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I am a programmer that has been working for fixed income financial companies for the past couple of years. As such, I have learned about a weird notation on fixed income products.

In the US, bonds are priced in 1/32 increments ("a tick") or 1/64 increments ("a plus").

Wikipedia explains the usage:

...a price is quoted as 99-30+, meaning 99 and 61/64 percent (or 30.5/32 percent) of the face value. As an example, "par the buck plus" means 100% plus 1/64 of 1% or 100.015625% of face value.

But in Europe, they are priced in 1/100 increments, represented in decimal.

I can't find much on the history of this system - why it's priced this way, notated this why, and why it only seems to be the US.

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    $\begingroup$ You have to remember that it wasn't so long ago that these markets were all paper and pencil ledgers and verbal trading. It is a lot easier to memorize and do the math of 8th and 16th in your head, quickly, especially when the figure wasn't changing that often and you traded round lots. Regulators felt that investors were at too much of a disadvantage to the market makers however, so they narrowed spreads by instituting 32nds and 64ths. It also allows for greater spreads. 0.005625 makes a big difference when you are trading in lots of 10MM and more, which you lose if you go to 1/100ths. $\endgroup$
    – AMR
    Dec 31, 2015 at 2:32
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    $\begingroup$ You actually might get a better answer to this particular question on Personal Finance & Money SE. There is probably an old bond trader lurking that remembers what it was like back in the day. It is more of a financial markets question than a math history one. $\endgroup$
    – AMR
    Jan 2, 2016 at 0:16
  • $\begingroup$ As other comments have noted, it's a legacy convention or practice. Not noted is that until the SEC ordered conversion to a decimal system in 2001, stocks were traded in fractions. investopedia.com/terms/d/decimal-trading.asp $\endgroup$
    – DJohnson
    Dec 3, 2022 at 18:43

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The US debt markets are a relatively recent addition to the financial markets - the US government did not issue debt until the early twentieth century.

When the US debt markets started trading, they took their cue from the already established US stock markets where prices were quoted in eighths.

The site How Stuff Works give the following description of this tradition:

These early stockbrokers looked to Europe for a model to build their system on and decided to base it on the system of Spain. This was largely due to the fact that the U.S. dollar's value had been based on the value of the Spanish real.

The real was the Spanish silver dollar and was divided into eight parts.

This strongly implies the following route to thirty-seconds, which I give as an "educated guess" without reference:

As market liquidity increased, pressure on the bid/offer spreads prompted brokers (buyers and sellers) to "meet half way", thus introducing sixteenths pricing. Continued increasing liquidity and a "meet half way" attitude finally introduced thirty-seconds pricing. (Each of these pricing refinements would have cut into the brokers profit margins, so their loss would have to have been made up by increased liquidity. Otherwise, they would have resisted the change.)

This would then be the pricing practise inherited by the debt markets when they started trading in the early 20th century. The later introduction of options trading and the "hyper-liquidity" of modern debt markets introduced the final refinement of sixty-fourths.

As late as 1997 some of the older stocks in the stock market were still quoting in 32nds. This ended with the introduction of the "Common Cents Stock Pricing Act". The debt markets however appear to have decided to stick with the historic pricing practice, perhaps because the nominal price of a treasury bond is $1000 making further fractional price increments cutting into the brokers spreads undesirable to the market makers.

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The gilt-edged market in the UK used halves and quarters and eighths for its stock prices at least up to the early 1980s. The weird people who deal in very short-dated gilts may even have gone as far as sixteenths.

It has nothing to do with Spanish coin: it is simply the easiest way to handle “a price half way between two other prices”.

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This isn't going to be an answer. But it will be informative. I am not sure how this community treats this type of thing. Feel free to erase if it's out of line.


Storing decimal numbers as floating points introduces round off error regardless of how many bits of precision are stored. For example, there is no way to express 0.1 as a floating points binary fraction precisely.

However small the round off error may be, the amounts traded on the bond markets are so large that in practical terms it may end up being thousands of dollars, that someone gains or loses on every trade. \$1000 is only .00001 of \$100M.


There are 2 possible solutions to this.

Either switch to fixed-point decimal fractions (and keep 2 integers for each number - the whole and the decimal parts).

Or keep using binary floating points numbers, and quote the prices using binary fractions.

Binary fractions can be stored precisely as floating-points binary numbers. When fractions are stored precisely, there are no round-off errors in additions and subtractions.


So regardless of why the bond trading started in binary fractions, there was a good reason to keep it in binary fractions. Again, it meant not having a loss/gain associated with every large trade.

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I can only speculate that it is the legacy of peso de ocho popularity. The "piece of eight" coin was often physically cut into 8 bits (mostly to obtain change - a solid peso contained too much value for everyday circulation, almost an ounce of fine silver). The bit was still large enough to accurately halve and even quarter it, giving 1/16 and 1/32 of original value.

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    $\begingroup$ Not likely. More the ease of doing the math in your head, quickly in the days before computer trading when quotes were in 8ths and 16ths. You just remembered the 4ths and halved or quartered those. with a little practice you can rattle off this prices very fast. It takes longer if you have to work out the price at par and 42 on an odd lot. $\endgroup$
    – AMR
    Dec 31, 2015 at 2:37

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