tk roy and sk mazumder 2007 multi objective mean

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Unformatted text preview: µ) + 1 u￿￿ (µ)σ 2 + 2 ˜ variance: σ 2 = E(W − µ)2 1 ￿￿￿ 3! u (µ)γ + 1 ￿￿￿￿ 4! u (µ)κ + ··· ˜ third central moment: γ = E(W − µ)3 , ˜ fourth central moment: κ = E(W − µ)4 γ κ related to skewness (i.e. 3 ) and kurtosis (i.e. 4 ) σ σ http://mvpprograms.com/help/mvpstats/distributions/SkewnessKurtosis K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 30 1 1 ˜ E[u(W )] ≈ u(µ) + 1 u￿￿(µ)σ 2 + 3! u￿￿￿(µ)γ + 4! u￿￿￿￿(µ)κ 2 ˜ Now define V (µ, σ 2 , γ , κ) := E[u(W )] ∂V 1 = u￿￿ (µ) 2 ∂σ 2 If investor is risk averse, then u￿￿ < 0 and investors dislike variance ∂V 1 = u￿￿￿ (µ) ∂γ 3! ∂V 1 = u￿￿￿￿ (µ) ∂κ 4! K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 31 Skewness and Kurtosis Standard utility theory imposes no constraints on u￿￿￿ & u￿￿￿￿ . Behavioral studies suggest the following: investors tend to like skewness and dislike kurtosis A higher probability of major upside upswing than downswing is considered “better" than equal probability of each Investors do no...
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This note was uploaded on 01/04/2012 for the course ACTSC 372 taught by Professor Maryhardy during the Fall '09 term at Waterloo.

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