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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 > 0 for nonzero vector c.
e, µ are linearly independent.
K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 18 (Mean-Variance) Efﬁcient Portfolio
A portfolio x∗ is called (mean-variance) efﬁcient if there exists
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 & CAPM – p. 19 Mean-Variance Optimization Formulations
max µT x subject to xT Σx = σ and eT x = 1
x for a given σ
ˆ Formulation II:
min xT Σx subject to µT x = µ and eT x = 1
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.
- Fall '09