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Unformatted text preview: g a portfolio of different assets can reduce the variance. This is called Diversification. Remark By varying the portfolio weights (1,2), we can trace out the whole meanvariance- frontier. Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 25 2 The Mean-variance ( , ) - frontier PF α1 ² σ1 ² 2α1 α 2 σ12 α 2 ² σ 2 ² α1 ² σ1 ² 2α1 α 2 12 1 2 α 2 ² σ 2 ² 2 PF α1 1 α 2 2 Example Asset 1: 1 0.1 and 12=0.3 Asset 1: 1 0.2 and 12=0.4 12=-0.2 Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 26 Portfolio Frontier (Rho=-0.2) Mean 0,30 0,25 0,20 0,15 0,10 0,05 0,00 0,10 0,20 0,30 0,40 Variance Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 27 Remark The set of portfolios in (, ) space is a line if one asset is riskless. Suppose asset 1 is riskless: 1 0 and 12 0 . 2 PF α1 ² σ1 ² 2α1 α 2 σ12 α 2 ² σ 2 ² α 2 ² σ 2 ² PF α1 rf α 2 2 Note α1 α 2 1 α1 1 α 2 PF α 2 σ 2 PF (1 α 2 ) rf α 2 2 rf 2 ( 2 rf ) Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 29 Remark The tangent point between the line and the curve is called the market portfolio. Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 30 Mean Variance Portfolio Management (N assets) Suppose you want a portfolio wit...
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This document was uploaded on 02/16/2014 for the course ECON w4280 at Columbia.

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