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The variance covariance matrix of the returns is a table of I rows and I columns. If a table representing a variance covariance matrix has 10 rows and 10 columns, then the entry in the table (row 1, column 3) is the covariance of the return in the first security with that of the third. The (5,5) term would be the variance of the fifth security. Covariance matrices or tables are symmetric. Let be the rate of return on risky security i . Let be the covariance between two returns and . Of course, . Let be the share of your wealth devoted to security i . Then the expected return of your portfolio is and the variance of the portfolio is. A question we might care about is finding a minimum variance portfolio made up of a given set of securities. The solver tool can handle this. We would set the objective to the EXCEL formula for , we would ask it to minimize this objective, by changing the weights , with the constraints that and all the weights are between 0
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Unformatted text preview: and 1, so . The spreadsheet “Variance Minimization.xlsx” has an example. As an exercise create your own spreadsheet for a portfolio of 2 stocks with variance covariance matrix 1.5E-06-3.1E-07-3.1E-07 1.99E-06 And mean returns of 0.00808 5 0.002376 Start with weights of ½ and ½ and find the mean return and the variance of the return of such a portfolio. Change the weights by hand (note they must sum to 1) to find a minimum variance portfolio. Now do it using the solver tool. Next add third security. With covariance matrix 1.5E-06-3.1E-07 1.07E-07-3.1E-07 1.99E-06-3.3E-07 1.07E-07-3.3E-07 2.12E-06 And expected returns 0.00808 5 0.002376 0.003128 Start with the solution you got for the first two and weight of zero for the new security. Now add the security and vary weights to find a new minimum variance portfolio made up of the three securities. You can do it by hand, but easier to do it using the solver tool....
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This document was uploaded on 03/18/2012.

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