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Annualization and leap years … there’s the rub!

by | Dec 13, 2013

Nine years ago I was reviewing a client’s performance system, and noticed on one of their reports they showed “annualized” and “cumulative” returns for the prior one, two, three, five, … years.

It struck me as quite odd that the prior year’s cumulative and annualized returns were different: how could this be? Recall that we annualize returns by taking the cumulative return, adding one, and either (a) taking the nth root, where “n” is the number of years or (b) raising the number to the transposition of n, and then subtracting one. Well, any number raised to the 1/1 (i.e., one) power, or having the 1st root, will yield that number, meaning the annualized return HAS TO equal the cumulative. But why not in this case?

Well, after some reflection I realized they weren’t using the number of years (which in this case would have been “1”) but rather the number of days in the period (366, since the prior year was 2004, a leap year) and dividing by 365. Oops!

This started me on a quest; sadly, one not unlike Don Quixote’s, which has yet to get me to my desired goal of a definitive and clear answer to the question: what to do?

A client asked us this week about this very subject, and my colleagues (John Simpson and Jed Schneider) and I engaged in a back-and-forth discussion on it. Space does not allow me to do much here, other than to say that there is no “rule” on this subject, there are a variety of ways firms handle it (some not so good, some okay), and that the “right” way is rather complex. And finally, one must weigh the complexity with the error that results from using something other than the “right” method. I suspect that most folks would deem it “immaterial.”

I will take this subject up in this month’s newsletters, and expand upon it further in an upcoming article.

The Journal of Performance Measurement

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