 Abstract cryptocurrencies have been gaining popularity in recent years due to their potential to revolutionize the way money is transacted. Research has shown that price returns come very significantly from one cryptocurrency to another, but little is known about how this variation depends on the age of the currency and its market capitalization. In this study, we investigate the tail behavior of price returns for more than 7000 cryptocurrencies and show that tail exponents follow power law functions over the entire history of the considered cryptocurrency portfolio. Furthermore, our results suggest that the tail exponent is not constant over time, but rather it decreases with the age of the currency and increases with its market capitalization. Additionally, we observe that the trend in tail exponents points to mixed directions, suggesting that the probability of large price variations becoming less frequent is low. This article was offered by Arthur A. B. Pessar, Magda Perk and Geraldo V. Rebelle. We are article.tv, links in the description below.