For those interested, I was able to find one of my favorite articles on the WaybackMachine:
Risk and Time, by John Norstad
https://web.archive.org/web/20170911171 ... -time.html
The Fallacy of Time Diversification
Portfolio theory teaches that we can decrease the uncertainty of a portfolio without sacrificing expected return by diversifying over a wide range of assets and asset classes. Some people think that this principle can also be used in the time dimension. They argue that if you invest for a long enough time, good and bad returns tend to "even out" or "cancel each other out," and hence time diversifies a portfolio in much the same way that investing in multiple assets and asset classes diversifies a portfolio.
While the basic argument that the standard deviations of the annualized returns decrease as the time horizon increases is true, it is also misleading, and it fatally misses the point, because for an investor concerned with the value of his portfolio at the end of a period of time, it is the total return that matters, not the annualized return. Because of the effects of compounding, the standard deviation of the total return actually increases with time horizon. Thus, if we use the traditional measure of uncertainty as the standard deviation of return over the time period in question, uncertainty increases with time.
Common variants of this time diversification argument can be found in many popular books and articles on investing, including those by highly respected professionals and even academics. For example, John Bogle used this argument in his otherwise totally excellent February, 1999 speech The Clash of the Cultures in Investing: Complexity vs. Simplicity (see his chart titled "Risk: The Moderation of Compounding 1802-1997," which if it had been properly drawn might well have been titled "Risk: The Exacerbation of Compounding 1802-1997"). Burton Malkiel uses a similar argument and chart in his classic book A Random Walk Down Wall Street (see chapter 14 of the sixth edition). (I deliberately chose two of my all-time favorite authors here to emphasize just how pervasive this fallacy is in the literature.)
The fact that some highly respected, justly admired and otherwise totally worthy professionals use this argument does not make it correct. The argument is in fact just plain wrong - it's a fallacy, pure and simple. When you see it you should dismiss it in the same way that you dismiss urban legends about alligators in sewers and hot stock tips you find on the Internet (you do dismiss those, don't you? :- ). It's difficult to do this because the argument is so ubiquitous that it has become an unquestioned assumption in the investment world.
For more details on this fallacy, see the textbook Investments by Bodie, Kane, and Marcus (fourth edition, chapter 8, appendix C), or sections 6.7 and 6.8 of my own paper Random Walks.