Long-term investment optimization based on Markowitz diversification

The article introduces a long-term investment algorithm that identifies optimal solutions in lower dimensional spaces constructed through principal component analysis or kernel principal component analysis. Portfolio weights optimization is carried out using the Markowitz method. Hyperparameters of the model include window size, smoothing parameter, rebalancing period and the fraction of explained variance in dimensionality reduction methods. The algorithm presented incorporates weights regularization taking into account portfolio rebalancing transaction costs. Hyperparameters' selection is based on the Martin coefficient, which allows us to consider the maximum drawdown for the suggested algorithms. The results demonstrate that the proposed algorithm, trained from 1990 to 2016, shows higher returns and Sharpe ratios compared to the S&P 500 benchmark from 2017 to 2022. This indicates that weights optimization can improve the algorithm's performance through rebalancing.