Should Stocks Trade in Increments of $.0001?

In Modern Principles Tyler and I explain that price floors create wasteful increases in quality. The classic story is the Civil Aeronautics Board’s regulation of airline prices between 1938 and 1978. Through entry, exit and price regulation, the CAB kept prices above market levels and airlines earned excess profits with every customer. Although the airlines were not allowed to compete on price they could compete to attract customers by offering better meals, wider seats and more frequent flights. Airline quality, as a result, was high but it was inefficiently high; for example, too many flights flew half empty. More fundamentally, if airlines compete by lowering prices by $100, customers are automatically better off by $100. But when airlines have no choice but to compete by spending $100 on “quality” customers are not necessarily better off by $100. Indeed, enforced non-price competition will always result in more spending than value creation on the margin. If given the choice, customers would have preferred lower prices to higher quality but until deregulation in 1978 they were not given the choice. Thus, price floors create wasteful increases in quality.

Ok, so where does stock pricing come into play? Chris Stucchio, a high-frequency trader, argues that the sub-penny rule, SEC Rule 612, “essentially acts as a price floor on liquidity – it is illegal to sell liquidity at a price lower than $0.01.” As a result, traders compete on speed (latency) rather than on price.

As with a classical minimum wage, two parties are harmed – the purchaser (who must pay extra) and the lower priced seller (who is pushed out of the market).

Similarly, at prices higher than $0.01, it makes price movements lumpy – on a bid ask spread of $0.05, it is illegal for someone to enter the market at price $0.049 or $0.045. Thus, at any price point, speculators are forced to compete on latency rather than on price. Price competition is only possible if one market maker is willing to offer a price at least $0.01 better than another, which is often not the case.

When price competition is impossible, market makers must compete for business via other methods – in this case latency.

As with the airlines, the increase in speed–now such that 40,000 trades can be executed in the literal blink of an eye and relativity matters–is profitable for the traders even though it doesn’t add nearly as much to customer or social welfare. As I wrote earlier:

A small increase in speed over one’s rivals has a large effect on who wins the race but no effect on whether the race is won and only a small effect on how quickly the race is won.  We get too much investment in innovations with big influences on distribution and small (or even negative) improvements in efficiency and not enough investment in innovations that improve efficiency without much influencing distribution (i.e. innovations in goods with big positive externalities).

Penny pricing (and before that 1/16th pricing) made sense when stocks were mostly traded by humans and we needed to conserve cognition but, as Stucchio points out, most trading today is done by computers and pricing in hundredths of a penny (or less) would not impose any extra effort on the computers. Pricing in 1/100ths of a penny, however, would dramatically increase price competition and reduce wasteful quality competition.

Here are previous MR posts on HFT about which Tyler and I have debated.


The classic minimum price is a penny for you thought.

This explains poor thoughts.

Wait, shouldn't we expect inefficiently high quality thoughts?

Or an inefficiently quick rate of thought exchange?

Why dictate the increment at all?

As some trades will still be operated manually, leaving room for error, pricing in 1/100th would also increase the effects of a fat finger trade by 100

I don't think so. You are right about the error in terms of what the trader intended. But the absolute price difference among errors should fall if errors are in any way distributed among the different digits. Keeping errors constant, the dollar outcomes will be less painful for those who err.

Infinitesimal increments. A 64 bit binary digit price allows quite fine increments in price.

Only if floating point- 56 bits of precision and 8 digits of exponent plus sign. By allowing negative prices, the problems of liquidity will be solved - you will always be able to unload those dogs in your portfolio.

Please PLease PLEASE don't use floating point numbers to represent financial quantities.

In floating point, it is not the case that if you add 0.01 to zero 100 million times you get 1000000 . DO try this at home -- it'll take about a second or two if you have a reasonably modern computer and you write it in a compiled language or in java. Also, if you add 0.03 to zero 100 million times you don't get the same answer as if you add 0.01 to zero 300 million times.

Instead, use 64 bit numbers. If we impose a ceiling of $1 trilliion on the total value of a single transaction you get a breakage of $0.0000001 , which is probably fine enough. If AAPL ever reaches a market cap of $1 trillion and you decide you want to buy it all you will not be able to place an ordinary order on an ordinary exchange ... sorry about that.


or we could use bigints and not have to worry about that at all.

Do you think that politician's ability to create hyper-inflation can be crammed into mere 64 bits?

(OK, I provoke a bit.)

One problem with decreasing the minimum increment is that it dramatically increases the number of ways that an HFT player can game the market. It also increases the value for lower latency trading in the following way. As the minimum increment decreases relative to a stock's price, the queues for that stock also decrease. It is easier to play games when the queues are small because then each order is a much large percentage of top of book than when the queues are very large.

