# Collective Dynamics, Diversification and Optimal Portfolio Construction for Cryptocurrencies

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## Abstract

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## 1. Introduction

## 2. Data

## 3. Collective Dynamics and Uniformity

## 4. Portfolio Sampling

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Normalized leading eigenvalue ${\tilde{\lambda}}_{1}\left(t\right)$ of the cross-correlation matrix as a function of time, for (

**a**) the entire collection of cryptocurrencies and (

**b**) the ten deciles. Like the equity market, collective correlations spike during market crises, such as COVID-19, and the collapse of exchanges BitMEX and FTX.

**Figure 2.**Uniformity $h\left(t\right)$ of the leading eigenvector ${\mathbf{v}}_{1}$ of the cross-correlation matrix as a function of time, for (

**a**) the entire collection of cryptocurrencies and (

**b**) the ten deciles. The results are dramatically different compared to the equity market, with numerous deciles exhibiting strikingly low uniformity scores over time.

Cryptocurrency | Ticker | Decile |
---|---|---|

Bitcoin | BTC | 1 |

Ethereum | ETH | 1 |

Tether | USDT | 1 |

Binance Coin | BNB | 1 |

USD Coin | USDC | 2 |

XRP | XRP | 2 |

Cardano | ADA | 2 |

Polygon | MATIC | 2 |

Dogecoin | DOGE | 3 |

Litecoin | LTC | 3 |

TRON | TRX | 3 |

Wrapped Bitcoin | WBTC | 3 |

Chainlink | LINK | 4 |

Cosmos | ATOM | 4 |

UNUS SED LEO | LEO | 4 |

OKB | OKB | 4 |

Ethereum Classic | ETC | 5 |

Filecoin | FIL | 5 |

Monero | XMR | 5 |

Bitcoin Cash | BCH | 5 |

Stellar | XLM | 6 |

VeChain | VET | 6 |

Crypto.com Coin | CRO | 6 |

Algorand | ALGO | 6 |

Quant | QNT | 7 |

Fantom | FTM | 7 |

Tezos | XTZ | 7 |

Decentraland | MANA | 7 |

EOS | EOS | 8 |

Bitcoin BEP2 | BTCB | 8 |

Theta Network | THETA | 8 |

TrueUSD | TUSD | 8 |

Rocket Pool | RPL | 9 |

Chiliz | CHZ | 9 |

USDP Stablecoin | USDP | 9 |

Huobi Token | HT | 9 |

KuCoin Token | KCS | 10 |

Bitcoin SV | BSV | 10 |

Dash | DASH | 10 |

Zcash | ZEC | 10 |

**Table 2.**Average ${\mu}_{m,n}$ of the median normalized eigenvalue ${\tilde{\lambda}}_{m,n}^{0.50}\left(t\right)$ for different pairs of m sectors and n cryptocurrencies per sector. In red we display a greedy path that aims to increase the total diversification benefit (by decreasing ${\mu}_{m,n}$) at each step. We identify a best value cryptocurrency portfolio consisting of 4 sectors and 4 cryptocurrencies per sector. This (4,4) portfolio has nearly the same diversification benefit as the largest possible (10,4) portfolio, as we will also show in the next experiment.

Number of Cryptocurrencies per Sector | ||||
---|---|---|---|---|

Number of Sectors | 1 | 2 | 3 | 4 |

1 | 1 | 0.759 | 0.668 | 0.645 |

2 | 0.774 | 0.651 | 0.598 | 0.587 |

3 | 0.681 | 0.605 | 0.581 | 0.576 |

4 | 0.641 | 0.587 | 0.572 | 0.565 |

5 | 0.613 | 0.583 | 0.565 | 0.559 |

6 | 0.607 | 0.57 | 0.565 | 0.557 |

7 | 0.593 | 0.565 | 0.559 | 0.555 |

8 | 0.582 | 0.564 | 0.557 | 0.552 |

9 | 0.552 | 0.565 | 0.557 | 0.553 |

10 | 0.581 | 0.560 | 0.554 | 0.552 |

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**MDPI and ACS Style**

James, N.; Menzies, M.
Collective Dynamics, Diversification and Optimal Portfolio Construction for Cryptocurrencies. *Entropy* **2023**, *25*, 931.
https://doi.org/10.3390/e25060931

**AMA Style**

James N, Menzies M.
Collective Dynamics, Diversification and Optimal Portfolio Construction for Cryptocurrencies. *Entropy*. 2023; 25(6):931.
https://doi.org/10.3390/e25060931

**Chicago/Turabian Style**

James, Nick, and Max Menzies.
2023. "Collective Dynamics, Diversification and Optimal Portfolio Construction for Cryptocurrencies" *Entropy* 25, no. 6: 931.
https://doi.org/10.3390/e25060931