{ "category": "Financial functions", "display_name": "MDURATION", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.MDURATION", "implementation_state": { "answer_bank": { "excel_builds": [ "20131", "?" ], "larger_numeric": 0, "last_bit": 157, "matched": 1103, "other_mismatch": 0, "refused": 0, "rows": 1260, "unread": 0, "worst_ulp": 3 }, "detail": "Everything else matches (1,260 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: 157 of 1,266 recorded answers differ in the last bits, worst 3 ULP", "workbook_corpus": { "cells": 6, "matched": 6 } }, "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#L141-L144", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/bond_core_family.rs#L654-L667" ], "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#L141-L144", "state": "close", "suite": null, "summary": "Close: 157 of 1,266 recorded answers differ in the last bits, worst 3 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.MDURATION.json", "name": "MDURATION", "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- **[DURATION](FUNC.DURATION.md)** — Macaulay duration, the numerator. The relation\n `MDURATION = DURATION/(1 + yld/frequency)` is exact in the definition and is the natural\n metamorphic test for both functions at once.\n- **`PRICE`** — the price whose sensitivity `MDURATION` measures. Together they give the standard\n first-order estimate `ΔP ≈ −MDURATION × P × Δy`, and comparing that estimate against a direct\n re-pricing at the shifted yield is the honest way to see how far first order gets you.\n- **`YIELD`** — the usual source of `yld`.\n- **`COUPNUM` / `COUPDAYBS` / `COUPDAYS`** — the schedule instruments for localizing a\n disagreement, exactly as for `DURATION`.\n- **Confused with**: Macaulay duration itself. The two differ by a factor that, for a semi-annual\n bond at a 6% yield, is about 3% — small enough to look like a rounding difference and large\n enough to matter in a hedge ratio.\n- **Not available**: convexity, the second-order term. Excel provides no function for it.\n\n\n", "how-to-implement": "\n### Numerical notes\n\n\nThe additional arithmetic is one division by `1 + yld/frequency`, a quantity of order 1 for any\nadmissible input. It introduces one rounding and no instability: there is no cancellation, no\noverflow, and the divisor cannot approach zero inside the admissible domain because `yld < 0` is\nrejected.\n\nThat makes `MDURATION` a clean amplifier for whatever `DURATION` does. All the genuine numerical\ndifficulty — the backwards coupon schedule with its end-of-month rule, the 30/360 accrual variants\nand the order in which their start-date and end-date adjustments apply, the two different `pow`\nstagings for integer and fractional discount exponents — belongs to `DURATION` and is discussed on\nthat page. `MDURATION` inherits every one of them and can add at most one ULP of its own.\n\nOne consequence worth stating: because the two functions differ by an exactly specified division, a\ndisagreement between an implementation's `MDURATION` and `DURATION/(1 + yld/f)` computed on the\nsheet is diagnostic. If the identity holds, any error is in the schedule or the discounting; if it\nfails, the implementation has computed modified duration by some other route.\n\n\n", "quirks": "\n### Result and edge cases\n\n\nReturns `Number` — a modified duration in years.\n\n- **`settlement ≥ maturity`** is a domain error.\n- **`yld = 0`** makes `MDURATION` and `DURATION` identical; that equality is a useful self-test.\n- **One remaining coupon**: inherits `DURATION`'s single-term branch, then divides.\n- **Every day-count and schedule subtlety of `DURATION` is present here unchanged.** Modified\n duration adds no new calendar behaviour whatsoever; it adds one division. If an `MDURATION`\n answer looks wrong, check `DURATION` first — the fault is almost certainly upstream of the\n division.\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 `MDURATION` 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\nThe `yld < 0` restriction deserves the same note it gets on the `DURATION` page: a negative-yield\nbond has **no modified duration in Excel**, even though the sensitivity is perfectly well defined\nand is precisely the quantity a desk holding negative-yielding paper needs. This is a documented\ndomain restriction, not a mathematical one.\n\n", "sources": "- Microsoft, \"MDURATION function\" —\n \n (syntax, the \"Macauley modified duration\" description, argument meanings, frequency values, the\n day-count basis table, the truncation remarks, and the documented `#VALUE!` and `#NUM!`\n conditions).\n- Handbook, [DURATION](FUNC.DURATION.md) — the Macaulay numerator, its schedule construction and the\n numerical discussion this page defers to.\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.MDURATION.json` and\n `data/presence/FUNC.MDURATION.json`.\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 | 1,260 |\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.MDURATION.json).", "what-it-does": "\n`MDURATION(settlement, maturity, coupon, yld, frequency, [basis])` returns the **modified duration**\nof a coupon bond with an assumed par value of 100.