Capital-Asset--Pricing-Theory-资本资产价格理论

Chapter 13Capital Asset Pricing Theory Learning Objectives Capital market line (CML) Capital Asset Pricing Model (CAPM) Beta compared to Standard Deviation Applying CAPM to security analysis Estimating Beta Beta - good news and bad newsCapital Asset Pricing Model (CAPM) Equation that quantifies security risk and defines a risk/return relationship Based on the idea that investors accept a higher risk only for a higher return Other assumptions are not realistic, but necessary to develop the modelAssumptions of the CAPM Investors have equal information and perceptions, leading to equal expectations Frictionless capital marketsNo transaction costsNo taxes Portfolios may be divided among securities in any proportion for optimization Investors are rational and seek to maximize their expected utility functions All investment is for the same time period All investors can borrow or lend at the risk-free rateEfficient Frontier andthe Optimal Risky Portfolio The efficient frontier is a series of portfolios representing the highest return for a given level of risk or the lowest risk for a given expected return Any individual security will lie inside the efficient frontier, but may be a part of portfolios on the efficient frontier Choosing the optimal efficient frontier depends on individual preferences for risk and return Measuring risk aversion and utility curves still wont provide an objective portfolio choiceDeveloping the Capital Market Line (CML)ERp = (X) ERp1 + (1 - X) RFSDP = (X) SDP1Combinations of risk-free assets and risky portfolios can be used to create portfolios along a line connecting the apex of the efficient frontier and the risk-free rateThe Capital Market Line (CML) Describes the percentage holdings in the risk free asset and the risky diversified market portfolio, surpassing the efficient frontier except at the point of intersection Utility curves may cross the CML, indicating appropriate portfolio selections Borrowing-lending line is the CML, divided where it intersects the efficient frontier (point M) with the lending line on the left and borrowing on the right Portfolio separation theorem allows investors to separate the decision of selecting the risky portfolio from the investors risk preferenceMarket PortfolioThe Market Portfolio (point M) must be the only risky portfolio chosen by all risk-averse investors. Because it is demanded by all investors, it must contain all the securities and other traded assetsCapital Asset Pricing Model Portfolio Ms risk = Market risk Security risk = total risk Security risk = Market risk + firm-specific risk Portfolio Ms risk = (Security 1s market risk + Security 2s market risk + + Security Ns market risk)Relative Risk Relative risk contribution of security i Total risk contribution of security i divided by Total risk of market portfolio, M Known as beta, b, it measures security risk, or volatility relative to the market portfolio Beta greater than 1.0 is riskier than the marketUnderstanding Beta All security betas are measured relative to the market portfolio beta, which equals 1.0 A beta greater than 1.0 means the security contributes more than the average risk to the well-diversified market portfolio The value of beta implies something about returns relative to the market The index used to approximate the market portfolio can affect the beta estimateRisk recap Market risk Firm-specific risk Securitys total risk is market risk plus firm-specific risk Relative market risk for a security is its beta Securitys total risk is beta plus firm-specific risk Beta is the systematic or nondiversifiable risk Diversifiable risk is irrelevant in a well diversified portfolio Decisions made by total risk (standard deviations) instead of beta ignore the systematic risk and diversifiable risk components of total riskDeriving the CAPM All risk averse investors will invest in one risky portfolio, M, which must be the market portfolio of all traded securities Mmust have the same slope as the CML ERi = RF + Risk premium (ERi - RF) = Risk premium The left side is the reward for accepting security riskRisk/return relationships Security systematic risk, beta, can be defined as a ratio to the market return ERi = RF + bi (ERM - RF) Security market line (SML) shows the risk/return relationship for securities and a graphical representation of the CAPM Equation of a line is Y = a + bXa is the y-intercept and b is the slope The y-intercept is the risk-free rate The slope is (ERM - RF) The equation of the SML isERi = RF + (ERM - RF) bi equal to equation for CAPM and similar to CMLDifferences between CML and SML Capital market line measures risk by standard deviation, or total risk Security market line measures risk by beta to find the securitys risk contribution to portfolio M CML graphs only defines efficient portfolios SML graphs efficient and nonefficient portfolios CML eliminates diversifiable risk for portfolios SML includes all portfolios that lie on or below the CML, but only as a part of M, and the relevant risk is the securitys contribution to Ms risk Firm specific risk is irrelevant to each, but for different reasonsCAPM and Security Analysis Value Line provides beta estimates for stocks Ibbotson Associates gives an average yield spread between the S&P 500 Index and the U. S. Treasury bill rate Negative beta means the security is negatively correlated to the market and can significantly reduce portfolio risk With the equation: ERi = RF + bi (ERM - RF) we can estimate the required return for a security, on an SML graph Calculate the predicted return for the security based on todays price, a predicted price a year from today, and expected dividends in the coming yearPredict a holding period return and compare to the SML expected returnIf a security seems likely to have a higher return than its risk level justifies, then it is undervalued (good investment)A lower expected return than its risk would justify suggests a security is overvalued (not a good investment)Estimating Beta A beta estimate measures the changes of a securitys return relative to the market return A security characteristic line graphs the relationship between the return on the market portfolio and a security return The market model uses linear regression to estimate the relationship between the market return and the security returnRegression analysis to estimate BetaDifferences between the SML and Security Characteristic Line SML graphs required return against betas of many securities Security Characteristic Line measures security returns against the market portfolios returns The SML has a slope the Expected rate less the risk-free rate, and an intercept of the risk-free rate The SCL is used to determine how a security return correlates to a market index return and it can be used to estimate beta, the slope of the SCL The SML is used to estimate the required return for a security relative to its risk measured by beta The beta value for the SML comes from the slope estimate of the SCLBeta: good news/bad news The SCL estimates beta and the