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# How to determine such efcient portfolios ks tanactsc

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Unformatted text preview: es on returns investors are risk averse returns r.v. follows a normal distribution OR investors have quadratic utility function Σ is positive deﬁnite; i.e. cT Σc &gt; 0 for nonzero vector c. e, µ are linearly independent. K.S. Tan/Actsc 372 F11 Modern Portfolio Theory &amp; CAPM – p. 18 (Mean-Variance) Efﬁcient Portfolio A portfolio x∗ is called (mean-variance) efﬁcient if there exists 2 2 no portfolio x with µx ≥ µx∗ and σx ≤ σx∗ (and at least one inequality is strict). In other words, a mean-variance efﬁcient portfolio provides the greatest expected return for a given level of risk, or the lowest risk for a given level of expected return. What is the difference between an investment feasible set and an efﬁcient portfolio? How to determine such efﬁcient portfolios? K.S. Tan/Actsc 372 F11 Modern Portfolio Theory &amp; CAPM – p. 19 Mean-Variance Optimization Formulations Formulation I: max µT x subject to xT Σx = σ and eT x = 1 ˆ x for a given σ ˆ Formulation II: min xT Σx subject to µT x = µ and eT x = 1 ˆ x for a given µ. ˆ K.S. Tan/Actsc 37...
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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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