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 Build mean-variance efficient portfolios Include a risk-free rate Separation property 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 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 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 Empirical work Interpretation
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10 Issue/Motivation How to estimate the input parameters of the Markowitz model? Equilibrium analysis An equilibrium characterizes a situation where no one wants to deviate 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 The market portfolio is the tangency portfolio on the efficient frontier:
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