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Unformatted text preview: 1 Equities Anna A. Obizhaeva BMGT 343: Investments Prof. Anna Obizhaeva Office: VMH 4428 Phone: (301) 4057934 Email: obizhaeva@rhsmith.umd.edu Section 0101 T Th 9:3010:45 am in VMH 1336 Section 0201 T Th 11:0012:15 pm in VMH 1336 Section 0301 T Th 12:301:45 pm in VMH 1336 Office Hours : Thu 3:004:00 pm or by appointment Equities Anna A. Obizhaeva Equities Topic 8: Empirical Tests of The CAPM 2 Equities Anna A. Obizhaeva What We Learned So Far In Topic 7 (The CAPM), we study how investors asset demand determines the relation between assets risk and return in a market equilibrium : How expected returns E(R) are determined. How they are related to risk. ( ) ( ) ( ) M M n n f M n f n R V R R Cov R R E R R E , , ) ( ) ( = = Equities Anna A. Obizhaeva Our Goal The main goal of this Topic is to design empirical tests of the CAPM to examine the empirical evidence on whether the CAPM holds or not. We will heavily rely on regression analysis . 3 Equities Anna A. Obizhaeva Outline for Topic 8 Regression Analysis Analysis of Asset Returns Statistical Tests of the CAPM Stock Characteristics and the CAPM FamaFrench Factors and the CAPM Equities Anna A. Obizhaeva 1. Regression Analysis Regression analysis is a technique used for the modeling and analysis of data. It is useful when we need to identify the relation between different variables, i.e. dependent variable Y and explanatory variable X. 4 Equities Anna A. Obizhaeva History of Regression Analysis The term "regression " was introduced by Francis Galton, a cousin of Charles Darwin, who studied a biological phenomenon, namely that the progeny of exceptional individuals tend on average to be less exceptional than their parents and more like their more distant ancestors. For Galton, regression had only this biological meaning, but his work was later extended to a more general statistical context. Equities Anna A. Obizhaeva Regression Equation Consider two random variables X and Y. We can always decompose Y into two parts 1) explained by X and 2) unexplained by X. So, we can always write Y as where constants random variable (noise), such that This equation is called regression equation . + + = X Y ) ( ) , ( = = E and X Cov : , : 5 Equities Anna A. Obizhaeva Regressions Equation (contd) It is useful to think about the mechanism how Y is generated in regression equation : Parameters are given. For each observation, an X and are randomly drawn. Then, Y is determined according to regression equation. + + = X Y , Equities Anna A. Obizhaeva Regression Analysis In general, we do not know parameters However, we can estimate them using regression analysis....
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 Fall '08
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