markowitz

# Markowitz

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Unformatted text preview: Allocation Line (CAL) linear slope of CAL reward-to-variability ⇔ Sharpe Ratio ⇔ price of risk a measure of extra return (risk premium) per unit of extra risk The CAL must also correspond to the efﬁcient frontier under this economy! K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 35 N Risky Assets and One Risk-free Asset Economy The economy: N risky assets µ and Σ, and one risk-free asset with equal lending and borrowing rate rf What is the efﬁcient frontier under this economy? There are at least two ways of deriving Markowitz model in the presence of a risk-free asset. Method I: use the same optimization approach as in the N risky assets case Method II: via the capital allocation line K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 36 Method I: via Standard Optimization Method Let x0 denote the proportion of wealth invested in the risk-free asset ˆ Portfolio weights: Let eT = (1, 1, . . . , 1) ∈ ￿N +1 , then ˆ ˆˆ xT = (x0 , x1 , . . . , xN ) = (x0 , xT ), eT x = 1, Expected return and variance are given by ￿￿ ￿ ￿x 0 E[Rx ] = µx = rx0 + µ1 x1 + · · · + µN xN = r µT = µT x ˆˆ ˆ ˆ x ￿ ￿￿ ￿ ￿ ￿ 0 0T x 0 2 ˆ ˆˆ V ar(Rx ) = σx = xT Σx = x0 x...
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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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