07.b - 7/16/2011 Chapter7 OptimalRiskyPortfolios Covariance...

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7/16/2011 1 Covariance Chapter 7 Optimal Risky Portfolios -Part±I Portfolios of Two Risky Assets / Markowitz Calculations -Part±II Diversification / Efficient Frontier - Part III Recall the equation we derived in Chapter 6: Two Risky Assets          2 2 CA A B B A A B B s ps wr s wr s wEr    In section 7.2, BKM consider a portfolio p consisting of 2 risky assets: (1) A risky bond fund, D (2) A risky equity fund, E           22 2 A A B B A B AA BB s w w ww psrs Er rs Er    The weights of these funds in the portfolio are: D E w,w
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7/16/2011 2 Now we can rewrite the 2-asset variance equation using covariance notation (as in equation 7.5): Two Risky Assets   22 2 2 2 2, P DD EE DE ww w w C o v r r   Or, using correlation coefficient notation (as in equation 7.7): We now have two equations to describe the characteristics of portfolios consisting of different combinations of assets D and E : 2 2 2 2 P DEDED E w w      p Er wEr    2 2 2 PD D E E D E D E w w C o v r r Two Risky Assets     p Note that if one of the assets is risk-free, say asset D : (1) The asset D variance term is zero (2) The covariance term is zero   2 2 2 D E E D E D E w w C o v r r Which means we are back to the linear E- σ relationship derived in Chapter 6.
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7/16/2011 3 Two Risky Assets 22 2 2 2 2, P SKX NKE ww w w C o v r r   w SKX w NKE E σ -1.00 2.00 -1.86 32.9 -0.50 1.50 -0.33 20.7 -0.40 1.40 -0.02 18.4       pS K X S K XN K E N K E Er w Er  -0.30 1.30 0.28 16.2 -0.20 1.20 0.59 14.2 -0.10 1.10 0.90 12.4 0.00 1.00 1.20 11.0 0.10 0.90 1.51 10.1 0.20 0.80 1.81 9.8 0.30 0.70 2.12 10.2 0.40 0.60 2.42 11.2 0.50 0.50 2.73 12.7 0.60 0.40 3.04 14.5 070 4.00 6.00 8.00 Average Return Skechers-Nike Combination Line 0.70 0.30 3.34 16.5 0.80 0.20 3.65 18.7 0.90 0.10 3.95 21.0 1.00 0.00 4.26 23.4 1.10 -0.10 4.56 25.8 1.20 -0.20 4.87 28.2 1.30 -0.30 5.18 30.7 1.40 -0.40 5.48 33.2 1.50 -0.50 5.79 35.8 2.00 -1.00 7.32 48.6 -4.00 -2.00 0.00 2.00 0.0 10.0 20.0 30.0 40.0 50.0 60.0 Standard Deviation Two Risky Assets    pD DE E
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07.b - 7/16/2011 Chapter7 OptimalRiskyPortfolios Covariance...

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