Slides6_HD - Corporate Finance(ECON W4280 Lecture 6 Tri Vi...

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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 1 Corporate Finance (ECON W4280) Lecture 6 Tri Vi Dang Columbia University
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 3 Midterm Exam The midterm exam is on 10/23 - during regular class time and place. It is an open book exam. - Textbook, lecture notes and your own notes can be used - Scientific calculator is allowed - NOT allowed are all other electronic devices (e.g. laptops, tablet PCs, smartphones)
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 4 Lecture 6 I.1. Valuation concepts N. Portfolio mechanics, diversification O. CAPM P. Other pricing models, market efficiency
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 5 I.1.N. Portfolio Mechanics
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 6 Remark - Suppose investors care about mean and variance of asset returns. - This section discusses mean-variance portfolio management and introduces the key tools for deriving desirable portfolios. Motivating Example Investing $10K in Apple AT&T Exxon Walmart
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 7 Share Price
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 9
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 11 Remark - Investing $3K in Apple $2K in AT&T $2K in Exxon $3K in Walmart generate an expected return of 0.0675% and variance of 0.0072% per day - Expected return is higher than AT&T, Exxon and Walmart - Variance is lower than any single stocks - What is the smallest possible variance?
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 12 Review Properties of the mean Suppose 1 ,.... , N R, und X 1 ,.... , X N random variables (M1) E[ 1 X 1 ]= 1 E[X 1 ] (M2) E[X 1 +.... +X N ]= E[X 1 ]+….+E[X N ] (M3) E[ 1 X 1 +….+ 2 X 2 ]= 1 E[X 1 ]+….+ N E[X N ]
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 13 Covariance-Matrix V X 1 ,.... ,X N are random variables, i ² is varianz of X i und ij is covariance between X i und X j . V is the Kovarianz-Matrix ² σ σ σ σ ² σ σ σ σ ² σ V N N2 N1 2N 2 21 1N 12 1 Note, ij = ji .
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 15 Properties of Variance Suppose 1 ,.... , N R, =( 1 ,.... , N ) a N-vector, X 1 ,.... , X N random variables and V the Covariance Matrix. (V1) Var[ 1 X 1 ]= 1 ² Var[X 1 ] (V2) Var[ 1 X 1 +….+ N X N ]= V Remark Formula (V2) plays a central role in portfolio theory (and asset management).
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Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 16 Example S1 (0.25) S2 (0.5) S3 (0.25) X 1 10 20 30 X 2 30 40 10 Interpretation X 1 generates a return of 10% in state 1, 20% in state 2, 30% in state 3.
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Slides6_HD - Corporate Finance(ECON W4280 Lecture 6 Tri Vi...

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