The continuous development of information technologies and the Internet intensified work on existing ideas of digital money. As a result, the computer program of the Bitcoin protocol was released to the public on January 9th 2009, creating an infrastructure for the first cryptocurrency with an open source software license that is free to the public. This means that anyone with an interest can replicate an existing protocol, create a new cryptocurrency, and release it to the public. The latter enabled the creation of a series of new cryptocurrencies with different characteristics and the expansion of their use first in payment transactions and then in the context of their trading on a new secondary market. The aim of this paper is to formally identify and describe the possibility of forming portfolios created according to different optimization goals, whose components represent cryptocurrencies as a new type of marketable assets. The first group of the portfolio was formed and modeled through the value of the bitcoin cryptocurrency, the second group through the dollar currency. For this purpose, five different optimization strategies were implemented, and the results of the strategy with equal shares in the portfolio were presented. The initial components of the portfolio are defined according to the development of the program code and the size of the community. The results of the portfolio which are expressed through units of bitcoin cryptocurrency suggest that the dynamics of historical cryptocurrency returns provides the possibility of modeling a portfolio in bitcoin currency. Such results are justified given that the return dynamics of the optimization strategy achieved a cumulative return higher than the cumulative return of the most successful component of the portfolio. On the other hand, the results of the portfolio expressed in dollar value did not achieve a cumulative return higher than the cumulative return of the selected comparison standard, so it is concluded that the applied fundamental indicators are not a good indicator for the initial selection of portfolio components.