# Crypto Asset Portfolio Selection

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

## 3. Empirical Findings

## 4. Conclusions and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Tail dependence networks among crypto assets. A red link indicates a negative dependence; a green link a positive effect, and the bolder the link the higher the magnitude of the correlation. (

**a**) 2018, (

**b**) 2019, (

**c**) 2020.

**Table 1.**Statistics for crypto-assets returns and first-difference of conditional value at risk (CVaR).

Returns | Δ CVaR | ||||||||
---|---|---|---|---|---|---|---|---|---|

Code | Name | Mean | Sd | Skew | Ex.Kurt | Mean | Sd | Skew | Ex.Kurt |

BTC | Bitcoin | 0.17 | 4.15 | −1.08 | 15.61 | −0.00 | 1.63 | −3.56 | 213.77 |

BCH | Bitcoin-Cash | −0.03 | 6.78 | 0.07 | 10.40 | 0.00 | 2.98 | 2.15 | 104.04 |

LTC | Litecoin | 0.07 | 5.54 | 0.37 | 9.02 | 0.00 | 1.91 | −1.80 | 117.23 |

ETH | Ethereum | 0.08 | 5.09 | −1.22 | 13.19 | 0.00 | 1.88 | −4.94 | 240.10 |

BNB | Binance-Coin | 0.33 | 6.09 | 0.23 | 12.99 | −0.01 | 1.72 | −5.59 | 265.12 |

