Table 1.
Glossary of abbreviations (alphabetically ordered).
Table 2.
Overview of studies on stock return prediction via machine learning.
Fig 1.
Training sample extraction via sliding window.
Fig 2.
Prediction results for the CNN model (Case study I):
Akhaber (top left), Asia (top middle), Foulad (top right), Hkshti (middle left), Mafakher (center), Nori (middle right), Satran (bottom left), Shasta (bottom middle), and Tejarat (bottom right). The different prediction scenarios are shown as light blue dashed lines, the single prediction trajectory without bootstrapping is shown as a green solid line, and the actual prices are shown as a red solid line. The horizontal axis denotes the number of days, and the vertical axis denotes the asset prices.
Fig 3.
Prediction results for the GRU model (Case study I):
Akhaber (top left), Asia (top middle), Foulad (top right), Hkshti (middle left), Mafakher (center), Nori (middle right), Satran (bottom left), Shasta (bottom middle), Tejarat (bottom right). The different prediction scenarios are plotted in light blue dashed lines, the single prediction trajectory without bootstrapping is plotted in a green solid line, and the real prices are also plotted in a red solid line. The horizontal axis denotes the number of days, and the vertical axis denotes the asset prices.
Table 3.
MSE and MAE means (standard deviation) with bootstrapping for the CNN model - Case study I.
Table 4.
MSE and MAE without bootstrapping for the CNN model - Case study I.
Table 5.
MSE and MAE means (standard deviation) with bootstrapping for the GRU model - Case study I.
Table 6.
MSE and MAE without bootstrapping for the GRU model - Case study I.
Fig 4.
Prediction results of the CNN model in Case Study II for 15 assets: prediction scenarios (light-blue dashed), single-step prediction (green solid), and actual prices (red solid).
Fig 5.
Prediction results for the GRU model in Case Study II for 15 assets: prediction scenarios (light blue dashed), single prediction (green solid), actual prices (red solid).
Table 7.
MSE and MAE means (standard deviation) with bootstrapping for the CNN model - Case study II.
Table 8.
MSE and MAE without bootstrapping for the CNN model - Case study II.
Table 9.
MSE and MAE means (standard deviation) with bootstrapping for the GRU model - Case study II.
Table 10.
MSE and MAE without bootstrapping for the GRU model - Case study II.
Fig 6.
Flowchart of the scenario-based portfolio optimization.
Table 11.
Portfolio Deviation for CNN model - Case study I. Lower λ values emphasize higher expected returns at greater risk levels, whereas larger λ values prioritize risk minimization and yield more conservative portfolios.
Table 12.
Portfolio Deviation for GRU model - Case study I. Lower λ values emphasize higher expected returns at greater risk levels, whereas larger λ values prioritize risk minimization and yield more conservative portfolios.
Fig 7.
Box plot of Portfolio Deviation values obtained from 10 replications of the tracking model using CNN model - Case study I.
Fig 8.
Box plot of Portfolio Deviation values obtained from 10 replications of the tracking model using GRU model - Case study I.
Fig 9.
Pareto frontiers for the CNN model - Case study I:
The tracking model (11) (left), model (6) without bootstrapping (middle), and model (6) with true return values (right). The horizontal axis denotes risk, and the vertical axis denotes return.
Fig 10.
Pareto frontiers for the GRU model - Case study I:
The tracking model (11) (left), model (6) without bootstrapping (middle), and model (6) with true return values (right). The horizontal axis denotes risk, and the vertical axis denotes return.
Table 13.
Portfolio Deviation for CNN model - Case study II. Lower λ values emphasize higher expected returns at greater risk levels, whereas largerλ values prioritize risk minimization and yield more conservative portfolios.
Table 14.
Portfolio Deviation for GRU model - Case study II. Lower λ values emphasize higher expected returns at greater risk levels, whereas larger λ values prioritize risk minimization and yield more conservative portfolios.
Fig 11.
Pareto frontiers for the CNN model - Case study II:
The tracking model (11) (left), model (6) without bootstrapping (middle), and model (6) with true return values (right). The horizontal axis denotes risk, and the vertical axis denotes return.
Fig 12.
Pareto frontiers for the GRU model - Case study II:
The tracking model (11) (left), model (6) without bootstrapping (middle), and model (6) with true return values (right), for the GRU model - Case study II. The horizontal axis denotes risk, and the vertical axis denotes return.
Fig 13.
Sensitivity analysis of PD values for the tracking model with varying bootstrap samples.
Fig 14.
Architecture of a CNN (Adapted from [59, Fig 3]).
Fig 15.
Graph and mathematical formulas of activation functions used in CNN.
Fig 16.
A cell of a GRU (Adapted from [65, Fig 2]).
Table 15.
Optimal solution, risk and return for the CNN model for - Case study I.
Table 16.
Optimal solution, risk and return for the CNN model for - Case study I.
Table 17.
Optimal solution, risk and return for the CNN model for - Case study I.
Table 18.
Optimal solution, risk and return for the CNN model for - Case study I.
Table 19.
Optimal solution, risk and return for the CNN model for - Case study I.
Table 20.
Optimal solution, risk and return for the CNN model for - Case study I.
Table 21.
Optimal solution, risk and return for the CNN model for - Case study I.
Table 22.
Optimal solution, risk and return for the CNN model for - Case study I.
Table 23.
Optimal solution, risk and return for the CNN model for - Case study I.
Table 24.
Optimal solution, risk and return for the GRU model for - Case study I.
Table 25.
Optimal solution, risk and return for the GRU model for - Case study I.
Table 26.
Optimal solution, risk and return for the GRU model for - Case study I.
Table 27.
Optimal solution, risk and return for the GRU model for - Case study I.
Table 28.
Optimal solution, risk and return for the GRU model for - Case study I.
Table 29.
Optimal solution, risk and return for the GRU model for - Case study I.
Table 30.
Optimal solution, risk and return for the GRU model for - Case study I.
Table 31.
Optimal solution, risk and return for the GRU model for - Case study I.
Table 32.
Optimal solution, risk and return for the GRU model for - Case study I.
Table 33.
Optimal solution, risk and return for the CNN model for - Case study II.
Table 34.
Optimal solution, risk and return for the CNN model for - Case study II.
Table 35.
Optimal solution, risk and return for the CNN model for - Case study II.
Table 36.
Optimal solution, risk and return for the CNN model for - Case study II.
Table 37.
Optimal solution, risk and return for the CNN model for - Case study II.
Table 38.
Optimal solution, risk and return for the CNN model for - Case study II.
Table 39.
Optimal solution, risk and return for the CNN model for - Case study II.
Table 40.
Optimal solution, risk and return for the CNN model for - Case study II.
Table 41.
Optimal solution, risk and return for the CNN model for - Case study II.
Table 42.
Optimal solution, risk and return for the GRU model for - Case study II.
Table 43.
Optimal solution, risk and return for the GRU model for - Case study II.
Table 44.
Optimal solution, risk and return for the GRU model for - Case study II.
Table 45.
Optimal solution, risk and return for the GRU model for - Case study II.
Table 46.
Optimal solution, risk and return for the GRU model for - Case study II.
Table 47.
Optimal solution, risk and return for the GRU model for - Case study II.
Table 48.
Optimal solution, risk and return for the GRU model for - Case study II.
Table 49.
Optimal solution, risk and return for the GRU model for - Case study II.
Table 50.
Optimal solution, risk and return for the GRU model for - Case study II.