HFT versus the sub-optimal Tick

Felix Salmon has an interesting follow-up to my post, Should Stocks Trade in Increments of $.0001?  First he notes (as did Chris Stuccio) that for stocks above say $50 the sub-penny rule doesn’t make much difference.

Here’s the chart, from Credit Suisse via Cardiff Garcia:


The y-axis shows the bid-offer spread on any given stock, in basis points; the x-axis shows the price of the stock, in dollars. Clearly, there’s an artificial clustering around that curve. For a lot of stocks trading at less than $50 a share, the market would happily provide bid-offer spreads of less than a penny if it could; but it can’t. And when stocks get really cheap, the bid-offer spread becomes enormous. For instance, an eye-popping 3.766 billion shares of Citigroup were traded on December 17, 2009, when the stock fell 7.25% to $3.20. At that level, a one-penny bid-offer spread is equivalent to a whopping 31 basis points; if Apple traded at a 31bp spread, then its bid-offer spread would be almost $2.

Clearly, the traders were the big winners when Citi was trading at a very low dollar price — if you make the assumption that traders capture half the bid-offer spread on each trade, then the traders made almost $20 million trading Citigroup alone, in one day.

On the other hand, it seems that the market almost never trades stocks at a bid-offer spread much below 2bp. Which in turn means that for stocks over $50 per share, we’re pretty much already living in Stuccio’s ideal world, where the spread is determined by traders, rather than by an artificial rule barring increments of less than a penny.

Salmon then makes another point – firms may use stock splits and IPO pricing to deliberately price their stocks below $50. Salmon says this is in part to grease their relationship with Wall Street but one could also say this is done in order to create more liquidity. In fact, there is good evidence for Salmon’s hypothesis that firms care about nominal share price; In Tick Size, Share Prices, and Stock Splits (JSTOR, H/T OneEyedMan) James Angel makes the interesting point that even as the S&P and CPI soared between 1924 and 1994 the average nominal price of a stock was very flat near $32. Angel’s explanation is that firms use the IPO price and splits to keep a consistent relationship between tick size and share price because:

A large relative tick size also encourages dealers to make a market in a stock….a larger tick provides a higher minimum round-trip profit to a dealer who can buy at the bid and sell at the offer.

Angel even notes the potential for rent-seeking that motivated the original argument to eliminate the sub-penny rule:

If the relative tick size is too big, the profits from a wider tick size may be dissipated through vigorous competition for order flow and payment for order flow.

Overall, I find these arguments continue to favor eliminating the sub-penny rule but these results indicate that firms already have some control over the extent of HFT so the net benefits may be smaller than at first imagined. It is probably easier to split than to combine shares to raise price, however, and social benefits may exceed private benefits so I still see an argument for eliminating the rule. See Felix’s post also for a number of very good comments.


So, the idea is to allow pricing in millionths of a cent so google can be split 5000 to 1 to turn it into a penny stock to increase liquidity?

Why isn't Warren Buffett who has influenced the google founders on stock price more correct on where stock prices should be?

What changes in corporations in terms of the value of their productive capital assets that requires rapid changing of the pricing to track value on a second by second basis? Is the market tracking the progress of the internet company building a quantum transport that would allow a train load of coal to be shipped over the internet cheaper than Warren's trains?

Why would the price of something that cost $100,000 to make yesterday and will cost $100,000 to make tomorrow move between $99,000 and $101,000 in the same day? Is all microeconomic theory wrong on price equilibrium and economy of scale? I find it odd that while physics jumps into time (t) almost right away in basic classical theory, economist ignore time for the most part other than to talk of "the long run" and "short run".

Perhaps I'm being like Einstein facing quantum theory in refusing to believe god plays dice with the universe, but I think I'm with Warren Buffett in thinking you are advocating destructive economic theory where price has nothing to do with cost, or even return on invest capital so the market is purely random motion and it is possible for the value to be in two places at one time, but quantum entangled so if a $100,000 cost asset goes to $110,000 it also goes to $90,000 at the same instant.

Alex - I think that the reason the average share price stayed constant throughout that period is because retail investors, for one reason or another, "prefer" to own 100 shares of a $30 stock instead of 1 share of a $3,000 stock. Retail investors drove stock splits!

Part of this preference used to have some basis in reality - when investors found it more difficult to trade odd lots - but that basis is no longer relevant, in my opinion.

As you are probably aware, there is still a massive cognitive bias in many novice investors' brains that if they own a $50 stock, in order for it to double, it has to go up $50... but if that stock splits 10-1, and they now own a $5 stock, all the stock has to do is go up FIVE MEASLY DOLLARS in order for them to get a double!!! It's *so* much easier for a stock to go up $5 than it is to go up $50, so investors prefer the lower prices... I don't think Wall Street has anything to do with it.

and yes, I am being sarcastic, trying to channel my inner muppet in the "so much easier" logic in the prior paragraph...

as evidence for my claim, I submit simply: the reaction of stock prices when a split was declared during the peak of the internet bubble... Declared stock splits were worth a 5% increase in stock price! The only explanation for that is that investors are ig'nant and prefer lower priced stocks...

