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No need to invent your own algorithm for random portfolio weights. There is a very simple algorithm to generate a random point in a simplex (i.e. to generate $e_i,i=1,k$ such that $e_i\ge 0$ and $\sum_{i=1}^k e_i=1$). It is due to Rubinstein and Melamed (1998): Generate k independent exponential random variables $Y_1,\cdots,Y_k$ (for example they can be ...