LNK | Chain-Link | 0.34 | 7.76 | 0.18 | 6.93 | −0.01 | 2.06 | −0.13 | 224.65 |

XRP | Ripple | 0.02 | 6.34 | 0.98 | 20.64 | 0.04 | 2.91 | 6.97 | 118.03 |

EOS | EOS | 0.12 | 6.70 | 0.20 | 7.10 | 0.01 | 2.27 | −0.66 | 96.15 |

TRX | Tron | 0.19 | 8.27 | 1.94 | 20.58 | −0.02 | 2.79 | 0.87 | 178.97 |

XLM | Stellar | 0.20 | 6.89 | 1.41 | 13.12 | −0.02 | 2.21 | 3.75 | 117.72 |

CRX | CRIX | 0.17 | 4.19 | −1.37 | 13.94 | 0.00 | 1.61 | −2.02 | 181.68 |

**Table 2.**The correlation matrix of asset returns, based on data from 20 September 2017–31 December 2020.

BTC | BCH | LTC | ETH | BNB | LNK | XRP | EOS | TRX | XLM | CRX | |
---|---|---|---|---|---|---|---|---|---|---|---|

BTC | 1 | 0.63 | 0.74 | 0.76 | 0.63 | 0.46 | 0.51 | 0.64 | 0.54 | 0.53 | 0.11 |

BCH | 0.63 | 1 | 0.66 | 0.72 | 0.49 | 0.41 | 0.54 | 0.67 | 0.44 | 0.49 | 0.05 |

LTC | 0.74 | 0.66 | 1 | 0.82 | 0.59 | 0.45 | 0.60 | 0.69 | 0.51 | 0.55 | 0.03 |

ETH | 0.76 | 0.72 | 0.82 | 1 | 0.62 | 0.56 | 0.66 | 0.73 | 0.58 | 0.61 | 0.03 |

BNB | 0.63 | 0.49 | 0.59 | 0.62 | 1 | 0.44 | 0.44 | 0.55 | 0.44 | 0.47 | 0.04 |

LNK | 0.46 | 0.41 | 0.45 | 0.56 | 0.44 | 1 | 0.43 | 0.46 | 0.40 | 0.46 | -0.01 |

XRP | 0.51 | 0.54 | 0.60 | 0.66 | 0.44 | 0.43 | 1 | 0.61 | 0.52 | 0.64 | 0.04 |

EOS | 0.64 | 0.67 | 0.69 | 0.73 | 0.55 | 0.46 | 0.61 | 1 | 0.56 | 0.56 | 0.04 |

TRX | 0.54 | 0.44 | 0.51 | 0.58 | 0.44 | 0.40 | 0.52 | 0.56 | 1 | 0.44 | 0.08 |

XLM | 0.53 | 0.49 | 0.55 | 0.61 | 0.47 | 0.46 | 0.64 | 0.56 | 0.44 | 1 | 0.06 |

CRX | 0.11 | 0.05 | 0.03 | 0.03 | 0.04 | −0.01 | 0.04 | 0.04 | 0.08 | 0.06 | 1 |

**Table 3.**Optimal portfolios with EDH, comparing the years 2018, 2019 and 2020 and two alternative values of the risk aversion parameter: $\tau =0.5$ and $\tau =5$.

Year | $\mathit{\tau}$ | BTC | BCH | LTC | ETH | BNB | LNK | XRP | EOS | TRX | XLM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2018 | 0.5 | 0.05 | 0.06 | 0.10 | 0.11 | 0.11 | 0.06 | 0.14 | 0.13 | 0.06 | 0.17 | |

2018 | 5 | 0.05 | 0.06 | 0.10 | 0.11 | 0.11 | 0.06 | 0.14 | 0.13 | 0.06 | 0.17 | |

2019 | 0.5 | 0.13 | 0.14 | 0.08 | 0.09 | 0.07 | 0.08 | 0.10 | 0.10 | 0.11 | 0.10 | |

2019 | 5 | 0.13 | 0.14 | 0.09 | 0.09 | 0.07 | 0.08 | 0.10 | 0.10 | 0.11 | 0.10 | |

2020 | 0.5 | 0.19 | 0.03 | 0.11 | 0.03 | 0.09 | 0.06 | 0.19 | 0.09 | 0.07 | 0.13 | |

2020 | 5 | 0.19 | 0.02 | 0.12 | 0.04 | 0.10 | 0.07 | 0.19 | 0.07 | 0.06 | 0.13 |

**Table 4.**Optimal portfolios with Markowitz, comparing the years 2018, 2019 and 2020 and two alternative values of the risk aversion parameter: $\tau =0.5$ and $\tau =5$.

Year | $\mathit{\tau}$ | BTC | BCH | LTC | ETH | BNB | LNK | XRP | EOS | TRX | XLM | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2018 | 0.5 | 0.80 | 0 | 0 | 0.15 | 0 | 0.02 | 0.02 | 0 | 0 | 0 | |

2018 | 5 | 0.80 | 0 | 0 | 0.17 | 0 | 0.01 | 0.01 | 0 | 0 | 0 | |

2019 | 0.5 | 0.77 | 0 | 0 | 0 | 0.12 | 0.03 | 0.08 | 0 | 0 | 0 | |

2019 | 5 | 0.76 | 0 | 0 | 0 | 0.11 | 0.01 | 0.12 | 0 | 0 | 0 | |

2020 | 0.5 | 0.57 | 0 | 0 | 0 | 0.04 | 0.02 | 0.36 | 0 | 0 | 0.01 | |

2020 | 5 | 0.53 | 0 | 0 | 0 | 0.04 | 0.01 | 0.40 | 0 | 0 | 0.02 |

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**MDPI and ACS Style**

Ahelegbey, D.F.; Giudici, P.; Mojtahedi, F.
Crypto Asset Portfolio Selection. *FinTech* **2022**, *1*, 63-71.
https://doi.org/10.3390/fintech1010005

**AMA Style**

Ahelegbey DF, Giudici P, Mojtahedi F.
Crypto Asset Portfolio Selection. *FinTech*. 2022; 1(1):63-71.
https://doi.org/10.3390/fintech1010005

**Chicago/Turabian Style**

Ahelegbey, Daniel Felix, Paolo Giudici, and Fatemeh Mojtahedi.
2022. "Crypto Asset Portfolio Selection" *FinTech* 1, no. 1: 63-71.
https://doi.org/10.3390/fintech1010005