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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
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
N risky assets µ and Σ, and
one risk-free asset with equal lending and borrowing
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
Portfolio weights: Let eT = (1, 1, . . . , 1) ∈ N +1 , then
xT = (x0 , x1 , . . . , xN ) = (x0 , xT ), eT x = 1, Expected return and variance are given by
E[Rx ] = µx = rx0 + µ1 x1 + · · · + µN xN = r µT
= µT x
0 0T x
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.
- Fall '09