1. Introduction
In recent years, the unpredictability, complexity, and uncertainty of financial markets have alarmed investors. These factors have significantly raised financial risks and market instability [
1]. Thus, more concerted effort is required from researchers and investors to develop effective and efficient strategies for predicting emerging market returns and risks. Doing so will significantly mitigate the impact of catastrophic events and asset losses. The future of these markets will play a crucial role in portfolio management and investment. With rapid advancements in machine learning and optimization, new opportunities are emerging for portfolio management. These technologies can be incorporated and integrated to improve investment strategies. The goal is to maximize returns and minimize risk, especially in uncertain and rapidly changing market conditions [
2]. Identifying and selecting the best asset for wealth investment requires an effective approach, strategy, and policy. A well-structured investment plan helps achieve higher returns while minimizing risk. In addition, it is important to note that assets possess distinct characteristics and qualities. These attributes vary from one asset to another. There is a dramatic need to develop a dynamic portfolio optimization scheme to adapt to market dynamics. Consequently, this requires an approach with high precision and accuracy to predict market dynamics and returns.
Portfolio optimization has seen a significant rise in usage and demand within the financial industry, as it helps maximize returns while effectively managing risk. Harry Markowitz pioneered and developed the concept of traditional portfolio optimization in the 1950s based on mean-variance optimization. This approach determines the trade-off between expected return and risk. In today’s rapidly changing and interconnected financial markets, traditional portfolio strategies struggle to adapt. They fail to account for the dynamic nature of market conditions and evolving investor preferences. Portfolio management, optimization, and resource allocation have real-world applications in areas such as transaction cost, risk, trade constraint, and asset return prediction. These techniques help investors make informed decisions by balancing risk and return while considering market constraints. Predicting future returns has been a major concern for managers in today’s financial world. This primarily involves using the model to predict short-term and long-term returns and observe the key factors affecting asset returns [
3].
Dynamic portfolio optimization is a powerful strategy for managing investments in a rapidly evolving financial landscape. By continuously adjusting portfolios based on real-time data and market trends, investors can enhance returns and manage risk effectively. However, successful implementation requires overcoming challenges related to complexity, data requirements, and model uncertainty [
4,
5,
6,
7,
8,
9,
10]. Dynamic portfolio optimization is crucial, as it significantly aids in the selection and management of assets in challenging and uncertain market conditions. It requires an efficient and strategic approach to asset and resource selection to maximize profits while minimizing risk. Market dynamics influence returns through various factors. The underutilized data collected from different financial institutions and markets can be useful in studying market dynamics and patterns. Dynamic portfolio optimization provides an effective solution to the limitations of conventional approaches. It adjusts portfolio compositions in response to changing market conditions, economic indicators, and risk preferences. Furthermore, it provides better market opportunities and risk management and enhances investment performance.
Machine-learning techniques will enable effective learning of financial data patterns [
11]. They will also support and manage dynamic portfolio optimization and decision-making. In addition, there have been no studies related to the application of the logistic regression approach in dynamic portfolio optimization. This gap presents an opportunity to enhance investment strategies and improve returns. The primary aim of this study is to combine logistic regression with dynamic portfolio optimization to enhance the prediction accuracy and precision of asset returns. The proposed approach enables efficient and accurate financial predictions. This advancement makes a significant contribution to the financial industry and investment strategies. Consequently, it will save investors time and ensure effective investment decisions. The proficiency of the proposed approach has been evaluated using performance metrics based on real-world DJIA and HSI historical data. It has also been compared with other machine-learning techniques to assess its effectiveness. Therefore, we used these datasets to evaluate the consistency of the approaches across various time periods and market conditions.
