Chap009 The Capital Asset Pricing Mode(金融工程-南开大学,王小麓))l.ppt

Chapter 9 The Capital Asset Pricing Model Capital Asset Pricing Model (CAPM) It is the equilibrium model that underlies all modern financial theory. Derived using principles of diversification with simplified assumptions. Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development. Assumptions Individual investors are price takers. Single-period investment horizon. Investments are limited to traded financial assets. No taxes and transaction costs. Assumptions (cont’d) Information is costless and available to all investors. Investors are rational mean-variance optimizers. There are homogeneous expectations. Resulting Equilibrium Conditions All investors will hold the same portfolio for risky assets – market portfolio. Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value. Resulting Equilibrium Conditions (cont’d) Risk premium on the the market depends on the average risk aversion of all market participants. Risk premium on an individual security is a function of its covariance with the market. Capital Market Line Slope and Market Risk Premium  M = Market portfolio rf = Risk free rate E(rM) - rf = Market risk premium E(rM) - rf = Market price of risk  = Slope of the CAPM Expected Return and Risk on Individual Securities The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio. An individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio. Security Market Line SML Relationships ????????????????????= [COV(ri,rm)] / ?m2 Slope SML = E(rm) - rf = market risk premium SML = rf + ?[E(rm) - rf] Betam = [Cov (ri,rm)] / sm2 = sm2 / sm2 = 1 Sample Calculations for SML E(rm) - rf = .08 rf = .03 ?x = 1.25 E(rx) = .03 + 1.25(.08) = .13 or 13% ?y = .6 e(ry) = .03 + .6(.08) = .078 or 7.8% Graph