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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
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:
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
i + N
x i Ri i=1 N
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.
- Fall '09