From 5 February 2021:

Okay let’s do payment for order flow again, because people are talking about it and that always stresses me out. Here’s an intuitive description of how it works. A million people come to a broker to trade GameStop Corp. stock. Half of them want to buy shares, half of them want to sell shares. One share each, all using market orders, all at precisely the same time. The stock exchange has half a million shares of GameStop available for sale at $58.25, and orders to buy half a million shares for $58. The broker could send all of its customers' orders to the stock exchange, where the buy orders would be filled at $58.25 and the sell orders would be filled at $58; the broker would pay the exchange a small fee for executing these orders.

But! The broker realizes, look, all these people who want to buy shares could be matched up with all these people who want to sell shares. I don’t have to pay a fee to the exchange, the buyers don’t have to pay $58.25, and the sellers don’t have to get $58. The buyers could pay $58.15 and save 10 cents, the sellers could get $58.10 and make an extra 10 cents, and I could keep 5 cents (and avoid the exchange’s fee) for my trouble. That’s a good deal for everyone!

This is called “internalizing”: Your broker executes your order internally, against its other orders, rather than sending it out to the exchange. In practice a typical retail broker doesn’t have the ability to do this, so it sends its orders to what is usually, in the business, called a “wholesaler” (or sometimes “internalizer”), and usually, outside of the business, called a “high-frequency trader."[3] Popular wholesalers include Citadel Securities, G1X Execution Services LLC, Two Sigma Securities LLC, Virtu Financial Inc., Wolverine Securities, etc. The wholesaler does the thing I just said: It pays the sellers more for their shares than the exchange offers, charges the buyers less for shares than the exchange would, and keeps 5 cents for itself. Well, it keeps, say, 3 cents for itself, and sends 2 cents back to the retail broker who sent it the trade. The broker has subcontracted the internalizing job to the wholesaler, and they share the profits.

Also a good debunking of this myth:

Otherwise normal people will start out mainstream explainer articles by saying, like, “Robinhood sells your order to Citadel so Citadel can front-run it.” No! First of all, it is illegal to front-run your order, and the Securities and Exchange Commission does, you know, keep an eye on this stuff. Second, the wholesaler is ordinarily filling your order at a price that is better than what’s available in the public market, so “front-running”—going out and buying on the stock exchange and then turning around and selling to you at a profit—doesn’t work. Third, because retail orders are generally uninformative, the wholesaler is not rubbing its hands together being like “bwahahaha now I know that Matt Levine is buying GameStop, it will definitely go up, I must buy a ton of it before he gets any!” The whole story is widely accepted but also completely transparent nonsense.

Posted here for all eternity, as this is a good reference and quick explanation about what PFOF is. Handy to have around.

Update 5 October 2021, with another section in today’s Money Stuff making an interesting point:

…if you were going to “ban payment for order flow,” would you ban payment for order flow, or would you ban internalization? The way the stock market works right now is that if you are a retail customer looking to buy or sell a stock, your order generally does not go to the stock exchange: Your broker routes it to one of a handful of big electronic market makers, who generally sells you the stock (or buys it from you) at a price that is slightly better than what’s available on the public exchange (“price improvement”), and pays your broker for the chance to do so (“payment for order flow”). You could ban that whole thing and make brokers send retail orders to the stock exchange. Or you could leave everything in place and just ban the payments from market makers to brokers; the brokers would just have to send orders to the market makers who offered the best price improvement, not the ones who pay.

I think either is a more or less plausible answer. If your concerns with payment for order flow are about conflicts of interest (retail brokers route orders to market makers who pay), or about gamification (payment for order flow enables free trading and probably too much of it, and higher payment for options orders gives brokers incentives to push options on customers), or about execution quality (higher payment for order flow means less price improvement), then I suppose banning payment for order flow would make sense. If your concerns are about opacity (so you want all orders to go to lit exchanges), or the market dominance of a handful of market makers (so you don’t want them to get all the retail orders), or about spreads on lit markets (so you don’t want retail orders to all be siphoned off to retail market makers, leaving only toxic orders on the lit exchanges), then I suppose you would need to ban internalization more broadly. Just banning payment for order flow would leave everything as it is right now except that, instead of paying Robinhood Markets Inc. for retail orders, the market makers would get them for free.

