Lecture07 Asset Pricing Models

Lecture07 Asset Pricing Models - Asset Pricing Models Tyler...

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Asset Pricing Models Tyler R. Henry 1 FINA 4310 Outline Contents 1 CAPM 1 1.1 SML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 SCL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Multi-Factor Models 13 2.1 APT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 FF3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1 CAPM Capital Asset Pricing Model (CAPM) The CAPM is an equilibrium model of security markets that attempts to answer the question: "What is the relationship between risk and expected returns?" CAPM is a single factor asset pricing model, that describes the risk-return rela- tionship for individual assets, where an asset’s risk is characterized by its contri- bution to the risk of an efficient, diversified portfolio. The single factor is the market portfolio (more on that later), and an asset’s rele- vant risk is the risk that cannot be diversified away by including it in the market portfolio. 1
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CAPM Assumptions Investors are rational mean-variance optimizers : they form their portfolios based on mean returns and variances. Homogeneous expectations : All investors possess the same probability distribu- tion of future asset returns. In other words, they all agree on the same means, variances, and covariance of future asset returns. Markets are perfectly competitive and investors are price takers. Investors have a single-period investment horizon. No market frictions such as taxes or transactions costs. All investors can borrow and lend at the same risk-free rate. Note: Clearly, these assumptions are not satisfied in reality. They are assumptions necessary to simplify the model’s approx- imation of reality. The success of a model is based on the accuracy of its predictions not on the realism of its assumptions. CAPM Equilibrium Outcome Under the assumptions of CAPM, all investors have the same investment opportunity set (e.g., they have access to the same set of risky assets), and the same risk-free rate. Therefore, they will also have the same optimal risky portfolio and the same efficient frontier. Under these conditions, the equilibrium outcome is: All investors hold the same optimal risky portfolio, and this portfolio is called the Market portfolio ( M ). The market portfolio will be on the efficient frontier, and is the optimal risky portfolio. The CAL that runs from the risk-free rate through M is the best CAL, and is called the Capital Market Line (CML). Capital Market Line (CML) Capital Market Line (CML Capital Market Line (CML) () P Er CML All investors are on th CAL hi h M M the same CAL, which is the CML. Where they lie on the CML depends on their risk r f aversion, and is reflected through the proportion of their wealth invested in the P σ M wealth invested in the risk-free asset versus M . Mf Pf P M r r =+ CML: 10/08/2007 FINA 4310 5 E ( r P ) = r f + ± E ( r M ) - r f σ M ² σ P 2
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The Market Portfolio Market portfolio contains all risky assets and the proportion of each asset is its market value as a percentage of total market value.
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This note was uploaded on 06/06/2011 for the course FINA 4310 taught by Professor Staff during the Spring '08 term at University of Georgia Athens.

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Lecture07 Asset Pricing Models - Asset Pricing Models Tyler...

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