Calculating Year Fractions Across Multiple Years

Summary

The document asks how to calculate a year fraction between dates spanning many years under Act/365. The answer says to count the actual calendar days between the dates and divide that full count by 365 for the fixed convention. This differs from counting complete calendar years first and applying the day-count rule only to the leftover part of the interval.

It also distinguishes Act/365 fixed from conventions that account for leap years. Under the actual variant described, the denominator is 365 in regular years and 366 in leap years; the answer groups this behavior with Act/Act. The example highlights that a convention’s name alone may not fully specify the calculation, since the asker did not state which Act/365 variant was intended. The post gives a brief explanation rather than a comprehensive treatment of market-specific day-count rules or the different forms of Act/Act.

Key ideas

• For Act/365 fixed, divide the full actual day count between the dates by 365.
• Do not split a multi-year interval into whole years plus a separately calculated remainder under that convention.
• Act/365 has variants, so the intended convention should be specified.
• The described actual variant adjusts its denominator to 366 for leap years.
• The post notes a similar leap-year adjustment for Act/Act without surveying its different market conventions.

Tags

# Day-Time conventions spanning across years


# Day-Time conventions spanning across years












I have 2 dates, let's say 2010-01-01 and 2020-01-02, and I am interested in calculating the year fraction between them according to the Act/365 time convention.

Would this be just $$ \frac{\text{raw # of days between the dates}}{365} = \frac{3653}{365} = 10 \tfrac{3}{365} $$ or will I have to convert the years normally, and then only apply the convention to the segment which is under a year, resulting in $$ 10+\frac{\text{# of days between Jan 1st and Jan 2nd}}{365} = 10 \tfrac{1}{365}? $$

Additionally, is it correct that if we use Act/Act it will be $10 \frac{1}{366}$ since 2020 is a leap year?

Thank you very much.

## Answer by KevinT (score 1, accepted)

https://quant.stackexchange.com/a/70827

As @Kermittfrog has indicated in the comment, it's the former of your two versions, i.e. Date2 - Date1, divided by 365 (in your case 10.00822). Do note that you did not further specify, and we "assumed" it to be Act/365 fixed

(because there is also the Act/365 Actual convention, which accounts for leap years: 365 in all regular yrs, 366 in leap years --> the very same holds for act/act convention).

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.