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since you've assumed that all returns are independent, the covariance matrix, $C,$ is diagonal. In the comments, you are assuming that the investor is a mean-variance investor. It's a general result that every portfolio that maximizes return for a given variance is a tangent portfolio for some risk-free rate, $R.$ Let $e=(1,1,...,1).$ and let $\mu$ be the ...


If you only need to pick 5 out of 10 and want equal weights then just enumerate all 252 possibilities (as pointed out above) and compute the portfolio volatility $(\textbf{1}'K^{(i)}\textbf{1})^{1/2} = \left( \sum_{ij}K^{(i)}_{ij} \right)^{1/2}$, where $K^{(i)}$ is the covariance matrix for the $i$th subset. Then use whatever subset gives the lowest ...

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