7 - 1Copyright 2002 Harcourt, Inc. AII rights reserved.CHAPTER 7Risk and Return:Portfolio Theory and Asset Pricing ModelsCapitaI Asset Pricing ModeI (CAPM)Efficient frontierCapitaI Market Line (CML)Security Market Line (SML)Beta caIcuIationArbitrage pricing theoryFama-French 3-factor modeI7 - 2Copyright 2002 Harcourt, Inc. AII rights reserved.What is the CAPM?%he CAPM is an equiIibrium modeI that specifies the reIationship between risk and required rate of return for assets heId in weII-diversified portfoIios.It is based on the premise that onIy one factor affects risk.What is that factor?7 - 3Copyright 2002 Harcourt, Inc. AII rights reserved.Investors aII think in terms ofa singIe hoIding period.AII investors have identicaI expectations.Investors can borrow or Iend unIimited amounts at the risk-free rate.What are the assumptions of the CAPM?(More...)7 - 4Copyright 2002 Harcourt, Inc. AII rights reserved.AII assets are perfectIy divisibIe.%here are no taxes and no transactions costs.AII investors are price takers, that is, investors' buying and seIIing won't infIuence stock prices.Quantities of aII assets are given and fixed.7 - 5Copyright 2002 Harcourt, Inc. AII rights reserved.ExpectedPortfoIio Return, kpRisk, 9pEfficient SetFeasibIe SetFeasibIe and Efficient PortfoIios7 - 6Copyright 2002 Harcourt, Inc. AII rights reserved.%he feasibIe set of portfoIios represents aII portfoIios that can be constructed from a given set of stocks.An efficient portfoIio is one that offers:the most return for a given amount of risk, orthe Ieast risk for a give amount of return.%he coIIection of efficient portfoIios is caIIed the efficient set or efficient frontier.7 - 7Copyright 2002 Harcourt, Inc. AII rights reserved.IB2 IB1IA2IA1OptimaI PortfoIioInvestor AOptimaI PortfoIioInvestor BRisk 9pExpectedReturn, kpOptimaI PortfoIios7 - 8Copyright 2002 Harcourt, Inc. AII rights reserved.Indifference curves refIect an investor's attitude toward risk as refIected in his or her risk/return tradeoff function.%hey differ among investors because of differences in risk aversion.An investor's optimaI portfoIio is defined by the tangency point between the efficient set and the investor's indifference curve.7 - 9Copyright 2002 Harcourt, Inc. AII rights reserved.When a risk-free asset is added to the feasibIe set, investors can create portfoIios that combine this asset with a portfoIio of risky assets.%he straight Iine connecting kRF with M, the tangency point between the Iine and the oId efficient set, becomes the new efficient frontier.What impact does kRF have onthe efficient frontier?7 - 10Copyright 2002 Harcourt, Inc. AII rights reserved.MZ.AkRF9MRisk, 9pEfficient Set with a Risk-Free Asset %he CapitaI MarketLine (CML):New Efficient Set..BkM^ExpectedReturn, kp7 - 11Copyright 2002 Harcourt, Inc. AII rights reserved.%he CapitaI Market Line (CML) is aII Iinear combinations of the risk-free asset and PortfoIio M.PortfoIios beIow the CML are inferior.%he CML defines the new efficient set.AII investors wiII choose a portfoIio on the CML.What is the CapitaI Market Line?7 - 12Copyright 2002 Harcourt, Inc. AII rights reserved.kp = kRF +SIope Intercept^9p.%he CML EquationkM - kRF^9MRisk measure7 - 13Copyright 2002 Harcourt, Inc. AII rights reserved.%he expected rate of return on any efficient portfoIio is equaI to the risk-free rate pIus a risk premium.%he optimaI portfoIio for any investor is the point of tangency between the CML and the investor's indifference curves.What does the CML teII us?7 - 14Copyright 2002 Harcourt, Inc. AII rights reserved.kRF9MRisk, 9pI1I2CMLR = OptimaI PortfoIio.R.MkRkM9R^^ExpectedReturn, kp7 - 15Copyright 2002 Harcourt, Inc. AII rights reserved.%he CML gives the risk/return reIationship for efficient portfoIios.%he Security Market Line (SML), aIso part of the CAPM, gives the risk/return reIationship for individuaI stocks.What is the Security Market Line (SML)?7 - 16Copyright 2002 Harcourt, Inc. AII rights reserved.%he measure of risk used in the SML is the beta coefficient of company i, bi.%he SML equation:ki = kRF + (RPM) bi%he SML Equation7 - 17Copyright 2002 Harcourt, Inc. AII rights reserved.Run a regression Iine of past returns on Stock i versus returns on the market.%he regression Iine is caIIed the characteristic Iine.%he sIope coefficient of the characteristic Iine is defined as the beta coefficient.How are betas caIcuIated?7 - 18Copyright 2002 Harcourt, Inc. AII rights reserved.IIIustration of beta caIcuIationYear kMki1 15% 18%2 -5 -103 12 16ki_kM_-5 0 5 10 15 202015105-5-10...ki = -2.59 + 1.44 kM^ ^7 - 19Copyright 2002 Harcourt, Inc. AII rights reserved.(More...)Method of CaIcuIationAnaIysts use a computer with statisticaI or spreadsheet software to perform the regression.At Ieast 3 year's of monthIy returns or 1 year's of weekIy returns are used.Many anaIysts use 5 years of monthIy returns. 7 - 20Copyright 2002 Harcourt, Inc. AII rights reserved.If beta = 1.0, stock is average risk.If beta > 1.0, stock is riskier than average.If beta < 1.0, stock is Iess risky than average.Most stocks have betas in the range of 0.5 to 1.5.7 - 21Copyright 2002 Harcourt, Inc. AII rights reserved.Interpreting Regression ResuIts%he R2measures the percent of a stock's variance that is expIained by the market.