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CHAPTER 6

CHAPTER 6. Efficient Diversification. Diversification and Portfolio Risk. Market risk Systematic or nondiversifiable Firm-specific risk Diversifiable or nonsystematic. Portfolio Risk as a Function of the Number of Stocks in the Portfolio. Portfolio Diversification.

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CHAPTER 6

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  1. CHAPTER 6 Efficient Diversification

  2. Diversification and Portfolio Risk Market risk Systematic or nondiversifiable Firm-specific risk Diversifiable or nonsystematic

  3. Portfolio Risk as a Function of the Number of Stocks in the Portfolio

  4. Portfolio Diversification

  5. Covariance and Correlation Portfolio risk depends on the correlation between the returns of the assets in the portfolio Covariance and the correlation coefficient provide a measure of the way returns two assets vary

  6. Two-Security Portfolio: Return

  7. Two-Security Portfolio: Risk = Variance of Security D = Variance of Security E = Covariance of returns for Security D and Security E

  8. Covariance Cov(rD,rE) = DEDE D,E = Correlation coefficient of returns D = Standard deviation of returns for Security D E = Standard deviation of returns for Security E

  9. Correlation Coefficients: Possible Values Range of values for 1,2 + 1.0 >r> -1.0 If r = 1.0, the securities would be perfectly positively correlated If r = - 1.0, the securities would be perfectly negatively correlated

  10. Descriptive Statistics for Two Mutual Funds

  11. Three-Security Portfolio 2p = w1212 + w2222 + w3232 + 2w1w2 Cov(r1,r2) Cov(r1,r3) + 2w1w3 + 2w2w3 Cov(r2,r3)

  12. Computation of Portfolio Variance From the Covariance Matrix

  13. Expected Return and Standard Deviation with Various Correlation Coefficients

  14. Portfolio Expected Return as a Function of Investment Proportions

  15. Portfolio Standard Deviation as a Function of Investment Proportions

  16. Portfolio Expected Return as a Function of Standard Deviation

  17. The relationship depends on the correlation coefficient -1.0 << +1.0 The smaller the correlation, the greater the risk reduction potential If r = +1.0, no risk reduction is possible Correlation Effects

  18. The Opportunity Set of the Debt and Equity Funds and Two Feasible CALs

  19. The Sharpe Ratio Maximize the slope of the CAL for any possible portfolio, p The objective function is the slope:

  20. The Opportunity Set of the Debt and Equity Funds with the Optimal CAL and the Optimal Risky Portfolio

  21. Determination of the Optimal Overall Portfolio

  22. The Proportions of the Optimal Overall Portfolio

  23. Markowitz Portfolio Selection Model Security Selection First step is to determine the risk-return opportunities available All portfolios that lie on the minimum-variance frontier from the global minimum-variance portfolio and upward provide the best risk-return combinations

  24. The Minimum-Variance Frontier of Risky Assets

  25. Markowitz Portfolio Selection Model Continued We now search for the CAL with the highest reward-to-variability ratio

  26. The Efficient Frontier of Risky Assets with the Optimal CAL

  27. The Efficient Portfolio Set

  28. Capital Allocation and the Separation Property The separation property tells us that the portfolio choice problem may be separated into two independent tasks Determination of the optimal risky portfolio is purely technical Allocation of the complete portfolio to T-bills versus the risky portfolio depends on personal preference

  29. Capital Allocation Lines with Various Portfolios from the Efficient Set

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