# Optimization and Diversification of Cryptocurrency Portfolios: A Composite Copula-Based Approach
## 3 Data Analysis and Empirical Results
### Data Description  
We chose to apply our methodology to cryptoassets portfolios. The latter are sourced from the top 100 cryptoassets by market capitalisation (which ensures that the analysis will not be affected by liquidity risk issues) from yahoo finance ([[https://finance.yahoo.com/](https://finance.yahoo.com/)]([https://finance.yahoo.com/](https://finance.yahoo.com/)), accessed on 3 May 2022) powered by coinmarketcap ([[https://coinmarketcap.com/](https://coinmarketcap.com/)]([https://coinmarketcap.com/](https://coinmarketcap.com/)), accessed on 3 May 2022) form 1 May 2017 to 30 April 2022. We then eliminate those with less than 700 observation and this operation has produced 58 cryptoassets with 1830 daily prices. The machine learning algorithm K-means (supported by the hierarchical clustering method) is used to select a diversified portfolio of eight cryptocurrencies and cryptotokens, representing about 50% of the whole crypto-market share (see Table 3). It is evident from Table 3 that Bitcoin reigns supreme over the cryptoassets market. As a result it controls the price formation of all altcoin.  
Figures 1 and 2 show respectively the evolution of the price and return dynamics for the eight cryptoassets under investigation. Visual inspection shows many signs of discrepancies than commonality signs in the returns and prices of all the eight virtual assets, testifying thus a certain dissimilarity in their behaviours over the considered period. Volatility clustering patterns are observed in the return dynamics of all eight cryptocurrencies.  
The descriptive statistics of the selected cryptocurrencies examined in this paper are shown in Table 4. All currencies display positive standard deviation and mean close to zero. With the exception of LEO, FIL, WAVES and ONE coin, the other cryptocurrencies are skewed left. In addition, the Jarque-Bera (JB) test and kurtosis for each series are positive and far from zero; that is, they possess heavy tailed and non normal distribution, which is consistent with the behaviour of most financial assets.  
Figure 1: Cryptoasset prices evolution from May 2017 to April 2022.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Rank** & **Symbols** & **Category** & **Consensus** & **Value** & **Maximum** & **\% of Total** \\  & & & **Mechanism** & **Proposition** & **Supply (10\({}^{6}\))** & **Marketcap** \\ \hline
1 & BTC & crytocurrency & PoW & digital gold & 21 & 43.33\% \\
20 & LEO & utility token & PoS & fund reimbursement & 985 & 0.36\% \\
25 & LINK & application token & N/A & oracle network & 1000 & 0.65\% \\
38 & FIL & storage network & PoRep & secure decentralised & 2000 & 1.83\% \\  & & token & & storage network & & \\
48 & THETA & application token & PoS & video streaming & 1000 & 1.93\% \\  & & & & network & & \\
49 & TUSD & stablecoin & N/A & digital fiat & N/A & 0.06\% \\
74 & WAVES & application token & LPoS & Web 3.0 application \& & 108,325 & 0.13\% \\  & & & & decentralised solution & & \\
80 & ONE & crypto-token & FBFT & deep sharding technology & 12,600 & 1.77\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Description of selected cryptoassets.  
Figure 2: Cryptoasset returns in the sample spanning from May 2017 to April 2022.