# Average Annual Total Return - How to calculate fractional number of years?

Per the SEC Form N-1A,

P(1+T)n = ERV

Where:

P=a hypothetical initial payment of \$1,000.

T=average annual total return.

n =number of years.

ERV= ending redeemable value of a hypothetical \$1,000 payment made at the beginning of the 1-, 5-, or 10-year periods at the end of the 1-, 5-, or 10-year periods (or fractional portion).

However, I was unable to find SEC guidance on how to calculate n.

For example, what value should `n` be when calculating average annual total return for a mutual fund with a return start date of Feb 1 2020 and end date of March 31 2021?

• Would I divide the number of days between those dates (inclusive of start and end date) by either 362.25, 365.2425 (average Gregorian year), 365, or 360?

• Would I include Feb 29 2020 in my day count?

Does the SEC provide guidance on how to calculate the number of years when it has a fractional part? If so, where can I find this documentation?

• Are you actaully filing SEC reports or just trying to calculate return on your own? My assumption was that they reported the returns for the exact 1-, 5-, and 10-year periods, meaning not interpolated, and if a fund has only been active for 9 months there would not be a 1-year return (let alone a 5- or 10-year return). May 18, 2021 at 22:12
• I'm trying to calculate the return on my own (but for others to consume) and I need it to adhere to SEC regulations if there is one on this or standard practice if not one. I'm looking to calculate returns for funds that have been active greater than a year. But I need to calculate more than just the 1, 5 and 10 year (or some other whole number of years). For example, I need to calculate the average annual return of the fund for March 6, 2008 - Dec 20, 2020 or any other random date range that falls within the active dates of the fund. May 18, 2021 at 22:21
• I'd also note that you shouldn't get significantly different return amounts by using any of the methods you suggest. Only using 360 would get you a significant difference (and still fairly small) May 18, 2021 at 22:23

## 1 Answer

I don't think there's and SEC guidance since that document (from what I can tell) is not meant for fractional year reporting, only actual exact 1-, 5- and 10-year returns.

I need to calculate the average annual return of the fund for March 6, 2008 - Dec 20, 2020

One method would be to calculate the fractional part separately (i.e. number of days from 3/6/2020 to 12/20/2020 divided by 365 (or 366 for a leap year) and add the number of whole years (12).

A simpler method would to just take the total number of days divided by 365.25. At worst you mae be off by a day or two from the more accurate method.

I would NOT divide by 360 to get an annualized return, but using 365, 365.25, or 365.2425 should not make a significant difference - maybe one hundredth of a percent at best.

• Thanks. When the return is large and the period is small, the return difference between methodologies can be material. For example, I've seen .07% return difference in actual data using 365 vs 365.25. Perhaps that is considered immaterial to some... May 19, 2021 at 23:15