KD, I don't doubt that the forces you point to are also a factor. Some of the evidence in Angel, however, suggests specifically that there is a relationship between tick size and share price. In particular, he finds that countries that have multiple tick limits (i.e. a tick that gets smaller when the share price is smaller), thus keeping a more constant relationship between bid-ask spreads and share price, have a wider variance of share prices.

Relaxing the tick rules would put further downward pressure on average share prices. One complication is that exchanges have minimum share prices for their listings. The minimum price rules have real bite and they trigger the vast majority of reverse-splits. Firms tend to do that only when in serious trouble because it is interpreted as a sign the firm is in serious trouble.Those rules were designed (I believe) to discourage "boiler room" penny stock trading but plausibly the SoX listing and reporting requirements have made penny stock listings unprofitable.

SoX exemption is based on market capitalization = share price * shares outstanding.

All this talk about fractions of one cent--is this what microeconomics excels in? No wonder they call it "micro" economics! And still no cure for the business cycle. Reminds me of the adage: "penny wise, pound foolish".

The business cycle is a macro topic and has been cured: http://mises.org/document/2745/Money-Bank-Credit-and-Economic-Cycles

This is an interesting microeconomics question and I think Alex is on point, although I wish he would elaborate on "social benefits may exceed private benefits". Shouldn't we look at the net private benefit/cost between consumers of financial products and traders of those products?

I don't think $50 is the cut-off point for irrelevance of the tick size. These are average spreads we're talking about, so if the average spread for a $100 stock is 2bps, it means that many times (maybe more than half the time) the spread is less than 2 bps.

I'm not sure we don't already have sub-penny ticks. My online limit orders can be placed only in increments of a penny, but my orders often fill in increments of a tenth, or even a hundredth, of a penny.
So it seems that the size of a tick depends on who you are...

There are a lot of implementation details that are being ignored. What bothers me most is that bid-ask spread is not the be all and end all of liquidity. Angel claims that too low a tick leads to reduced liquidity, though I am skeptical.

I claim: It is legal to transact in sub-penny increments, but it is illegal to quote sub-penny prices, but I don't know what that means. I think it has to do with the difference between trading on an exchange and advertising a price that people on other exchanges can accept. Also, the price of the last transaction has legal consequences (eg, the uptick rule) and I think that this is another "quoted" price that is rounded to the penny.

Roughly correct. Essentially, in the US no one can publicly quote (offer to undertake a transaction at) a specific sub-penny price, but the trades themselves are allowed to occur away from sub-pennies. E.g. a market maker might provide his clients a certain amount of "price improvement" on average - i.e. promising transaction prices better _on average_ than the prevailing best quotes - so you might be the lucky recipient of this from time to time (but you won't be promised this in advance, vis-a-vis a specific transaction at a specific price). Some order types can be placed that, if executed against someone similar, will price at the mid-quote say (so may be on a half/penny), but still no-one was actually quoting "I'll trade at $10.005". There are also other corner cases and venues where you might get a better price that you asked for or offered. Also, orders can execute against quotes on multiple price levels (today, this is possible even if under 100 shares) so the blended price your broker reports can by pretty much anything.

Professional traders also face the fee or rebate structure of US trading venues, which weakly reproduce some of the advantages (and drawbacks - which are big also; this conversation is ignoring this side of things!) of more flexible pricing. I can quote on one exchange and be assured of an extra 0.3 cents rebate if I trade, and quote the same limit penny-compliant ice on another but have to pay 0.02c if I trade. Economically, this is not dissimilar to having a finite set of sub-penny quoting options available to me. The implications of fee/rebate competition are complex.

The New York Stock Exchange is currently working with the SEC to get approval for a pilot program (Retail Liquidity Plan) which, in a roundabout way, can be seen as offering a way to get sub-penny pricing but only for "retail" orders.

A share split and consolidation are equally easy as they use the same process. From the boardrooms I've been sitting in the driver of the decision has more to do with the price of a board lot falling inside the desired range for liquidity.

I wonder more about a minimum-size 'tick' in the time dimension. What if all pending trades were matched and cleared only every N seconds? (With N>1, maybe even >60.)

Might that cap the zero-sum gaming around HFT while still serving the market's price-finding/order-clearing purposes?

I think the Arizona Stock Exchange was an early attempt at this, where N was so large that trades crossed only once or twice daily. (It was not really conceptualized with "N" -- rather a combination of ideas aiming at good price discovery without the participants needing to disclose size.)

Graph note: What is so wrong with units, percentages and logs?

An interesting place to look at is Hong Kong, where because of its 0.1% stamp duty, HFT is non-existent.
However, a proposal to reduce the bid/ask spread a few years ago has received strong opposition from the broker community (especially small local ones). The exchange finally abandoned the plan to reduce the spread further for stocks with price below HK$5.The bid/ask spread (as a % of stock price) is astonishingly high for stocks with low nominal prices. Small local brokers got a substantial part of their revenue from trading of medium and small cap stocks (which usually have low nominal prices)
You can have a look here for a summary:

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