Capital Asset Pricing and Arbitrage Pricing Theory - PowerPoint Presentation

Capital Asset Pricing and Arbitrage Pricing Theory Bodie, Kane and MarcusEssentials of Investments 9th Global Edition 7

7.1 The Capital Asset Pricing Model  

7.1 The Capital Asset Pricing Model AssumptionsMarkets are competitive, equally profitableNo investor is wealthy enough to individually affect pricesAll information publicly available; all securities publicNo taxes on returns, no transaction costsUnlimited borrowing/lending at risk-free rateInvestors are alike except for initial wealth, risk aversionInvestors plan for single-period horizon; they are rational, mean-variance optimizersUse same inputs, consider identical portfolio opportunity sets

7.1 The Capital Asset Pricing Model Hypothetical EquilibriumAll investors choose to hold market portfolioMarket portfolio is on efficient frontier, optimal risky portfolioRisk premium on market portfolio is proportional to variance of market portfolio and investor’s risk aversionRisk premium on individual assets Proportional to risk premium on market portfolioProportional to beta coefficient of security on market portfolio

Figure 7.1 Efficient Frontier and Capital Market Line

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

7.1 The Capital Asset Pricing Model Risk Premium of Market PortfolioDemand drives prices, lowers expected rate of return/risk premiumsWhen premiums fall, investors move funds into risk-free assetEquilibrium risk premium of market portfolio proportional to Risk of marketRisk aversion of average investor

7.1 The Capital Asset Pricing Model  

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

Figure 7.2 The SML and a Positive-Alpha Stock

7.1 The Capital Asset Pricing Model Applications of CAPMUse SML as benchmark for fair return on risky assetSML provides “hurdle rate” for internal projectsIn setting pricing for government offerings and tenders

7.1 The Capital Asset Pricing Model What is the expected rate of return for a stock that has a beta of 1 if the expected return on the market is 15%? a.   15%. b.   More than 15%. c.   Cannot be determined without the risk-free rate.

7.2 CAPM and Index Models  

7.2 CAPM and Index Models  

Table 7.1 Monthly Return Statistics 01/06 - 12/10 Statistic (%)T-Bills S&P 500 Google Average rate of return 0.184 0.239 1.125 Average excess return - 0.055 0.941 Standard deviation* 0.177 5.11 10.40 Geometric average 0.180 0.107 0.600 Cumulative total 5-year return 11.65 6.60 43.17 Gain Jan 2006-Oct 2007 9.04 27.45 70.42 Gain Nov 2007-May 2009 2.29 -38.87 -40.99 Gain June 2009-Dec 2010 0.10 36.83 42.36 * The rate on T-bills is known in advance, SD does not reflect risk.

Figure 7.3A: Monthly Returns

Figure 7.3B Monthly Cumulative Returns

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

Table 7.2 SCL for Google (S&P 500), 01/06-12/10 Linear Regression Regression Statistics R 0.5914   R-square 0.3497   Adjusted R-square 0.3385   SE of regression 8.4585   Total number of observations 60   Regression equation: Google (excess return) = 0.8751 + 1.2031 × S&P 500 (excess return) ANOVA     df SS MS F p -level   Regression 1 2231.50 2231.50 31.19 0.0000   Residual 58 4149.65 71.55   Total 59 6381.15       Coefficients Standard Error t -Statistic p -value LCL UCL   Intercept 0.8751 1.0920 0.8013 0.4262 -1.7375 3.4877   S&P 500 1.2031 0.2154 5.5848 0.0000 0.6877 1.7185   t-Statistic (2%) 2.3924   LCL - Lower confidence interval (95%)   UCL - Upper confidence interval (95%)            

7.2 CAPM and Index Models Estimation resultsSecurity 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

7.2 CAPM and Index Models Predicting BetasMean reversionBetas move towards mean over timeTo predict future betas, adjust estimates from historical data to account for regression towards 1.0

True or False Stocks with a beta of zero offer an expected rate of return of zero.The CAPM implies that investors require a higher return to hold highly volatile securities.You can construct a portfolio with beta of .75 by investing .75 of the investment budget in T-bills and the remainder in the market portfolio.

10) The market price of a security is $ 30. Its expected rate of return is 10%. The risk-free rate is 4%, and the market risk premium is 8%. What will the market price of the security be if its beta doubles (and all other variables remain unchanged)? Assume the stock is expected to pay a constant dividend in perpetuity.

15) If the CAPM is valid, is the below situation possible?

16) If the CAPM is valid, is the below situation possible?

24) Two investment advisers are comparing performance. One averaged a 19% return and the other a 16% return. However, the beta of the first adviser was 1.5, while that of the second was 1.Can you tell which adviser was a better selector of individual stocks (aside from the issue of general movements in the market)? If the T-bill rate were 6% and the market return during the period were 14%, which adviser would be the superior stock selector? c.   What if the T-bill rate were 3% and the market return 15%?

