tailieunhanh - Lecture Investments (8th edition): Chapter 7 - Zvi Bodie, Alex Kane, Alan J. Marcus

In this chapter, we first motivate the discussion by illustrating the potential gains from simple diversification into many assets. We then proceed to examine the process of efficient diversification from the ground up, starting with an investment menu of only two risky assets, then adding the risk-free asset, and finally, incorporating the entire universe of available risky securities. We learn how diversification can reduce risk without affecting expected returns. | CHAPTER 7 Optimal Risky Portfolios Diversification and Portfolio Risk Market risk Systematic or nondiversifiable Firm-specific risk Diversifiable or nonsystematic Figure Portfolio Risk as a Function of the Number of Stocks in the Portfolio Figure Portfolio Diversification 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 Two-Security Portfolio: Return = Variance of Security D = Variance of Security E = Covariance of returns for Security D and Security E Two-Security Portfolio: Risk Two-Security Portfolio: Risk Continued Another way to express variance of the portfolio: D,E = Correlation coefficient of returns Cov(rD,rE) = DE D E D = Standard deviation of returns for Security D E = Standard deviation of returns for Security E Covariance Range of values for 1,2 + > r > If r = , the securities would | CHAPTER 7 Optimal Risky Portfolios Diversification and Portfolio Risk Market risk Systematic or nondiversifiable Firm-specific risk Diversifiable or nonsystematic Figure Portfolio Risk as a Function of the Number of Stocks in the Portfolio Figure Portfolio Diversification 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 Two-Security Portfolio: Return = Variance of Security D = Variance of Security E = Covariance of returns for Security D and Security E Two-Security Portfolio: Risk Two-Security Portfolio: Risk Continued Another way to express variance of the portfolio: D,E = Correlation coefficient of returns Cov(rD,rE) = DE D E D = Standard deviation of returns for Security D E = Standard deviation of returns for Security E Covariance Range of values for 1,2 + > r > If r = , the securities would be perfectly positively correlated If r = - , the securities would be perfectly negatively correlated Correlation Coefficients: Possible Values Table Descriptive Statistics for Two Mutual Funds 2p = w12 12 + w22 12 + 2w1w2 Cov(r1,r2) + w32 32 Cov(r1,r3) + 2w1w3 Cov(r2,r3) + 2w2w3 Three-Security Portfolio Table Computation of Portfolio Variance From the Covariance Matrix Table Expected Return and Standard Deviation with Various Correlation Coefficients Figure Portfolio Expected Return as a Function of Investment Proportions Figure Portfolio Standard Deviation as a Function of Investment Proportions Minimum Variance Portfolio as Depicted in Figure Standard deviation is smaller than that of either of the individual component assets Figure and combined demonstrate the relationship between portfolio risk Figure Portfolio Expected Return as a Function of Standard Deviation The relationship depends on the correlation coefficient < < + The .