S tanactsc 372 f11 modern portfolio theory capm p 36

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Unformatted text preview: the optimization and tend to lead to a model that is not tractable. 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 The Economy: One risky asset with stochastic return Rrisky and risk-reward characteristics: (σrisky , µrisky ) one risk-free asset with equal lending and borrowing rate rf 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 + σP σrisky also known as Capital...
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