Capital Asset Pricing and Arbitrage Pricing Theory Chapter 7 Capital Asset Pricing and Arbitrage Pricing Theory Describes the financial instruments traded in primary and secondary markets. Discusses Market indexes. Discusses options and futures. 1

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 Think of a world where individuals are all very similar except their initial wealth and their level of risk aversion. ( I was born poor and chicken) “Price Takers” means that individuals do not effect prices. (Big assumption! An individual’s behavior does not effect price.) 7-2

alpha and beta E(rM) = 14% βS = 1.5 rf = 5% Required return = rf + β S [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% Get Beta of portfolio by the sum of each weight times the beta of the asset. Get the risk premium of the portfolio by the sum of each weight times the risk premium of the asset. Or, by the portfolio Beta times the Market risk premium. 17% - 18.5% = -1.5% 7-3 3

Adjusted Betas Adjusted β = 2/3 (Calculated β) + 1/3 (1) = Calculated betas are adjusted to account for the empirical finding that betas different from _ tend to move toward _ over time. 1 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) Adjusted β = = 2/3 (Calculated β) + 1/3 (1) 2/3 (1.276) + 1/3 (1) 1.184 The adjusted beta forecast is adjusted to account for the empirical finding that betas tend to have a regression toward the mean. A firm with a high beta (Beta >1) will tend to have a beta closer to 1 in the future, and vice versa. 7-4 4

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

Evaluating the CAPM practicality 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. not as useful estimating the market portfolio Still widely used and well understood. 7-6

Fama-French (FF) 3 factor Model http://mba. tuck. dartmouth 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

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 Firm size variable SMB 7-8

Arbitrage Pricing Theory (APT) 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 The arbitrage pricing theory was created by Stephen Ross and it is similar to the CAPM but it requires far fewer limiting assumptions. Arbitrage example Apples cost 1 per pound Pie crust cost 1 dollar. Pie cost 3 dollars and a pie is simply the apples thrown into the crust. With efficient markets, profitable arbitrage opportunities will quickly disappear 7-9

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 = ___ 6% 1.3 2% 0.9 1% WP = and WQ = ; Then βp = αp = -2.25 3.25 Note: Σ W = 1 (-2.25 x 1.3) + (3.25 x 0.9) = 0 (-2.25 x 2%) + (3.25 x 1%) = - 1.25% 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. Formulas for the weights are in the text. 7-10 10

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 RS is the excess return on a portfolio with a beta of 1 relative to systematic factor “S” AND has a beta of zero to all other systematic factors. These are called factor portfolios. 7-11 11