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optimization and tend to lead to a model that is not
N is in the order of hundreds in practice
⇒ large scale optimization problem
often resort to numerical software such as Matlab,
Cplex, Excel Solver, etc.
K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 33 One Risky Asset and One Risk-free Asset Economy
One risky asset with stochastic return Rrisky and
risk-reward characteristics: (σrisky , µrisky )
one risk-free asset with equal lending and borrowing
What is the investment opportunity set (and efﬁcient
frontier) under this economy?
Construct a portfolio P with proportion w in the risky asset
and 1 − w in the risk-free asset
RP = (1 − w )rf + wRriksy
E(RP ) = µP = (1 − w )rf + wµrisky = rf + w (µrisky − rf )
s.d.(RP ) = σP = w σrisky
K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 34 Capital Allocation Line (CAL)
Investment opportunity set:
µrisky − rf
µP = rf +
also known as Capital...
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- Fall '09