Fractions, Decimals and the Math of Markets

Editor's Note: This column is a special bonus for readers. This piece originally appeared on RealMoney today. To sign up for RealMoney, where you can read Paul Kedrosky's commentary regularly, please click here for a free trial.

Earlier this week, Securities and Exchange Commission Chairman William Donaldson suggested on CNBC that he would review decimalization. Not the Dewey decimal system, and not the whole edifice of modern mathematics, but the change over the last few years whereby stocks began trading in decimals rather than fractions.

The morning after Donaldson's interview, I posted a comment here on RealMoney on the subject. It became clear from emails that opinions on decimalization are only slightly less divided (and heated) than they are about the current Bush tax cuts. I decided to revisit the subject in longer form.

How did math become such a hot-button topic? It has do with market participants (and some regulators, ahem) fusing stock pricing with minimum stock price differences.

Where It Began

Some brief history first. Until its recent switch to decimals, the U.S. markets stood alone in quoting stock prices in anything but decimals. Why the infatuation with fractions? You can trace its roots back to the Buttonwood Agreement in 1792 that helped create a formal U.S. market for stocks. In trying to set up domestic markets, brokers at the time looked for another market on which to base their own.

For a number of reasons, not least of which was that the U.S. dollar's value was loosely based on the value of the Spanish real, early traders decided to base U.S. markets on the Spanish one. The real had eight parts.

Why eight parts? It had to do with a then-current method of counting on the hands, one that used the thumbs to carry the total you had worked out on your eight fingers. That system led naturally to dividing stock prices into eighths, thus making the smallest possible price change one-eighth, or 12.5 cents.

Pressure began mounting, however, in the latter part of the last century. First, in 1975, commissions were deregulated, so trading costs began coming down. Having obtained a taste of lower trading costs, many investors (and regulators) began looking for other ways to reduce costs for market participants. That 12.5-cent spread started to seem awfully juicy.

Then in 1997 the pressure grew even more. After Canada began pricing its stocks in decimals, the U.S. was left as the only major market still using fractions. Under pressure from some investors' groups, legislators proposed a new act that would compel the major U.S. markets to follow suit. The arguments were myriad, overlapping and confusing, but the gist was that the elimination of fractions would make U.S. markets more competitive by simplifying price quotations, and by reducing overall transaction costs.

About Ticks

The former objective has certainly been met. There can be little doubt that quoting a stock at 11 1/8 is more confusing to many investors than quoting it at $11.125. Not only that, the change makes it easier to imagine what it might cost to buy, say, 100 shares. And that increased clarity around pricing has been a good thing for the markets, whatever retrograde fans of fractions might say.

The trouble, however, is that the push to decimalization was really about two things. There was the obvious -- replacing fractions with decimals, something only lovers of vacuum tubes and treadle sewing machines would quibble with. But the change also included a decrease in the minimum tick size.

Far from being an entomological term, minimum tick size refers to the smallest price difference by which a stock price can change. Orthodox economics might appear to say that prices shouldn't be stipulated at all. No one tells corner stores that they can only price Pepsi in 12.5-cent increments, so why are stock quotes different?

Understandably, perhaps, brokers, specialists firms and some large institutional investors will tell you that tick size is different. They have a point. Tick size provides a number of services to the market. First, it implicitly pays providers of liquidity. In other words, that 12.5-cent spread becomes, in a sense, my payment for standing ready to trade with all comers. It's good money (or at least it was) if you can get it. Because, so the argument goes, if you want liquidity and immediacy, you have to be willing to pay for it.

Second, a minimum tick size helps keep people from jumping around orders.

Say there's a limit order to sell a particular stock at $10 and stocks are quoted in eighths. If a market order comes in that would have hit that limit order, a specialist can pick off the order by offering a higher price. When stocks are quoted in eighths the specialist would have to bid at least 10 1/8 -- a 1.25% premium.

