The Fallacy of Time Diversification: Mea Culpa?
By Bryan Caplan
How many times have I made this argument:
“At your young age, you have enough time to recover from any dips in the market, so you can safely ignore bonds and go with an all stock retirement portfolio.” This kind of statement makes the implicit assumption that given enough time good returns will cancel out any possible bad returns. This is nothing more than a popular version of the supposed “principle” of time diversification. It is usually accepted without question as an obvious fact, made true simply because it is repeated so often, a kind of mean reversion with a vengeance.
In the investing literature, the argument for this principle is often made by observing that as the time horizon increases, the standard deviation of the annualized return decreases. I most frequently see this illustrated as a bar chart displaying a decreasing range of historical minimum to maximum annualized returns over increasing time periods. Some of these charts are so convincing that one is left with the impression that over a very long time horizon investing is a sure thing.
John Norstad says it’s all wrong, and enough smart people agree that I’m close to conceding. What’s the problem?
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.
For an example of a bar chart which shows a better picture of uncertainty and risk over time, see the Appendix below.
Smart people also assure me that this doesn’t make the equity premium puzzle go away. This further confuses me, but I’ll follow the advice I’ve often given to others: Once you strongly suspect that you’ve been wrong about something, stop talking about it and cede the floor to clearer heads.
Perhaps you’re one of them? If so, please enlighten us.
HT: John Nye