Tài chính doanh nghiệp - Chapter 9: The capital asset pricing model

Chapter 9The Capital Asset Pricing ModelIt is the equilibrium model that underlies all modern financial theory.Derived using principles of diversification with simplified assumptions.Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development.Capital Asset Pricing Model (CAPM)Individual investors are price takersSingle-period investment horizonInvestments are limited to traded financial assetsNo taxes and transaction costs.AssumptionsInformation is costless and available to all investors.Investors are rational mean-variance optimizers.There are homogeneous expectations.Assumptions (cont’d)All investors will hold the same portfolio for risky assets – market portfolio.Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value.Resulting Equilibrium ConditionsRisk premium on the the market depends on the average risk aversion of all market participants.Risk premium on an individual security is a function of its covariance with the market.Resulting Equilibrium Conditions (cont’d)Capital Market LineE(r)E(rM)rfMCMLm M = Market portfolio rf = Risk free rate E(rM) - rf = Market risk premium E(rM) - rf = Market price of risk = Slope of the CAPMMSlope and Market Risk PremiumThe risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio.An individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio.Return and Risk For Individual SecuritiesSecurity Market LineE(r)E(rM)rfSMLbbM = 1.0= [COV(ri,rm)] / m2Slope SML = E(rm) - rf = market risk premium SML = rf + [E(rm) - rf] Betam = [Cov (ri,rm)] / sm2 = sm2 / sm2 = 1SML RelationshipsE(rm) - rf = .08 rf = .03x = 1.25 E(rx) = .03 + 1.25(.08) = .13 or 13%y = .6 e(ry) = .03 + .6(.08) = .078 or 7.8%Sample Calculations for SMLGraph of Sample CalculationsE(r)Rx=13%SMLb1.0Rm=11%Ry=7.8%3%1.25bx.6by.08Disequilibrium ExampleE(r)15%SMLb1.0Rm=11%rf=3%1.25Suppose a security with a  of 1.25 is offering expected return of 15%.According to SML, it should be 13%.Under-priced: offering too high of a rate of return for its level of risk.Disequilibrium Example (cont.)Black’s Zero Beta ModelAbsence of a risk-free assetCombinations of portfolios on the efficient frontier are efficient.All frontier portfolios have companion portfolios that are uncorrelated.Returns on individual assets can be expressed as linear combinations of efficient portfolios.Black’s Zero Beta Model FormulationEfficient Portfolios and Zero CompanionsQPZ(Q)Z(P)E[rz (Q)]E[rz (P)]E(r)sZero Beta Market ModelCAPM with E(rz (m)) replacing rfCAPM & LiquidityLiquidityIlliquidity PremiumResearch supports a premium for illiquidity.Amihud and MendelsonCAPM with a Liquidity Premiumf (ci) = liquidity premium for security if (ci) increases at a decreasing rateLiquidity and Average ReturnsAverage monthly return(%)Bid-ask spread (%)