One reason these games are so prevalent is because participants are not charged for placing orders (a classic case of the free rider problem). After an entity has put their infrastructure in place, the marginal cost of placing an extra order is zero. This entices HFT to engage in practices such as quote stuffing, deceptive trading and continual probing of the market. If instead each participant were charged a small fee for each order, (which would be rebated when a trade was completed in a revenue neutral way), then much of the games would be eliminated, and the advantages to smaller bid/offer spreads would be better transmitted to the average participant rather than the HFT player.

Could it be argued that these strategies simply provide better price discovery and maintain a finer grained price uniformity? How does one classify a HFT strategy into efficient arbitrage versus gaming?

Albert, could you explain all the new ways that subpenny pricing allows gaming the system, and why they are harmful? You are correct that the size of the queue at each individual price point would shrink, but similarly being at the "top of the book" would be less relevant. Traders would just use the cumulative view rather than the ladder view.

Also, do you believe that if we went back to pricing in 1/8ths, we would reduce the number of ways for HFTs to game the system? If not, why not? What makes $0.01 the optimal pricing increment?

A shorter queue need not make it "easier to play games." (For those not in trading, market participants' orders at a given price wait in a queue and trade first-in-first-out). If we assume that the current liquidity would be distributed across several, strictly non-worse price levels, a semi-competent trader would simply aggregate the quantities. Of course, displayed size would not stay constant--it would probably decrease, as it did when the markets moved to penny pricing. This is a bad thing, but not because of increased susceptibility to gaming.

As for your other gripes, I'll concede quote stuffing. However, probing? It's not ok to discover the state of the market? Deceptive trading? Since when do traders show their hand? Charging fees for orders? I think you understand neither the degree to which market-makers *are* the market, nor the damage this would do to them. Or perhaps you do, and you don't mind making appointments to trade... "the advantages to smaller bid/offer spreads would be better transmitted to the average participant rather than the HFT player." Huh? If retail can go out right now and buy equities at lower spreads, how are those spreads not being transmitted to the average participant?

For the record, I am in favor of spreads tighter than a penny and I certainly do not want to go back to the days of the specialist. However decreasing spreads is not an pure gain unless you also charge for placing orders. For an example of the types of games that the HFT players can play, see the website: . Also, it annoys me that I have to spend substantial extra money on computer systems to process quotes that would not exist were it not for the free rider problem I mentioned above.

"Also, it annoys me that I have to spend substantial extra money on computer systems to process quotes that would not exist were it not for the free rider problem I mentioned above."

Are you speaking from an Exchange point of view? Which other participant needs to bear the burden of equipment?

You process price feeds, don't you?

Jesus do you know what you are talking about? I costs a $$$$$ to host co-lo, $$$$ all price feeds direct, etc, etc,etc. That's for a participant.

I'm all for fees for message. It encourages efficiency, and reduces the number of idiots in the market.

Ah, so you are a participant complaining about having to keep up with a competitor who otherwise will eat away your profits because he has better technology?

This is why God gave us reverse stock splits.

Trades aren't continuous in the time domain either, are they? Whats the tick frequency for the queues?

Another surprising benefit of inflation...

This would be expected due to dis-inflation - Not inflation. Inflation would alleviate the need for this.

Actually what I meant. Inflation reduces this problem automatically.

There becomes a point where market-makers can "step-ahead" of others in the auction market for an economically insignificant improvement in price. That is why sub-penny pricing has been banned by the SEC for stocks that trade > $1. I would argue that if sub-penny pricing is allowed, it will cause a massive surge in message traffic (order cancels/replaces/etc...) that will further deteriorate market quality.

Why do you believe it is harmful to "step-ahead" of others by offering a better price? And why do you believe that anything below $0.01 is economically insignificant?

Also, if messaging becomes a significant issue, the exchanges can introduce a messaging fee (assuming this is not banned by the SEC). Due to competition among exchanges, each one has an incentive to protect market quality.

I dont think stepping ahead is harmful - a market-makers job is to improve the spread if possible. I think stepping ahead for an economically insignificant amount creates no value for a liquidity taker and has negative externalities on a shared resource, the market. 1/100th of a penny on a product like SPY is 7/1000th of a basis point. SPY turns over $24bn a day - assuming every share was improved by 1/100th of a penny, this would amount to roughly $18k a day. Ok, a small benefit to the liquidity seekers - but at what cost? If you believe messaging rates will increase, every market participant will have to invest in new hardware and software to even be able to handle the influx of market data.

Here is a simple technical solution to the issue of increased messaging rates: the exchange can offer a penny feed which rounds prices appropriately. I.e., a bid of $10.0023 is rounded to $10.00 and an ask of $10.0409 is rounded to $10.05.

A replace order from $10.0023 to $10.0028 is simply not reported in this feed.

