How U.S. Bond Price Fractions Differ from Bond Yields
Summary
The note distinguishes quoted bond prices from bond yields. It explains that a U.S. bond price such as 99 1/8 represents 99.125 per 100 of par, while a yield is the discount rate that equates the present value of coupon and principal cash flows with the bond’s clean price. A coupon rate or quoted yield therefore cannot be read by converting its fractional part directly into a decimal percentage.
It also notes that U.S. bond price quotes may use fine fractional increments, including Treasury thirty-seconds and subdivisions, and that yields are not subject to the same tick convention. The discussion is conceptual rather than a worked yield calculation: it omits day-count details and assumes a flat term structure for simplicity. Quote conventions can vary by market, so the stated fractions should not be generalized to all bond prices.
Key ideas
- Bond price fractions express a price per par amount, while yield is a discount rate derived from cash flows and price.
- A price of 99 1/8 corresponds to 99.125 per 100 of par.
- Yield calculation depends on coupon and principal cash flows, time to maturity, and pricing assumptions.
- U.S. bond price quotes can use fractional subdivisions, while yields can be reported at much finer precision.
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Full text
# Corporate bond quote convention # Corporate bond quote convention I'm not a quant practitioner, but a student so this may be a very simple question. I was of the understanding corporate US bonds were quoted 1/8 increments and US treasuries in 1/32 increments. Such that a quote of 99 1/8 represents 99.125%. I came across some study notes, from a fairly reputable source that equated a Nominal 3 5/8 bond to a yield of 3.275% (but 5/8 = 0.625) and a TIPS which was quoted as 1 7/8 to a yield of 1.237% (7/8 = .875) ... am I missing something? ## Answer by owner (score 1) https://quant.stackexchange.com/a/22045 Your confusion is certainly coming from a distinction between Price and Yield. 1 - You're definitely right in regards to Bond Price `as 99 1/8 = 99.125`. Likewise `99 1/32 = 99.0313` (assuming 100 PAR). It's worth highlighting on the fact that this convention is only applicable to US bond prices, as far as I am concerned. 2 - By contrast, Bond Yield is the discount rate at which the present value of all future cash flows from the bond (coupons and principal included) is equal to its price (see the below). Where: ``` P = Bond price (Clean) C = Coupon payments, derived from Coupon frequency as well as Coupon Rate F = Face value of the bond t = Time to maturity ``` - For simplicity purposes, let's assume a flat term structure of interest rates, thus `r` is constant. - Refer to Excel YIELD() or Matlab YLDMAT() functions to sort `r` out from the above equation (excluding day count convention for simplicity purposes.) Hope it helps ## Answer by Helin (score 0) https://quant.stackexchange.com/a/21771 US bond prices are routinely quoted at much finer intervals. For example, you may see a quote of 99-103, which translates into $99+10/32 + 3/256$. Further, although there may be a minimum tick size for "prices," so such constraints are imposed on "yields" (at least in the US). In fact, yields are frequently computed up to 15-20 decimal places.
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