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Chapter 7

Chapter 7. Capital Asset Pricing and Arbitrage Pricing Theory. CAPM: Simplifying Assumptions. Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets No taxes and no transaction costs

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Chapter 7

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  1. Chapter 7 Capital Asset Pricing and Arbitrage Pricing Theory

  2. CAPM: Simplifying Assumptions Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets No taxes and no transaction costs Information is costless and available to all investors Investors are rational mean-variance optimizers Homogeneous expectations 7-2

  3. alpha and beta E(rM) = βS = rf = Required return = rf + βS [E(rM) – rf] = If you believe the stock will actually provide a return of ____, what is the implied alpha?  = Portfolio Beta is the weighted average of underlying Betas 14% 1.5 5% 5 + 1.5 [14 – 5] = 18.5% 17% 17% - 18.5% = -1.5% 7-3

  4. Adjusted Betas Adjusted β = = = 1 1 Calculated betas are adjusted to account for the empirical finding that betas different from _ tend to move toward _ over time. A firm with a beta __ will tend to have a ___________________ in the future. A firm with a beta ___ will tend to have a ____________________ in the future. >1 lower beta (closer to 1) < 1 higher beta (closer to 1) 2/3 (Calculated β) + 1/3 (1) 2/3 (1.276) + 1/3 (1) 1.184 7-4

  5. Evaluating the CAPM The CAPM is “false” based on the ____________________________. validity of its assumptions The CAPM could still be a useful predictor of expected returns. That is an empirical question. Huge measurability problems because the market portfolio is unobservable. Conclusion: As a theory the CAPM is untestable. 7-5

  6. Evaluating the CAPM However, the __________ of the CAPM is testable. Betas are ___________ at predicting returns as other measurable factors may be. More advanced versions of the CAPM that do a better job at ___________________________ are useful at predicting stock returns. practicality not as useful estimating the market portfolio Still widely used and well understood. 7-6

  7. Fama-French (FF) 3 factor Modelhttp://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html Fama and French noted that stocks of ____________ and stocks of firms with a _________________ have had higher stock returns than predicted by single factor models. smaller firms high book to market Problem: Empirical model without a theory Will the variables continue to have predictive power? 7-7

  8. Fama-French (FF) 3 factor Model FF proposed a 3 factor model of stock returns as follows: rM – rf = Market index excess return Ratio of ______________________________________ measured with a variable called ____: HML: High minus low or difference in returns between firms with a high versus a low book to market ratio. _______________ measured by the ____ variable SMB: Small minus big or the difference in returns between small and large firms. book value of equity to market value of equity HML SMB Firm size variable 7-8

  9. Arbitrage Pricing Theory (APT) Arbitrage: Zero investment: Efficient markets: Arises if an investor can construct a zero investment portfolio with a sure profit, e.g. Credit Card B/T Since no net investment outlay is required, an investor can create arbitrarily large positions to secure large levels of profit With efficient markets, profitable arbitrage opportunities will quickly disappear 7-9

  10. Arbitrage Pricing Example Suppose Rf = ___ and a well diversified portfolio P has a beta of ___ and an alpha of ___ when regressed against a systematic factor S. Another well diversified portfolio Q has a beta of ___ and an alpha of ___. If we construct a portfolio of P and Q with the following weights: What should αp = ___ 3.25 -2.25 Note: Σ W = 1 1.3 6% 2% 0.9 1% WP = and WQ = ; Then βp = αp = (-2.25 x 1.3) + (3.25 x 0.9) = 0 (-2.25 x 2%) + (3.25 x 1%) = - 1.25% 0 αp = -1.25% means an investor will earn rf – 1.25% or 4.75% on portfolio PQ. In theory one could short this portfolio and pay 4.75%, and invest in the riskless asset and earn 6%, netting the 1.25% difference. Arbitrage should eliminate the negative portfolio alpha quickly. 7-10

  11. Arbitrage Pricing Model The result: For a well diversified portfolio Rp = βpRS (Excess returns) (rp,i – rf) = βp(rS,i – rf) and for an individual security (rp,i – rf) = βp(rS,i – rf) + ei Advantage of the APT over the CAPM: RS is the excess return on a portfolio with a beta of 1 relative to systematic factor “S” • No particular role for the “Market Portfolio,” which can’t be measured anyway • Easily extended to multiple systematic factors, for example • (rp,i – rf) = βp,1(r1,i – rf) + βp,2(r2,i – rf) + βp,3(r3,i – rf) + ei 7-11

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