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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 ...

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Could you please be more specific with your question and post the text here? This will be more helpful for other people visiting the site. Now as far as to where the 1/2 went, usually people put 1/2 in front of the second order term because this will simplify to 1 after the derivation: $$\frac{\partial x^2}{\partial x} = 2x$$ vs  \frac{1}{2} \cdot ...

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Assuming that we are talking about volatility as the standard deviation of uncorrelated random variables (in this case this would mean no autocorrelation) the variance is additive, which means that we get $\sqrt{.15^2+.2^2}=.25=25\%$. You can illustrate this result by simulation in R: > sd(rnorm(1e7,sd=.15)+rnorm(1e7,sd=.2)) [1] 0.2500001 If you want ...

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7 years ago I had to solve the problem of a efficiency frontier under linear constraints on the asset weights and also stumbled upon Markowitz Critial Line Algorithm. I still have a directory with some resources in it. Since Bryce already gave a practical implementation with R code by Eric Zivot, I will concentrate on some papers which might help. I ...

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