# Tag Info

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In addition to the previous comments, I would like to add that are plenty of definitions for market neutrality. You can for instance be market neutral in dollars, or market neutral in beta or running a spread based on some other mechanics (f.ex. cointegration) Some more info would help better answer your question.

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Try to formulate the problem as a constrained optimization problem, and examine the KKT (Karush-Kuhn-Tucker) complementary slackness conditions.

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You wrote: $$d[5] = (DJIR[5] - \mu) * Covariance$$ but you left out half of it (the inverse and the transposed vector on the right side). The correct formula is $$d[5] = (DJIR[5] - \mu)^2 / Var[DJIR]$$ The covariance "matrix" becomes the variance in a 1-dimensional case (in other words $x_i$ and $y_i$ are both equal to DJIR[i] in this case) and the "matrix ...

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Market-neutral portfolios seek to eliminate market risk, so sum of the weights could be even a zero. That would mean that you bought a lot of some equity, and then borrowed some other equity and sold it. You have cash now, but you also have risks, because you will have to return the borrowed equity in the end, and who knows how much you will have to pay to ...

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Yes, it is normal for a L/S fund to have a lot of cash. When you short securities your account is credited with the proceeds from the sales. So if you short 1 million of stock you end up with 1 million cash and -1 million short stock position. Another way to look at it is: as you mentioned, the weights as a fraction of NAV have to add up to 1.0 by definition ...

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Here is a simple way of solving the above: Take future returns (use the daily return matrix of all the assets for the future investment horizon), calculate covariance matrix. Calculate weights using future perfect data. Repeat for all time periods. Pick whichever method of estimating the covariance matrix you prefer the most and plug it into 1), likewise ...

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First and foremost you are using bad data. min(data) gets me -3.67 (it's random remember) which would be -367% as in the position went bankrupt and took out two other ones (could be possible in a levered porftolio). However for the sake of an reproducible answer lets use the edhec data set, very little changes to your original code need to be done. ...

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An approach to consider is: Computing the total return streams of all the instruments in the portfolio Calculate the risk parameters using 1 Weight appropriately (Equal risk contribution, min variance etc)

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