Section 11

# Section 11 - ECON 136 Financial Economics Section 11(Nov...

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ECON 136: Financial Economics Section 11 (Nov 13th) Xing Huang 1 Economics Department, UC Berkeley 1 Review 1.1 The Capital Asset Pricing Model (CAPM) The capital asset pricing model (CAPM) assumes (1) all investors are price takers (2) all investors care about returns measured over one period (3) all assets are traded (4) investors can borrow or lend at a given risk-free rate (5) investors pay no taxes or transactions costs (6) all investors are mean-variance optimizers (7) all investors perceive the same means, variances, and covariances for returns. If the CAPM assumptions are true, then the market portfolio is the tangency portfolio. Note: the market portfolio is the value-weighted portfolio of all traded assets in the economy. Why? Because all investors are mean-variance optimizers, we know by the mutual fund the- orem that they hold various combinations of the risk-free asset and the tangency portfolio. Because the market supply of risky assets must equal the market demand for assets, the mar- ket portfolio must be the tangency portfolio that investors are demanding. In other words, this result says that all investors hold combinations of the risk-free asset and the value-weighted portfolio of all traded assets. return R i , E [ R i ] ± R f = i ( E [ R m ] ± R f ) where R m is the return on the market portfolio and i = Cov ( R i ; R m ) =V ar ( R m ) . Why? The formal argument is long, but it is based on the idea that the market return is mean-variance e¢ cient, so you cannot increase the expected return of the market portfolio by making an adjustment into asset i without increasing your portfolio variance. Note that the expected return-beta representation of CAPM has the nice interpretation: E[excess return] = quantity of risk*price of risk. 1 These notes are enormously bene±ted from previous GSIs: Keith Jacks Gamble, Dan Hartley and Congyan Tan. Thank you all very much !! 1

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1.2 Testing the CAPM In practice the CAPM can be tested by estimating the time-series regression: R i;t R f;t = a i + i ( R m;t R f;t ) + e i;t Here a i = the estimated expected excess return on asset i that is not due to its risk, which is captured by
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Section 11 - ECON 136 Financial Economics Section 11(Nov...

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