1 / 15

Efficient Diversification I

Efficient Diversification I. Covariance and Portfolio Risk Mean-variance Frontier Efficient Portfolio Frontier. Some Empirical Evidence. In 2000, 40% of stocks in Russell 3000 had returns of -20% or worse. Meanwhile, less than 12% of U.S. stock mutual funds had returns of -20% or below.

december
Télécharger la présentation

Efficient Diversification I

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Efficient Diversification I Covariance and Portfolio Risk Mean-variance Frontier Efficient Portfolio Frontier

  2. Some Empirical Evidence • In 2000, 40% of stocks in Russell 3000 had returns of -20% or worse. • Meanwhile, less than 12% of U.S. stock mutual funds had returns of -20% or below. • Of the 2,397 U.S. stocks in existence throughout 1990s, 22% had negative returns. • In contrast, 0.4% of U.S. equity mutual funds had negative returns.

  3. Diversification and Portfolio Risk • “Don’t put all your eggs in one basket” • Effect of portfolio diversification  Diversifiable risk, non-systematic risk, firm-specific risk, idiosyncratic risk Non-diversifiable risk, systematic risk, market risk 5 15 10 20 # of securities in the portfolio

  4. Covariance and Correlation • Covariance and correlation • Degree of co-movement of two stocks • Covariance: non-standardized measure • Correlation coefficient: standardized measure r2 r2 r2 r1 r1 r1 0<12 <1 -1<12 <0 12 =0

  5. Covariance and Correlation • Example: Two risky assets • Calculating the covariance Means Std. Dev. Cov. Corr.

  6. Diversification and Portfolio Risk • A portfolio of two risky assets • w1: % invested in bond • w2: % invested in stock • Expected return • Variance

  7. Diversification and Portfolio Risk • Example: Portfolio of two risky securities • w in security 1, (1 – w) in security 2 • Expected return (Mean): • Variance • What happens when w changes? • Expected return decreases with increasing w • How about variance ?..

  8. Mean-Variance Frontier • w from 0 to 1 GMVP: Global Minimum Variance Portfolio Mean-variance frontier Security 2 GMVP Security 1

  9. Mean-Variance Frontier • Global Minimum Variance Port. (GMVP) • A unique w • Associated characteristics

  10. Efficient Portfolio Frontier • 67% in Security 1 and 33% in Security 2, what’s so special? • Efficient portfolio has < 67% in 1, and > 33% in 2 w1=0 P Efficient Frontier w1 = .6733 GMVP Inefficient Frontier w1=1

  11. Efficient Portfolio Frontier • Portfolio “P” dominates Security 1 • The same standard deviation • The higher expected return • How to find it? • Since the portfolio has the same standard deviation as Security 1 • Solve the quadratic equation • w = 1 (Security 1) or w = .3465 (Portfolio P)

  12. Efficient Portfolio Frontier • The effect of correlation • Lower correlation means greater risk reduction • Ifr= +1.0, no risk reduction is possible

  13. Efficient Portfolio Frontier • Efficient Portfolio of Many securities • E[rp]: Weighted average of n securities • p2: Combination of all pair-wise covariance measures • Construction of the efficient frontier is complicated • Analytical solution without short-sale constraints • Numerical solution with short-sale constraints • General Features • Optimal combination results in lowest risk for given return • Efficient frontier describes optimal trade-off • Portfolios on efficient frontier are dominant

  14. Efficient Frontier E[r] Efficient frontier Individual assets Global minimum variance portfolio Minimum variance frontier St. Dev.

  15. Wrap-up • How to estimate portfolio return and risk? • What is the mean-variance frontier? • What is the efficient portfolio frontier? • Why do portfolios on efficient frontier dominate other combinations?

More Related