This study proposes a dynamic portfolio return classification algorithm that incorporates PALR to enhance accuracy and precision. The price-aware dynamic portfolio return classification scheme for uncertain financial markets primarily uses logistic regression to classify and predict returns. It leverages market price values and dynamics to enhance predictive accuracy. The proposed scheme makes a significant contribution to the field of financial analytics and portfolio optimization and introduces an innovative approach to classifying portfolio returns, improving both accuracy and reliability. In contrast with traditional methods, PALR demonstrates an ability to dynamically adjust to changing market conditions. Ultimately, this ensures that the model remains robust and relevant across various financial environments. It effectively captures the nuances inherent in the stock market. The contributions are as follows:
Introduces a PALR model incorporating price movements and historical financial indicators for return classification.
Develops a mathematical framework for price deviation and market dynamics to enhance adaptability and performance.
Achieves high performance from the proposed new approach in classifying the dynamic portfolio return in an unpredictable market environment.
Compares the performance of the proposed PALR with traditional machine learning using DJIA and HSI historical data.
The rest of the paper is organized as follows:
Section 2 focuses mainly on related works.
Section 3 presents the dynamic portfolio return mathematical framework and concept and the data used.
Section 4 introduces the PALR dynamic portfolio return prediction scheme. The experiments and results are discussed in
Section 5. In
Section 6, the summary and conclusions are presented.
2. Related Works
To examine and review related works in portfolio optimization, return, risk, and uncertainty, it is essential to explore the concepts related to dynamic portfolios and previous studies in the field. Several studies have been conducted, but only the most relevant ones will be discussed. The foundational concept of portfolio optimization was introduced by Markowitz. Since then, numerous research efforts have sought to further explore and enhance this field. In [
12], the trade-off between return and risk in portfolio selection is demonstrated. Additionally, ref. [
13] examines the dynamic mean-variance approach to portfolio selection, accounting for stochastic interest rates and liabilities. Furthermore, an approach for selecting a portfolio based on dynamic mean variance to critically analyze the market timing is proposed in [
14].
A fuzzy-based portfolio has been proposed as an alternative tool for portfolio studies by [
15]. It is reported in [
16] that a portfolio for different investments can be accomplished by using a fuzzy multi-period portfolio selection approach. Similarly, ref. [
17] introduces a financial portfolio selection method based on a fuzzy approach, which considers return, liquidity, and risk. In [
18], a fuzzy multi-objective portfolio selection strategy integrating efficiency and higher returns is proposed and developed. A mean absolute semi-deviation and triangular fuzzy approach can be integrated into multi-period portfolio optimization to achieve optimal performance, as reported in [
19]. These studies offer useful ideas for dynamic portfolio optimization, but they also have some common problems. The models are often too complex, hard to use in practice, based on fixed assumptions, and not well-tested in different market situations. Fixing these issues could make the models more useful and reliable in real-world investment.
In addition, a machine-learning approach for stock prediction has been developed and introduced into the portfolio variance mean model, as reported in [
20]. In [
21], a multi-period model is proposed to incorporate both market environment fluctuations and transaction costs. Ref. [
22] proposes an LSTM prediction approach based on the hit ratio; it outperforms both RNN and gate recurrent approaches in terms of performance. More importantly, ref. [
23] presents a hybrid deep-learning scheme for stock price prediction using Black–Litterman model inputs. Ref. [
24] reports a machine-learning-based technique using the Omega portfolio and mean variance to predict daily trading investment. In summary, these studies provide useful ideas about portfolio optimization and prediction methods. However, they often miss key dynamic aspects like adjusting to market changes, including transaction costs, and updating models in real time.
Furthermore, it has been reported in [
25] that different machine-learning techniques are used to predict the return for the stock exchange markets. A model based on augmentation and LSTM has been developed for predicting the stock market index, as reported in [
26]. In [
27], an approach for predicting financial time series using a stochastic time neural network and principal component analysis is proposed and developed. Additionally, the approach presented in [
28] utilizes reinforcement learning, with a primary focus on discrete single-asset trading. In contrast, ref. [
29] develops a multi-asset trading scheme that does not account for transaction costs. Although these papers use modern AI and deep learning for forecasting or trading, they do not adjust portfolio weights continuously based on changing risk and return. They also do not consider how relationships among assets change over time.
