Calculating U.S. Treasury Pricing
Pricing U.S. Treasury bonds, notes and futures can look at first glance to be much different than the pricing of other investment products.
Cash bonds and futures based on U.S. Treasury securities do not trade in decimal format but in full percentage points, plus fractions of a 1/32 of par value. For example, if you were to see a quote on a broker/dealer screen showing U.S. Treasury prices you might encounter something like this:
10 YR 2.250 2/15/27 99-032 / 99-03+ 10/20
This quotation would indicate the current on-the-run (OTR), or most recently auctioned, 10-year note with a coupon of 2.250% and a maturity date of February 15, 2027 is currently 99-032 bid and offered at 99-03+, $10 million bid with $20 million offered.
The bid-side price of 99-032 is not 99.032 but rather 99 full points of par value plus 3.25 1/32s of a point. In the cash market, the third digit might be two, plus or six. The two constitutes 2/8, or ¼, of a 1/32. A plus constitutes ½ of 1/32, and six constitutes 6/8, or ¾, of 1/32. So our bid-side quote converted from 1/32 to a decimal would be: 99-032 (1/32s) = 99.1015625, or 99.1015625 percent of par. The offer-side price would convert to 99-03+ = 99.109375.
If you were to view a U.S. Treasury futures price quotation you might encounter something like this: TNM7 134-010/134-015.
The same concept as the cash market convention applies. The bid-side quote represents 134 full points plus 1/32 of a point. The converted price into decimal would be 134-010 = 134.03125, and so forth for the offer-side price. In futures you might see 134-012 for 1-1/4 (1/32), 134-015 for 1-1/2 (1/32), or 134-017 for 1-3/4 (1/32).
While seemingly complicated, it becomes second nature after a while. Cash Treasuries and futures based on U.S. Treasuries trade in points and fractions of points (1/32). But when doing any mathematical calculations, we must first convert from 1/32 to decimal, do the calculation, then convert back to 1/32 price convention.