4 ms·

The funny thing is that if you're dealing with (US Treasury) bonds, (EDIT: binary) floats are actually kind-of the right thing, since they trade in 32nds of a d

The funny thing is that if you're dealing with (US Treasury) bonds, (EDIT: binary) floats are actually kind-of the right thing, since they trade in 32nds of a dollar (and binary fractions thereof)[1][2] > Unlike U.S. equity markets, which switched to decimal pricing in 2001, U.S. Treasury securities still trade in fractions. In particular, prices are quoted in 32nds of a point, where a point equals one percent of par, with the 32nds themselves split into fractions. On the BrokerTec platform, for example, 3- and 5-year notes trade in quarters of 32nds, whereas 7-, 10-, and 30-year securities trade in halves of 32nds. The quoted price for a 5-year note might be 98-15¼, for example, indicating a price in decimal form of 98.4765625 (that is, 98 + 15⁄32 + ¼⁄32). [1] https://www.newyorkfed.org/aboutthefed/fedpoint/fed07.html https://www.newyorkfed.org/aboutthefed/fedpoint/fed07.html [2] https://www.bloomberg.com/opinion/articles/2020-01-15/it-s-not-insider-trading-if-the-president-does-it https://www.bloomberg.com/opinion/articles/2020-01-15/it-s-n...

jleahy 7y ago
Unfortunately it's 32nds of a 100th, so they still don't work in floats (because floats are stored normalised, as 1.x in binary). Eg. 117.125
- andreareina 7y ago
  Is it? The NY Fed site says it's 32nds of a dollar: > • Prices are quoted in 32nds of a dollar. > [...] Note and bond prices are quoted in dollars and fractions of a dollar. By market convention, the normal fraction used for Treasury security prices is 1/32.
  - jleahy 7y ago
    Right, but the price is about 100, not 1. If you had a price of 1.25 then you could represent this as a float as (binary) 1.01. However if you have 117.25 then that's (decimal) 1.83203125 * 2^-6. You can see how you quickly run out of bits.
dragonwriter 7y ago
Arbitrary precision rationals are the general solution for when some aspects of the calculation work better are in binary (power-of-two denominator) fractions and some are in decimal fractions.

jleahy 7y ago

Unfortunately it's 32nds of a 100th, so they still don't work in floats (because floats are stored normalised, as 1.x in binary). Eg. 117.125

andreareina 7y ago
Is it? The NY Fed site says it's 32nds of a dollar: > • Prices are quoted in 32nds of a dollar. > [...] Note and bond prices are quoted in dollars and fractions of a dollar. By market convention, the normal fraction used for Treasury security prices is 1/32.
- jleahy 7y ago
  Right, but the price is about 100, not 1. If you had a price of 1.25 then you could represent this as a float as (binary) 1.01. However if you have 117.25 then that's (decimal) 1.83203125 * 2^-6. You can see how you quickly run out of bits.

dragonwriter 7y ago

Arbitrary precision rationals are the general solution for when some aspects of the calculation work better are in binary (power-of-two denominator) fractions and some are in decimal fractions.