{ "category": "Financial functions", "display_name": "DURATION", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.DURATION", "implementation_state": { "answer_bank": { "excel_builds": [ "20131", "20228", "?" ], "larger_numeric": 0, "last_bit": 333, "matched": 7551, "other_mismatch": 0, "refused": 0, "rows": 7884, "unread": 0, "worst_ulp": 3 }, "detail": "Everything else matches (7,884 in the answer bank and 6 workbook cells). Last-bit means a finite number within 16 ULP of Excel's.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "close", "state_label": "Close: last-bit deviations remain", "summary": "Close: 335 of 7,890 recorded answers differ in the last bits, worst 3 ULP", "workbook_corpus": { "cells": 6, "last_bit": 2, "matched": 4, "worst_ulp": 1 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/bonds.rs#L137-L140" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/bonds::or", "catalogue/bonds::bond_out", "catalogue/financial::date_1900", "locale::days_from_civil", "locale::civil_from_days", "locale::excel_serial_from_ymd", "locale::ymd_from_excel_serial", "ported/bond_core_family::max_serial", "ported/bond_core_family::derr", "ported/bond_core_family::dyear", "ported/bond_core_family::dim", "ported/bond_core_family::act", "ported/bond_core_family::basis", "ported/bond_core_family::freq", "ported/bond_core_family::dser", "ported/bond_core_family::rate", "ported/bond_core_family::addm", "ported/bond_core_family::d360eu", "ported/bond_core_family::dc", "ported/bond_core_family::ctx", "ported/bond_core_family::period", "ported/bond_core_family::excel_bond_pow", "ported/bond_core_family::duration_kernel", "ported/bond_core_family::last_day_of_feb", "ported/bond_core_family::diff360_us", "ported/bond_core_family::days_between_num", "ported/bond_core_family::map_bond_core_error_to_ws", "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_pow_chain", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric/x87::mul", "ported/excel_numeric/x87_chains::pow2_positive", "ported/excel_numeric/x87_chains::pow2", "ported/excel_numeric/x87_chains::exp_ext", "ported/excel_numeric/x87_chains::exp_with", "ported/excel_numeric/x87_chains::excel_exp", "ported/excel_numeric/x87_chains::log_with", "ported/excel_numeric/x87_chains::excel_log" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/bonds.rs#L137-L140", "state": "close", "suite": null, "summary": "Close: 335 of 7,890 recorded answers differ in the last bits, worst 3 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.DURATION.json", "name": "DURATION", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n### Relationships\n\n\n- **[MDURATION](FUNC.MDURATION.md)** — modified duration, defined as `DURATION/(1 + yld/frequency)`.\n Same arguments, same errors, one extra division. If you want a price-sensitivity number, that is\n the one.\n- **`PRICE`** — the denominator of the duration quotient *is* the dirty price. The two functions\n share their coupon schedule, their day counts and their discount ladder, so a `DURATION`\n discrepancy and a `PRICE` discrepancy on the same bond are usually the same bug seen twice.\n- **`YIELD`** — the inverse of `PRICE`, and the usual source of the `yld` argument. Note the loop:\n compute `yld` from a market price with `YIELD`, feed it to `DURATION`, and any day-count\n disagreement enters twice.\n- **`COUPNUM` / `COUPDAYBS` / `COUPDAYS` / `COUPDAYSNC`** — the schedule quantities `DURATION`\n computes internally. They are the right instruments for localizing a disagreement: if `COUPDAYBS`\n differs, the duration will differ, and you have found the day count rather than the discounting.\n- **`ACCRINT`** — accrued interest, which uses the same accrual span as the fractional offset.\n- **Confused with**: the everyday sense of \"duration\" as time to maturity. For a coupon bond\n duration is always *less* than time to maturity, and a reader who expects the two to match will\n read every answer as wrong.\n- There is **no convexity function** in Excel. The second-order term has to be built by hand.