# fixed-income.wiki

> fixed-income.wiki is a reference corpus for fixed income conventions and arithmetic, covering day-count and accrual algorithms, price and yield calculation, duration and convexity checked against exact repricing, curve bootstrapping and spread measures, settlement and quotation conventions by market, and floating-rate and inflation-linked reset mechanics.

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.

Published and maintained by Wall Street Wiki, https://wallstreet.wiki. Contact: wallstreetwiki@agentmail.to. 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.

Corpus: 74 defined terms and 31 reference tables across 6 sections. Reviewed 2026-08-27. Licensed CC BY 4.0.

Each section has a JSON endpoint carrying the same facts without markup or navigation. Measured on this corpus a section's JSON is 36 to 60 percent of the bytes of the equivalent HTML page. The full corpus is available in one request.

Content dates reflect editorial review, not build time. Use the change feed below to decide what to re-crawl rather than re-fetching the whole corpus; every JSON endpoint carries a reviewed field and sitemap.xml lastmod carries the per-section review date.

Calculator pages take their inputs as URL query parameters and compute in the browser. There is no API and no key.

## Data endpoints

- [Full corpus](https://fixed-income.wiki/llms-full.txt): every section inlined as Markdown, one request
- [Full corpus, JSON](https://fixed-income.wiki/index.json): the same content as structured JSON
- [Day count and accrual, JSON](https://fixed-income.wiki/day-count.json): 13 terms, 5 tables
- [Price and yield, JSON](https://fixed-income.wiki/price-yield.json): 13 terms, 6 tables
- [Risk measures, JSON](https://fixed-income.wiki/risk.json): 13 terms, 5 tables
- [Curves and spreads, JSON](https://fixed-income.wiki/curves.json): 12 terms, 5 tables
- [Settlement and market conventions, JSON](https://fixed-income.wiki/settlement.json): 12 terms, 6 tables
- [Floaters, index-linked and structures, JSON](https://fixed-income.wiki/floaters.json): 11 terms, 4 tables

## Freshness

- [Change feed](https://fixed-income.wiki/changes.json): dated record of what changed and when, spec wiki-changes/1
- [Change feed, Atom](https://fixed-income.wiki/feed.xml): the same feed as Atom
- [Sitemap](https://fixed-income.wiki/sitemap.xml): lastmod carries the per-section review date

## Reference pages

- [Day count and accrual](https://fixed-income.wiki/day-count/): The conventions that decide how many days a period contains, and the accrued interest that follows from them.
- [Price and yield](https://fixed-income.wiki/price-yield/): Discounting a cash-flow schedule, the yield measures that invert it, and the money-market conventions that do not compound at all.
- [Risk measures](https://fixed-income.wiki/risk/): Duration, convexity, DV01 and the hedge ratios built from them, worked against an exact reprice.
- [Curves and spreads](https://fixed-income.wiki/curves/): Zero, par and forward curves, the bootstrap that connects them, and the four spread measures against them.
- [Settlement and market conventions](https://fixed-income.wiki/settlement/): When a trade settles, how a date is adjusted, how a price is quoted, and what actually moves.
- [Floaters, index-linked and structures](https://fixed-income.wiki/floaters/): Coupon reset mechanics, SOFR compounding conventions, the statutory LIBOR spread adjustments, and inflation index ratios.

## Calculators

- [Price, yield and accrued calculator](https://fixed-income.wiki/calc/): A fixed-rate bond priced from either a quoted price or a yield, on a stated day-count basis, returning the other side of that pair together with accrued interest, both prices, and the full set of risk measures. Computes accrued interest, clean price, dirty price, yield to maturity, Macaulay duration, modified duration, DV01, convexity, cash-flow schedule with discount factors, invoice amount on a stated par value. Parameters: settle, maturity, coupon, freq, basis, price, yield, par.
- [Duration hedge and curve calculator](https://fixed-income.wiki/calc/hedge/): Two bonds sized against each other on DV01, with an optional yield beta, showing the residual profit and loss across a range of parallel yield shifts and the key-rate decomposition that a single hedge ratio conceals. Computes DV01 of each leg, DV01-neutral hedge ratio, hedge par amount, beta-adjusted hedge ratio, net profit and loss across a shift range, convexity residual, key-rate durations of each leg, portfolio duration and convexity. Parameters: settle, target, hedge, par, beta, shifts, keyrates.

