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@vanguard2k and @Theja provide useful information. In my experience, unequal starting points is most common, so I'll try to focus on that. The technique that @vanguard2k mentioned for unequal starting points can be thought of like a regression. You start with the longest available data and get the covariance matrix of that. For the next set of available ...


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One really nice book that comes to my mind is Little, Rubin, Statistical Analysis with Missing Data I read part of it but probably it is too much information in your case. For your application, i think you can categorize the problem into two possible subproblems: First, time series that have unequal starting points (when some stocks' history is ...


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A simpler question would be the following: suppose you want to find the covaraince between the returns of two stocks and each of their time series has missing values at different places. What is the best way to compute covariance here? One very sensible way to approach this is to throw away the observations where ony one of the stocks has a return value. Of ...


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Most portfolios offer positive returns, and minimum variance portfolios are not exceptions to this rule. But by offering "minimum variance," they also offer the lowest possibility of a negative deviation large enough to pull the actual return (expected return minus deviation), into negative territory.


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Your question is formulated in a very general way, this is why any answer will need to be general as well. In a nutshell and in full generality you need to estimate the joint distribution from your historical data since in most cases correlations alone are not sufficient to define the joint distribution. In a second step you can calculate the distribution ...


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If $\Sigma$ is the covariance matrix of all assets and $w$ is the column vector of weightings of the asset in a certain portfolio. Then $$ w^T \Sigma w = VAR $$ is the variance of the portfolio. The contribution to volatility of asset $i$ is given by $$ w_i (\Sigma w)_i/\sqrt{VAR}, $$ where $(\Sigma w)_i$ is the $i_{th}$ entry in the vector $\Sigma w$. Note ...



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