两基金分离定理和资产定价模型ppt课件

1、CHAPTER THREE: Portfolio Theory, Fund Separation and CAPMMarkowitz Portfolio Selection There is no single portfolio that is best for everyone. The Life Cycle different consumption preference Time Horizons different terms preference Risk Tolerance different risk aversion Limited Variety of Portfolio

2、Limited “finished products in marketsThe Trade-Off Between Expected Return and Risk E r1 2rE121w2w Expected Return Risk WeightAsset 1Asset 2 E rwE rw E rwwww122212222121121 Portfolio of two assets 11is correlation coefficient:Markowitzs contribution 1: The measurement of return and riskMini Case 1:

3、Portfolio of the Riskless Asset and a Single Risky Asset 0,22frrE E rrw E rrwff11 wE rrE rrE rrE rrffff111Suppose , how to achieve a target expected return ? %20%,14%,611rErf %11rE %5 .12%20%5 .62%5 .62%6%14%6%1111wrrErrEwffIs the portfolio efficient ? The Diversification PrincipleMini Case 2: Portf

4、olio of Two Risky Assetswwww122212211 1ww121The Diversification Principle The standard deviation of the combination is less than the combination of the standard deviations. Asset 1 Asset 2Expected Return 0.14 0.08Standard Deviation 0.20 0.15Correlation Coefficient 0.6R0100% 8% 0.15C 10% 90% 8.6%0.14

5、79Minimum Variance Portfolio 17% 83%9.02%0.1474D 50% 50% 11%0.1569Symbol Proportion in Asset 1Proportion in Asset 2Portfolio Expected ReturnPortfolio Standard DeviationS100%0 14% 0.20Hyperbola Frontier of Two Risky Assets Combination.2000C0.1569.1500.1479.0860.0902.1100.1400SDR.0800 rEMinimum Varian

6、ce PortfolioThe Optimal Combination of Two Risky Assets Diversificationwnini11,Suppose , Thennininijjijininjninijjijniiiijnnnnnn11122211112122111111Let ,n0ninijjijijnn1121Let ,1121221nnnijjj inijinijSystematic ExposureMarkowitzs contribution 2: Diversification.Mini Case 3: Portfolio of Many Risky As

7、sets E riin1,Expected return: :ijCovariance: :i jn,1 E rw E rwwiiinijijjnin121120? min. .wijijjniniiiniinwws tw E rE rw211111Resolving the quadratic programming, get the minimum variance frontier Efficient Frontier of Risky Assets The Mean-Variance Frontier E rmin0Indifference Curve of UtilityOptima

8、l Portfolio of Risky AssetsProposition!The variance of a diversified portfolio is irrelevant to the variance of individual assets. It is relevant to the covariance between them and equals the average of all the covariance. Systematic risk cannot be diversifiedProposition!Only unsystematic risks can

9、be diversified.Systematic risks cannot be diversified. They can be hedged and transferred only.Markowitzs contribution 3: Distinguishing systematic and unsystematic risks.Proposition!There is systematic risk premium contained in the expected return. Unsystematic risk premium cannot be got through tr

10、ansaction in competitive markets. iirE,Only systematic risk premium contained, no unsystematic risk premium contained.Both systematic and unsystematic volatilities containedTwo Fund SeparationThe portfolio frontier can be generated by any two distinct frontier portfolios.Theorem:Practice:If individu

11、als prefer frontier portfolios, they can simply hold a linear combination of two frontier portfolios or mutual funds. E r0Orthogonal Characterization of the Mean-Variance FrontierOrthogonal Characterization of the Mean-Variance FrontierP(x)=0P(x)=1R*1E=0E=1Re*ieiinrwrr*in*eiirwrrProposition: Every r

12、eturn ri can be represented as 0 Efficient Frontier of Risky Assets The Portfolio Frontier: where is R*? E r0R*w1w2w3inSome Properties of the Orthogonal Characterization Capital Market Line (CML)rfM E r0Indifference Curve 2Indifference Curve 1CAL 1CAL 2CMLPP can be the linear combination of M and rf

13、CAL Capital Allocation Line Combination of M and Risk-free SecuritywM The weight invested in portfolio M1 wM The weight invested in risk-free security E rrE rrwpfmfMppMM Market Portfolio Definition: Definition: A portfolio that holds all assets in A portfolio that holds all assets in proportion to t

14、heir observed market proportion to their observed market values is called the Market Portfolio.values is called the Market Portfolio.Security Market Value CompositionStock A $66 billion 66%Stock B $22 billion 22%Treasury $12 billion 12%Total $100 billion 100%M is a market portfolio of risky assetsTw

15、o fund separationMarket clearing!Substitute: Market IndexCapital Asset Pricing Model (CAPM) Assumptions: 1. Many investors, they are price takers. The market is perfectly competitive. 2. All investors plan for one identical holding period. 3. Investments to publicly traded financial assets. Financin

16、g at a fixed risk free rate is unlimited. 4. The market is frictionless, no tax, no transaction costs. 5. All investors are rational mean variance optimizers. 6. No information asymmetry. All investors have their homogeneous expectations.Derivation of CAPM Portfolio of risky assetsppijijjninww1112wi

17、ni:,1The weightsIf (market portfolio), Mp njijMjiMw1)(211)(niiMMiMwThe exposure of the market portfolio of risky assets is only related to the correlation between individual assets and the portfolio.M E rMrf E r01.0SMLDerivation of CAPM: Security Market LineE(rM)-rFiiMMiMirr221iiMM2)(irE E rrE rrifM

18、fMiM2 Security Market Line (SML) E rrE rrifMfMiM2iiMM2 E rrE rrifiMfpiiinw1 are additive E rrE rrpfpMf Model ModelUnderstanding Risk in CAPM In CAPM, we can decompose an assets return into three pieces:ifMiifirrrr)(0),(0)(iMirCovrEwhere Three characteristic of an asset: Beta Sigma AplhaM E rMrf E r01.0SMLThe market becomes more aggressiveThe market becomes more conserva