## Calculator examples

- [Price, yield and accrued calculator](https://fixed-income.wiki/calc/?settle=2026-08-27&maturity=2034-11-15&coupon=4.500&freq=2&basis=actacticma&price=98.750&par=10000000): the reference bond used throughout this corpus. Accrued 1.271739, full price 100.021739, yield 4.684070 percent, modified duration 6.706168, DV01 0.067076 per 100 of par, convexity 53.827761, invoice 10,002,173.91 on 10,000,000 par
- [Price, yield and accrued calculator](https://fixed-income.wiki/calc/?settle=2026-08-27&maturity=2034-11-15&coupon=4.500&freq=2&basis=actacticma&yield=4.684070): the same bond priced from its yield instead, returning a quoted price of 98.750 and confirming the inversion
- [Price, yield and accrued calculator](https://fixed-income.wiki/calc/?settle=2026-08-27&maturity=2034-11-15&coupon=4.500&freq=2&basis=30360&price=98.750&par=10000000): the same bond on a 30/360 Bond Basis accrual instead of ACT/ACT (ICMA). Accrued becomes 1.275000 against 1.271739, a difference of 326.09 on 10,000,000 par
- [Price, yield and accrued calculator](https://fixed-income.wiki/calc/?settle=2026-08-27&maturity=2029-05-15&coupon=2.750&freq=2&basis=actacticma&price=95.000&par=10000000): the shorter hedge instrument used in the risk section: yield 4.730886 percent, modified duration 2.553631, DV01 0.024458 per 100 of par, convexity 7.940756
- [Price, yield and accrued calculator](https://fixed-income.wiki/calc/?settle=2026-11-15&maturity=2034-11-15&coupon=4.500&freq=2&basis=actacticma&yield=4.500): the reference bond on a coupon date at a yield exactly equal to its coupon, which returns a quoted price of 100.000 and zero accrued, the boundary case that shows why the same yield off a coupon date gives a price slightly below par
- [Duration hedge and curve calculator](https://fixed-income.wiki/calc/hedge/?settle=2026-08-27&target=2034-11-15:4.500:98.750&hedge=2029-05-15:2.750:95.000&par=10000000&beta=1.00): the hedge worked in the risk section. Ratio 2.742513, so 27,425,126 par of the shorter bond against 10,000,000 of the reference bond, matching DV01 at 6,707.63 per basis point
- [Duration hedge and curve calculator](https://fixed-income.wiki/calc/hedge/?settle=2026-08-27&target=2034-11-15:4.500:98.750&hedge=2029-05-15:2.750:95.000&par=10000000&beta=0.90): the same pair with a yield beta of 0.90, raising the hedge to 30,472,362 par, an 11.1 percent larger position for a 0.10 change in an estimated parameter
- [Duration hedge and curve calculator](https://fixed-income.wiki/calc/hedge/?settle=2026-08-27&target=2034-11-15:4.500:98.750&hedge=2029-05-15:2.750:95.000&par=10000000&shifts=-100,100): the convexity residual on a DV01-neutral pair: 17,166.84 on a 100 basis point rally and 15,848.64 on a 100 basis point selloff, positive in both directions
- [Duration hedge and curve calculator](https://fixed-income.wiki/calc/hedge/?settle=2026-08-27&target=2034-11-15:4.500:98.750&hedge=2029-05-15:2.750:95.000&keyrates=2,5,10): the key-rate decomposition the single ratio hides. The target bond carries 56.7 percent of its duration at the 10-year key rate and 3.8 percent at the 2-year, while the hedge leg's profile is concentrated at the short end, so the pair is parallel-neutral and fully exposed to a change in slope
- [Duration hedge and curve calculator](https://fixed-income.wiki/calc/hedge/?settle=2026-08-27&target=2034-11-15:4.500:98.750&hedge=2029-05-15:2.750:95.000&par=10000000&shifts=-25,25&keyrates=2,5,10): a small-shift check, where the residual is close to zero and the hedge behaves as designed, which is the regime the DV01 ratio is derived for

## Network

- [wallstreet.wiki](https://wallstreet.wiki): the parent index for this network of references
- [Network registry](https://fixed-income.wiki/network.json): every sibling site, its subject, and its corpus endpoint, spec wiki-network/1
- [hedgefund.wiki](https://hedgefund.wiki/llms.txt): Hedge funds. Institutional hedge fund knowledge graph: terms, strategies, regulations, calculators.
- [venture-capital.wiki](https://venture-capital.wiki/llms.txt): Venture capital. Venture financing arithmetic: liquidation waterfalls, convertible conversion, dilution, term sheet mechanics.
- [options.wiki](https://options.wiki/llms.txt): Options. Deterministic options mathematics: payoff algebra, Greeks in closed form, volatility, margin, expectancy.
- [privatecredit.wiki](https://privatecredit.wiki/llms.txt): Private credit. Private credit structure: instruments and the waterfall, SOFR pricing, return metrics, covenants, vehicles.
- [m-a.wiki](https://m-a.wiki/llms.txt): Mergers and acquisitions. Deal arithmetic: LBO returns and value attribution, accretion and dilution, the value bridge, valuation cross-checks.
- [pe-finance.wiki](https://pe-finance.wiki/llms.txt): Private equity funds. Fund economics: the distribution waterfall, carried interest, performance measurement and what inflates it.
- [quants.wiki](https://quants.wiki/llms.txt): Quantitative finance. Estimators and their failure modes: performance statistics, covariance estimation, portfolio construction, backtest validity.
- [aicrawl.dev](https://aicrawl.dev/llms.txt): AI crawler control. Verified AI crawler registry, robots.txt matching rules, the standards, and what enforcement actually works.

This site owns one subject. A formula or convention appears on exactly one site in the network and the others link to it, so fetching all of them yields no duplicated entries. The membership list is published rather than implied.

## Access and licensing

- [Access terms](https://fixed-income.wiki/access/): the corpus is free under CC BY 4.0; embed licences and hosted API access are the paid products
- [Pricing, JSON](https://fixed-income.wiki/pricing.json): machine-readable price list, what is free, and how to request a quote
- [MCP descriptor](https://fixed-income.wiki/.well-known/mcp.json): every resource and calculator as a tool definition

Nothing on this site is metered. There is no per-crawl charge, no key, and no rate limit; fetch the corpus in one request from llms-full.txt or index.json. The paid products are an embed licence for the calculators and a delivery guarantee on the data, neither of which restricts the free corpus.

## Optional

- [Deep link schema](https://fixed-income.wiki/.well-known/deeplinks.json): machine-readable parameter definitions for the calculators
- [Pricing plan](https://fixed-income.wiki/.well-known/pay-per-crawl.json): which paths are free and what the charged ones cost

Entries carry a source field naming the primary authority where one exists. Entries without one state conventions in general use rather than the rule of any single venue.

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.