Those who don't want to invest in new computer equipment can subscribe to this feed with no change to their systems. The only effect on them is that their brokerage accounts will show slightly more money than they predicted.

Also, I suspect that spreads will drop by an average of $0.0050, not $0.0001. If a market maker currently offers a bid of $10.00, all we know is that their reserve price lies in [10.00, 10.01). It could just as easily be $10.0099 as $10.0001.

Also worth noting, sub-penny quoting is outlawed by the regulators, but sub-penny pricing is not - which is why much of the sub-penny prints come from dark pools and ATSs. the distinction is purely technical. If you are looking for price-improvement, a smart order router will typically ping the dark-pools first..

Shouldn't we be able to test this empirically today? Since stocks must be traded in whole number increments, a penny will represent 1/1000th of a $10 stock but but 1/10000th of a $100 stock. If the sub penny rule truly hindered market making, we should see more HFT on lower-priced stocks (where latency matters) than on higher-priced stocks where more liquidity is implied.

I have anecdotes suggesting this is the case, but no hard data. I.e., most of the HFTs I know say they don't make a huge amount of money off AAPL (and no HFTs will touch BRK.A).

Also note that such a comparison must be done carefully - high price stocks are often high volume, and the increase in trading due to volume might swamp the decrease in trading due to a smaller relative spread.

Let's just let them trade in doubles.

This is a terrible idea. See the article "What Every Computer Scientist Should Know About Floating Point Arithmetic" by David Goldberg.

If we used floats for money, then money at close might not be equal to money at open.

I'm a mathematician, and I did floating point validation for AMD. NEVER use anything but integers for money.


64 bit integers FTW

Scratch that, we should just use bigints instead.

Is there any standard datatype that handles (a fixed number of?) decimals without the imprecision drawbacks of a float? Without having to hack around by defining everything in pennies or micropennies?

Even a bigint will impose an arbitrary increment, although trivial. Is there an implementation for retaining precision and arbitrarily small increments, both?

We could of course have the prices in integral multiples of 1/2048 of a penny, or 1/1048576 of a dollar, or even 1/3579 of 1¢, as long as we all agreed on the book-keeping standard.

Profits at $.00000001 instead of at $1.00, $.0125, $.0625 or $.01. The diminishing rate of profit continues to diminish.

Hard to get fired up about this one. Our financial markets have many serious problems. Distortions in stock pricing in low value stocks due to rounding errors that can also be addressed with reverse stock splits if they get out of hand is not one of them. It might be a little better, but is unlikely to make a material difference in anything that is materially wrong with the system.

I would say that the flash crash, as well as some of the melt-ups indicate that there ARE serious problems driven by faux-volume.

Those worrying about whole number increments should remember that for 200 years or so the increments reflected the doubloons and bits from the Spanish dollar that we adopted at Independence, those 1/8 increments being worth 12 and a half cents. Yeah, the good old days!

Oh, and those 1/16 increments were the old Spanish picayunes worth 6 and 1/4 cents, even more off from a whole unit. The paper in New Orleans is named for them, and you can find them for sale on Royal Street in the French Quarter. Great increments!

It seems to me Chris that the hole in your analysis is that you assume that all rents currently go to HFT. If all liquidity provision is via HFT, and non-HFT always takes liquidity, then it's true that by allowing HFT providers to compete on price, rather than quantity, you lower ex-post rents, reducing transaction costs for non-HFT "fundamental" traders and thus make the market more efficient.

However in practice currently a lot of limit orders on the book are placed by institutions that do not have HFT capability (at least, not on co-location timescales). Some of these are placed by human traders, some by shortfall minimization or other algorithms working on non-HFT timescales. At a .01 price point, such traders are able to execute a subset of orders by passively waiting on the book; this allows such traders to recapture some of the rents they typically pay to HF market makers. In practice (at least as of last year, when I left the industry) you could still get quite a lot executed in such a manner without HF infrastructure. As a result the ex-ante rent extracted by HF is potentially far smaller than .01/share.

For a .0001 tick to be superior, we need the ex-ante rents at a tick of .01 > the ex-ante rents at a tick of .0001. In other words, P({needing to take liquidity | tick = .01}) * (bid-ask spread at a minimum of .01) > P({needing to take liquidity | tick = .0001}) * (bid-ask spread at a minimum of .0001). Note that if P({needing to take liquidity | tick = .01} = 1, then this always holds if (bid-ask spread at a minimum of .01) > (bid-ask spread at a minimum of .0001), which I'll grant, and which I think is your point.

However I would assert that while P({needing to take liquidity | tick = .0001}) is roughly 1 (assuming that the bid-ask spread at a minimum tick of .0001 > .0001, and thus HFT in this case would always have a profitable front-running strategy), currently P({needing to take liquidity | tick = .01}) >0 (perhaps on the order of .3-.4 for realistic values depending on the size of the latent block being executed, risk aversion, riskiness of the stock, etc. etc.).

