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I am wondering how PFOF (Payment For Order Flow) works and why people say that hedge funds make wider spread using PFOF.

If a client sends an order A then the broker is going to redirect that order to a hedge fund B. Then B is not allowed to offer a worse price than what's available in the market. Hence if on the exchanges the tighter spread is $s$ then B can makes at most $s$, but B needs to pay a percentage of $s$ to the broker.

Hence I don't see how PFOF widen the spreads, and what are typical algos employed by hedge funds to execute these orders.

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Consider a scenario with two kinds of trader:

  • Informed traders, who are price sensitive and trade when they expect the price to move in their favour
  • Noise traders, who do not have any edge and trade randomly.

You can map these onto "institutions" and "retail" for the purposes of this answer, which isn't perfect (some institutions have no edge and some retail traders do have an edge) but is directionally accurate.

What would happen if there was no PFOF and all orders were routed to the exchange?

Market makers would face a mix of informed flow and noisy flow, and their spreads would reflect the mix of flow that they face. More informed flow would lead them to quote wider spreads, and more noisy flow would lead them to quote narrower spreads. Say that the spread on the exchange in this scenario is $S$, and all traders (both informed traders and noise traders) pay the same spread.

Now introduce PFOF, which means that noise trader orders can be routed to market making firms directly, and informed orders still go to the exchange. Then a market maker on the exchange faces a greater fraction of informed flow, so they will need to quote a wider spread, $S'>S$.

The market makers who are paying for order flow only see noisy orders, so they will be able to offer price improvement, and quote a spread $S'' = S' - I$ where $I$ is the amount of price improvement.

Under which scenario do noise traders pay less? In the first scenario they pay $S$, and in the second scenario they pay $S'-I$, so they do better in the second scenario if

$$ S' - I < S $$

which can be written as

$$ I > S' - S $$

In order for noise traders to get tighter spreads under PFOF, the amount of price improvement needs to be greater than the amount by which spreads needed to widen as a consequence of routing a greater fraction of informed flow to the exchange. Whether this is true or not is an empirical question that can only be answered with data (either a randomised trial, which is unlikely to ever happen, or more likely a natural experiment where e.g. you compare spreads in a market which has PFOF to one which does not have PFOF).

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  • $\begingroup$ great answer thank you! I just have two quick follow-up questions: 1- PFOF is more prolific in options, is there a reason for that? 2- Can MM firm use this information they get from flows to implement taking strategies? (for ex. all the flow on the market that is orthogonal to the flow PFOF is informed...) Thank you! $\endgroup$ Commented Feb 25 at 13:32
  • $\begingroup$ 1. Probably because the gap between a retail options trader and an informed options trader is much wider than the gap between a retail stock trader and an informed stock trader. 2. As long as they are not front-running their clients, they are largely free to use the information in any way they wish. $\endgroup$ Commented Feb 25 at 13:43
  • $\begingroup$ That makes sense! Thanks a lot $\endgroup$ Commented Feb 25 at 13:48

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