17 markowitz modern portfolio theory 1952 markowitzs

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Unformatted text preview: es the percentage of the portfolio’s total value invested in the i-th asset xi can be negative ⇒ short selling “budget constraint": ￿N T T T i=1 xi = 1 or e x = x e = 1 where e = (1, 1, · · · , 1) K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 16 Portfolio Risk and Return For any portfolio x: Portfolio rate of return r.v.: Rx = N ￿ x i Ri i=1 Portfolio Expected Return: N N ￿ ￿ E[Rx ] ≡ µx = xi E[Ri ] = xi µi = µT x i=1 i=1 Portfolio Variance: Var(Rx ) ≡ = N ￿ i=1 K.S. Tan/Actsc 372 F11 2 σx = Var 2 x2 σi i + ￿ N ￿ x i Ri i=1 N N ￿￿ ￿ = NN ￿￿ xi xj σij i=1 j =1 xi xj σij = xT Σx i=1 j =1,i￿=j Modern Portfolio Theory & CAPM – p. 17 Markowitz Modern Portfolio Theory (1952) Markowitz’s problem: How to construct an optimal portfolio x from a given set of N risky assets? Assumptions: single period investment horizon the economy has N risky assets assets are perfect divisible no transaction costs investors pay no tax...
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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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