# 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.

• I found a couple of questions on day-count conventions, but did not see this asked explicitly. May 9, 2022 at 15:34
• PDF Page 14f: quant.opengamma.io/…. It is defined as the day difference between d1 and d2 divided by 365 if it is Act/365 fixed. May 9, 2022 at 17:51
• Also asked Bloomberg, they are implementing direct difference as well May 11, 2022 at 3:08