Week 2: Capital Asset Pricing Model (CAPM) PDF

1\. Regression Analysis \- Key equation: Y = α + βX + ε \- β = cov(X,Y) / var(X) \- R-squared: Measures explained variation 2\. CAPM and Asset Returns \- Stock return equation: (r\_it - r\_f) = α\_i + β\_i(r\_Mt - r\_f) + ε\_it \- Decomposes return into systematic (β\_i\^2 \* σ\_M\^2) and idio...

1\. Regression Analysis \- Key equation: Y = α + βX + ε \- β = cov(X,Y) / var(X) \- R-squared: Measures explained variation 2\. CAPM and Asset Returns \- Stock return equation: (r\_it - r\_f) = α\_i + β\_i(r\_Mt - r\_f) + ε\_it \- Decomposes return into systematic (β\_i\^2 \* σ\_M\^2) and idiosyncratic (σ\_ε\^2) risk 3\. Estimating Expected Returns \- E(r\_j) = r\_f + β\_j\[E(r\_M) - r\_f\] \- Requires estimates of risk-free rate, market risk premium, and stock\'s beta 4\. CAPM Implications \- Expected excess returns are linear in beta \- Slope of SML is market risk premium \- Expected returns depend only on beta 5\. Testing CAPM \- Time-series approach: Tests if α\_i = 0 for all assets \- Two-pass approach: 1\. Estimate betas for each stock 2\. Run cross-sectional regression: (r\_it - r\_ft) = γ\_0 + γ\_1β\_i + ε\_i \- If CAPM holds: γ\_0 = 0 and γ\_1 = (r\_Mt - r\_ft) 6\. Empirical Evidence \- Fama-MacBeth (1973) method: portfolio formation, rolling betas, cross-sectional regressions \- Findings: \- Returns and betas are approximately linearly related \- Risk-return relation flatter than CAPM predicts \- High-beta stocks: lower returns than CAPM predicts \- Low-beta stocks: higher returns than CAPM predicts 7\. Roll\'s Critique \- CAPM tests using market proxies may not actually test CAPM \- True market portfolio (including all assets) needed for proper testing \- CAPM potentially untestable due to inability to observe true market portfolio 8\. Reasons for CAPM Rejection \- Estimation error in betas \- Use of market proxies instead of true market portfolio \- Incomplete market representation (should include bonds, real estate, foreign assets, human capital)