Update 8 December 2021, with some evidence that PFOF might be increasing retail trading costs (aka not getting the best execution price), but nothing definitive. First, additional background on PFOF! I love these explanations. First we have The Good Model:

I think there are two different intuitive models of payment for order flow. Let’s call them the Good Model and the Bad Model.

The Good Model goes like this. Lots of retail investors go to their brokerage looking to buy XYZ stock, and lots of retail investors go to their brokerage looking to sell XYZ stock. XYZ is available on the stock exchange; you can buy it for $10.02 or sell it for $9.98. Those prices on the stock exchange are called the “national best bid and offer,” or NBBO, and are set essentially by market makers, high-frequency electronic traders who are in the business of buying from sellers and selling to buyers. The spread — the $0.04 difference between the buying price (the offer) and the selling price (the bid)[1] — is due to the fact that the market makers take lots of risk: If they buy stock on the stock exchange, probably some smart hedge fund is selling, and it will probably go down. So they need to buy at a fairly low price ($9.98) and sell at a fairly high price ($10.02) to compensate for this risk of “adverse selection,” this risk that whoever they trade with knows something that they don’t.

If the brokerage just sends all of its customers' orders to the stock exchange, they will buy at $10.02 and sell at $9.98, which is not so great. Also the brokerage will pay a little fee — customarily $0.003 per share — to the exchange for executing the order.

But the market makers come to the brokerage and say: Look, we hate trading with all these hedge funds on the public stock exchange. So much adverse selection. If we could just trade with your delightful retail customers, who trade small lots and never know anything we don’t know, we would never lose money. So we could afford to charge them a much lower spread. So if you send your orders to us directly, we will let your customers buy at $10.01 and sell at $9.99. They will get a better price than they would on the stock exchange, but we will still make money. Not only that! We’ll make so much money that we can pay you some of it. We’ll give you $0.003 per share for your trouble. Instead of you paying an exchange to execute your customers' orders, we’ll pay you to execute them. With that money, you can fund your business. It can replace commissions! You can offer free trades! Good deal for everyone.

The Good Model has very intuitive market-structure economics. I have discussed it in more detail a few times, mainly here.

And then, The Bad Model:

The Bad Model goes like this. XYZ is available on the stock exchange, and the posted prices are in fact $10.02 to buy and $9.98 to sell. But only naive rubes pay those posted prices. There is a “real” price to buy XYZ, a savvy-customer price that you can get by knowing where XYZ is on sale. The real price is, say, $10.001 to buy and $9.999 to sell. You have to be smart, you have to know about order types and hidden liquidity and dark pools, you can’t just send a market order to the big stock exchange and expect to get the real price. But lots of people are smart; there are smart order routers that are commercially available and that are good at finding the real price.

High-frequency electronic traders, for instance, are smart, and know where to find the real price. They can easily buy XYZ for $10.001 and sell it for $9.999. Retail customers of retail brokerages are not particularly smart, and frankly the retail brokerages aren’t all that smart; they don’t know where to find the real price. All they know is that the posted price, the NBBO, is $9.98 / $10.02.

So the electronic traders — the market makers — go to the brokerages and say: Look. Instead of sending your customers' orders to the exchange, having them pay $10.02 and get $9.98 and you paying $0.003 in fees, send their orders to us. We’ll give them a better price; we’ll charge them $10.01 to buy and pay them $9.99 to sell. And we’ll even pay you $0.003 for your trouble. This is a good deal for the brokerage (it gets paid for order flow instead of paying for execution), and it looks like a good deal for the customers (they pay $10.01 instead of $10.02, etc.).

But meanwhile the market makers are doing this very simple trade:

Customer comes to them to buy stock.

  1. It sells them stock for $10.01.
  2. It turns around and buys stock at the real price, $10.001.
  3. It makes $0.009 in instant risk-free profit.
  4. It pays $0.003 of that to the brokerage for the opportunity.

