Asset Allocation with Crypto: Application of Preferences for Positive Skewness

Abstract

Bitcoin (BTC) returns exhibit pronounced positive skewness with a third central moment of approximately 150% per year. They are well characterized by a mixture of Normals distribution with one “normal” regime and a small probability of a “bliss” regime where the price appreciation is more than 100 times at the annual horizon. The large right-tail skew induces investors who prefer positive skewness to add significant BTC holdings to equity-bond portfolios. Even when BTC is forecasted to lose half its value in the normal regime, investors with power utility optimally add 3% allocations to BTC when the probability of the bliss regime is around 1%. Cumulative Prospect Theory investors are even more sensitive to positive skewness. They hold BTC allocations of about 3% when the probability of the bliss regime is 0.0006, and the mean of BTC in the normal regime corresponds to a loss of 90%.