On Taking a Skewed Risk More Than Once

Abstract

This paper collects results on the repeated risk-taking of skewed risks. An extensive body of theoretical and experimental literature has shown that, in one-time decision situations, humans are skewness-seeking and dislike risks that feature unlikely but large losses (i.e., negatively skewed risks). We show that, contrary to intuition, the often-observed phenomenon of penny-picking—repeatedly taking negatively skewed risks—is not at odds with skewness-seeking, but, to the contrary, may even be caused by it. The skewness of the distribution that results from repeatedly taking a skewed risk depends in non-trivial ways on the risk-taking strategy and may even differ in sign from that of the individual risk. With sufficient time available, every risk—no matter how negatively skewed—can be gambled in such a way that, in total, skewness is positive. Because recent work has shown that skewness is decisive whether risk is taken, this result may be important for economics and finance on a fundamental level.