Interestingly, ref. [
30] proposes a linear rebalancing rule for obtaining an optimal portfolio that uses trading constraints to determine the near-optimal solution. In [
31], an approach for determining the impact of ambiguity on returns and its prediction signal is proposed. More importantly, ref. [
32] proposes a scheme for selecting a portfolio in environments with multiple risk assets. Collin-Dufresne et al. [
33] introduce a regime-switching approach that incorporates trading costs, volatility, and expected returns in portfolio selection. Additionally, ref. [
34] introduces a continuous-time approach derived from the discrete-time model previously proposed in [
35]. The impact of transaction costs on equilibrium return in continuous time is studied in [
36]. These studies often rely on simple assumptions like fixed rebalancing rules and predictable returns, which do not reflect real market conditions. Many also ignore factors like liquidity shocks and market friction, making them less useful for dynamic portfolio optimization.
A CNN-LSTM model with high performance capability has been developed to capture the spatial and temporal features of stock market data, as reported in [
37]. In [
38], a method that accounts for both volatility and noise in financial time series data to predict stock prices is proposed. In addition, ref. [
39] proposes a hybrid scheme to improve prediction performance by utilizing the strengths of CNN and bidirectional LSTM. Furthermore, ref. [
40] proposes a cost-sensitive scheme that assigns varying costs to different types of prediction errors, resulting in higher prediction accuracy. In [
41], it is demonstrated that high-frequency predictions can be achieved by extracting features using a deep neural network informed by prior knowledge. In contrast, ref. [
42] proposes a scheme for predicting stock market indices and indicators without prior knowledge. Furthermore, ref. [
43] proposes an approach that simultaneously correlates and predicts multiple time series of financial data. These articles use deep learning to effectively predict financial trends. However, they do not focus on dynamic portfolio optimization, such as managing risk, allocating assets, or building performance-driven portfolios based on their forecasts.
We also reviewed studies that applied ensemble-learning techniques in finance. Son et al. [
44] show that XGBoost is effective for identifying key factors in predicting company bankruptcy. Qian et al. [
45] use models like AdaBoost, XGBoost, Random Forest, and GBDT to predict financial distress in Chinese firms. In [
46], a new model combines ARMA with CNN-LSTM to capture both linear and nonlinear patterns in financial data. The study in [
47] uses regression tree-based ensemble learning for portfolio valuation and risk management. In [
48], ensemble learning is applied to imbalanced data to predict financial distress. Study [
49] introduces a blending ensemble method using recurrent neural networks for stock prediction. Lastly, ref. [
50] uses ensemble methods with Empirical Mode Decomposition (EMD) to improve forecasting of financial products. These articles mainly focus on predicting financial distress, bankruptcy, and stock prices. However, they do not address dynamic portfolio optimization, as they ignore changing market risks and do not adjust portfolio weights over time.
4. Proposed Dynamic Portfolio Return Classification Model
This section is aimed at explaining the proposed dynamic portfolio model used for the prediction of the dynamic portfolio based on return (gain or loss). The key fundamental components were explained in the previous section. This section explores the concept of the dynamic portfolio return model, both mathematically and methodologically.
First, we assume that the dynamic portfolio problem allows for return prediction while considering risk factors. In essence, assets are allocated with varying weights over time (t) to achieve optimal or maximum returns. Both the return and risk can be observed under different times (t, t(t + 1), ……, t(n − 1)) to critically examine the dynamics of the portfolio. The number of assets is assumed to be
N, which defines the dimensions of the problem. The price of the asset changes over time. Each of the dimensions is represented by w
t. While each component of w represents the weight at time t, and it varies from t
1 to t
N.