But things change if the minimum tick size falls to a penny, as it has in many cases under decimalization. In that case a specialist firm could jump around the limit order by bidding as little $10.01, a miniscule one-tenth of a percent more than that limit order sitting on the books. They could then, of course, turn around and hit the limit order, neatly profiting from the difference in the transaction.

It's a legitimate concern. Not just because of the gaming problem, but because of the effect it would have on the order book. If you were a large institutional investor and you know that this sort of tomfoolery would be going on, you would be more likely to hide your real trading interest. You might avoid limit orders, you might route through electronic markets, you might break your orders up into smaller pieces. All of these actions make markets less open and transparent, and potentially increase the time and cost involved in closing trades.

Altering Spreads

So, has it happened? Well, there is a tsunami of academic literature on the subject, so I won't bore you with it all. There are two main results. First, spreads have tightened anywhere from 20% to 50%, depending on the exchange, the stock price, the volume of trading and the perceived risk of the stock. That is, of course, generally good for investors, large and small. They pay less of a premium to trade.

On the other hand, the overall depth of visible liquidity has decreased. The limit order book is generally thinner, and investors -- especially large ones -- are clearly hiding their orders. But complex trades are still being completed, and a recent study (Chakravarty, Panchapagesan and Wood (2002)) has shown the institutional costs have declined around $220 million a year overall, despite what some feared. Obviously there's considerably more liquidity in the market than is apparent through limit orders outside the best bid and offer.

All of this brings us back to SEC Chairman Donaldson's musings this week about decimalization.

Some readers who emailed me after my original comments muttered darkly about Donaldson's conflict of interest. He was, they argued, the co-founder of Donaldson Lufkin & Jenrette; in proposing a rethink of decimalization, these readers contended, he was just offering a leg up to his former colleagues by returning them to happier days of larger spreads.

Minimum Considerations

That seems like conspiratorial "black helicopter" talk to me. More realistically, Chairman Donaldson is being assailed with conflicting research and analysis about changes to the minimum tick size, and he took the rhetorical short cut of equating minimum tick size with decimalization. They're not the same thing, of course, and it's too bad he perpetuated the confusion.

Nevertheless, having waded through many of the studies, I feel for the guy. The minimum tick size topic is wearying stuff, and it may yet turn out that there are defensible reasons to increase the minimum tick. Perhaps Donaldson and the SEC will find a flaw in the aforementioned study, or others like it. If so, there may be a small increase in the minimum tick size for stocks over some price, or depending on volume. Anything is possible.

But whatever happens, it has nothing to do with decimalization. And that's here to stay.

We hope you've enjoyed today's special bonus from RealMoney, our premium sister site. To sign up for RealMoney, where you can read commentary like this in real time, please click here for a free trial.

Paul Kedrosky advises various hedge funds and private equity firms in the U.S. and Europe and serves as an adjunct professor at the University of California in San Diego. Formerly a high-ranked sell-side technology equity analyst, Kedrosky has also started various technology companies and worked in product management at Digital Equipment Corp. At time of publication, Kedrosky held no positions in any of the securities mentioned in this column, although holdings can change at any time. Under no circumstances does the information in this column represent a recommendation to buy or sell stocks. While Kedrosky cannot provide investment advice or recommendations, he welcomes your feedback.

More from Opinion

Apple Needs to Figure Out Its Self-Driving Vehicle Strategy

Apple Needs to Figure Out Its Self-Driving Vehicle Strategy

Throwback Thursday: Tesla, Chip Stocks, TheStreet's Picks

Throwback Thursday: Tesla, Chip Stocks, TheStreet's Picks

12 Stocks That Our Writers and Their Sources Recommend You Buy Here

12 Stocks That Our Writers and Their Sources Recommend You Buy Here

Musk Goes on Unoriginal Media Tirade

Musk Goes on Unoriginal Media Tirade

What's Happening in Video Games This Week: On the Road to E3

What's Happening in Video Games This Week: On the Road to E3