McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Capital Asset Pricing and Arbitrage Pricing Theory 7 Bodie, Kane, and Marcus Essentials of Investments, 9 th Edition

The Capital Asset Pricing Model

The Capital Asset Pricing Model Assumptions Markets are competitive, equally profitable No investor is wealthy enough to individually affect prices All information publicly available; all securities public No taxes on returns, no transaction costs Unlimited borrowing/lending at risk-free rate Investors are alike except for initial wealth, risk aversion Investors plan for single-period horizon; they are rational, mean-variance optimizers Use same inputs, consider identical portfolio opportunity sets

The Capital Asset Pricing Model Hypothetical Equilibrium All investors choose to hold market portfolio Market portfolio is on efficient frontier, optimal risky portfolio

The Capital Asset Pricing Model Hypothetical Equilibrium Risk premium on market portfolio is proportional to variance of market portfolio and investor’s risk aversion Risk premium on individual assets Proportional to risk premium on market portfolio Proportional to beta coefficient of security on market portfolio

7-6 Figure 7.1 Efficient Frontier and Capital Market Line

The Capital Asset Pricing Model Passive Strategy is Efficient Mutual fund theorem: All investors desire same portfolio of risky assets, can be satisfied by single mutual fund composed of that portfolio If passive strategy is costless and efficient, why follow active strategy? If no one does security analysis, what brings about efficiency of market portfolio?

The Capital Asset Pricing Model Risk Premium of Market Portfolio Demand drives prices, lowers expected rate of return/risk premiums When premiums fall, investors move funds into risk-free asset Equilibrium risk premium of market portfolio proportional to Risk of market Risk aversion of average investor

The Capital Asset Pricing Model

The Capital Asset Pricing Model The Security Market Line (SML) Represents expected return-beta relationship of CAPM Graphs individual asset risk premiums as function of asset risk Alpha Abnormal rate of return on security in excess of that predicted by equilibrium model (CAPM)

7-11 Figure 7.2 The SML and a Positive-Alpha Stock

The Capital Asset Pricing Model Applications of CAPM Use SML as benchmark for fair return on risky asset SML provides “hurdle rate” for internal projects

CAPM and Index Models

CAPM and Index Models

7-15 Table 7.1 Monthly Return Statistics 01/ /10 Statistic (%)T-BillsS&P 500Google Average rate of return Average excess return Standard deviation* Geometric average Cumulative total 5-year return Gain Jan 2006-Oct Gain Nov 2007-May Gain June 2009-Dec * The rate on T-bills is known in advance, SD does not reflect risk.

7-16 Figure 7.3A: Monthly Returns

7-17 Figure 7.3B Monthly Cumulative Returns

7-18 Figure 7.4 Scatter Diagram/SCL: Google vs. S&P 500, 01/06-12/10

7-19 Table 7.2 SCL for Google (S&P 500), 01/06-12/10 Linear Regression Regression Statistics R R-square Adjusted R-square SE of regression Total number of observations 60 Regression equation: Google (excess return) = × S&P 500 (excess return) ANOVA dfSSMSFp-level Regression Residual Total CoefficientsStandard Errort-Statisticp-valueLCLUCL Intercept S&P t-Statistic (2%) LCL - Lower confidence interval (95%) UCL - Upper confidence interval (95%)

CAPM and Index Models Estimation results Security Characteristic Line (SCL) Plot of security’s expected excess return over risk-free rate as function of excess return on market Required rate = Risk-free rate + β x Expected excess return of index

CAPM and Index Models Predicting Betas Mean reversion Betas move towards mean over time To predict future betas, adjust estimates from historical data to account for regression towards 1.0

CAPM and the Real World CAPM is false based on validity of its assumptions Useful predictor of expected returns Untestable as a theory Principles still valid Investors should diversify Systematic risk is the risk that matters Well-diversified risky portfolio can be suitable for wide range of investors

Multifactor Models and CAPM

Multifactor Models and CAPM

7-25 Table 7.3 Monthly Rates of Return, 01/06-12/10 Monthly Excess Return % *Total Return SecurityAverage Standard Deviation Geometric Average Cumulative Return T-bill Market index ** SMB HML Google *Total return for SMB and HML ** Includes all NYSE, NASDAQ, and AMEX stocks.

7-26 Table 7.4 Regression Statistics: Alternative Specifications Regression statistics for:1.A Single index with S&P 500 as market proxy 1.B Single index with broad market index (NYSE+NASDAQ+AMEX) 2. Fama French three-factor model (Broad Market+SMB+HML) Monthly returns January December 2010 Single Index SpecificationFF 3-Factor Specification EstimateS&P 500Broad Market Indexwith Broad Market Index Correlation coefficient Adjusted R-Square Residual SD = Regression SE (%) Alpha = Intercept (%)0.88 (1.09)0.64 (1.08) 0.62 (0.99) Market beta1.20 (0.21)1.16 (0.20) 1.51 (0.21) SMB (size) beta (0.44) HML (book to market) beta (0.37) Standard errors in parenthesis

Arbitrage Pricing Theory Arbitrage Relative mispricing creates riskless profit Arbitrage Pricing Theory (APT) Risk-return relationships from no-arbitrage considerations in large capital markets Well-diversified portfolio Nonsystematic risk is negligible Arbitrage portfolio Positive return, zero-net-investment, risk-free portfolio

Arbitrage Pricing Theory Calculating APT Returns on well-diversified portfolio

7-29 Table 7.5 Portfolio Conversion *When alpha is negative, you would reverse the signs of each portfolio weight to achieve a portfolio A with positive alpha and no net investment. Steps to convert a well-diversified portfolio into an arbitrage portfolio

7-30 Table 7.6 Largest Capitalization Stocks in S&P 500 Stock Weight

7-31 Table 7.7 Regression Statistics of S&P 500 Portfolio on Benchmark Portfolio, 01/06-12/10 Linear Regression Regression Statistics R R-square Adjusted R-square Annualized Regression SE Total number of observations60 S&P 500 = × Benchmark Coefficients Standard Errort-statp-level Intercept Benchmark

7-32 Table 7.8 Annual Standard Deviation PeriodReal RateInflation RateNominal Rate 1/1 / /31/ /1/ /31/ /1/ /31/

7-33 Figure 7.5 Security Characteristic Lines

Arbitrage Pricing Theory Multifactor Generalization of APT and CAPM Factor portfolio Well-diversified portfolio constructed to have beta of 1.0 on one factor and beta of zero on any other factor Two-Factor Model for APT

7-35 Table 7.9 Constructing an Arbitrage Portfolio Constructing an arbitrage portfolio with two systemic factors