The asset return and asset covariance are represented by (
) and (∑t), respectively, as shown in Equation (17). The change in price is due to many factors and it affects the return as well. The change in return can be due to inflation and production within the period. Therefore, this can be represented in matrix form to track variations in returns for future predictions. The matrix conical representation of return variation is as follows:
The return variation for m records and each record can be track at any time t (t, t + 1, …, t + n). As stated earlier, the return can be on a daily, weekly, monthly, quarterly, or yearly basis. Therefore, Equation (18) shows the return at different times.
Similarly, the risk associated with the asset return presented in Equation (18) can be expressed mathematically using Equation (19), as follows:
Furthermore, it can be observed that the variance of the portfolio return is represented by the component
, as illustrated in Equation (19) above. Also, the risk under different time conditions can be represented in matrix form as follows:
Ultimately, risk can be quantified using volatility. This measure aligns with the dynamic nature of the portfolio. Since the summation of all the weights will result in total investment, the weights can be normalized using the mathematical expression below:
where K represents total investment, and the normalized asset weight was calculated based on the historical dataset to determine the best possible return with minimum potential risk. Subsequently, we used the computed returns to predict market returns during the study period.
Additionally, the fundamentals of the proposed scheme can be explained based on the concept of logistic regression and portfolio optimization. It is worth noting that the PALR scheme primarily uses historical data for training and testing, based on data captured from the DJIA and HSI. The parameters we considered include price (open, close, low, and high), volume, return, date, and volatility. These parameters significantly assist in determining the market performance at any time. The daily return was computed based on Equation (1), and it was identified as the target to be classified. In addition, the return deviation was tracked using Equation (5). It enables the PALR scheme to learn the variation patterns in the dataset during training. After selecting the input features and identifying the target variable, the data were standardized to ensure they were appropriately scaled for the logistic regression model.
The portfolio was optimized using dynamic mean-variance optimization (MVO). This is an extension of Markowitz’s classical mean-variance model that adjusts portfolio allocations over time in response to changing market conditions. More importantly, the dynamic MVO continuously or periodically updates the portfolio using new data on returns, risk, and other factors, allowing it to adapt to changing market conditions. This dynamic adaptation helps the portfolio respond to changing financial market conditions. To solve this optimization problem, we applied Lagrangian functions, a mathematical technique used to handle constraints effectively and derive optimal weight allocations.
As shown in
Figure 1, the procedure for dynamic portfolio classification using logistic regression begins with data preprocessing, where historical financial data are collected and cleaned. This step involves handling missing values, normalizing continuous variables, and encoding categorical features. It is important to note that all predictor variables used in this study were z-score normalized prior to training the logistic regression model. The dataset is structured to enable the model to learn from historical patterns and adjust dynamically over time. Next, feature selection was performed to extract informative predictors—such as volatility measures and return—that influence portfolio behavior.
Once the features were prepared, a target variable was defined, often as a classification label indicating portfolio movement based on predefined return thresholds. The labelling was used to compare logarithmic return rates, using 0 and 1 to distinguish between negative and positive returns [
57,
58]. The missing values were addressed by using mean imputation. Subsequently, we used the z-score to identify outliers. Seventy percent (70%) of the financial market data was allocated for training, and the remaining thirty percent (30%) was used for testing [
59,
60]. The logistic regression model was trained on the historical (in-sample) data, where it learned the relationship between the features and the class labels using the logistic function.
Historical financial market data were used as inputs to the proposed scheme. These inputs included open, low, high, and close prices, as well as trading volume. More importantly, return and market volatility were derived from price data and employed as predictive features for market movement classification. Logistic regression, along with baseline models, was used to track market trends and estimate corresponding probabilities. These predictions were subsequently utilized to adjust the model’s weight dynamically based on the predicted probabilities. The portfolio optimization problem was addressed using the Lagrangian method, with the resulting weights applied to anticipate future market conditions. The logistic regression model’s tuning parameters were selected through L1 regularization guided by cross-validation, enhancing generalization. We used L1 regularization to prevent overfitting, especially in high-dimensional settings. The hyperparameter tuning was accomplished through the regularization strength for L1 penalties.
