Distinguishing Actual/Actual Day Count Conventions

Article Quant Q&A · Author: Attack68

Summary

The document clarifies naming and interpretation of Actual/Actual day count conventions used in bond and interest rate calculations. It outlines the questioner’s uncertainty about whether the ICMA and Bond definitions differ, particularly around leap days and how to determine the number of interest periods in a year. The accepted response says the two descriptions refer to the same convention and explains that the labels have changed over time.

It traces the naming relationship through references to QuantLib and ISDA: the ISMA convention is now known as ICMA, while earlier ISDA material described the ISMA approach as Actual/Actual (Bond). The answer also distinguishes this convention from the ISDA or historical approach and the AFB or Euro approach. This is useful guidance for interpreting convention names in documentation and software, but it is not a detailed implementation specification or worked calculation. Users still need to follow the governing contract’s definitions and schedule details when computing accrual fractions.

Key ideas

Actual/Actual day count labels have varied across standards bodies and over time.
The response identifies the ISMA approach as the convention now called ICMA.
It explains that earlier ISDA material called the ISMA approach Actual/Actual (Bond).
The document distinguishes these names from the ISDA historical and AFB Euro conventions.
It provides naming clarification rather than a full calculation procedure or implementation example.

Tags

Fixed income Statistics

Full text

# Implementation of Act/Act IDSA / ICMA / Bond Day Count Convention


# Implementation of Act/Act IDSA / ICMA / Bond Day Count Convention












I read the following definitions of day count rules

> (ii) if “Actual/Actual (ISDA)” or “Act/Act (ISDA)” is specified, the actual number of days in the Interest Period divided by 365 (or, if any portion of that Interest Period falls in a leap year, the sum of (1) the actual number of days in that portion of the Interest Period falling in a leap year divided by 366 and (2) the number of days in that portion of the Interest Period falling in a non-leap year divided by 365);

> (iii) if “Actual/Actual (ICMA)” is specified, the number of days in the Interest Period, including February 29 in a leap year, divided by the product of (1) the actual number of days in such Interest Period and (2) the number of Interest Periods in the calendar year;

> (iv) if “Actual/Actual (Bond)” is specified, the number of calendar days in the Interest Period, divided by the number of calendar days in the Interest Period multiplied by the number of Interest Periods in the calendar year;

It seems very difficult to obtain precise calculations for these. In particular I think ii) is well defined but iii) and iv) might require a subjective assessment. In particular I read iii) and iv) as the same since a calendar day includes a leap, but the very fact of different presentation alludes to the fact they are different.

Has anyone specifically implemented these into their quant finance libraries, or can offer an opinion?

## Answer by AKdemy (score 4, accepted)

https://quant.stackexchange.com/a/71892

Daycount rules can be daunting and I sometimes feel like "everyone" uses a different name for the same definition and names frequently change.

For short:

iii) and iv) are the same

Long answer:

You can check for example quantlib's where you can see

> the ISDA convention, also known as "Actual/Actual (Historical)", "Actual/Actual", "Act/Act", and according to ISDA also "Actual/365", "Act/365", and "A/365"; the ISMA and US Treasury convention, also known as "Actual/Actual (Bond)"; the AFB convention, also known as "Actual/Actual (Euro)".

Now ISMA is the same as ICMA, you can see that on ISDA where Act/Act (Bond) is not even mentioned as an alternative name for ICMA.

However, ISDA mentions it here (with examples showing that there is no subjective assessment) where it is written that:

> The existing ISDA approach will be retained, to be known as "Actual/Actual (Historical)", the AFB approach will be introduced, to be known as "Actual/Actual (Euro)". The ISMA approach will also be introduced, to be known as "Actual/Actual (Bond)". These changes will be taken forward when ISDA revises and consolidates its existing interest rate swap definition booklets in the course of 1999.

As you can see, back in 1999, ISDA called "Actual/Actual (Bond)" the ISMA approach, which is known as ICMA since 2011 🙃

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.