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Portfolio Managment 3-228-07 Albert Lee Chun

Portfolio Managment 3-228-07 Albert Lee Chun. Capital Asset Pricing Model . Lecture 5. 23 Sept 2007. Today’s Lecture. Portfolio Seclection Criteria of Roy, Kataoka and Tessler. Power of Diversification Market Portfolio Revisited 2 Excel Examples

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Portfolio Managment 3-228-07 Albert Lee Chun

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  1. Portfolio Managment3-228-07Albert Lee Chun Capital Asset Pricing Model Lecture 5 23 Sept 2007

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

  3. Other Portfolio Selection Models

  4. Safety First Criterion • 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. • We look at 3 criteria, that of Roy, Kataoka and Tessler.

  5. Roy’s Criterion Fix RL Minimize Prob (Rp< RL) Maximize k = (E(RP) - RL)/P Example: RL = 5% Mean Return 10% 14% 17% Standard Deviation 5% 4% 8% Difference from 5% (k) -1 -2.25 -1.5

  6. Roy`s Criteria Maximize k kB kC kA k  + RL = E(RP) RL

  7. Kataoka’s Criterion Maximize RL s.t. prob(RP < RL) <= α Ex: α =.05 RP = RL+1.65

  8. Tessler’s Criterion Fix RL Maximize E(Rp) s.t. prob(RP < RL) <= α Ex: α =.05 E(RP) >= RL+1.65

  9. Power of Diversification Risk Nonsystematic Risk (idiosyncratic, diversifiable) PortfolioRisk Market Risk Systematic Risk Number of Stocks 8

  10. Market Portfolio

  11. The Market Portfolio • 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. • This is an example of a value weighted portfolio.

  12. 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 wi=1%

  13. Capital Asset Pricing Model

  14. 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 http://www.afajof.org/association/historyfinance.asp

  15. Capital Asset Pricing Model

  16. 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.

  17. 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.

  18. Betas are Linear Betas are linear Beta(aA+bB) = a *Beta(A)+b*(Beta(B) because cov(aA +bB,M) = a*cov(A,M)+b*cov(B,M)

  19. Security Market Line Security market Line

  20. Example Assume:Rf = 5% (0.05) RM = 9% (0.09) Implied market risk premium = 4% (0.04) E(RA) = 0.05 + 0.70 (0.09-0.05) = 0.078 = 7.8% E(RB) = 0.05 + 1.00 (0.09-0.05) = 0.090 = 09.0% E(RC) = 0.05 + 1.15 (0.09-0.05) = 0.096 = 09.6% E(RD) = 0.05 + 1.40 (0.09-0.05) = 0.106 = 10.6% E(RE) = 0.05 + -0.30 (0.09-0.05) = 0.038 = 03.8%

  21. All Efficient Securities Lie on the SML Security Market Line Negative Beta

  22. When Not in Equilibrium Return Lies Above the SML Stock is Undervalued Droite de marché Return Lies Below the SML Stock is Overvalued

  23. For NextWeek Next week we will: - Continue our discussion of the CAPM • Do some more examples • Talk about preparing for the Midterm • You should read Chapter 8, Section 8.1 – 8.3

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