Discussion2_linear_eq

Discussion2_linear_eq - Discussion 2: Review Solving Linear...

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Unformatted text preview: Discussion 2: Review Solving Linear Equations Rosanna Chan September 14, 2006 1 The problem Assets 1 2 3 Return 6% 12% 15% Variance 30% 50% 60% Covariance 10% ( 12 ) 5%( 23 ) 15%( 13 ) Table 1: 3 Hypothetical Assets Table 1 lists the return on 3 assets as well as their variance and covariance. A typical problem that you will be asked to solve is to work out the weights on these assets if you were to make a portfolio of them such that it will minimize risk (ie variance) and will give you a return, of say, 10%. In other words, you will be asked to solve an optimization problem subject to constraints- like any other econ problem you have done. Here, rather than maximizing pro ts or utility, we're maximizing the negative variance of the portfolio - ie minimize the variance. max- ( w 2 1 2 1 + w 2 2 2 2 + w 2 3 2 3 + 2 w 1 w 2 12 + 2 w 2 w 3 23 + 2 w 1 w 3 13 ) st w 1 R 1 + w 2 R 2 + w 3 R 3 = 0 . 10 w 1 + w 2 + w 3 = 1 Where: w i- weights on asset i 2 i-variance of asset i...
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Discussion2_linear_eq - Discussion 2: Review Solving Linear...

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