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What does 'simulate a covariance matrix' mean? If the question means, generate an arbitrary correlation matrix for 1000 stocks, then we can choose any symmetric matrix with all 1s down the diagonal, so long as every element is between -1 and 1 and the matrix is positive semi-definite. The large size of the matrix means that putting random values in every ...


3

Just to expand on Alex answer. Empirically it is simply not true. Focusing on the diagonal of the variance-covariance matrix, we know that there is a large variance risk premium. Take a look at table 3 from Carr and Wu (2009). Regarding covariances we do not have much evidence, because there are no options on every single pair of stocks. However, we do know ...


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I will just clarify Point 2 in StackG excellent answer. (It's really a comment, but it's too long and has too much math symbols to fit in the comment field.) Suppose you're given a covariance matrix $C$ for the returns of $n$ assets. (1000 $\times$ 1000 is 1 million entries - should not be too large for modern computers to work with, but do be mindful of ...


2

I assume you found these weights by Markowitz Optimization? It is quite common that MVO will deliver extreme weights with some weights well above 100 percent (implying leverage, i.e. buying the stock on borrowed money) and others massively negative meaning a leveraged short position. These weights are not usable in a real portfolio. Let's examine the first ...


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