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Backtesting on a past realization does not provide any meaningful "estimate", as the variance of the "estimate" would be undefined. More meaningful would be to make distributional assumptions and get estimates through extensive Monte Carlo simulations. Clearly, the estimates that you get would be "meaningful" under your specific distributional assumption, ...

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The concrete (general) answer to part (ii) of my question seems to be contained in Equation 8 of the following link: http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-portfolio-I.pdf In particular, interpreting $\sigma$ as volatility, take for example $E_A=0.10,\sigma_A=0.15,E_B=0.25,\sigma_B=0.40$ and $\rho =−0.2$. I get that about 83 percent of the ...

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Firstly, to answer your question for part (i), this part of the question makes no sense - your expected return is unbounded and is asymptotically linear with respect to risk. Let ${\bf w}\in\mathbb{R}^{2}$ denote your vector of weights, $\Omega$ denote the covariance matrix and $\iota$ denote a unit exposure vector (defined by \$\iota_{j}:=1\ \forall j, j ...

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