Week 3_CAPM - Risk and Return CAPM Last Time Markowitz...

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Risk and Return CAPM
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2 Last Time ± Markowitz Model ² Build mean-variance efficient portfolios ± Include a risk-free rate ± Separation property ² When investors have the same parameter estimates and when there is a risk-free asset, the optimal portfolio of risky assets is the same for everyone, which is the market portfolio
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3 Optimal Capital Allocation P CAL σ E(r) r f Less risk-averse investors More risk- averse investors h h h h h h
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4 Markowitz portfolio optimization 1 w w w r ) r ( E w ) r ( E w ) r ( E w . t . s ) r , r ( Cov w w 2 ) r , r ( Cov w w 2 ) r , r ( Cov w w 2 w w w Min C B A C C B B A A C B C B C A C A B A B A 2 C 2 C 2 B 2 B 2 A 2 A 2 P W i = + + = + + + + + σ + σ + σ = σ
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5 Efficient frontier & minimum variance set A C Efficient Frontier Minimum Variance Set (MVS) σ E(r) MVP B
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6 The Separation Property ± The optimal portfolio of risky assets, P*, is independent of each individual’s risk preference. ± P * is the market portfolio. σ P * * 1 C * 2 C * 3 C CAL Efficient Frontier r f E(r)
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7 Optimal Complete Portfolio ) r ( E P σ P * f r CAL * C 2 p f p * C y 1 and A 01 . 0 r ) r ( E y σ = C * Portfolio weights of C * are given by
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8 Text reference ± This week lecture: Chapter 9 ² Tutorial problems due this week: ± Ch6: 1-19,26-28, CFA: 1-9 ± Ch7: 1-11,13-19, CFA: 4-13 ± Next week lecture: Chapter 8 ² Tutorial problems due next week: ± Ch9: 1-17, CFA: 1-12
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9 Today ± Explore implications of the separation property ± Develop a risk model ± Present β ± Capital market line (CML) ± Security market line (SML) ± Zero- β CAPM ± Discuss CAPM history ² Empirical work ² Interpretation
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10 Issue/Motivation ± How to estimate the input parameters of the Markowitz model? ± Equilibrium analysis ² An equilibrium characterizes a situation where no one wants to deviate ² If everyone behaves according to Markowitz, what should be the expected price or return?
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11 The CAPM Assumptions ± All investors are price takers, mean-variance optimisers ± All investors have identical information and holding periods (single period, equilibrium) ± All assets are marketable and divisible. The market portfolio includes ALL assets ± There is a single risk-free rate at which one can borrow or lend any amount ± No market imperfections (no taxes, short selling restriction, transaction costs, etc)
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12 CAPM Conclusion ±
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This note was uploaded on 05/02/2010 for the course ACCT 3756 taught by Professor Leung during the Three '09 term at University of Sydney.

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Week 3_CAPM - Risk and Return CAPM Last Time Markowitz...

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