Lecture 7 Sep 28 2011

Lecture 7 Sep 28 2011 - FINA FINA3104:

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FINA 3104 FINA 3104: Investment Analysis and Portfolio Management Lecture 7 – Portfolio Analyses and the Markowitz Portfolio Selection Model (continued) Darwin Cho Darwin Choi September 28, 2011 Recap from Last Lecture Optimal Complete Portfolio First Order Condition, Utility Function, Utility Indifference Portfolios of Two Risky Asset Portfolios of Two Risky Assets Different Correlations Minimum Variance & Optimal Portfolio Portfolio Opportunity Set Efficient Frontier Optimal Risky Portfolio 2
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Outline of Today’s Lecture Outline of Today s Lecture Optimal Complete Portfolio Diversification Markowitz Selection: N Risky Assets Passive Investing as a Strategy Allocation with No Riskfree Asset Riskfree Lending, No Borrowing Borrowing Rate > Riskfree Rate 3 Portfolio Weights Example (Cont’d Portfolio Weights Example (Cont d) so Optimal Risky Portfolio: w D = 40% in bond w E = 60% in stock * * E( r P* ) = w D E( r D ) + w E E( r E ) = 11% * * P* 2 = w D 2 D 2 + w E 2 E 2 + 2 w D w E DE = 2.0164% ** * * Solve y* = [E( r P* ) – r f ] ÷ A P* 2 y* = [0.11 – 0.05] ÷ 4(0.020164) y =006 ÷ 0 080656 = 74 39% y* = 0.06 ÷ 0.080656 = 74.39% 4
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Portfolio Weights Example Asset E( r ) Uyw Riskfree 5% 0% 5 00% (1 (F) 5.00% y ) Bond Fund (D 8% 12% 5.12% (1 w ) (D) y Stock Fund (E) 13% 20% 5.00% w Min Var. (A) 8.90% 11.45% 6.28% w D = 0.82 w E = 0.18 Opt. Risky (P * ) 11.00% 14.20% 6.97% w D = 0.40 w E = 0.60 Opt. Comp. (C) 9.46% 10.56% 7.23% y = 0.74 5 Optimal Complete Portfolio 74.39% in the Optimal Risky Portfolio means Bonds, Stocks, 25.61% in the Riskfree Asset 29.76% 44.63% 40% of the Optimal Risky Portfolio in bonds (60% in stocks) means 29.76% (40% x 74.39%) Riskfree and 44.63% (60% x 74.39%) of the Complete portfolio is in bonds and stocks Riskfree, 25.61% bonds and stocks. 6
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Outline of Today’s Lecture Outline of Today s Lecture Optimal Complete Portfolio Diversification Markowitz Selection: N Risky Assets Passive Investing as a Strategy Allocation with No Riskfree Asset Riskfree Lending, No Borrowing Borrowing Rate > Riskfree Rate 7 H F C Di ifi ti G? How Far Can Diversification Go? Combining risky securities could lower portfolio standard deviation, if the securities are not perfectly correlated Adding more risky securities strengthens this result (efficient frontier shifts left (efficient frontier shifts left) 8
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This note was uploaded on 11/27/2011 for the course FINA 3104 taught by Professor Darwin during the Spring '11 term at HKUST.

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Lecture 7 Sep 28 2011 - FINA FINA3104:

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