0 Portfolio Managment Albert Lee Chun Capital Asset Pricing Model Lecture 5 23 Sept 2007

Albert Lee Chun Portfolio Management 1 Today’s Lecture Portfolio Seclection Criteria of Roy, Kataoka and Tessler. Portfolio Seclection Criteria of Roy, Kataoka and Tessler. Power of Diversification Power of Diversification Market Portfolio Revisited Market Portfolio Revisited 2 Excel Examples 2 Excel Examples Intro to the Capital Asset Pricing Model Intro to the Capital Asset Pricing Model

Albert Lee Chun Portfolio Management 2 Other Portfolio Selection Models

Albert Lee Chun Portfolio Management 3 Safety First Criterion Investors may find it too complex to go through a utility maximization algorithm. Investors may find it too complex to go through a utility maximization algorithm. They may want to avoid bad outcomes, such a scenario where they lose a significant portion of their wealth. They may want to avoid bad outcomes, such a scenario where they lose a significant portion of their wealth. We look at 3 criteria, that of Roy, Kataoka and Tessler. We look at 3 criteria, that of Roy, Kataoka and Tessler.

Albert Lee Chun Portfolio Management 4 Roy’s Criterion Example: R L = 5% Mean Return10%14%17% Standard Deviation 5%4%8% Difference from 5% (k)-1   -1.5  Fix R L Minimize Prob (R p < R L ) Maximize k = (E(R P ) - R L )/  P

Albert Lee Chun Portfolio Management 5 Roy`s Criteria kAkA RLRL kCkC kBkB k  + R L = E(R P ) Maximize k

Albert Lee Chun Portfolio Management 6 Kataoka’s Criterion Maximize R L s.t. prob (R P < R L ) <= α Ex: α =.05 R P = R L 

Albert Lee Chun Portfolio Management 7 Tessler’s Criterion Fix R L Maximize E(R p ) s.t. prob (R P < R L ) <= α Ex: α =.05 E(R P ) >= R L 

Albert Lee Chun Portfolio Management 88 Power of Diversification Risk Number of Stocks Market Risk Systematic Risk Portfolio Risk Nonsystematic Risk (idiosyncratic, diversifiable)

Albert Lee Chun Portfolio Management 9 Market Portfolio

Albert Lee Chun Portfolio Management 10 The Market Portfolio The market portfolio represents the entire market of risky securities. The market portfolio represents the entire market of risky securities. The weight on each security is therefore its market weight, given by the ratio of the market capitalization of the security divided by the total market capitalization. The weight on each security is therefore its market weight, given by the ratio of the market capitalization of the security divided by the total market capitalization. This is an example of a value weighted portfolio. This is an example of a value weighted portfolio.

Albert Lee Chun Portfolio Management 11 Market Portfolio Example Suppose the total value of the market is $100,000,000 dollars. Suppose there exists 500,000 shares of a security in circulation with market price of $2 per share. This security comprises 1% of the total market capitalisation ($1,000,000 / $100,000,000 ) Thus, the weight of this security in the market portfolio is w i =1%

Albert Lee Chun Portfolio Management 12 Capital Asset Pricing Model

Albert Lee Chun Portfolio Management 13 William Sharp 1990 Nobel Prize in Economics for his contributions to the theory of price formation for financial assets, the so- called, Capital Asset Pricing Model (CAPM) Interview with Sharp and Markowitz

Albert Lee Chun Portfolio Management 14 Capital Asset Pricing Model

Albert Lee Chun Portfolio Management 15 Expected Returns Depends on Beta The expected return on an asset is determined by the beta of asset, which also measures the covariance between the return on the asset and the return on the market portfolio. The expected return on an asset is determined by the beta of asset, which also measures the covariance between the return on the asset and the return on the market portfolio.

Albert Lee Chun Portfolio Management 16 Excess Returns and Beta The expected excess return of a security is proportional to the expected excess return of the market. The proportionality factor is beta. It is the covariance of an asset with the market that determines the excess returns! Assets with a negative beta reduces the overall risk of the portfolio and investors are willing to accept a rate of return that is lower than the risk-free rate of return.

Albert Lee Chun Portfolio Management 17 Betas are Linear Betas are linear Beta(aA+bB) = a *Beta(A)+b*(Beta(B) Beta(aA+bB) = a *Beta(A)+b*(Beta(B)because cov(aA +bB,M) = a*cov(A,M)+b*cov(B,M) cov(aA +bB,M) = a*cov(A,M)+b*cov(B,M)

Albert Lee Chun Portfolio Management 18 Security Market Line Security market Line

Albert Lee Chun Portfolio Management 19 Example Assume: Rf = 5% (0.05) R M = 9% (0.09) R M = 9% (0.09) Implied market risk premium = 4% (0.04) E(R A ) = ( ) = = 7.8% E(R B ) = ( ) = = 09.0% E(R C ) = ( ) = = 09.6% E(R D ) = ( ) = = 10.6% E(R E ) = ( ) = = 03.8%

Albert Lee Chun Portfolio Management 20 All Efficient Securities Lie on the SML Negative Beta Security Market Line

Albert Lee Chun Portfolio Management 21 When Not in Equilibrium Return Lies Above the SML Stock is Undervalued Return Lies Below the SML Stock is Overvalued Droite de marché

Albert Lee Chun Portfolio Management For Next Week Next week we will: - Continue our discussion of the CAPM - Do some more examples - Talk about preparing for the Midterm You should read You should read Chapter 8, Section 8.1 – 8.3 Chapter 8, Section 8.1 –