CAPM Extended

CAPM Formula

E(Ri) = Rf + βi(E(Rm) - Rf); expected return = risk-free rate + market premium × beta.

Meaning of Beta

Measures a stock’s sensitivity to market movements; β > 1 = more volatile, β < 1 = less volatile.

Interpretation of CAPM

Only systematic (market) risk is priced; unsystematic (firm-specific) risk can be diversified away.

Market Risk Premium

(E(Rm) - Rf); the additional return investors demand for holding the market portfolio instead of risk-free assets.

Long-Short Strategy

Objective: exploit difference between low P/E (value) and high P/E (growth) stocks.

How Long-Short Works

Short-sell high P/E stocks, use proceeds to buy low P/E stocks, rebalance monthly.

Expected Return of Strategy

E(Rstrategy) = (βLowP/E - βHighP/E) × (E(Rm) - Rf)

Key Insight

Value stocks outperform growth stocks even though betas are similar → CAPM can’t explain it fully.

Beta of Portfolio

Weighted average of component betas; measures total market exposure.

Meaning of Similar Betas

If both long and short portfolios have similar betas, CAPM predicts zero excess return → anomaly evidence.

Fama-French 3-Factor Model

E(Ri) = Rf + βi(E(Rm) - Rf) + Si(SMB) + Hi(HML)

SMB (Small Minus Big)

Size factor; small-cap stocks outperform large-cap stocks on average.

A negative SMB beta means the stock behaves like a large-cap company — more stable, less risky, and generally earns lower expected returns.

HML (High Minus Low)

Value factor; high book-to-market (value) stocks outperform low book-to-market (growth) stocks.

A negative HML beta means the stock behaves like a low B/P (growth) stock — it’s safer and typically has a lower expected return.

Purpose of 3-Factor Model

Expands CAPM by adding size and value risks to better explain stock returns.

Fama-French 5-Factor Model

E(Ri) = Rf + βi(E(Rm) - Rf) + si(SMB) + hi(HML) + ri(RMW) + ci(CMA)

RMW (Robust Minus Weak)

Profitability factor; firms with strong profits outperform weak ones.

CMA (Conservative Minus Aggressive)

Investment factor; firms that invest conservatively outperform aggressive investors.

Purpose of 5-Factor Model

Improves the 3-factor model by adding profitability and investment risk dimensions.

Interpreting Regression Coefficients

b (beta) = market exposure; s, h, r, c = exposures to other factors; a (alpha) = excess return not explained by risk.

Alpha (α) in Model

Positive / negative alpha = abnormal return; zero alpha = returns explained by risk factors.

Why Factors Matter

They explain average return differences across portfolios that CAPM cannot.

Systematic Risk

Market-wide risk (e.g., inflation, recession); cannot be diversified away; compensated in expected return.

Unsystematic Risk

Firm-specific risk (e.g., strikes, product failure); can be diversified away; not priced in expected return.

Total Risk Formula

σ² = β²σm² + σε²; total variance = systematic risk + unsystematic risk.

Diversification

Reduces unsystematic risk; in large portfolios, only systematic risk remains.

CAPM Risk Focus

Investors are compensated only for systematic risk, measured by beta.

Interpreting Proportions of Risk

If a stock’s risk is mostly unsystematic, it’s less reliable for CAPM-based valuation.

Why Use 5 Years Monthly Data

Provides enough observations (~60) to estimate beta accurately without daily noise.

Systematic Risk and Required Return

Only systematic risk influences required return since it cannot be diversified.

Unsystematic Risk and Portfolios

Typically ignored in expected return, but high unsystematic risk makes returns less predictable.

SMB Factor Interpretation

Positive SMB = behaves like a small company (riskier); Negative SMB = behaves like a large company (safer).

HML Factor Interpretation

Positive HML = behaves like a value stock; negative HML = behaves like a growth stock.

Momentum Factor (Winners Minus Losers, WML)

Measures return difference between recent winner and loser stocks; captures tendency of past winners to keep outperforming short term.

Positive Momentum Beta - Stock behaves like recent winners; benefits from continuing positive trends.

Negative Momentum Beta - Stock behaves like recent losers; riskier in momentum crashes but may earn reversal gains later.

Carhart 4-Factor Model E(Ri) = Rf + βi(E(Rm)-Rf) + si(SMB) + hi(HML) + mi(WML)

adds momentum to the Fama-French 3-factor model

RMW Factor (Robust Minus Weak)

Profitability factor; firms with strong (robust) profits earn higher returns than weakly profitable firms.

Positive ri​ → the stock behaves like a robust (profitable, safer) firm.
Negative ri → the stock behaves like a weak (less profitable, riskier) firm.

CMA Factor (Conservative Minus Aggressive)

Investment factor; firms that invest conservatively tend to outperform those that invest aggressively.

• Positive CMA beta ( + ) → stock behaves like a conservative firm (invests less, safer).

• Negative CMA beta ( – ) → stock behaves like an aggressive firm (invests more, riskier).

Key Fama-French Idea

Additional factors represent different kinds of systematic risks investors are compensated for.

Procyclical Stocks

Perform well when the market is strong; riskier because they fail during downturns → higher required return.

Countercyclical Stocks

Perform better in bad times (e.g., defensive stocks) → lower required return.

High ROE Firms

Considered higher risk if markets are efficient, since they must sustain performance expectations.

Low Liquidity Assets

Require higher expected returns since they are harder to sell (liquidity risk premium).

Beta and Return Relationship

Higher beta → higher expected return; lower beta → lower expected return.

Regression Analysis in Testing CAPM

Used to estimate relationship between excess returns and beta to verify if alpha = 0.

Why Long-Short Strategies Matter

Test whether extra returns come from risk exposure (factors) or inefficiency (alpha).

CAPM vs Fama-French Comparison

CAPM: 1 factor (market); Fama-French: adds size, value, profitability, and investment to explain returns.