Converting Treasury Bond Prices from Fractions to Decimals

Summary

The document explains how to convert a U.S. Treasury quote written in thirty-seconds into a decimal price. For a quote with a whole-number price followed by a dash and a fractional component, divide that component by 32 and add the result to the whole-number part. If the component includes a smaller fraction, first add that fraction to the integer component, then divide by 32. The worked example converts 99-26¾ to 99.8359375.

It also describes shorthand for eighths within a thirty-second: the symbols 2, plus, and 6 represent two, four, and six eighths, respectively. A second example applies this notation to a quote ending in 022. These rules are specific to the Treasury price convention described; the note does not discuss yield calculations, accrued interest, or other instruments’ quoting conventions.

Key ideas

• Treasury fractional price components are expressed in thirty-seconds of a point.
• Add any smaller fractional component to the integer thirty-second count before dividing by 32.
• The symbols 2, plus, and 6 can denote two, four, and six eighths of a thirty-second.
• The decimal fraction is added to the whole-number price to obtain the decimal quote.

Tags

# change fraction price of treasury to decimal form


# change fraction price of treasury to decimal form












How do I change the Price of 99-26 and 7/8 to decimal form ?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/82386

The part after "-" needs to be divided by $32$ to get decimals.

The fractional part after - of the form $a{}^b{}_c$, where $0<a<32$ and $b<c$, means $a+\frac{b}{c}$.

So, for example, $26{}^3{}_4$, following 99-, means $\frac{26+\frac{3}{4}}{32}=\frac{26.75}{32}= 0.8359375$, and in total the price is $99.8359375$.

P.S. Not in your example, but if instead of ${}^b{}_c$, the third digit might also be a single

2, which means $\frac{2}{8}\times\frac{1}{32}$;

+, which means $\frac{4}{8}\times\frac{1}{32}$;

6, which means $\frac{6}{8}\times\frac{1}{32}$.

E.g., -022 means $\frac{2+\frac{2}{8}}{32}=\frac{2.25}{32}=0.0703125$.

Related: https://stackoverflow.com/questions/20276971

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.