22) Assume the risk-free rate is 4% and the expected rate of return on the market is 15%. I am buying a firm with an expected perpetual cash flow of $ 600 but am unsure of its risk. If I think the beta of the firm is zero, when the beta is really 1, how much more will I offer for the firm than it is truly worth?

7.3 CAPM and the Real World CAPM is false based on validity of its assumptionsUseful predictor of expected returnsUntestable as a theoryPrinciples still validInvestors should diversifySystematic risk is the risk that mattersWell-diversified risky portfolio can be suitable for wide range of investors

7.3 CAPM and the Real World Consider the statement: “If we can identify a portfolio that beats the S& P 500 Index portfolio, then we should reject the single-index CAPM.” Do you agree or disagree? Explain.

7.4 Multifactor Models and CAPM  

7.4 Multifactor Models and CAPM  

Table 7.3 Monthly Rates of Return, 01/06-12/10   Monthly Excess Return % * Total Return Security Average Standard Deviation Geometric Average Cumulative Return     T-bill 0 0 0.18 11.65 Market index ** 0.26 5.44 0.30 19.51 SMB 0.34 2.46 0.31 20.70 HML 0.01 2.97 -0.03 -2.06 Google 0.94 10.40 0.60 43.17           *Total return for SMB and HML   ** Includes all NYSE, NASDAQ, and AMEX stocks.            

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 2006 - December 2010   Single Index Specification FF 3-Factor Specification Estimate S&P 500 Broad Market Index with Broad Market Index   Correlation coefficient 0.59 0.61 0.70 Adjusted R-Square 0.34 0.36 0.47 Residual SD = Regression SE (%) 8.46 8.33 7.61 Alpha = Intercept (%) 0.88 (1.09) 0.64 (1.08) 0.62 (0.99) Market beta 1.20 (0.21) 1.16 (0.20) 1.51 (0.21) SMB (size) beta - - -0.20 (0.44) HML (book to market) beta - - -1.33 (0.37)         Standard errors in parenthesis      

7.5 Arbitrage Pricing Theory ArbitrageRelative mispricing creates riskless profitArbitrage Pricing Theory (APT)Risk-return relationships from no-arbitrage considerations in large capital marketsWell-diversified portfolioNonsystematic risk is negligibleArbitrage portfolioPositive return, zero-net-investment, risk-free portfolio

7.5 Arbitrage Pricing Theory Calculating APT Returns on well-diversified portfolio

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

Figure 7.5 Security Characteristic Lines

7.5 Arbitrage Pricing Theory Multifactor Generalization of APT and CAPMFactor portfolioWell-diversified portfolio constructed to have beta of 1.0 on one factor and beta of zero on any other factorTwo-Factor Model for APT

7.5 Arbitrage Pricing Theory 29. Assume a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of 45%. Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 3.5%, and one-half have an alpha of –3%. The analyst then buys $ 1 million of an equally weighted portfolio of the positive-alpha stocks and sells short $ 1.7 million of an equally weighted portfolio of the negative-alpha stocks.What is the expected profit (in dollars), and what is the standard deviation of the analyst’s profitHow does your answer change if the analyst examines 50 stocks instead of 20? 100 stocks?

7.5 Arbitrage Pricing Theory 31) The APT itself does not provide information on the factors that one might expect to determine risk premiums. How should researchers decide which factors to investigate? Is industrial production a reasonable factor to test for a risk premium? Why or why not?

7.5 Arbitrage Pricing Theory 31) As a finance intern at Pork Products, Jennifer Wainwright’s assignment is to come up with fresh insights concerning the firm’s cost of capital. She decides that this would be a good opportunity to try out the new material on the APT that she learned last semester. As such, she decides that three promising factors would be (i) the return on a broad-based index such as the S& P 500; (ii) the level of interest rates, as represented by the yield to maturity on 10-year Treasury bonds; and (iii) the price of hogs, which are particularly important to her firm. Her plan is to find the beta of Pork Products against each of these factors and to estimate the risk premium associated with exposure to each factor. Comment on Jennifer’s choice of factors. Which are most promising with respect to the likely impact on her firm’s cost of capital? Can you suggest improvements to her specification?

7.5 Arbitrage Pricing Theory

My Problems 2 Validity of the CAPM3 Conceptual on CAPM6 CAPM10 Price if beta changes15 Are the numbers valid based on CAPM16 Are the numbers valid based on CAPM22 How much extra is paid when beta is incorrectly estimated24 Calculate alpha for portfolio managers27 Arbitrage Opportunity29 APT (well-diversified portfolios)31 What factors to use for the APT34 Choice of factors for APTCFA 13 investment strategy

TA Problems 4 Calculate r using CAPM5 Determine whether under- or over-priced7 CAPM17 Are the numbers valid based on CAPM18 Are the numbers valid based on CAPM23 CAPM (Calculate Beta)25 CAPM (E(r), r for Beta=0, underpriced)26 Stock Alpha & Portfolio Formation28 Solve for Rf using two stocks CAPM formulas32 Estimate r using APT33 Derive APT formula from 2 portfoliosCFA 3 Use CAPM to change risk and/or return of portfolio