fixed-income.wiki
Fixed income - conventions, formulas, and the arithmetic

About this reference

Who publishes it, how it is put together, what it deliberately does not do.

Who

This site is published by . A reference published by the wallstreet.wiki network. Every figure is stated as a formula and recomputed from it, every convention names the authority that sets it, and corrections are versioned and dated.

Why it exists

Fixed income has the highest ratio of formula to opinion of anything in finance, and it is still got wrong constantly, because the conventions that feed the formulas are numerous, market-specific, and almost never written down in one place. This reference states the conventions and the arithmetic. Every entry that changes a settlement amount, a yield, or a risk number carries an explicit formula and a worked example whose figures compute. It is not a glossary: definitions of bond terminology are free everywhere and worth nothing, while the day-count algorithm that decides whether an accrual is 180 or 182 days is not. One instrument runs through every section so the numbers tie together. The reference bond is a 4.500 percent semiannual bond with coupon dates of 15 May and 15 November, maturing 2034-11-15, settling 2026-08-27 at a quoted price of 98.750 per 100 of par, which is 98-24 in thirty-seconds. Its current accrual period runs 2026-05-15 to 2026-11-15, so A = 104 accrued days out of E = 184 in the period, with 80 days remaining to the next coupon. On ACT/ACT (ICMA) the accrued interest is 1.271739, the full price 100.021739, the street-convention yield 4.684070 percent nominal semiannual, the modified duration 6.706168, the DV01 0.067076 per 100 of par and the convexity 53.827761. Those figures reappear throughout. Where a section needs a second instrument, an illustrative curve, a repo rate or a call schedule, it says so explicitly at the point of use. Notation is uniform. P is the quoted or clean price per 100 of par and P_full = P + AI the full or dirty price, where AI is accrued interest per 100 of par. C is the annual coupon rate in percent of par, f the number of coupon periods per year and c = C/f the periodic coupon. y is an annual yield quoted nominal and compounded f times a year, so a discount factor over n periods is (1 + y/f) raised to the power -n. n_k counts coupon periods, possibly fractional, from settlement to cash flow k, and w = n_1 is the fraction of the current period still to run, equal to the days from settlement to the next coupon divided by E. A is accrued days and E days in the coupon period, in the ICMA sense, so A + (E - A) = E and w + A/E = 1. A day-count fraction is written D/B, where D is a convention's numerator in days and B its denominator. z(t) is a zero or spot rate at time t on a stated compounding basis and DF(t) the matching discount factor. s is a spread expressed as a decimal, and one basis point is 0.0001. D_mac, D_mod and Cx are Macaulay duration, modified duration and convexity, and DV01, also written PVBP, is the price change per 100 of par for a one-basis-point move. In money-market arithmetic d is a discount rate and t a day count. In compounded-in-arrears arithmetic r_i is an overnight fixing, n_i the calendar days it applies for, d_b the business days in the period and d_c its calendar days. QM is a quoted margin and DM a discount margin. IR is an inflation index ratio. Notional amounts in worked examples are 10,000,000 of par unless stated otherwise. Prices, coupons, curve levels, repo rates, discount rates, overnight fixings, index values, call schedules and option-model outputs used in worked examples are chosen to make the arithmetic legible. None of them is a market observation, a typical level, or a benchmark, and none should be read as one. Where a convention is fixed by a published rule the rule is named in the entry's source field; where a convention varies by market the entry says which market it describes.

How it is built

Every page here is generated from a single reviewed data file. That has consequences worth stating: the content is a data edit rather than a code change, every page has a JSON twin carrying the same facts without markup, and the review date attached to a page comes from the data file rather than from the build clock - so rebuilding without changing anything does not make the content look fresher than it is.

PropertyThis site
LicenceCC BY 4.0 - https://creativecommons.org/licenses/by/4.0/
Content reviewed2026-08-27
Machine-readable corpus/index.json and /llms-full.txt
Change feed/changes.json - poll this instead of re-crawling
Network9 sibling references, indexed at wallstreet.wiki
Third-party requestsNone. No fonts, no CDN, no analytics, no trackers on any page.
Contact[email protected], or the form. Corrections get answered first.

What is deliberately not here

No investment performance figures. Not because there are none, but because an unaudited return published on a commercial site is the specific thing securities counsel warns about, and the antifraud rules reach a publisher whether or not they are a registered adviser. If figures ever appear here they will have been reviewed first.

No recommendations. Nothing on this site says what to buy, when, or in what size. It states how the arithmetic works. That line is deliberate: impersonal, generally circulated financial writing is publishing, and personalised advice is something else with a different regulatory regime attached.

No market levels presented as fact. Every number in a worked example is an input chosen so the arithmetic can be checked, not an observation of where anything trades. Structures and formulas are durable; levels are not, and a stale level stated confidently is worse than no level at all.

Corrections

If a formula or a worked figure here is wrong, that is worth more to fix than anything else on the site, and the fastest route is the contact form. Corrections are recorded in the change feed with a date, so what changed and when is auditable rather than silently overwritten.

Reference data. Reviewed 2026-08-27. Corpus manifest: /llms.txt.

Published and maintained by · [email protected]. A reference published by the wallstreet.wiki network. Every figure is stated as a formula and recomputed from it, every convention names the authority that sets it, and corrections are versioned and dated. About this reference.

Reference information only. Not investment, legal, tax, or accounting advice. Day-count, settlement, quotation and reset conventions vary by market, by instrument class and by individual issue, and the convention that applies to a specific security is a term of that security. Verify every convention against the offering document, prospectus, indenture or confirmation before relying on any calculation here. All prices, rates, curve levels, index values and model outputs in worked examples are illustrative inputs chosen for arithmetic clarity and are not market levels, typical levels, or benchmarks.