This preview shows page 1. Sign up to view the full content.
Unformatted text preview: (1 − x1 )σ2 = µP · σ1 −σ2
µ1 − µ2 + µ1 σ2 −µ2 σ1
µ1 − µ2 ⇒ linear in the (σP , µP )-plane ρ = −1, ⇒ σP = |x1 σ1 − (1 − x1 )σ2 |
−1 < ρ < 1, σP = x2 σ1 + (1 − x1 )2 σ2 + 2x1 (1 − x1 ) · ρσ1 σ2
K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 14 Investment Opportunity Set or Feasible Set (Region)
The possible (µP , σP ) or (µP , σP ) pairs of all portfolios
that can be constructed from a given set of assets Describe the feasible set for a portfolio of two assets?
see Figure 11.4 What if there are three assets?
What if there are N assets?
see Figure 11.6 K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 15 General Case: N Risky Assets
the economy has N risky assets with return r.v.
R1 , . . . , RN .
assume their ﬁrst and second moments exist; i.e.
µT = (µ1 , . . . , µN ), with µi = E[Ri ], i = 1, . . . , N,
Σ = (σij )i,j =1,...,N , with σij = Cov(Ri , Rj ), i, j = 1, . . . , N.
note: σii = Cov(Ri , Ri ) = Var(Ri ) = σi A portfolio is constructed with portfolio weights
xT = (x1 , . . . , xN ), where xi denot...
View Full Document
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