Optimization of portfolios with cryptocurrencies: Markowitz and GARCH-Copula model approach

ArXiv ID: 2401.00507 “View on arXiv”

Authors: Unknown

Abstract

The growing interest in cryptocurrencies has drawn the attention of the financial world to this innovative medium of exchange. This study aims to explore the impact of cryptocurrencies on portfolio performance. We conduct our analysis retrospectively, assessing the performance achieved within a specific time frame by three distinct portfolios: one consisting solely of equities, bonds, and commodities; another composed exclusively of cryptocurrencies; and a third, which combines both ’traditional’ assets and the best-performing cryptocurrency from the second portfolio.To achieve this, we employ the classic variance-covariance approach, utilizing the GARCH-Copula and GARCH-Vine Copula methods to calculate the risk structure. The optimal asset weights within the optimized portfolios are determined through the Markowitz optimization problem. Our analysis predominantly reveals that the portfolio comprising both cryptocurrency and traditional assets exhibits a higher Sharpe ratio from a retrospective viewpoint and demonstrates more stable performances from a prospective perspective. We also provide an explanation for our choice of portfolio optimization based on the Markowitz approach rather than CVaR and ES.

Keywords: Markowitz optimization, GARCH-Copula, Vine Copula, Sharpe ratio, Portfolio optimization, Mixed (Cryptocurrencies + Traditional)

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced mathematics including GARCH, Copula, and Vine Copula models with explicit formulas and derivations, warranting a high math score. While it is retrospective with described data sources and performance metrics like Sharpe ratio, it lacks specific implementation details like code or exhaustive backtest metrics, placing it at moderate empirical rigor.
  flowchart TD
    A["Research Goal:<br>Impact of Cryptocurrencies<br>on Portfolio Performance"] --> B["Data Preparation:<br>Traditional Assets &<br>Cryptocurrencies Time Series"]
    B --> C{"Risk Structure Modeling"}
    C --> D["Markowitz Optimization<br>Minimize Variance"]
    C --> E["GARCH-Copula &<br>Vine Copula Methods"]
    D --> F{"Portfolio Analysis"}
    E --> F
    F --> G["Key Findings:<br>Mixed Portfolio = Highest Sharpe Ratio<br>& Most Stable Performance"]