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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-1 Chapter 8

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-2 Chapter Summary Objective: To discuss the nature and illustrate the use of arbitrage. To introduce the index model and the APT. The Single Index Model The Arbitrage Pricing Theory

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-3 Advantages: Reduces the number of inputs for diversification Easier for security analysts to specialize Drawback: the simple dichotomy rules out important risk sources (such as industry events) The Single Index Model

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-4 ß i = index of a securitys particular return to the factor F= some macro factor; in this case F is unanticipated movement; F is commonly related to security returns Single Factor Model Assumption: a broad market index like the S&P500 is the common factor

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-5 Single Index Model i = stocks expected return if markets excess return is zero i (r M -r i ) = the component of return due to market movements e i = the component of return due to unexpected firm-specific events

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-6 Let: R i = (r i - r f ) R m = (r m - r f ) Risk premium format R i = i + ß i R m + e i Risk Premium Format

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-7 Market or systematic risk: risk related to the macro economic factor or market index Unsystematic or firm specific risk: risk not related to the macro factor or market index Total risk = Systematic + Unsystematic Components of Risk

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-8 i 2 = total variance i 2 m 2 = systematic variance 2 (e i ) = unsystematic variance Measuring Components of Risk

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-9 Total Risk = Systematic +Unsystematic Examining Percentage of Variance

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-10 Security Characteristic Line Excess Returns (i) SCL Excess returns on market index R i = i + ß i R m + e i

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-11 Using the Text Example from Table 8-1 Excess X Returns Excess Mkt Returns January February December Mean Std Deviation

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-12 Regression Results Estimated coefficient Std error of estimate(1.547)(0.309) Variance of residuals = Std dev of residuals = R-SQR = 0.575

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-13 Index Model and Diversification

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-14 Risk Reduction with Diversification Number of Securities St. Deviation Market Risk Unique Risk 2 (e P )= 2 (e) / n P 2 M 2

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-15 Industry Prediction of Beta BMO Nesbitt Burns and Merrill Lynch examples BMO NB uses returns not risk premiums has a different interpretation: + r f (1-) Merill Lynchs adjusted Forecasting beta as a function of past beta Forecasting beta as a function of firm size, growth, leverage etc.

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-16 Multifactor Models Use factors in addition to market return Examples include industrial production, expected inflation etc. Estimate a beta for each factor using multiple regression Chen, Roll and Ross Returns a function of several macroeconomic and bond market variables instead of market returns Fama and French Returns a function of size and book-to-market value as well as market returns

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-17 Summary Reminder Objective: To discuss the nature and illustrate the use of arbitrage. To introduce the index model and the APT. The Single Index Model The Arbitrage Pricing Theory

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-18 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

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-19 Arbitrage Example (pp ) StockCurrent Price ($) Expected Return (%) Standard Deviation (%) A B C D

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-20 Arbitrage Portfolio MeanStandard Deviation Correlation Portfolio of A, B & C D stock

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-21 Arbitrage Action and Returns Action: Short 3 shares of D and buy 1 of A, B & C to form portfolio P Returns: You earn a higher rate on the investment than you pay on the short sale E(r) P D

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-22 APT & Well-Diversified Portfolios F is some macroeconomic factor For a well-diversified portfolio e P approaches zero The result is similar to CAPM

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-23 F E(r)(%) Portfolio F E(r)(%) Individual Security Portfolio & Individual Security Comparison

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-24 E(r)% Beta for F Risk Free = 4 A D C.51.0 Disequilibrium Example

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-25 Disequilibrium Example Short Portfolio C Use funds to construct an equivalent risk higher return Portfolio D D is comprised of A & Risk-Free Asset Arbitrage profit of 1%

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-26 M Beta (Market Index) Risk Free 1.0 [E(r M ) - r f ] Market Risk Premium E(r) APT with Market Index Portfolio

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Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 8-27 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 APT and CAPM Compared

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