The Bad Model is what pretty much everyone believes about payment for order flow. It is the explicit model of Michael Lewis’s “Flash Boys.” I have discussed it in more detail here, when we talked about an institutional brokerage that followed it more or less exactly and got in trouble with the Securities and Exchange Commission. The brokerage told its customers that it did smart routing to try to find them the best price. But it didn’t: It secretly sold their orders to market makers who filled the orders at a better-than-the-NBBO-but-worse-than-the-best-price price, and then went out and traded for themselves at the best price.

And now for the upshot, a Medium post published by Public, a retail stock brokerage.

Still, the two models do make different empirical predictions. In particular they make different predictions about what would happen if a retail brokerage — or every retail brokerage — stopped using payment for order flow and routing orders to market makers:

  1. On the Good Model, internalizing retail orders allows them to get better prices than they could get in public markets, so getting rid of this model would lead to worse prices for retail.
  2. On the Bad Model, internalizing retail orders allows them to get worse prices than they could get in the (“real”) public markets, so getting rid of this model would lead to better prices for retail, if retail brokers can do a good job of finding the real best public price.

Last week Public, a retail stock brokerage, put out a Medium post titled “Delivering on Price Execution Without PFOF.” (Felix Salmon wrote about it here.) Earlier this year Public said that it would stop taking payment for order flow; instead, it routes its orders to public venues. Here’s how that’s going:

The takeaway: The data available to us strongly suggests that Public delivers better execution quality on average to customers than our peer firms that accept PFOF from market makers. …

We want our customers to get the best possible price on every single order. So, working with our partners at Apex Clearing, Instinet and the execution venues, we use smart order routing (“SOR”) software to locate the best price for each order available across 28 different lit exchanges and alternative trading systems (“ATSs”), and then route that order to the venue that offers the best price.

When a customer submits an order to Public, the SOR first tries to execute that order at the “midpoint” price that is halfway between the Best Bid and Best Offer by scanning venues that are often not included in NBBO, including retail-specific lit venues and alternative trading systems that are designed to pair natural buyers and sellers at the midpoint.

If we are unable to find a NBBO midpoint (or similar) execution during this first sweep, we route to the exchange with the best available posted price (often called the “inside quote”) as well as the highest likelihood of executing the order at or better than the NBBO. Most often, these are high-quality lit exchanges, including Nasdaq and IEX.

This approach is working. We’re able to deliver better prices for our investors, in aggregate, than the PFOF-based model. This is based largely on delivering significantly better prices for a meaningful percentage of our investors' orders.

There are some statistics comparing execution quality and suggesting that Public gets better prices without the payment-for-order-flow model than it would with that model. Which suggests that the Bad Model of PFOF might predominate.

Some caveats:

  1. There are different ways to measure execution quality across lots of trades, none of the data is that transparent, and no study is ever really definitive. Some orders presumably get better execution with a PFOF/internalizer model, but others get better execution without it; Public’s aggregate numbers are good “based largely on delivering significantly better prices for a meaningful percentage of our investors' orders.” I think that means something like “we trade at the midpoint” — $10.00 in my schematic examples above — “a lot of the time, which is way more price improvement than internalizers offer, but when we don’t get a midpoint fill we are more likely to end up trading at the NBBO, which is less price improvement than internalizers would offer.”
  2. This is not complete support for the Bad Model, because part of how Public gets good prices is by sending orders to “retail-specific lit venues,” that is, places for people who want to trade with retail due to, basically, the economic theory of the Good Model. “It is desirable to trade against retail,” the basic theory of the Good Model, does seem to be true.
  3. Public doesn’t get paid for order flow, and in fact often pays exchanges to execute orders, which means that its business is not subsidized by PFOF, which makes it harder to offer free trading. (Public offers free trading, but gently requests tips.) If you think free trading is good then this is a drawback to getting rid of PFOF. (If you think free trading is bad and encourages gambling and churn, then this is a benefit!)

Still all in all this does count as evidence for the Bad Model: You can find stock for sale at better prices than the NBBO, if you look for it, so you don’t have to use payment for order flow to get good execution for retail orders.

Find Matt Levine at Bloomberg.