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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% ( σ 12 ) 5%( σ 23 ) 15%( σ 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 σ 2 1 + w 2 2 σ 2 2 + w 2 3 σ 2 3 + 2 w 1 w 2 σ 12 + 2 w 2 w 3 σ 23 + 2 w 1 w 3 σ 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 σ 2 ivariance of asset i...
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 Fall '08
 CHABOT
 Economics, Linear Equations, Variance, Optimization, Elementary algebra

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