# Bond's price expressed as a % of par

the following is causing a bit of confusion...

In some countries, e.g. Brazil, I saw the bonds are quoted in "Unitary prices" (PU).

If we pick an example where:

Unitary price = 10,400 (Market price)
Par value = 1,000


What is the math behind to convert the market price to a "% of par price"? I saw Anbima, the main brazilian exchange, quotes price as 10,400; while some brokers as say 1,040 (which would be the price as "% of par").

Is it accurate to say the below?

Price as % of par = (Traded price / Par value) * 100

Bond price quoting conventions differ in different countries... In the vast majority of markets, they are quoted as percentage of par. But there are a few exceptions.

If you're looking at Brazil LTN's (BLTN on Bloomberg) or NTN-F's, for example, 1,000 is the par price, so 950 quote means 95% of par.

If you're looking at Mexican cete's (MCET on Bloomberg), 10 is the par price, so 9.5 quote means 95% of par.

On Bloomberg, there is a yes/no field saying whether this bond is quoted as percentage of par. If it is false, then another field contains the par value used for quotes.

Also, in Brazil, coupon bond prices are quoted dirty (with accrued), not clean (without accrued), like in most markets.

But, as they say in TV infomercials, that's not all!

If you're looking at inflation-linked Brazil bonds like NTN-B's or (rarely seen these days) NTN-C's, then the P.U. also includes the inflation index adjustment. (Israeli inflation-linked bonds are also quoted this way - I'm not sure if all or some.)

• Yes, I was looking at LTN's (introducing myself to this market). Maybe I am missing something very silly, but how is it that 1,000 is the par price, so 9500 quote means 95% of the par? Beside this, as example, suppose 2026 LTN is quoted at 10200 in Bloomberg (seems they quote in "Unitary Price"). Then I saw that the price as "% of par" is 1020. Would you know how they derive to this 1020? (I know basically divide by 10, but probably something more intuitive as the formula I added in the post) – F0l0w Mar 17 at 23:51
• Sorry! I simply made a typo. price 950 means 95% of par. But price 10200 doesn't sound right. Do you see it in ALLQ? If you load BXT and type in a reasonable yield like 10%, do you see a price like 950? You may like this tutorial LTNs are on page 3, and this page 19. Finally, please note that yield of LTNs having more than a year left to maturity uses annual compounding . – Dimitri Vulis Mar 18 at 0:29
• Looking at anbima I actually don't seem see any LTN price quotes, only yields. But if I click on one bond's details I currently see P.U. 991,66171700 (note they use , for decimal) for yield (taxa) 2,9740 – Dimitri Vulis Mar 18 at 0:42
• I think in my last example I messed up with LFT prices. Was looking here: anbima.com.br/pt_br/informar/taxas-de-titulos-publicos.htm There is a section for LFT, in the column "PU" (Unitary Price). – F0l0w Mar 18 at 0:53
• Of course. LFT Letras Financeiras do Tesouro (and also LBC Letras do Banco Central , BBCA ) are unusual floaters that are issued at par and the principal accrues overnight index every day. The principal today is principal yesterday * (1 + index/3000). This can grow to be a large number since the year 2000, almost 11,000. – Dimitri Vulis Mar 18 at 1:16