S tanactsc 372 f11 modern portfolio theory capm p 5

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Unformatted text preview: 7 = 5.83% E(RB ) = 5.96% s.d.(RB ) = 0.72% Cov(RA , RB ) = 0.000412 ⇒ ρ = Cov(RA , RB ) = 0.98 σA σB K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 5 Historical Estimates Recall that if {ri ; i = 1, . . . , N } is the empirical rate of ˆ return in period i Then sample mean and sample variance are estimated as: E(R) = N 1￿ ri = µ ˆ ˆ N i=1 N 1￿ 1 Var(R) = (ˆi − µ)2 = r ˆ N −1 N −1 i=1 ￿ N ￿ i=1 ri − N µ2 ˆ2 ˆ ￿ = σ2 ˆ Similarly for estimating sample covariance and sample correlation K.S. Tan/Actsc 372 F11 Modern Portfolio Theory & CAPM – p. 6 Portfolio of Two Assets with Return r.v. (R1 , R2) Dollar amount w1 in asset 1 and w2 in asset 2 Portfolio P Asset 1 Asset 2 dollar amt. invested w1 w2 w = w1 + w2 w1 w2 % amt. invested x1 = w x2 = w x1 + x2 = 1 Let RP be the rate of return r.v. for the above portfolio, then dollar return over the period initial investment amount 1 = ( w 1 R1 + w 2 R2 ) = x 1 R1 + x 2 R2 w RP = E(RP ) = µP = E(x1...
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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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