Essentials of Investments: Chapter 7 - Capital Asset Pricing and Arbitrage Pricing Theory presents Capital Asset Pricing Model, Resulting Equilibrium Conditions, Capital Market Line, Slope and Market Risk Premium, Expected Return and Risk on Individual Securities.
1 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Chapter Capital Asset Pricing and Arbitrage Pricing Theory Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 2 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 3 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Assumptions • Individual investors are price takers • Single-period investment horizon • Investments are limited to traded financial assets • No taxes, and transaction costs Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 4 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Assumptions (cont.) • Information is costless and available to all investors • Investors are rational mean-variance optimizers • Homogeneous expectations Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 5 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 6 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Resulting Equilibrium Conditions (cont.) • 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 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 7 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Capital Market Line E(r) E(rM) CML M rf sm Irwin / McGraw-Hill s © 2001 The McGraw-Hill Companies, Inc All rights reserved 8 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Slope and Market Risk Premium M rf E(rM) - rf = = = Market portfolio Risk free rate Market risk premium E(rM) - rf = Market price of risk = Slope of the CAPM sM Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 9 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 10 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Security Market Line E(r) SML E(rM) rf ß M = 1.0 Irwin / McGraw-Hill ò â 2001 The McGraw-Hill Companies, Inc All rights reserved 11 Bodie • Kane • Marcus Essentials of Investments Fourth Edition SML Relationships b = [COV(ri,rm)] / sm2 Slope SML = E(rm) - rf = market risk premium SML = rf + b[E(rm) - rf] Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 12 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Sample Calculations for SML E(rm) - rf = 08 rf = 03 bx = 1.25 E(rx) = 03 + 1.25(.08) = 13 or 13% by = e(ry) = 03 + 6(.08) = 078 or 7.8% Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 13 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Graph of Sample Calculations E(r) SML Rx=13% Rm=11% Ry=7.8% 3% 08 1.0 1.25 ßy ßm ßx Irwin / McGraw-Hill ß © 2001 The McGraw-Hill Companies, Inc All rights reserved 14 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Disequilibrium Example E(r) SML 15% Rm=11% rf=3% 1.0 1.25 Irwin / McGraw-Hill ò â 2001 The McGraw-Hill Companies, Inc All rights reserved 15 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 16 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Security Characteristic Line Excess Returns (i) SCL Excess returns on market index R = a + ß R + e i Irwin / McGraw-Hill i i m i © 2001 The McGraw-Hill Companies, Inc All rights reserved 17 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Using the Text Example p 245, Table 8.5: Jan Feb Dec Mean Std Dev Irwin / McGraw-Hill Excess GM Ret 5.41 -3.44 2.43 -.60 4.97 Excess Mkt Ret 7.24 93 3.90 1.75 3.32 © 2001 The McGraw-Hill Companies, Inc All rights reserved 18 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Regression Results: rGM - rf = a + ß(rm - rf) a ß Estimated coefficient -2.590 1.1357 Std error of estimate (1.547) (0.309) Variance of residuals = 12.601 Std dev of residuals = 3.550 R-SQR = 0.575 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 19 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 20 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Arbitrage Example from Text pp 255257 Current Stock Price$ A 10 B 10 C 10 D 10 Irwin / McGraw-Hill Expected Return% 25.0 20.0 32.5 22.5 Standard Dev.% 29.58 33.91 48.15 8.58 © 2001 The McGraw-Hill Companies, Inc All rights reserved 21 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Arbitrage Portfolio Portfolio A,B,C D Irwin / McGraw-Hill Mean Return Stan Dev Correlation Of Returns 25.83 6.40 0.94 22.25 8.58 © 2001 The McGraw-Hill Companies, Inc All rights reserved 22 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Arbitrage Action and Returns E Ret * P * D St.Dev Short shares of D and buy of A, B & C to form P You earn a higher rate on the investment than you pay on the short sale Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 23 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved ... rGM - rf = a + ß(rm - rf) a ß Estimated coefficient -2 .590 1.13 57 Std error of estimate (1.5 47) (0.309) Variance of residuals = 12.601 Std dev of residuals = 3.550 R-SQR = 0. 575 Irwin / McGraw-Hill... McGraw-Hill Excess GM Ret 5.41 -3 .44 2.43 -. 60 4. 97 Excess Mkt Ret 7. 24 93 3.90 1 .75 3.32 © 2001 The McGraw-Hill Companies, Inc All rights reserved 18 Bodie • Kane • Marcus Essentials of Investments... McGraw-Hill © 2001 The McGraw-Hill Companies, Inc All rights reserved 19 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Arbitrage Pricing Theory Arbitrage - arises if an investor