  Portfolio management is essential for any investment decision. Yet,
traditional methods in the literature are ill-suited for the characteristics
and dynamics of cryptocurrencies. This work presents a method to build an
investment portfolio consisting of more than 1500 cryptocurrencies covering 6
years of market data. It is centred around Topological Data Analysis (TDA), a
recent approach to analyze data sets from the perspective of their topological
structure. This publication proposes a system combining persistence landscapes
to identify suitable investment opportunities in cryptocurrencies. Using a
novel and comprehensive data set of cryptocurrency prices, this research shows
that the proposed system enables analysts to outperform a classic method from
the literature without requiring any feature engineering or domain knowledge in
TDA. This work thus introduces TDA-based portfolio management of
cryptocurrencies as a viable tool for the practitioner.
