FA-61296 / Bond day-count conventions / Open access
Rate conversion across day-count basis and compounding: the basis rescaling is applied after compounding conversion · case 01
Combined basis and compounding conversions drift from the contract value.
ROOT CAUSE
The basis factor is applied to the converted output instead of the input nominal rate.
THE FAILURE
The basis factor is applied to the converted output instead of the input nominal rate.
Unsuccessful approach: Rescaling the effective annual rate instead of the nominal rate is still out of order.
Case contract
Inputs a nominal rate, from/to day-count year basis (360 or 365), from/to compounding frequency (0 = continuous). First rescale the nominal rate by to_basis/from_basis, then convert compounding through the effective annual rate: EAR = (1+r/m)^m - 1 or e^r - 1; target nominal = m*((1+EAR)^(1/m)-1) or ln(1+EAR). Return rounded to 10 decimals.
Why this case matters
Bond accrual and pricing systems depend on exact day-count arithmetic; a single-day error changes settlement cash.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(rate, from_basis, to_basis, from_comp, to_comp):
def ear(r, m):
return math.exp(r) - 1 if m == 0 else (1 + r / m) ** m - 1
def nominal(e, m):
return math.log(1 + e) if m == 0 else m * ((1 + e) ** (1 / m) - 1)
return round(nominal(ear(rate, from_comp), to_comp) * to_basis / from_basis, 10)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression conversion order 1', [0.0125, 360, 365, 12, 0], 0.0126669233], ['regression conversion order 2', [0.03, 365, 360, 2, 0], 0.0293722984], ['partial repair probe 1', [0.001, 365, 360, 12, 12], 0.0009863014], ['partial repair probe 2', [0.03, 360, 365, 2, 2], 0.0304166667], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 360, 2, 2], 0.05], ['normal control 1', [0.15, 365, 365, 2, 0], 0.1446413232], ['normal control 2', [0.15, 365, 365, 2, 2], 0.15]], [['regression conversion order 1', [0.0125, 360, 365, 4, 0], 0.0126535759], ['regression conversion order 2', [0.03, 365, 360, 1, 4], 0.0292662784], ['partial repair probe 1', [0.0125, 360, 365, 0, 0], 0.0126736111], ['partial repair probe 2', [0.0125, 365, 360, 12, 12], 0.0123287671], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 360, 360, 2, 2], 0.05], ['normal control 1', [0.03, 360, 360, 0, 1], 0.030454534], ['normal control 2', [0.03, 365, 365, 1, 12], 0.0295952373]], [['regression conversion order 1', [0.0125, 360, 365, 0, 4], 0.0126937099], ['regression conversion order 2', [0.08, 365, 360, 1, 4], 0.0766713681], ['partial repair probe 1', [0.001, 365, 360, 0, 0], 0.0009863014], ['partial repair probe 2', [0.08, 360, 365, 4, 4], 0.0811111111], ['boundary control 1', [0.05, 360, 360, 2, 2], 0.05], ['boundary control 2', [0.05, 365, 365, 0, 0], 0.05], ['normal control 1', [0.03, 360, 360, 0, 2], 0.0302261292], ['normal control 2', [0.08, 365, 365, 4, 0], 0.0792105092]], [['regression conversion order 1', [0.15, 360, 365, 2, 12], 0.1474772429], ['regression conversion order 2', [0.08, 360, 365, 4, 0], 0.0802996855], ['partial repair probe 1', [0.0475, 365, 360, 4, 4], 0.0468493151], ['partial repair probe 2', [0.03, 360, 365, 12, 12], 0.0304166667], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 360, 360, 2, 2], 0.05], ['normal control 1', [0.0125, 365, 365, 2, 1], 0.0125390625], ['normal control 2', [0.001, 365, 365, 4, 2], 0.001000125]], [['regression conversion order 1', [0.001, 365, 360, 1, 0], 0.0009858153], ['regression conversion order 2', [0.001, 360, 365, 2, 4], 0.0010137604], ['partial repair probe 1', [0.0125, 360, 365, 12, 12], 0.0126736111], ['partial repair probe 2', [0.08, 360, 365, 2, 2], 0.0811111111], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 360, 360, 2, 2], 0.05], ['normal control 1', [0.0475, 365, 365, 1, 12], 0.0464962199], ['normal control 2', [0.0125, 360, 360, 1, 0], 0.01242252]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression conversion order 1 | 0.0126670149 | 0.0126669233 | Failed |
| regression conversion order 2 | 0.0293693178 | 0.0293722984 | Failed |
| partial repair probe 1 | 0.0009863014 | 0.0009863014 | Passed |
| partial repair probe 2 | 0.0304166667 | 0.0304166667 | Passed |
