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 outcome distribution's spread to be too narrow-band and they estimate the median and the mode to lie too close to the distribution's center. The observed bias in expectations is irrespective to risk preferences and it appears under a variety of conditions regarding feedback, incentive size, and market contexts. The bias is largely consistent with a behavioral model in which geometric growth is confused with linear growth. This misperception is a possible explanation of investors' difficulties with real-world financial products like leveraged ETFs and is also related to issues regarding real estate investments, retirement savings plans or investments in college funds.