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The sigma is the same short as if you were long. Imagine you held exactly the opposite portfolio. It stands to reason that volatility of holding both is net zero; and they're -100% correlated. It therefore stands to reason that you have to have the same sigma (for the same value) for them to cancel out thus, as they must. Alternatively, just look at the ...


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This is the result of the Sherman-Morrison inversion for the sum of an invertible matrix and an outer product. You will find this (and many other helpful methods) in the Matrix Cookbook. Specifically, this is equation 160 on p 18: $$ \left(\boldsymbol{A}+\boldsymbol{bc}^T\right)^{-1}=\boldsymbol{A}^{-1}-\frac{\boldsymbol{A}^{-1}\boldsymbol{bc}^T\boldsymbol{A}...


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While the close vote might be reasonable, there is mathematical arguments that show there is a limit to how negatively correlated a set of assets can be. It is even a classic quant interview question: Let the correlation matrix be $$\Omega = \rho \mathbf{1} + (1-\rho)I_d,$$ where $\mathbf 1$ is the $d \times d$ matrix with 1's everywhere. What is the range ...


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As a first step it is helpful to draw a 'time circle' from 0000 to 2359 GMT/UTC and plot on this circle the opening and closing times of the major markets/exchanges. This gives an overview of the situation and makes it easy to answer questions like "at xxxx GMT what markets are open and what markets are closed". (Actually you may need to have ...


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