Principal component analysis based construction and evaluation of cryptocurrency index

摘要

Decentralized nature of cryptocurrencies, irrational cryptocurrency valuations and severe price volatility in cryptocurrency market makes it a formidable task for investors to pick individual coins, and rather investors would prefer to invest money on the entire cryptocurrency market accurately represented by a cryptocurrency index. This paper proposes the design of a Principal Component Analysis based methodology to construct a dynamic cryptocurrency index that accurately tracks the movement of the entire cryptocurrency market. Our analysis on real market data shows why first component derived from PCA is sufficient to construct the cryptocurrency index and how to determine the number of constituents while building the index. Proposed PCA based tool, tested on actual historical cryptocurrency data, takes into account the changing dynamics of the cryptocurrency market by regularly shifting the number of constituents as well as the weights and is able to capture the evolving pattern in the cryptocurrency market. The proposed index has been validated by three-factor pricing model, consisting of market, size and momentum factors. Subsequently, the proposed index has been compared with other existing indexes based on the results of three-factor model. In summary, the paper presents a robust mathematical model for construction of a dynamic cryptocurrency index that can be used as a tool to analyze the return on investments as well as to study the fluctuations present in the cryptocurrency market.