Optimal Risky Portfolios参考.ppt

Figure 7.13 Capital Allocation Lines with Various Portfolios from the Efficient Set The Power of Diversification Remember: If we define the average variance and average covariance of the securities as: The Power of Diversification We can then express portfolio variance as: Table 7.4 Risk Reduction of Equally Weighted Portfolios in Correlated and Uncorrelated Universes Optimal Portfolios and Nonnormal Returns Fat-tailed distributions can result in extreme values of VaR and ES and encourage smaller allocations to the risky portfolio. If other portfolios provide sufficiently better VaR and ES values than the mean-variance efficient portfolio, we may prefer these when faced with fat-tailed distributions. Risk Pooling and the Insurance Principle Risk pooling: merging uncorrelated, risky projects as a means to reduce risk. increases the scale of the risky investment by adding additional uncorrelated assets. The insurance principle: risk increases less than proportionally to the number of policies insured when the policies are uncorrelated Sharpe ratio increases Risk Sharing As risky assets are added to the portfolio, a portion of the pool is sold to maintain a risky portfolio of fixed size. Risk sharing combined with risk pooling is the key to the insurance industry. True diversification means spreading a portfolio of fixed size across many assets, not merely adding more risky bets to an ever-growing risky portfolio. Investment for the Long Run Long Term Strategy Invest in the risky portfolio for 2 years. Long-term strategy is riskier. Risk can be reduced by selling some of the risky assets in year 2. “Time diversification” is not true diversification. Short Term Strategy Invest in the risky portfolio for 1 year and in the risk-free asset for the second year. INVESTMENTS | BODIE, KANE, MARCUS INVESTMENTS | BODIE, KANE, MARCUS Copyright ? 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin CHAPTER 7 Optimal Risky Portfolios The Invest