\n\nThe definition is one division applied to Macaulay duration:\n\n MDURATION = DURATION / (1 + yld/frequency)\n\nand that division is what converts a *time* into a *sensitivity*. Where Macaulay duration answers\n\"on average, how far away is my money\", modified duration answers \"if the yield moves, how much\ndoes the price move\":\n\n dP/dy = −MDURATION × P equivalently ΔP/P ≈ −MDURATION × Δy\n\nSo a modified duration of 7.2 means a one-percentage-point rise in yield costs roughly 7.2% of the\nprice. It is a **first-order** statement: the price/yield curve is convex, so the linear estimate\noverstates losses on a rise and understates gains on a fall, and the error grows with the square of\n`Δy`. Excel has no convexity function to supply the second-order correction.\n\nUnits are years, inherited from `DURATION`; the quantity is often read as \"per unit change in\nyield\", which is dimensionally the same thing because yield is per year.\n\nMicrosoft's page names the result **\"Macauley modified duration\"** — with that spelling of\nMacaulay. It is worth knowing so that searches match.\n\nLimiting cases follow `DURATION`'s directly, damped by the divisor:\n\n- **Zero coupon**: `MDURATION` is the time to maturity divided by `1 + yld/frequency`, so it is\n strictly less than the time to maturity for any positive yield.\n- **`yld = 0`**: the divisor is 1 and modified duration equals Macaulay duration exactly.\n- **`yld → −frequency`**: the divisor approaches zero and the quantity diverges — but that region is\n excluded from the admissible domain long before it is reached, because `yld < 0` is an error.\n\n\n\n### Arguments\n\n\n| Argument | Meaning | Default |\n|---|---|---|\n| `settlement` | The settlement date. Required. | — |\n| `maturity` | The maturity date. 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\nIdentical to [DURATION](FUNC.DURATION.md), and the same three traps apply: `coupon` and `yld` are\n**annual** rates even at `frequency = 2` or `4`; `frequency` admits only 1, 2 and 4; dates and\n`basis` are truncated to integers.\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\nBecause the extra division uses `yld/frequency`, the `frequency` argument enters the answer twice —\nonce through the coupon schedule and once through the divisor. Getting it wrong therefore moves the\nresult further than it moves `DURATION`.\n\n\n" }, "signature": { "display": "MDURATION(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": "Modified duration of a security with periodic coupons", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the Macauley modified duration for a security with an assumed par value of $100", "microsoft_url": "https://support.microsoft.com/en-us/office/mduration-function-b3786a69-4f20-469a-94ad-33e5b90a763c" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "MDURATION" }, { "locale": "bg-BG", "name": "MDURATION" }, { "locale": "cs-CZ", "name": "MDURATION" }, { "locale": "da-DK", "name": "MVARIGHED" }, { "locale": "de-DE", "name": "MDURATION" }, { "locale": "el-GR", "name": "MDURATION" }, { "locale": "en-AU", "name": "MDURATION" }, { "locale": "en-GB", "name": "MDURATION" }, { "locale": "en-US", "name": "MDURATION" }, { "locale": "es-ES", "name": "DURACION.MODIF" }, { "locale": "et-EE", "name": "MDURATION" }, { "locale": "fi-FI", "name": "KESTO.MUUNN" }, { "locale": "fr-FR", "name": "DUREE.MODIFIEE*" }, { "locale": "he-IL", "name": "MDURATION" }, { "locale": "hr-HR", "name": "MDURATION" }, { "locale": "hu-HU", "name": "MKAMATÉRZ" }, { "locale": "id-ID", "name": "MDURATION" }, { "locale": "it-IT", "name": "MDURATION" }, { "locale": "ja-JP", "name": "MDURATION" }, { "locale": "ko-KR", "name": "MDURATION" }, { "locale": "lt-LT", "name": "MDURATION" }, { "locale": "lv-LV", "name": "MDURATION" }, { "locale": "nb-NO", "name": "MVARIGHET" }, { "locale": "nl-NL", "name": "AANG.DUUR" }, { "locale": "pl-PL", "name": "ROCZ.PRZYCH.M" }, { "locale": "pt-BR", "name": "MDURATION" }, { "locale": "pt-PT", "name": "MDURAÇÃO" }, { "locale": "ro-RO", "name": "MDURATION" }, { "locale": "ru-RU", "name": "МДЛИТ" }, { "locale": "sk-SK", "name": "MDURATION" }, { "locale": "sl-SI", "name": "MDURATION" }, { "locale": "sr-Latn-RS", "name": "MDURATION" }, { "locale": "sv-SE", "name": "MLÖPTID" }, { "locale": "th-TH", "name": "MDURATION" }, { "locale": "tr-TR", "name": "MSÜRE işlevi" }, { "locale": "uk-UA", "name": "MDURATION" }, { "locale": "vi-VN", "name": "MDURATION" }, { "locale": "zh-CN", "name": "MDURATION" }, { "locale": "zh-HK", "name": "MDURATION" }, { "locale": "zh-TW", "name": "MDURATION" } ], "signature": { "display": "MDURATION(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": "MDURATION", "version_marker": null, "xlcall": { "code": "459", "symbol": "xlfMduration" } }, "microsoft": "https://support.microsoft.com/en-us/office/mduration-function-b3786a69-4f20-469a-94ad-33e5b90a763c" }, "try_it": { "formula": "=MDURATION(DATE(2024,1,1),DATE(2028,1,1),0.05,0.06,2)" }, "url": "https://handbook.dnacalc.com/functions/MDURATION.html", "variants": [], "versions": [ { "behaviour": "1,260 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.MDURATION.json" ] } ] }