Comparative Study of Portfolio Optimization Models for Cryptocurrency and Stock Markets

Since the introduction of Modern Portfolio Theory (MPT) in 1952, its practical applications, associated challenges, and computational efficiency on large and high-frequency datasets, particularly datasets not used to develop and optimize the model, have drawn extensive research interest. This study has examined the performance of various portfolio models that have explored the concept of MPT on U.S. stock and cryptocurrency markets, i.e., discrete Markowitz portfolio selection (DMPS), the optimal dynamic portfolio (ODP), the binary unconstrained ODP (BUODP) with a quantum annealing solver, and the 1/N naive diversification (ND). Their performance is then compared to the indices that measure the performance of corresponding market exchange-traded funds (ETFs) for stock markets. Our findings show that the DMPS and ODP perform better than other models, delivering better returns in a shorter period. Both run significantly faster than the BUODP (with quantum annealing) with computation time of approximately 0.5 seconds for the S&P 400, 500, and 600 markets whereas BUODP takes 30 seconds; they also mitigate risk and outperform ETFs and ND model for the out-of-sample test with diversified portfolios combining NASDAQ stocks and cryptocurrencies. Furthermore, we have analyzed the impact of data with different frequency intervals, i.e., weekly, daily, hourly, and one-minute, on portfolio performance of the stock markets. The results suggest that data collection frequencies do not make differences in portfolio selections and weights. This study contributes to the advancement of portfolio theory, providing insights and practical values, especially in addressing computational efficiency for high-frequency and large-scale datasets and saving computational costs.