Portfolio Management

Portfolio Management - FIN 6275 (PART I) Investment...

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FIN 6275 (P ART I) Investment Analysis and Global Portfolio Management P ORTFOLIO M ANAGEMENT H OMEWORK I A LEXANDER A BAWI A MANDA G OLDIN M Y L AN L E S AVANTHI S ILVA F EI X IE K UAN -Y ING C HEN F EBRUARY 18, 2012 1
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1. Analysis of Stand-Alone Risk and Return: a. Plot all portfolios in a Mean-Variance framework (i.e. return – standard-deviation graph). 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.009 0.0095 0.01 0.0105 0.011 0.0115 0.012 Standard Deviation Expected Return 6 Portfolios in Mean- Variance framework A B C F E D A: Durable D: Utilities B: Energy E: Health C: Business Equipment F: Money b. Is any of the portfolios dominated by any other portfolio? If yes, which one(s) is (are) dominated and by which other portfolio(s)? From the graph we can say that portfolio E(Health) dominates portfolio F(Money) and portfolio A (Durable). Portfolio D is also superior to portfolio A. Portfolio B dominates portfolio A and C. c. Calculate the utility of an investor with a risk-aversion of A=5 from holding each portfolio? Which portfolio would this investor prefer? Portfolio U @ A=5 Portfolio A - “Durbl” -0.0015 Portfolio B - “Enrgy” 0.0036 Portfolio C - “BusEq” -0.0026 Portfolio D - “Utils” 0.0060 Portfolio E - “Hlth” 0.0057 Portfolio F - “Money” 0.0028 It is obvious that this investor would prefer Utilities portfolio (D) 2
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d. Calculate the utility of an investor with a risk-aversion of A=2.5 from holding each portfolio? Which portfolio would this second investor prefer? Portfolio U @ A=2.5 Portfolio A - “Durbl” 0.0041 Portfolio B - “Enrgy” 0.0076 Portfolio C - “BusEq” 0.0039 Portfolio D - “Utils” 0.0080 Portfolio E - “Hlth” 0.0085 Portfolio F - “Money” 0.0067 This second investor would prefer Health portfolio (E). e. Based on your findings, is there a portfolio which is the best for all investors? There is not a best portfolio for all investors. As we can see from part c, d, the best portfolio for an individual depends on his risk-aversion level, i.e the risk aversion coefficient. f. What is the risk aversion coefficient, A, of an investor if he/she is indifferent between the preferred portfolio of investor A=5 (in 1.c.) and the preferred portfolio of investor A=2.5 (in 1.d.) ? Note: Solve this one analytically (i.e. by hand). What is the utility level of this investor from holding either portfolio? A = 4.0365 U(health) = U (utils) = 0.0068 g. From now on assume an investor has a risk aversion level of A=2.5. Plot this investor’s indifference curve across his preferred portfolio. What is the utility of this investor from holding this best portfolio 0 0.05 0.1 0.15 0 0.005 0.01 0.015 0.02 0.025 0.03 Standard Deviation Expected Return Indifference Curve with A=2.5 3
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h. Suppose now that this investor could also invest in the risk-free rate which is now 0.004 per month. If he decides to allocate his money between the risk-free rate and one of the portfolios, which portfolio would he choose? Plot the best
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Portfolio Management - FIN 6275 (PART I) Investment...

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