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## Optimal Risky Portfolios

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**Optimal Risky Portfolios**Chapter 7 Bodi Kane Marcus Ch 5**p(%)**35 Unique Risk (unsystematic risk) 20 0 Total Risk Market Risk (systematic risk) 10 20 30 40 1,000+ Number Stocks in Portfolio**Portfolios of two risky assets**=0.19 =19%**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.**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:**Bodi Kane Marcus Ch 5**Portfolios of two risky assets • If DE = 1**Bodi Kane Marcus Ch 5**Portfolio Expected Return as a function of investment proportion Expected Return, 13% Equity Fund 8% Debt Fund**Bodi Kane Marcus Ch 5**Problem 5 Expected Return, 20% Equity Fund 12% Debt Fund**Bodi Kane Marcus Ch 5**Portfolio Expected Return as a function of standard deviation =-1 E =.30 Expected Return, rp =0 =1 D Risk, p**Bodi Kane Marcus Ch 5**The Optimal Risky Portfolio with Two Risky Assets and a Risk-Free Asset A = the risk aversion parameter**Bodi Kane Marcus Ch 5**The reward-to-volatility (Sharpe) ratio**CAL(P)**The Determination of Complete Portfolio Expected Return, rp I2 I1 . Opportunity Set of Risky Assets M . ^ rM P ^ rR Optimal Risky Portfolio rRF Optimal Complete Portfolio Risk, p R M**Bodi Kane Marcus Ch 5**The optimal Complete Portfolio**The**Efficient frontier Expected Return, rp Individual Asset Global Minimum- Variance Portfolio 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, (%)**Bodi Kane Marcus Ch 5**The efficient portfolio set E( r ) Efficient Frontier Risky Assets E( r 3) E( r 2) E( r 1) **Bodi Kane Marcus Ch 5**Tugas Kelompok