\n\n\n", "how-to-implement": "\n### Numerical notes\n\n\n`DURATION` is a short sum of well-scaled terms, and the numerator and denominator are both positive\nand of similar magnitude, so the reduction itself is benign — no cancellation, no overflow for any\nrealistic bond. The difficulty is entirely in the *schedule* and in the *discount factor*.\n\n**The schedule is integer calendar arithmetic and is unforgiving.** Coupon dates are generated by\nmonth arithmetic backwards from maturity, with an end-of-month rule: a bond maturing on 31 August\npays on 28/29 February, and a naive \"same day number\" step lands on the wrong date. Every discount\nexponent depends on that schedule, so a single mis-stepped coupon date moves the answer far beyond\nany rounding concern.\n\n**The discount factor is a `pow`, and `pow` is not one function.** The exponents are integers when\nsettlement falls exactly on a coupon date and fractional otherwise. Integer exponents can be\nevaluated by binary exponentiation (square-and-multiply on plain multiplies) or by `exp(y·ln x)`,\nand the two differ in the last bits. Fractional exponents can be evaluated through a modern\ncorrectly-rounded `pow` or through a legacy `exp(ln)` chain, and those differ too. The reference\nengine deliberately implements both staging cases and documents that it selects them to match\nobserved Excel behaviour. The Handbook does **not** assert what Excel does internally; what it can\nsay is that this is the axis on which careful implementations of bond math disagree, and that any\nclaim of agreement that has not distinguished on-coupon from off-coupon settlement has not tested\nthe interesting half.\n\nFor the underlying mathematics, Macaulay's weighted-average-time construction and the\n`dP/dy = −D_mod·P` link are standard; any fixed-income text develops them, and the discrete-schedule\nform used by spreadsheet functions is the one in the market conventions literature rather than in\nthe continuous-time treatment.\n\n\n", "quirks": "\n### Result and edge cases\n\n\nReturns `Number` — a duration in **years**, not in periods and not in days.\n\n- **`settlement ≥ maturity`** is a domain error, not a zero or negative duration.\n- **Zero coupon** is admissible (`coupon = 0`) and gives time to maturity in years.\n- **Zero yield** is admissible and makes every discount factor 1, so `D` becomes the simple\n cash-flow-weighted average time.\n- **Non-integer `frequency` and `basis`** are truncated toward zero before the range check, so\n `frequency = 2.9` reads as `2`.\n- Empty, missing and error arguments follow the shared call model; see\n [The value universe](../model/01-value-universe.md) and\n [Coercion and lifting](../model/02-coercion-and-lifting.md).\n\n\n\n### Errors\n\n\nAs documented on Microsoft's `DURATION` page:\n\n| Error | Condition |\n|---|---|\n| `#VALUE!` | `settlement` or `maturity` is not a valid serial date number |\n| `#NUM!` | `coupon < 0` or `yld < 0` |\n| `#NUM!` | `frequency` is any number other than 1, 2 or 4 |\n| `#NUM!` | `basis < 0` or `basis > 4` |\n| `#NUM!` | `settlement ≥ maturity` |\n\n", "sources": "- Microsoft, \"DURATION function\" —\n \n (syntax, argument meanings, the frequency values, the day-count basis table, the truncation\n remarks, and the documented `#VALUE!` and `#NUM!` conditions).\n- Handbook, [MDURATION](FUNC.MDURATION.md) — the modified-duration sibling and the exact relation.\n- Handbook, [The value universe](../model/01-value-universe.md) and\n [Coercion and lifting](../model/02-coercion-and-lifting.md).\n- Handbook projections `data/functions/FUNC.DURATION.json` and `data/presence/FUNC.DURATION.json`\n (arity, classification axes, implementing module and the bond-family sibling set).\n\n", "version-differences": "The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.\n\n| Excel 16.0 build | Platform and CPU | Captured inputs |\n|---|---|---:|\n| 20131 | Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics | 7,620 |\n\nThe record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.DURATION.json).", "what-it-does": "\n`DURATION(settlement, maturity, coupon, yld, frequency, [basis])` returns the **Macaulay duration**\nof a coupon bond with an assumed par value of 100, expressed in **years**.