markowitz

# Ks tanactsc 372 f11 modern portfolio theory capm p

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Unformatted text preview: omposition of the (unique) optimal risky portfolio is 40% RIM and 60% SLF. Investor A, with investment amount \$10,000, decides to invest in equal amount in both risk-free and risky assets Investor B, also with the same investment amount but is more risk tolerance, is willing to invest 90% in the risky asset and 10% in the risk-free asset Implications? K.S. Tan/Actsc 372 F11 Modern Portfolio Theory &amp; CAPM – p. 42 Principle of Diversiﬁcation Let Var(Ri ) = σ 2 , Cov(Ri , Rj ) = ρσ 2 , xi = 2 σx = N ￿ i=1 2 x2 σi + i N N ￿￿ i 1 N i, j = 1, . . . N xi xj σij j =1,i￿=j 1 1 = N × 2 · σ 2 + N (N − 1) × 2 · ρσ 2 N￿ N ￿ 12 1 = σ + 1− ρσ 2 = ρσ 2 as N → ∞ N N An Example (suppose σ = 1.0) N 1 2 5 10 100 500 ∞ ρ = 0 1.0 0.50 0.20 0.10 0.010 0.002 0.000 ρ = 0.3 1.0 0.65 0.44 0.37 0.307 0.301 0.300 K.S. Tan/Actsc 372 F11 Modern Portfolio Theory &amp; CAPM – p. 43 Systematic vs Nonsystematic Risks The total risk of an asset (or a portfolio) can be decomposed into two components: systematic, undiversiﬁable, or market risk: examples: inﬂation rate, recession, poli...
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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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