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1 Optimal Risky Portfolios Chapter 7 Bodi Kane Marcus Ch 5 p (%) 35 0 Total Risk 20 Unique Risk (unsystematic risk) Market Risk (systematic risk) 10 20 30 40 1,000+ Number Stocks in Portfolio Portfolios of two risky assets rˆP w D rˆD w E rˆE Note : w E 1 - w D (Cov rD , rE ) P w w 2w D w E ρ DE D E 2 D 2 D 2 E 2 E rˆP expected return of portfolio rˆD expected return of stock D r̂E expected return of stock E D Standard deviation of Stock D E Standard deviation of Stock E P Standard deviation of Portfolio w D Proportion of stock D to the entire portfolio w E Proportion of stock E to the entire portfolio DE the Coefficien t Correlatio n between Stock A and Stock B Portfolios of two risky assets rˆP w D rˆD w E rˆE Note : w E 1 - w D (Cov rD , rE ) P w w 2w D w E ρ DE D E 2 D 2 D 2 E 2 E P (0.16 * 0.0225) (0.36 * 0.09) 2 * 0.4 0.6 0.1* 0.15 0.3 =0.19 =19% 5 Bodi Kane Marcus Ch 5 Covariance • A measure of the degree to which returns on two risky assets move in tandem. A positive covariance means that asset returns move together. A negative covariance means returns move inversely. 6 Bodi Kane Marcus Ch 5 Correlation Coefficient A measure that determines the degree to which two variable's movements are associated. The correlation coefficient is calculated as: 7 Bodi Kane Marcus Ch 5 Portfolios of two risky assets • If DE = 1 P wD D wE E 8 Expected Return, Bodi Kane Marcus Ch 5 Portfolio Expected Return as a function of investment proportion 13% Equity Fund 8% Debt Fund - 0.5 0 1 2.0 W stocks 1.5 1 0 -1.0 W bonds 9 Expected Return, Bodi Kane Marcus Ch 5 Problem 5 20% Equity Fund 12% Debt Fund - 0.5 0 1 2.0 W stocks 1.5 1 0 -1.0 W bonds 10 Bodi Kane Marcus Ch 5 Expected Return, rp Portfolio Expected Return as a function of standard deviation =-1 E =.30 =0 =1 D Risk, p 11 The Optimal Risky Portfolio with Two Risky Assets and a Risk-Free Asset Bodi Kane Marcus Ch 5 E (rD ) E (rE ) A( D E DE ) wD 2 2 A( D E 2 D E DE ) 2 E A = the risk aversion parameter 12 Bodi Kane Marcus Ch 5 The reward-to-volatility (Sharpe) ratio sA E (rA ) rf Max sP A E (rP ) rf P Expected Return, rp I2 ^ rM ^ rR . . I1 M Opportunity Set of Risky Assets P Optimal Risky Portfolio rRF Optimal Complete Portfolio R M Risk, p The Determination of Complete Portfolio CAL(P) 14 Bodi Kane Marcus Ch 5 The optimal Complete Portfolio The Expected Return, rp Efficient frontier Global MinimumVariance Portfolio Individual Asset Minimum-Variance Frontier Risk, p The Opportunity Set of The Debt and Equity funds with the optimal CAL and the optimal risky portfolio Expected Return, (%) The Capital Allocation Line (CAL): E P Opportunity set of risky asset rRF D Risk, (%) 17 Bodi Kane Marcus Ch 5 The efficient portfolio set E( r ) Efficient Frontier Risky Assets E( r 3) E( r 2) E( r 1) 18 Tugas Kelompok Klp Felix -ffs RDPU Venny Schroder Dana Likuid Schroder Dana Obl Panin Dana Ekstra Unggulan Timothy Manulife DK Manulife Obl Ngr Hilda Mathew Ivana Gentry Mandiri Investa PU Mandiri Investa DU Mandiri Investa Mandiri Investa Aktif Atraktif Mandiri Investa PU Fortis rUPIAH Plus Panin Dana Schroder Dana II Unggulan Prestasi Plus Manulife Manulife Manulife Dana Manulife Dana DanaPasar Uang Pendapatan Tetap Berimbang Ekuitas Batavia Dana Kas Manulife Obl Neg Manulife Dana Panin Dana Prima Maxima Indonesia Bertumbuh Berimbang Manulife Dana Kas Manulife Obl Manulife Dan Stabil Manulife Dana Unggulan Berimb Saham Mandiri Investa PU Mandiri Investa DU Manulife Dana Manulife Saham Campuran II Andalan Danny Dyson-ffs RDPT Bodi Kane Marcus Ch 5 Mandiri Investa PU Fortis Prima II RDC RDS Fortis Pesona Schroder Dana Prestasi Plus Panin Dana Maxima Fortis Ekuitra Manulife Saham Andalan 19 Bodi Kane Marcus Ch 5 In order to run this model, you must have your Excel's "solver add-in" installed to your computer. To install the "solver add-in", 1. From the menu, choose "TOOLS", 2. Choose, "ADD-INS", 3. In the "Add-Ins Available" list, have your "SOLVER ADD-IN" checked. If you have not chosen the full installment option when you had been installing your Microsoft Office, you might need your original Microsoft Office disks during this configuration. METIN KILIC