\n\nMacaulay duration is the present-value-weighted average time to receipt of a security's cash flows:\n\n D = ( Σ t_k · C_k · v^(t_k) ) / ( Σ C_k · v^(t_k) ) with v = (1 + y/f)^(−f)\n\nwhere `t_k` is the time in years from settlement to cash flow `k`, `C_k` the cash flow (a coupon of\n`100·coupon/f`, plus 100 at maturity), `y` the annual yield and `f` the coupon frequency. The\ndenominator is the dirty price; the numerator is that price with each term weighted by its own\nmaturity. So **duration is a weighted mean of times, and it carries units of years** — that is the\nwhole content of the definition, and it is why a zero-coupon bond's duration is exactly its time to\nmaturity.\n\nTwo identities are worth holding on to:\n\n1. **Zero coupon.** With `coupon = 0` the only cash flow is the redemption, so `D` is the time to\n maturity in years. This is the sanity check that catches most implementation errors.\n2. **The price-sensitivity link.** With `P(y)` the price,\n\n dP/dy = −(D / (1 + y/f)) · P\n\n which is why the *modified* duration `D/(1 + y/f)` — see [MDURATION](FUNC.MDURATION.md) — is the\n number risk desks actually quote. Macaulay duration is the time; modified duration is the\n sensitivity.\n\nBehaviour in the limits: `D` increases with maturity, decreases with coupon rate, and decreases\nwith yield. For a perpetual-style long bond `D` approaches `(1 + y/f)/y` from below rather than\ngrowing without bound, which is why a 30-year and a 100-year bond have far more similar durations\nthan their maturities suggest. As `y → −f` the discount base `1 + y/f` approaches zero and the\nexpression has a pole; the admissible domain excludes it (see Errors).\n\n### How Excel measures the time axis\n\nThe one place where a textbook formula and a spreadsheet function part company is the *time* axis.\nExcel does not measure `t_k` from settlement in calendar years. It works in **coupon periods**:\n\n- the coupon schedule is generated backwards from `maturity` at `12/frequency`-month steps until\n the first date at or before `settlement`, giving `n` remaining coupons;\n- the settlement's position inside the current coupon period is expressed as a fraction, and the\n exponent for the `k`-th remaining coupon is that fraction plus `k`;\n- the final quotient is divided by `frequency` to convert periods into years.\n\nThe fractional offset is the accrual measurement, and it depends on `basis`. This is why two calls\nthat differ only in `basis` can differ in the third decimal of the answer: the day count is not a\npresentational choice, it changes the exponent on every discount factor.\n\n\n\n### Arguments\n\n\n| Argument | Meaning | Default |\n|---|---|---|\n| `settlement` | The settlement date — when the security trades to the buyer. Required. | — |\n| `maturity` | The maturity date — when the security expires. Required. | — |\n| `coupon` | The security's **annual** coupon rate, as a decimal fraction. Required. | — |\n| `yld` | The security's **annual** yield, as a decimal fraction. Required. | — |\n| `frequency` | Coupon payments per year: `1` annual, `2` semi-annual, `4` quarterly. Required. | — |\n| `basis` | The day-count basis. Optional. | 0 |\n\nThe day-count basis values are the standard five: `0` or omitted = US (NASD) 30/360, `1` =\nActual/actual, `2` = Actual/360, `3` = Actual/365, `4` = European 30/360.\n\nThree argument traps, in decreasing order of how often they bite:\n\n1. **`coupon` and `yld` are annual rates even when `frequency` is 2 or 4.** A 6% semi-annual bond is\n `coupon = 0.06`, `frequency = 2` — not `0.03`. The function divides by `frequency` internally.\n2. **`frequency` admits only 1, 2 and 4.** There is no monthly bond here; `frequency = 12` is an\n error, not a slow path.\n3. **Dates and `basis` are truncated to integers**, as documented for the whole bond family. There\n is no `issue` date argument: `DURATION` assumes settlement falls inside a regular coupon period.\n Odd first or last periods need `ODDFPRICE`-family thinking, and `DURATION` will not tell you it\n was the wrong function.