 The Formula

$r_{e} = r_{f} + β \cdot (r_{m} - r_{f})$

Term	Meaning	Typical Value
`re`	Expected return on asset	What we solve for
`rf`	Risk-free rate	~4–5% (10-yr US Treasury)
`β`	Beta — systematic risk	1.0 = market average
`(rm − rf)`	Equity Risk Premium (ERP)	~5–6% historically

🔑 Understanding Beta (β)

Beta measures how much a stock moves relative to the market:

Beta	Interpretation
β = 0	No correlation to market (e.g. T-bills)
β = 0.5	Half as volatile as market
β = 1.0	Moves in lockstep with market
β = 1.5	50% more volatile than market
β = 2.0	Twice as volatile (e.g. small-cap tech)
β < 0	Inversely correlated (e.g. gold sometimes)

High beta stocks: Technology, startups, commodities
Low beta stocks: Utilities, consumer staples, REITs (defensive)

🎯 The Security Market Line (SML)

The SML plots expected return vs. beta for all assets:

On the SML: Fairly priced
Above the SML: Undervalued (higher return than CAPM predicts) → Buy
Below the SML: Overvalued → Sell

This is the foundation of alpha generation in active portfolio management.

📊 CAPM in Practice: Computing Cost of Equity

Apple (hypothetical):

β = 1.2 (from financial data providers)
rf = 4.5% (current 10-year Treasury)
ERP = 5.5% (Damodaran estimate)

$r_{e} = 4.5% + 1.2 \times 5.5% = 11.1%$

→ This 11.1% feeds into WACC as the cost of equity component.

🔬 Levered vs. Unlevered Beta

When comparing companies with different capital structures, use the Hamada equation to lever/unlever beta:

$β_{L} = β_{U} \times [1 + (1 - T) \times \frac{D}{E}]$

Process:

Find comparable companies’ levered betas
Unlever each beta to remove debt effects
Average unlevered betas
Re-lever at your company’s target capital structure

⚠️ CAPM Limitations

Limitation	Issue
Single-factor model	Only beta matters for returns (empirically untrue)
Beta is backward-looking	Historical beta ≠ future beta
Normal distribution assumed	Returns are fat-tailed in reality
Market portfolio unobservable	We use S&P 500 as a proxy
Ignores liquidity, size effects	Fama-French adds size + value factors

Fama-French 3-Factor Model addresses some limitations: $r = r_{f} + β_{m} (r_{m} - r_{f}) + β_{s} \cdot SMB + β_{h} \cdot H M L$

🔗 Connected Concepts

WACC — CAPM’s output is the cost of equity input
Beta and Systematic Risk — deeper dive into β
Efficient Market Hypothesis — the theoretical backdrop
DCF Valuation — uses WACC (which uses CAPM)
Portfolio Theory — Markowitz foundation for CAPM

🏫 School Context

Booth: Fama-French originated here; CAPM taught with heavy critique
Wharton: Rigorous derivation; applied to real portfolio construction
HBS: Emphasizes practitioner judgment — e.g., which ERP to use

← 📊 Finance MOC | Related: WACC · Beta and Systematic Risk · DCF Valuation

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