Skip to content
All library documents

Calculating ACT/ACT Year Fractions Across Leap Years

Article Quant Q&A · Author: FelB
Read the original

Summary

The document addresses how to calculate an ACT/ACT year fraction when a date interval spans both leap and non-leap years. Instead of dividing the entire number of elapsed days by a single denominator, the answer separates the interval into day counts associated with each type of year. Days in non-leap years are divided by 365, and days in leap years are divided by 366; the resulting fractions are then added.

For the dates in the question, the response gives 1,155 non-leap-year days and 366 leap-year days, producing a stated year fraction of 4.164. This is a concise worked example rather than a comparison of different ACT/ACT variants or a detailed treatment of endpoint conventions. Users should verify which convention their instrument or application requires, since the document does not discuss alternative definitions or explain how to handle every possible date-boundary case.

Key ideas

  • For the illustrated ACT/ACT calculation, split elapsed days between leap and non-leap years.
  • Divide non-leap-year days by 365 and leap-year days by 366.
  • Add the two resulting fractions to obtain the year fraction.
  • The example does not compare ACT/ACT variants or specify endpoint conventions for other applications.

Tags

Fixed incomeStatistics
Full text
# Day count convention confusion


# Day count convention confusion












For example I want to calculate a year fraction between the dates: 2011.03.31 and 2015.05.30.

There are 1521 days between the two dates, but 2012 was a leap year. So what should I use in the denominator? 366 or 365 if I want to use the ACT/ACT convention?

## Answer by Ami44 (score 2, accepted)

https://quant.stackexchange.com/a/29482

As I know act/act you are using the sum of 2 fractions. One with 365 and one with 366 in the denominator. In your example the number of days in non-leap-years is 1155 and we have 366 days in leap-years. The resulting year fraction would be 1155/365 + 366/366 = 4.164

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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