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

TL;DR

This paper evaluates the impact of cryptocurrencies on portfolio performance using advanced GARCH-Copula models and Markowitz optimization, finding that mixed portfolios with cryptocurrencies outperform traditional ones in risk-adjusted returns.

Contribution

It introduces a combined GARCH-Copula and Markowitz approach to optimize portfolios including cryptocurrencies, highlighting their effect on risk and return.

Findings

Mixed portfolios with cryptocurrencies have higher Sharpe ratios.

Cryptocurrency-inclusive portfolios show more stable performance.

The Markowitz approach is justified over CVaR and ES for optimization.

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.