PORTFOLIO THEORY notes

# PORTFOLIO THEORY notes - PORTFOLIO THEORY Taken from Bodie,...

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PORTFOLIO THEORY Taken from Bodie, Kane, and Marcus Risk and Risk Aversion 1. Investors avoid risk 2. There is a utility function that includes risk and reward 3. Risk is measured in the context of a portfolio w 1 = \$150,000 (up to) w = \$100,000 w 2 = \$80,000 (down to) E(w) = .6*150,000 + .4*80,000 = 122,000 σ 2 (w) = .6(150,000 – 122,000) 2 + .4(80,000-122,000) 2 = 1,776,000,000 σ(w) = 34,292.86 (std. dev) Consider Treasury Bills as an alternative addition to the portfolio profit \$50,000 (profit) risky asset \$100,000 \$-20,000 (loss) T Bills \$5000 (var = 0) Risk premium \$22,000 (expected value of the profit) - \$5,000 = \$17,000. Utility Function Utility function of the Association of Investment Management and Research U = E(r) - .005A σ 2 A an index of risk aversion .005 so that we can use % rather than decimals Example E(r) = 22%, σ = 34% risk premium 17% A = 3 – moderate risk aversion 22-.005*3*34 2 = 4.66% < 5% Stay with Treasuries

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higher E(r) utility Q E(r p ) p σ p σ Utility function indifference curves
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## This note was uploaded on 11/23/2009 for the course FIN 5208 taught by Professor Murphy during the Spring '09 term at Temple.

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PORTFOLIO THEORY notes - PORTFOLIO THEORY Taken from Bodie,...

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