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An argument I often hear (which was repeated here) against sending orders through "pay-for-flow" wholesalers is that those wholesalers can potentially determine if you are an "informed" trader (as opposed to an "uninformed" retail investor), in which case they can use the information embedded in your floor to your disadvantage.

If we accept that wholesalers can distinguish informed vs uninformed flow, what actions can they take to adversely impact the informed trades? E.g., are they allowed to front-run those trades? If they are on the NBBO are they allowed to yank their liquidity before processing the trade?

Or is the reality that even if they can determine that a particular trade is "informed" they cannot take any action that would adversely impact the trade, as compared to the trade going straight to the market?

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Short answer, yes, to an extent. Although this is off exchange, exchanges (NYSE, eg) have rules that even on exchange, a market maker (Specialist) may get first look at order flow to improve on pricing.

Wholesalers pay for order flow because it's assumed to be uninformed. Even if there are informed orders in the purchased flow, it is retail sized and less meaningful compared to institutional flow of the same size.

Now, all of this is caveated that laws and rules prohibit frontrunning and other forms of manipulative trading. For example, a market maker cannot use knowledge from an order flow arrangement to requote exchange posted prices prior to processing those orders.

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