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I know this is almost a month old, but... Unless it is a homework assignment, you could have a look at this paper by Del Moral and Shevchenko, which gives a different estimator than the one you're probably using. It gives both a crude Monte Carlo-estimator and a sequential Monte Carlo-estimator. You probably just want the crude Monte Carlo one. Eq. (27) ...


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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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