Bài giảng Essentials of Investments - Chapter 7 Capital Asset Pricing and Arbitrage Pricing Theory

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus1 Chapter 7 Capital Asset Pricing and Arbitrage Pricing Theory Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus2 Capital Asset Pricing Model (CAPM) • 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 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus3 Assumptions • Individual investors are price takers • Single-period investment horizon • Investments are limited to traded financial assets • No taxes, and transaction costs Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus4 Assumptions (cont.) • Information is costless and available to all investors • Investors are rational mean-variance optimizers • Homogeneous expectations Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus5 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 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus6 • Risk premium on 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 Resulting Equilibrium Conditions (cont.) Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus7 E(r) E(rM) rf M CML sm Capital Market Line s Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus8 M = Market portfolio rf = Risk free rate E(rM) - rf = Market risk premium E(rM) - rf = Market price of risk = Slope of the CAPM Slope and Market Risk Premium Ms Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus9 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 • Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus10 E(r) E(rM) rf SML M ßß = 1.0 Security Market Line Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus11 SML Relationships b = [COV(ri,rm)] / sm 2 Slope SML = E(rm) - rf = market risk premium SML = rf + b[E(rm) - rf] Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus12 Sample Calculations for SML E(rm) - rf = .08 rf = .03 bx = 1.25 E(rx) = .03 + 1.25(.08) = .13 or 13% by = .6 e(ry) = .03 + .6(.08) = .078 or 7.8% Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus13 E(r) Rx=13% SML m ß ß 1.0 Rm=11% Ry=7.8% 3% xß 1.25 yß .6 .08 Graph of Sample Calculations Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus14 E(r) 15% SML ß 1.0 Rm=11% rf=3% 1.25 Disequilibrium Example Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus15 Disequilibrium Example • Suppose a security with a b of 1.25 is offering expected return of 15% • According to SML, it should be 13% • Underpriced: offering too high of a rate of return for its level of risk Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus16 Security Characteristic Line Excess Returns (i) SCL . . ... . . . . .. . . . . . . .. . . . . . . .. . . . . . . . . . . . . . . . ... . . .. . Excess returns on market index Ri = a i + ßiRm + ei Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus17 Using the Text Example p. 245, Table 8.5: Jan. Feb. . . Dec Mean Std Dev 5.41 -3.44 . . 2.43 -.60 4.97 7.24 .93 . . 3.90 1.75 3.32 Excess Mkt. Ret. Excess GM Ret. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus18 Estimated coefficient Std error of estimate Variance of residuals = 12.601 Std dev of residuals = 3.550 R-SQR = 0.575 ß -2.590 (1.547) 1.1357 (0.309) rGM - rf = + ß(rm - rf) Regression Results: a a Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus19 Arbitrage Pricing Theory Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit • Since no investment is required, an investor can create large positions to secure large levels of profit • In efficient markets, profitable arbitrage opportunities will quickly disappear Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus20 Arbitrage Example from Text pp. 255- 257 Current Expected Standard Stock Price$ Return% Dev.% A 10 25.0 29.58 B 10 20.0 33.91 C 10 32.5 48.15 D 10 22.5 8.58 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus21 Arbitrage Portfolio Mean Stan. Correlation Return Dev. Of Returns Portfolio A,B,C 25.83 6.40 0.94 D 22.25 8.58 Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus22 Arbitrage Action and Returns E. Ret. St.Dev. * P * D Short 3 shares of D and buy 1 of A, B & C to form P You earn a higher rate on the investment than you pay on the short sale Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie • Kane • Marcus23 APT and CAPM Compared • APT applies to well diversified portfolios and not necessarily to individual stocks • With APT it is possible for some individual stocks to be mispriced - not lie on the SML • APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio • APT can be extended to multifactor models