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1

They are the same. The maximum growth rate is achieved when the Sharpe ratio is maximized. For the proof, see here.


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Sounds like PCA is not the approach you're looking for. If you're looking to transform a risk vector in terms of securities V into a risk vector in terms of securities W, then the basic approach would be to perform a linear regression of V against W. The resulting regression coefficients will form a matrix B which will give a change of basis between V and W. ...


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I think that the approach suggested by @Alex is pretty standard and I have seen such charts before but for a less orthodox approach that may clean up the graphics a bit, you might consider the final cumulative return as a segmented bar or pie chart (though I might discourage pie chart). See this example of a segmented bar for what I'm talking about. Each bar ...


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After Markowitz published his famous paper, William F. Sharpe published "A Linear Programming Algorithm for Mutual Fund Portfolio Selection" (1967). I haven't re-read it 20 years, but AFAIR it relies on a special structure for the covariance matrix and some assumptions about the utility. Maybe reading this paper would tell you if you are onto something new ...


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The Markowitz model for portfolio optimization (http://www.princeton.edu/~rvdb/542/lectures/lec17.pdf) is formulated as a quadratic programming (QP) problem, not an LP one. You cannot use an LP solver to solve a QP problem.


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Concerning the weighted portfolio returns. If you have weights $w_i$ and individual returns $r_i$ of your assets then it is only precisely true that the portfolio return $r$ is given by the scalar product $$ r = \sum_{i=1}^n w_i r_i $$ if $r_i$ is the usual arithmetic/simple return (not logreturn). Thereby I mean the simple return $$ r = P_{t+1}/P_t - 1 $$ ...



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