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Essentials of Investments: Chapter 6 - Efficient Diversification

Essentials of Investments: Chapter 6 - Efficient Diversification includes Two-Security Portfolio, Correlation Coefficients, Three Security Portfolio, Minimum Variance Combination, Extending Concepts to All Securities, Optimal Risky Portfolios. | 1 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Chapter 6 Efficient Diversification Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc. All rights reserved. 2 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Two-Security Portfolio: Return rp = W1r1 + W2r2 W1 = Proportion of funds in Security 1 W2 = Proportion of funds in Security 2 r1 = Expected return on Security 1 r2 = Expected return on Security 2 n S Wi = 1 i=1 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc. All rights reserved. 3 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Two-Security Portfolio: Risk sp2 = w12s12 + w22s22 + 2W1W2 Cov(r1r2) s12 = Variance of Security 1 s22 = Variance of Security 2 Cov(r1r2) = Covariance of returns for Security 1 and Security 2 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc. All rights reserved. 4 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Covariance Cov(r1r2) = r1,2s1s2 r1,2 = Correlation coefficient of returns s1 = Standard deviation of returns for Security 1 s2 = Standard deviation of returns for Security 2 Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc. All rights reserved. 5 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Correlation Coefficients: Possible Values Range of values for r 1,2 -1.0 < r < 1.0 If r = 1.0, the securities would be perfectly positively correlated If r = - 1.0, the securities would be perfectly negatively correlated Irwin / McGraw-Hill © 2001 The McGraw-Hill Companies, Inc. All rights .