Compounding can make things appear to be larger than they really are. This confusion can arise when the return from an event is compounded over a long holding period, and the return from compounding is described as the return from the event. In this article, McLean reviews several examples of this common mistake, which are found in a popular book on rare events, newspaper articles, investment advisors’ research reports, and finance journal articles. He also shows how compounding can distort inference in event studies and in the measurement of mutual fund performance. McLean describes alternative methods of return measurement that are not affected by compounding and shows that these methods can lead to different inferences than do measures that include compounding.
While the examples and reasoning in the paper aren’t novel or groundbreaking, it’s yet another example of how easy it is to be mislead by compound or exponential growth.
Related: McKenzie, C. R. M., & Liersch, M. J. (in press). Misunderstanding savings growth: Implications for retirement savings behavior. Journal of Marketing Research. [pdf]
People systematically underestimate exponential growth. The current studies illustrate this phenomenon, its implications, and potential interventions in the context of saving for retirement, where savings grow exponentially over long periods of time. Experiment 1 showed that the majority of participants expected savings over 40 years to grow linearly rather than exponentially, leading them to grossly underestimate their account balance at retirement. Experiment 2 demonstrated that this misunderstanding of savings growth led to underestimating the cost of waiting to save, which makes putting off saving more attractive than it should be. Finally, Experiments 3-5 showed that highlighting the exponential growth of savings motivated both college students and real employees to save more for retirement. Making clear to employees the exponential growth of savings — just before they make crucial decisions about how much to save — may be a simple and effective means of increasing retirement savings.