Lecture 6 Sep 26 2011

Lecture 6 Sep 26 2011 - FINA FINA3104:

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FINA 3104 FINA 3104: Investment Analysis and Portfolio Management Lecture 6 – Portfolio Analyses and the Markowitz Portfolio Selection Model Darwin Cho Darwin Choi September 26, 2011 Recap from Last Lecture Utility Indifference Risk & Return for Security Portfolios Mean Variance Criterion Allocation Decision Levels Asset Allocation & Security Selection Complete Portfolio Return & Risk A Risky Asset & A Riskfree Asset The Capital Allocation Line All Possible Complete Portfolios 2
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Outline of Today’s Lecture Outline of Today s Lecture Risk Tolerance & Portfolio Choice Portfolios of Two Risky Assets Minimum Variance & Optimal Portfolio Optimal Complete Portfolio 3 Risk Tolerance & Asset Allocation Given that: E( r C ) = r f + y [E( r P ) – r ] ) r f C = y P U C = E[ r C ] – ½A C 2 U C = r f + y [E( r P ) – r ] – ½A y 2 P 2 f What is the Optimal Asset Allocation, y* = ? 4
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Finding the Optimal Allocation How? Maximize Investor Utility (A=4) Max U C = r + y [E( r P ) – r ] – ½A y 2 P 2 f f Find y at U C / y = 0 (First order condition) i.e., [E( r P ) – r f ] – Ay P 2 = 0 Hence: y* = [E( r P ) – r f ] ÷ A P 2 Numerically: y* = [0.15 – 0.07] ÷ 4(0.22) 2 y* = 0.08 ÷ 4(0.0484) = 41.32% 5 Optimal Allocation: Graphicall 10% Optimal Allocation: Graphically U C = r f + y [E( r P ) – r f ] – ½A y 2 P 2 8% C* U( y* ) 8.65% Utility U( y ) 6% 4% y* = [E( r P ) – r f ] ÷ A P 2 U(y*) = r f + y* [E( r P ) – r f ] – ½A y* 2 P 2 2% y 0% 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 y* = 0.4132 6
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Optimal Allocation: Graphicall Optimal Allocation: Graphically The Optimal Portfolio, C *, involves y * = 41.32%. Its expected return Utility Indifference Curves (A=4) Return E( r ) Capital Its expected return, E( r C * ) = 10.28% and standard deviation, Allocation Line (CAL) C * = 9.02% E( r P ) C* E( r C* ) 10.28% with utility of 8.65% 15% P Utility, U = 4.653% Utility, U = 8.653% Suboptimal Optimal Unfeasible Ri k r f 7% F Utility, U = 12.653% C* = 9.02% Risk P = 22% 7 Some more details about CA Some more details about CAL Can we short sell the riskfree asset (1 – y* < 0)?
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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 6 Sep 26 2011 - FINA FINA3104:

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