The trade-off thus is a function of a stock's liquidity. Suppose at one extreme you had a stock so liquid that its actual bid-ask spread would be .0005 if that were the min tick. Then you would require P({needing to take liquidity | tick = .01}) > 5% to have a welfare improvement. This is certainly true, and that makes it a no-brainer to cut the tick size in the highly liquid case.

Now consider a stock with an equilibrium bid-ask spread of .009. The criterion is now P({needing to take liquidity | tick = .01}) * .01 > .008 -> P({needing to take liquidity | tick = .01}) > 90%. This seems to me unrealistically high (only 1 in 10 limit orders on the passive side of the book can get executed)?

For a more extreme example consider a stock in the Russell 2000 with an equilibrium bid-ask spread of 4 cents. In this case we expect that the bid-ask spread won't change at all, as the minimum tick is not currently binding. The condition is P({needing to take liquidity | tick = .01}) >= P({needing to take liquidity | tick=.0001}). This condition is clearly false if there is any possibility at all of lower-frequency traders currently getting a passive order executed in the book, assuming of course that if the current spread is .04 that an HFT would be willing to take a spread of .0399.

Bottom line, it depends. I could definitely get behind the standard European systems of altering the min tick based on the price of the stock (which should affect the "natural" bid-ask spread), and perhaps volatility and volume should be considered as well. But I think that a general move to $.0001 is likely to be counterproductive in all but the most liquid stocks (at least, toward the ends of efficient markets; it might be productive for HFTs...).

Isn't a transaction tax a simpler solution?

A transaction tax could cause HFTs to increase the spread, thereby reducing liquidity. This is undesirable, assuming you believe price discovery is beneficial.

I'm not persuaded that price discovery at this degree of precision is in the least bit meaningful. It's a feature, not a bug, that a transaction tax would increase bid/ask spreads--and reduce trading volume.

Even if not meaningful, how can over-precise price discovery ever be a bug?

Why is reducing trading volume a plus;unless current volumes are overwhelming servers or choking the system in other ways. Are they?

The minimum increment should be $1 - liquidity is overrated.

I wonder what would be the effect of restricting the arrival of orders to round them later to the nearest 1/10 of a second, with cancels likewise rounded up, but with a minimum appearance of 5 seconds.

This would trash the benefit of UHF trading; what else would it affect?

Bitcoin has increments of 10^08

I mean 10^-08

So, to improve liquidity in the real economy, the worst idea is eliminating the penny, and what the US Mint should be doing is going back to minting the "half cent" and "mill" coins. The increased liquidity will drive down prices and increase sales and boost the economy.

Online fine-graining has close to zero overhead costs. How much more does it cost to run a $0.0000001 system versus a $0.01 system?

How much does it cost to mint mils and half cents?

A few points:

1. Grocery stores get around this fine. Toilet paper couldn't be sold at less than a penny per sheet if priced individually. Therefore they put together a thousand sheets for $2.99.

2. This doesn't work for fees for management of index funds: the marginal unit cost of production is equal to the cost of moving a few electrons around, yet fees are not driven down to billionths of a percent. HFT is basically another case of moving a few electrons around, so like mp3's the unit cost should go to zero save something that distorts the market and causes deadweight loss (copyright for mp3's).

3. If I misunderstood the mechanism and my point (1) is incorrect (firms can't reduce effective unit prices by selling in bulk), I imagine that sub-penny pricing would allow established capital rich HFT firms to drive new competition out of business by simply underpricing liquidity until the new firm went bankrupt. The firm with the most money would be the only one left standing.

I think this is a confusion of what people with the biggest stake in the game want. Major shareholders of corporations want a depth of liquidity. Part of the incentive for quoting depth is to get time priority on the book, with 0.0001 price levels this incentive goes away and the depth of liquidity follows. Look at the difference between the depth of book on stocks below $1 (which have a 0.0001 mininc) and stocks above $1.

Also, it's not entirely true that the mininc is 0.01, there are many venues which support matching at 0.005 and the fee structure on the boston stock exchange is inverted so removers are paid 0.0015 for taking, but good luck getting TD ameritrade to pass that savings back to you.

A post about this but not facebook's IPO? Retreated to your ivory tower, then? Too concerned with the market for overpriced slow-service food in DC?

Our laws make it impossible for a man to keep his business private, he has to deal with an increasingly crooked set of bankers by law, and then people get ripped off by those bankers. It's all so predictable, yet, where is the real reform? Our banks are still too large and leveraged. Why haven't we re-instated the depression-era reforms that worked so well? Why don't we enforce physical money and stocks exchanging hands in our markets to cut down on IT shenanigans, improve transparency and help employment? Is there a real downside to preventing the next flash crash?

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