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I am analyzing the Markowitz models with uncertain returns as follows: after calculating the expected returns and the covariances of 30 monthly historical series of 30 stocks, I resolve the Markowitz model to determine the minimum and maximum expected returns. After randomly generating with uniform distribution five vectors of random returns with values ​​in the intervals $ [0.95 R_i, 1.05 R_i] $. For the original expected yield vector and for each yield vector generated, I resolve the Markowitz model with the required yield of $ R = 1/2 (R_ {max} -R_ {min})$ thus obtaining the exact portfolio and five perturbed portfolios .

I am asked to calculate the average of the disrupted portfolios and to compare it with the exact portfolio, for example by calculating the distance from the average portfolio to the exact one

By average portfolios do you mean the average odds found by solving the exact model? What should I expect? What do you think is the reason to analyze these perturbed portfolios?

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