\n\n\n" }, "signature": { "display": "DURATION(settlement, maturity, coupon, yld, frequency, [basis])", "parameters": [ { "description": null, "name": "settlement", "optional": false, "repeats": false }, { "description": null, "name": "maturity", "optional": false, "repeats": false }, { "description": null, "name": "coupon", "optional": false, "repeats": false }, { "description": null, "name": "yld", "optional": false, "repeats": false }, { "description": null, "name": "frequency", "optional": false, "repeats": false }, { "description": null, "name": "basis", "optional": true, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 6, "min": 5 }, "category": "Financial functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "Custom", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Macaulay duration of a security with periodic coupons, in years", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the annual duration of a security with periodic interest payments", "microsoft_url": "https://support.microsoft.com/en-us/office/duration-function-b254ea57-eadc-4602-a86a-c8e369334038" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "DURATION" }, { "locale": "bg-BG", "name": "DURATION" }, { "locale": "cs-CZ", "name": "DURATION" }, { "locale": "da-DK", "name": "VARIGHED" }, { "locale": "de-DE", "name": "DURATION" }, { "locale": "el-GR", "name": "DURATION" }, { "locale": "en-AU", "name": "DURATION" }, { "locale": "en-GB", "name": "DURATION" }, { "locale": "en-US", "name": "DURATION" }, { "locale": "es-ES", "name": "DURACIÓN" }, { "locale": "et-EE", "name": "DURATION" }, { "locale": "fi-FI", "name": "KESTO" }, { "locale": "fr-FR", "name": "DURÉE" }, { "locale": "he-IL", "name": "DURATION" }, { "locale": "hr-HR", "name": "DURATION" }, { "locale": "hu-HU", "name": "KAMATÉRZ" }, { "locale": "id-ID", "name": "DURATION" }, { "locale": "it-IT", "name": "DURATION" }, { "locale": "ja-JP", "name": "期間" }, { "locale": "ko-KR", "name": "지속 시간" }, { "locale": "lt-LT", "name": "DURATION" }, { "locale": "lv-LV", "name": "DURATION" }, { "locale": "nb-NO", "name": "VARIGHET," }, { "locale": "nl-NL", "name": "DUUR" }, { "locale": "pl-PL", "name": "ROCZ.PRZYCH" }, { "locale": "pt-BR", "name": "DURAÇÃO" }, { "locale": "pt-PT", "name": "DURAÇÃO" }, { "locale": "ro-RO", "name": "DURATION" }, { "locale": "ru-RU", "name": "ДЛИТ" }, { "locale": "sk-SK", "name": "DURATION" }, { "locale": "sl-SI", "name": "DURATION" }, { "locale": "sr-Latn-RS", "name": "TRAJANJE" }, { "locale": "sv-SE", "name": "LÖPTID" }, { "locale": "th-TH", "name": "DURATION" }, { "locale": "tr-TR", "name": "SÜRE işlevi" }, { "locale": "uk-UA", "name": "DURATION" }, { "locale": "vi-VN", "name": "DURATION" }, { "locale": "zh-CN", "name": "持续时间" }, { "locale": "zh-HK", "name": "DURATION" }, { "locale": "zh-TW", "name": "DURATION" } ], "signature": { "display": "DURATION(settlement, maturity, coupon, yld, frequency, [basis])", "parameters": [ { "description": null, "name": "settlement", "optional": false, "repeats": false }, { "description": null, "name": "maturity", "optional": false, "repeats": false }, { "description": null, "name": "coupon", "optional": false, "repeats": false }, { "description": null, "name": "yld", "optional": false, "repeats": false }, { "description": null, "name": "frequency", "optional": false, "repeats": false }, { "description": null, "name": "basis", "optional": true, "repeats": false } ], "trailing_repeats": false }, "surface_name": "DURATION", "version_marker": null, "xlcall": { "code": "458", "symbol": "xlfDuration" } }, "microsoft": "https://support.microsoft.com/en-us/office/duration-function-b254ea57-eadc-4602-a86a-c8e369334038" }, "try_it": { "formula": "=DURATION(DATE(2024,1,1),DATE(2028,1,1),0.05,0.06,2)" }, "url": "https://handbook.dnacalc.com/functions/DURATION.html", "variants": [], "versions": [ { "behaviour": "7,620 captured inputs are indexed for this environment. Capture dates: 2026-07-20 to 2026-07-20. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20131", "platform": "Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.DURATION.json" ] } ] }