%he typicaI R2is:0.3 for an individuaI stockover 0.9 for a weII diversified portfoIio7 - 22Copyright 2002 Harcourt, Inc. AII rights reserved.Interpreting Regression ResuIts (Continued)%he 95% confidence intervaI shows the range in which we are 95% sure that the true vaIue of beta Iies.%he typicaI range is:from about 0.5 to 1.5 for an individuaI stockfrom about .92 to 1.08 for a weII diversified portfoIio7 - 23Copyright 2002 Harcourt, Inc. AII rights reserved.92= b292+ 9e2.92= variance= stand-aIone risk of Stock j.b292= market risk of Stock j.9e2= variance of error term= diversifiabIe risk of Stock j.What is the reIationship between stand-aIone, market, and diversifiabIe risk.j jM jjjjM7 - 24Copyright 2002 Harcourt, Inc. AII rights reserved.Beta stabiIity tests%ests based on the sIope of the SMLWhat are two potentiaI tests that can be conducted to verify the CAPM?7 - 25Copyright 2002 Harcourt, Inc. AII rights reserved.%ests of the SML indicate:A more-or-Iess Iinear reIationship between reaIized returns and market risk.SIope is Iess than predicted.IrreIevance of diversifiabIe risk specified in the CAPM modeI can be questioned.(More...)7 - 26Copyright 2002 Harcourt, Inc. AII rights reserved.Betas of individuaI securities are not good estimators of future risk.Betas of portfoIios of 10 or more randomIy seIected stocks are reasonabIy stabIe.Past portfoIio betas are good estimates of future portfoIio voIatiIity.7 - 27Copyright 2002 Harcourt, Inc. AII rights reserved.Yes.Richard RoII questioned whether it was even conceptuaIIy possibIe to test the CAPM.RoII showed that it is virtuaIIy impossibIe to prove investors behave in accordance with CAPM theory. Are there probIems with the CAPM tests?7 - 28Copyright 2002 Harcourt, Inc. AII rights reserved.It is impossibIe to verify.Recent studies have questioned its vaIidity.Investors seem to be concerned with both market risk and stand-aIone risk.%herefore, the SML may not produce a correct estimate of ki.What are our concIusionsregarding the CAPM?(More...)7 - 29Copyright 2002 Harcourt, Inc. AII rights reserved.CAPM/SML concepts are based on expectations, yet betas are caIcuIated using historicaI data.A company's historicaI data may not refIect investors' expectations about future riskiness.Other modeIs are being deveIoped that wiII one day repIace the CAPM, but it stiII provides a good framework for thinking about risk and return.7 - 30Copyright 2002 Harcourt, Inc. AII rights reserved.%he CAPM is a singIe factor modeI.%he AP% proposes that the reIationship between risk and return is more compIex and may be due to muItipIe factors such as GDP growth, expected infIation, tax rate changes, and dividend yieId.What is the difference between the CAPMand the Arbitrage Pricing %heory (AP%)?7 - 31Copyright 2002 Harcourt, Inc. AII rights reserved.ki = kRF + (k1 - kRF)b1 + (k2 - kRF)b2 + ... + (kj - kRF)bj.bj = sensitivity of Stock i to economicFactor j.kj = required rate of return on a portfoIiosensitive onIy to economic Factor j.Required Return for Stock i under the AP%7 - 32Copyright 2002 Harcourt, Inc. AII rights reserved.%he AP% is being used for some reaI worId appIications.Its acceptance has been sIow because the modeI does not specify what factors infIuence stock returns.More research on risk and return modeIs is needed to find a modeI that is theoreticaIIy sound, empiricaIIy verified, and easy to use.What is the status of the AP%?7 - 33Copyright 2002 Harcourt, Inc. AII rights reserved.Fama-French 3-Factor ModeIFama and French propose three factors:%he excess market return, kM-kRF.the return on, S, a portfoIio of smaII firms (where size is based on the market vaIue of equity) minus the return on B, a portfoIio of big firms.%his return is caIIed kSMB, for S minus B.7 - 34Copyright 2002 Harcourt, Inc. AII rights reserved.Fama-French 3-Factor ModeI (Continued)the return on, H, a portfoIio of firms with high book-to-market ratios (using market equity and book equity) minus the return on L, a portfoIio of firms with Iow book-to-market ratios.%his return is caIIed kHML, for H minus L.7 - 35Copyright 2002 Harcourt, Inc. AII rights reserved.ki = kRF + (kM - kRF)bi + (kSMB)ci + (kHMB)dibi = sensitivity of Stock i to the market return.cj = sensitivity of Stock i to the size factor.dj = sensitivity of Stock i to the book-to-market factor.Required Return for Stock i under the Fama-French 3-Factor ModeI7 - 36Copyright 2002 Harcourt, Inc. AII rights reserved.ki = kRF + (kM - kRF)bi + (kSMB)ci + (kHMB)diki = 6.8% + (6.3%)(0.9) + (4%)(-0.5) + (5%)(-0.3)= 8.97%Required Return for Stock i: bi=0.9, kRF=6.8%, the market risk premium is 6.3%, ci=-0.5, the expected vaIue for the size factor is 4%, di=-0.3, and the expected vaIue for the book-to-market factor is 5%. 7 - 37Copyright 2002 Harcourt, Inc. AII rights reserved.CAPM:ki = kRF + (kM - kRF)biki = 6.8% + (6.3%)(0.9) = 12.47%Fama-French (previous sIide):ki = 8.97%CAPM Required Return for Stock i