Hidden Skewness: On the Difficulty of Multiplicative Compounding Under Random Shocks

Abstract

Multiplicative growth processes that are subject to random shocks often have an asymmetric distribution of outcomes. In a series of incentivized laboratory experiments, we show that a large majority of participants either strongly underestimate the asymmetry or ignore it completely. Participants misperceive the spread of the outcome distribution to be too narrowband, and they estimate the median and the mode to lie too close to the center of the distribution, failing to account for the compound nature of average growth. The observed biases are measured irrespective to risk preferences and they appear under a variety of conditions. The biases are largely consistent with a behavioral model in which geometric growth is confused with linear growth. This confusion is a possible driver of investors’ difficulties with real-world financial products like leveraged exchange-traded funds and retirement savings plans. Data and the online appendix are available at https://doi.org/10.1287/mnsc.2016.2618 . This paper was accepted by Teck-Hua Ho, behavioral economics.