As a new client of a broker I'm given $300 of free commission on trading (basically on everything: stocks, options, futures etc).
Is there a way to capitalize this bonus by creating some combination of trades?
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Yes, you can maximize this by having a series of entries with very small stop-losses in the most liquid market with the tightest bid-ask spreads possible.
You will probably use a "bonsai" entry strategy, which enters a position at a particular price with a fixed (but not arbitrary) stop. You would re-enter that position every time price returned to your entry after being stopped out. For a small stop, this can realistically happen many times, even with what is a very good entry in the grand scheme of things. Transaction costs and slippage therefore become a primary limiting factor.
The other limiting factor, however, is the quality and resolution of your trading system itself. Tight stops, free trades, and minimal spreads will not help much if you're entering at the wrong places. Also, some systems will naturally not fit the time frames that allow for tight enough stops to take advantage of free commissions, and so must be ruled out.
Finally, even though you can maximize the utility of free commissions like this, often spreads and slippage are significant enough that the overall savings is not that great. Furthermore, a system capable of capitalizing on tight, series-of-entries positions will still require significant development costs and (likely) automation. Finally, its profitability will be hurt when your free commissions have expired. So, I can't really suggest targeting free commissions as an effective long-term strategy, even though it is (temporarily) possible to do.