| boundary control 1 | 0.05 | 0.05 | Passed |
| boundary control 2 | 0.05 | 0.05 | Passed |
| normal control 1 | 0.1446413232 | 0.1446413232 | Passed |
| normal control 2 | 0.15 | 0.15 | Passed |
SHA-256 / 7a2994596344e2d33c5bd3b338970a56212b8d48eb5331597b0f9cd8c0ff4c00
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(rate, from_basis, to_basis, from_comp, to_comp):
def ear(r, m):
return math.exp(r) - 1 if m == 0 else (1 + r / m) ** m - 1
def nominal(e, m):
return math.log(1 + e) if m == 0 else m * ((1 + e) ** (1 / m) - 1)
return round(nominal(ear(rate, from_comp) * to_basis / from_basis, to_comp), 10)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression conversion order 1', [0.0125, 360, 365, 12, 0], 0.0126669233], ['regression conversion order 2', [0.03, 365, 360, 2, 0], 0.0293722984], ['partial repair probe 1', [0.001, 365, 360, 12, 12], 0.0009863014], ['partial repair probe 2', [0.03, 360, 365, 2, 2], 0.0304166667], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 360, 2, 2], 0.05], ['normal control 1', [0.15, 365, 365, 2, 0], 0.1446413232], ['normal control 2', [0.15, 365, 365, 2, 2], 0.15]], [['regression conversion order 1', [0.0125, 360, 365, 4, 0], 0.0126535759], ['regression conversion order 2', [0.03, 365, 360, 1, 4], 0.0292662784], ['partial repair probe 1', [0.0125, 360, 365, 0, 0], 0.0126736111], ['partial repair probe 2', [0.0125, 365, 360, 12, 12], 0.0123287671], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 360, 360, 2, 2], 0.05], ['normal control 1', [0.03, 360, 360, 0, 1], 0.030454534], ['normal control 2', [0.03, 365, 365, 1, 12], 0.0295952373]], [['regression conversion order 1', [0.0125, 360, 365, 0, 4], 0.0126937099], ['regression conversion order 2', [0.08, 365, 360, 1, 4], 0.0766713681], ['partial repair probe 1', [0.001, 365, 360, 0, 0], 0.0009863014], ['partial repair probe 2', [0.08, 360, 365, 4, 4], 0.0811111111], ['boundary control 1', [0.05, 360, 360, 2, 2], 0.05], ['boundary control 2', [0.05, 365, 365, 0, 0], 0.05], ['normal control 1', [0.03, 360, 360, 0, 2], 0.0302261292], ['normal control 2', [0.08, 365, 365, 4, 0], 0.0792105092]], [['regression conversion order 1', [0.15, 360, 365, 2, 12], 0.1474772429], ['regression conversion order 2', [0.08, 360, 365, 4, 0], 0.0802996855], ['partial repair probe 1', [0.0475, 365, 360, 4, 4], 0.0468493151], ['partial repair probe 2', [0.03, 360, 365, 12, 12], 0.0304166667], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 360, 360, 2, 2], 0.05], ['normal control 1', [0.0125, 365, 365, 2, 1], 0.0125390625], ['normal control 2', [0.001, 365, 365, 4, 2], 0.001000125]], [['regression conversion order 1', [0.001, 365, 360, 1, 0], 0.0009858153], ['regression conversion order 2', [0.001, 360, 365, 2, 4], 0.0010137604], ['partial repair probe 1', [0.0125, 360, 365, 12, 12], 0.0126736111], ['partial repair probe 2', [0.08, 360, 365, 2, 2], 0.0811111111], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 360, 360, 2, 2], 0.05], ['normal control 1', [0.0475, 365, 365, 1, 12], 0.0464962199], ['normal control 2', [0.0125, 360, 360, 1, 0], 0.01242252]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression conversion order 1 | 0.0126659205 | 0.0126669233 | Failed |
| regression conversion order 2 | 0.0293752504 | 0.0293722984 | Failed |
| partial repair probe 1 | 0.0009863076 | 0.0009863014 | Failed |
| partial repair probe 2 | 0.0304135457 | 0.0304166667 | Failed |
| boundary control 1 | 0.05 | 0.05 | Passed |
| boundary control 2 | 0.05 | 0.05 | Passed |
| normal control 1 | 0.1446413232 | 0.1446413232 | Passed |
| normal control 2 | 0.15 | 0.15 | Passed |
SHA-256 / 3a295e93d7b8dd2e0f0c09add58f8e1bd271bb6722654b872b7948e5f47ed288
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.
Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.
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Sign in to the archive ↗Verification & scope
A deterministic toy contract stated explicitly in the contract field; no claim of conformance to any published convention text. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:46:53.914757+00:00.
Case digest / 1a1cfaaff9ac23d0d6e96c40b2bd0ab8cc6218fa8cefdb10cade9a0b57c8ce76