L Pch9

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L Pch9

  1. 1. Investments Chapter 9: Portfolio Diversification
  2. 2. Diversification: The ‘Free Lunch ’ of Finance <ul><li>An investor can achieve higher returns for a given level of risk through diversification. </li></ul><ul><li>Principle: In terms of Chapter 8: diversification raises the Markowitz mean-variance efficient frontier. </li></ul>
  3. 3. Three Ways to Diversify <ul><li>Diversification across sectors and industries. </li></ul><ul><li>Diversification across asset classes. </li></ul><ul><li>Diversification across regions and countries. </li></ul>
  4. 4. Three Ways to Diversify – Illustration Exhibit 9.1 Correlation matrix for regions, sectors and asset classes (1994 –2003) Source: mba.tck.dartmouth.edu/pages/faculty/ken.french/
  5. 5. Systemic Risk vs. Nonsystemic Risk <ul><li>Systemic Risk </li></ul><ul><li>The risk that comes from the individual exposure of assets to their individual risk factors. Can be diversified away. </li></ul><ul><li>Nonsystemic Risk </li></ul><ul><li>The risk that comes from the common exposure of assets to economy-wide risk factors. Can ’t be diversified away. </li></ul>
  6. 6. International Diversification: I <ul><li>Principle: </li></ul><ul><li>Since international markets are not perfectly correlated investors can achieve reductions in risk BEYOND portfolios with only domestic assets. </li></ul>
  7. 7. International Diversification: II <ul><li>Nowadays, the benefits of international diversification seem to have diminished. </li></ul><ul><li>Reasons: </li></ul><ul><li>1. (For US investors) superior returns in US markets during the 1990s. </li></ul><ul><li>2. Increased correlation between developed countries. </li></ul><ul><li>3. Increased correlation during international market crises. </li></ul>
  8. 8. ‘ A Little Diversification Goes a Long Way’ <ul><li>The incremental contribution to the reduction of a portfolio ’s variance of adding extra assets to a portfolio REDUCES as the number of assets in a portfolio increases. </li></ul>
  9. 9. ‘ A Little Diversification Goes a Long Way’ – Illustration <ul><li>(The above results differ for different correlation coefficients. These coefficients can be interpreted as the systemic risk that cannot be diversified away) </li></ul>Exhibit 9.4(b) Effect of the number of assets and the correlation coefficient on a portfolio’s variance (individual assets are identical)
  10. 10. Barriers to Diversification <ul><li>Main Barriers: </li></ul><ul><li>1. Information Costs </li></ul><ul><li>2. Transaction Costs </li></ul><ul><li>Possible solution for small investors: </li></ul><ul><li>Mutual Funds </li></ul>
  11. 11. Estimation Error: I <ul><li>Construction of efficient portfolios requires the means, variances and covariances of all individual assets. </li></ul><ul><li>Often-used Method: </li></ul><ul><li>Assume historical observations are representative for the future return distribution of assets, assigning equal weight to all observations. </li></ul>
  12. 12. Estimation Error: II <ul><li>Problem: </li></ul><ul><li>Time variation of the return distribution. </li></ul><ul><li>Result: Estimation Errors. </li></ul><ul><li>Related Problem: </li></ul><ul><li>The construction of efficient portfolios is extremely sensitive to estimation errors. </li></ul><ul><li>Solution: Confidence Intervals. </li></ul>
  13. 13. Human Capital and Property Holdings <ul><li>Single most valuable asset most people have is their Human Capital. </li></ul><ul><li>Ideally, investors should incorporate their human capital in their portfolio analysis. </li></ul><ul><li>The same holds for property holdings. </li></ul>
  14. 14. Actual Diversification by Households <ul><li>Empirical evidence indicates household portfolios are often under-diversified. </li></ul>
  15. 15. Portfolio Risk as a Function of the Number of Stocks in the Portfolio Nondiversifiable risk; Systematic Risk; Market Risk Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk n  In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. Thus diversification can eliminate some, but not all of the risk of individual securities. Portfolio risk
  16. 16. The Efficient Set for Many Securities <ul><li>Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios . </li></ul>return  P Individual Assets
  17. 17. The Efficient Set for Many Securities <ul><li>Given the opportunity set we can identify the minimum variance portfolio . </li></ul>return  P minimum variance portfolio Individual Assets
  18. 18. The Efficient Set for Many Securities <ul><li>The section of the opportunity set above the minimum variance portfolio is the efficient frontier. </li></ul>return  P minimum variance portfolio efficient frontier Individual Assets
  19. 19. Optimal Risky Portfolio with a Risk-Free Asset <ul><li>In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills </li></ul>100% bonds 100% stocks r f return 
  20. 20. Riskless Borrowing and Lending <ul><li>Now investors can allocate their money across the T-bills and a balanced mutual fund </li></ul>100% bonds 100% stocks r f return  Balanced fund CML
  21. 21. Riskless Borrowing and Lending <ul><li>With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope </li></ul>return  P efficient frontier r f CML
  22. 22. Market Equilibrium <ul><li>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. </li></ul>return  P efficient frontier r f M CML
  23. 23. The Separation Property <ul><li>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. </li></ul>return  P efficient frontier r f M CML
  24. 24. The Separation Property <ul><li>Investor risk aversion is revealed in their choice of where to stay along the capital allocation line—not in their choice of the line. </li></ul>return  P efficient frontier r f M CML
  25. 25. Optimal Risky Portfolio with a Risk-Free Asset <ul><li>The optimal risky portfolio depends on the risk-free rate as well as the risky assets. </li></ul>100% bonds 100% stocks return  First Optimal Risky Portfolio Second Optimal Risky Portfolio CML 0 CML 1

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