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Лекц 14 Portfolio diversification

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- 1. Portfolio Diversification
- 2. The Efficient Set for Two Assets Risk Return 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50.00% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100% 8.2% 7.0% 5.9% 4.8% 3.7% 2.6% 1.4% 0.4% 0.9% 2.0% 3.08% 4.2% 5.3% 6.4% 7.6% 8.7% 9.8% 10.9% 12.1% 13.2% 14.3% 7.0% 7.2% 7.4% 7.6% 7.8% 8.0% 8.2% 8.4% 8.6% 8.8% 9.00% 9.2% 9.4% 9.6% 9.8% 10.0% 10.2% 10.4% 10.6% 10.8% 11.0% Portfolo Risk and Return Combinations Portfolio Return % in stocks 12.0% 11.0% 10.0% 9.0% 8.0% 7.0% 6.0% 5.0% 0.0% 100% stocks 100% bonds 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% Portfolio Risk (standard deviation) We can consider other portfolio weights besides 50% in stocks and 50% in bonds …
- 3. The Efficient Set for Two Assets Risk Return 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100% 8.2% 7.0% 5.9% 4.8% 3.7% 2.6% 1.4% 0.4% 0.9% 2.0% 3.1% 4.2% 5.3% 6.4% 7.6% 8.7% 9.8% 10.9% 12.1% 13.2% 14.3% 7.0% 7.2% 7.4% 7.6% 7.8% 8.0% 8.2% 8.4% 8.6% 8.8% 9.0% 9.2% 9.4% 9.6% 9.8% 10.0% 10.2% 10.4% 10.6% 10.8% 11.0% Portfolo Risk and Return Combinations 12.0% Portfolio Return % in stocks 11.0% 10.0% 100% stocks 9.0% 8.0% 7.0% 6.0% 100% bonds 5.0% 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% Portfolio Risk (standard deviation) Note that some portfolios are “better” than others. They have higher returns for the same level of risk. These comprise the efficient frontier.
- 4. return Two-Security Portfolios with Various Correlations 100% stocks ρ = -1.0 100% bonds ρ = 1.0 ρ = 0.2 σ Relationship depends on correlation coefficient -1.0 < ρ < +1.0 If ρ = +1.0, no risk reduction is possible If ρ = –1.0, complete risk reduction is possible
- 5. Perfect Positive Correlation Corr(RA, RB) = 1
- 6. Perfect Negative Correlation Corr(RA, RB) = −1
- 7. Zero Correlation Corr(RA, RB) = 0
- 8. Portfolio Risk as a Function of the Number of Stocks in the Portfolio σ Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk Portfolio risk Nondiversifiable risk; Systematic Risk; Market Risk n Thus diversification can eliminate some, but not all of the risk of individual securities.
- 9. return The Efficient Set for Many Securities σP Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios.
- 10. return The Efficient Set for Many Securities (contd.) minimum variance portfolio σP Given the opportunity set we can identify the minimum variance portfolio.
- 11. return The Efficient Set for Many Securities (contd.) c effi ie t i er ron nt f minimum variance portfolio σP The section of the opportunity set above the minimum variance portfolio is the efficient frontier.
- 12. return Optimal Risky Portfolio with a Risk-Free Asset rf σ In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills
- 13. return Riskless Borrowing and Lending CM L rf σ Now investors can allocate their money across the T-bills and a balanced mutual fund
- 14. return Choice of Capital Market Line CM L efficient frontier rf σP With a risk-free asset available and the efficient frontier identified, we choose the capital market line with the steepest slope
- 15. return Market Equilibrium CM L efficient frontier M rf σP With the capital allocation line identified, all investors choose a point along the line—some combination of the risk-free asset and the market portfolio M. In a world with homogeneous expectations, M is the same for all investors.
- 16. return Market Equilibrium (contd.) CM L rf σ Just where the investor chooses along the capital allocation line depends on his risk tolerance. The big point though is that all investors have the same CML (Capital Market Line).
- 17. return Market Equilibrium (contd.) CM L Optimal Risky Portfolio rf σ All investors have the same CML because they all have the same optimal risky portfolio given the riskfree rate.
- 18. return The Separation Property CM L efficient frontier M rf σP The Separation Property states that the market portfolio, M, is the same for all investors—they can separate their risk aversion from their choice of the market portfolio.
- 19. return The Separation Property (contd.) CM L efficient frontier M rf σP Investor risk aversion is revealed in their choice of where to stay along the capital market line—not in their choice of the line.
- 20. return The Separation Property (contd.) CM L Optimal Risky Portfolio rf σ The separation property implies that portfolio choice can be separated into two tasks: (1) determine the optimal risky portfolio, and (2) selecting a point on the CML.
- 21. Dependence of Optimal Risky return Portfolio on Risk-Free Asset 1 f 0 f r r L 0 CML 1 CM First Optimal Risky Portfolio Second Optimal Risky Portfolio σ The optimal risky portfolio depends on the riskfree rate as well as the risky assets.

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