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I have started exploring portfolio optimization results that pop out when I don’t constrain the weights to sum to 1. For instance, in a dollar-neutral portfolio, the weights sum to 0. Also, some dollar neutral portfolios are more “extreme” than others, as measured by the sum of the absolute values of the weights.

So how do I know if my broker will let me implement strategies like these? What are the accounting keywords that I have to understand to be able to answer this without resorting to the trial and error approach? I am looking for help converting some of this accounting language into mathematical language. Is the only that is necessary to consider my margin requirements?

For equities, the primary consideration appears to be Reg T. The end-of-day margin requirement is 50% for both long and short positions.

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In the US, Prime Brokers will generally follow either Reg T rules or Portfolio Margining rules. For Portfolio Margining accounts, assuming the account is somewhat diversified (not everything in one stock), they will generally allow 4 times gross leverage on the overall portfolio ($\sum_i |w_i|<=4$). This is negotiable and you may be able to get a higher limit, say 6 or 7 (as Ontic wrote) depending what securities you trade (based on the broker's internal risk model).

This is only a general guideline, but it should give you a starting point for designing your strategy. Then you can negotiate with brokers (maybe you are such a profitable customer that you can get a better deal ;) ).

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For equities, the primary consideration appears to be Reg T. The primary consideration is the end-of-day margin requirement, which is, for a Reg-T margin account, 50% for longs and shorts. However, the proceeds from a short sale cannot be used to increase your liquidity, unless you have a fancier account type, which is only available for those with a higher minimum account balance.

So, for a standard Reg T margin account, the sum of the absolute value of the weights of all your longs and all your shorts may not exceed $2.0$ by the end of the day. A broker (mine at least) wouldn't stop me from entering into a trade and going over this, though, because the initial margin requirements are lower than the end-of-day margin requirements. However, there would likely be a forced liquidation at the end of the day, and that also might count against the number of pattern day trades you are allowed.

Another interesting situation, say you put $1.99\%$ of your capital into a long position, and that position appreciates by $1\%$, then the total value of your longs is $2.0895\%$, and so you would trigger an end-of-day margin call.

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