When it comes to annualizing returns, most folks think that the rules are pretty straightforward and agreed by all. However, that truly is not the case. And, it is most notable when we’re dealing with a “point-to-point” cumulative return such as June 15, 2016 to January 8, 2019. How do we annualiize this? Well, I take this up in this video, though I do not provide any solution: I will, by the end of the year. Something to look forward to! As always, please chime in w/your thoughts!

I suggest that this is a case of “Perfect is the Enemy of Good.” A straightforward, clear, and clean approach is to annualize ONLY if the period is > 1 year. In cases where you’re having to annualize based on days, simply arrive at a convention and stand behind it. Use 365.25 or 365 and disclose which you’re using. Perhaps direct those who’re really interested to an explanation of why you chose the denominator you did.

Dave, I agree with you, the difference will be very small. Until GIPS standards address this and they should, there’s no wrong answer. But, for 1 year numbers, force the annualized number to be the cumulative.

Thanks for the vblog post.

Thanks for your comments, Pat.

I do not believe this should fall within the GIPS standards: note that the only thing GIPS speaks of re. annualization is (1) don’t annualize for periods < 1 year, (2) report 36-month annualized standard deviation, and (3) (w/2020 version) report 36-month annualized return. I don't believe this is something we need a STANDARD for, but rather some guidance, which I hope to do before 12/31/2019 (or, if you prefer, 31/12/2019).

If I understand correctly, a key question raised here is — how can you guarantee that cumulative return equals annualized return if the period is one year, calculated from any arbitrary day in the year to another day one year later. Doing the calculation involves calculating a fraction of the number of days in the period divided by the number of days in the year, which you want here to always equal 1. So I think the question can be re-framed this way: how can you guarantee that these two number of days calculations are equal for any possible starting date? At the risk of stating a truism, the answer is: by having the date ranges be identical. For example:

1. Use the beginning date for the return period as your beginning date for the “number of days in the year” calculation.

2. Project out one year from the beginning date to calculate the number of days in the year.

3. Use that same “one year out” date as your ending date for the cumulative return calculation.

One gotcha: if the ending date isn’t a date on which you have market pricing information (e.g., a non-business day), it may be inappropriate to use it in a calculation of total return.

Another gotcha: leap year handling. Because 2016 is a leap year, 02/29/2016 is a valid day. Tricky questions:

1. What is one year away from 02/28/2015? Naively, it is 02/28/2016 (365 days).

2. What is one year away from 03/01/2015? Naively, it is 03/01/2016 (366 days). But notice that we’ve skipped over 02/29/2016 as an ending date.

3. What is one year away from 02/28/2016? Naively, it is 02/28/2017 (366 days).

4. What is one year away from 02/29/2016? Here you have an arbitrary choice between 02/28/2017 (365 days) and 03/01/2017 (366 days).

Wow!

Joel, I’ll take this into consideration when I do my paper. Thanks!

I imagine most systems will use 365 calendar days to annualise returns, although I can understand why 365.25 would be used i.e. to average out the leap year impact over 4 years. I see no valid reason to just use 366 days, as there is not a leap year every year. However, some performance systems are clever enough to use an actual day count and work out how many times February 29th occurs during the period being annualised. For the example above there is no leap year impact between 15/06/2016 and 08/01/2019 (937 calendar days), therefore you are safe to use 365!

I have also come across instances (including some index vendors) where business/working/trading days (e.g. 252) are used instead. This would be fine if all global markets adopted the same holiday schedule and worked the same number of days each year. Plus you still have to factor in the leap year impact 1 in every 4, as well as any other ad-hoc market closures.

Whilst I’ve not tested the difference in the annualised returns over the period using both methods, I’d imagine the impact (difference) to be small, i.e. a few basis points here and there.

Dave,

I’m pleased to hear that you have now committed to a date!!! We’ve spoken on this subject more than once previously and I agree, some guidance would be good. I have a method I have used for at least 20 years – I doubt that I “invented” it, but it was that long ago, that I don’t remember – I’m happy to take the credit!! I do not believe there is a perfect solution as there will always be exceptions. However, I believe that consistency is what we should strive for. I have seen systems which report different figures for a 1 year annualized and cumulative return – this, to me, is wrong. So, my method is as follows:-

Method

Calculate the number of complete months in the period

Calculate the two part-month periods as fractions of the month using the actual number of days in the month

Calculate the number of months to use for annualisation by adding the above

Use the “standard” monthly annualisation formula to arrive at figure

Reasoning

Ensures that monthly calculations (month-end to month-end) are always consistent

Ensures that compounding works (chain-linking using this method is consistent)

As an example …

15 March 2003 – 15 March 2004

Number of complete months – 11

Initial fraction of months – 16/31

Final fraction of months – 15/31

Total number of months – 12

I have sent you a spreadsheet with numerous examples by email which I am happy that you share/use as you see fit.

Good luck with your work!

Anthony

Another great comment, that may make it into my paper.

Thanks, Anthony! I can’t be giving away my secrets too soon, can I?

Thanks for your contribution

Anthony, thanks for chiming in! You, and our fellow colleagues who have been compelled to share their thoughts, are providing fodder for my paper. Many thanks!

David,

I think that one needs to address this problem in a way that ensures that if one lengthens the period by adding on a day with a greater return than any day in the previous period (perhaps a year) that the annualized return for the period that is now one day longer is not smaller than the annualized return for the period without that additional day of higher return. I am not sure that the methods alluded to here always fulfill that requirement while also ensuring that the annualized return for a year is equal to the cumulative return for that same year-long period.

For example, it seems that monthly methods fail the second requirement for a period like from Feb 15, 2016 to Feb 14, 2017 or to Feb 15, 2017, since neither 14/28 nor 15/28 gives one when added to 14/29.

I look forward to seeing the exact calculations you suggest to see how they compare with what we do at Opturo.

Andre

Thanks, Andre!

Believe the late Damian Laker had solved for this in an elegant and logical way. This would have been published in the Journal of Performance Measurement (Summer 2008)

Thanks for the reminder; I’ll dig it out.