Week 2: Capital Asset Pricing Model (CAPM) PDF
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These notes provide a detailed explanation of the Capital Asset Pricing Model (CAPM). The document covers various aspects of CAPM, including regression analysis, asset returns, expected returns, and testing the model. The notes also examine empirical evidence supporting and contradicting CAPM and discuss Roll's critique.
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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)