The logistic regression equation models the probability of an outcome Y ∈ [0, 1] as a function of predictor variables X. In the presence of uncertainty, an uncertainty term was incorporated into the model. We derived the differential equation for logistic regression with an added uncertainty term. Subsequently, the logistic regression model predicted a binary outcome (gain or loss) based on historical data using the key equations explained below. The logistic regression equation that models the probability P(Y = 1∣X) is as follows:
where
Y is the binary target (e.g., positive or negative stock return);
X1, X2, …, Xn are predictor variables (e.g., stock indicators);
The expression can be represented by
β0 is the intercept, and β1, β2, …, βn are the coefficients.
The term ϵ has been added to account for the uncertainty arising from the dynamics of the market environment. To express it in the form of a differential equation, we considered the rate of change of P(Y = 1∣X) with respect to z. The sigmoid function satisfies
With the uncertainty, Equation (23) will eventually become
If we substitute P(Y = 1∣X) with P, Equation (24) becomes
We introduced ϵ as a noise or error term (Gaussian or random) in both Equations (26) and (27) to account for rapid fluctuations caused by uncertainty over time, thereby mimicking real-world conditions. In our study, we assumed that uncertainty evolves as market prices change, and we modeled this behavior as a stochastic process. The term ϵ captures the random noise or uncertainty present in the input signal z, which is a common approach in stochastic or probabilistic models where inputs are not perfectly deterministic. Ultimately, there is the need to integrate the explicit uncertainty dynamics. This will result in
where
This eventually forms a differential equation that captures both the logistic regression dynamics [
61] and the impact of time-varying uncertainty. The dynamic of the data input has a significant impact on the output [
62].
Logistic regression estimates the log-odds of the target variable. This ensures that predictions remain within the range of (0,1) for probabilities. The log-odd can be calculated using Equation (28), as shown below:
The decision rule is primarily based on Equation (4); it can alternatively be written as follows:
During the training process, logistic regression employed maximum likelihood estimation (MLE) to determine the optimal parameters (
). This approach maximized the probability of observing the given dataset. More importantly, the loss function (log loss) can be minimized using logistic regression to optimize the coefficients. Hence, the log loss can be computed as follows:
where
is the actual outcome and
is the predicted probability. The equations above played an integral role in predicting the outcomes based on historical data features. Hence, this eventually makes logistic regression a suitable technique for predicting markets and portfolios where probabilities are needed.
We used Lasso (L1) regularization in the logistic regression log-loss function by adding the term to Equation (30), where ζ is the regularization parameter that controls the penalty strength. The model weights are denoted by w, and d represents the number of features. This approach enhances model generalization by penalizing the absolute values of the coefficients, often resulting in sparse models with some coefficients reduced to zero. Consequently, it inherently performs feature selection by eliminating irrelevant features. Additionally, L1 regularization helps prevent overfitting, particularly in high-dimensional datasets.
Overfitting often occurs when the fitted model includes many feature variables with relatively large coefficient magnitudes. Incorporating regularization into logistic regression is essential for preventing overfitting. This is achieved by penalizing large coefficients, which helps ensure that the model remains simple and generalizable. More importantly, regularization mitigates the effects of multicollinearity by discouraging reliance on highly correlated predictors. The application of L1 regularization further enhances model performance by performing feature selection, assigning zero coefficients to less important predictors. Choosing the L1 regularization parameter (ζ) in logistic regression for financial market classification is a critical step, as it directly influences model sparsity, generalization capability, and the identification of meaningful predictors within noisy financial data. When ζ = 0, no regularization is applied, and the standard MLE solution is used. When ζ approaches ∞, all weights shrink toward zero, effectively nullifying the model. For values between 0 and ∞, a sparse solution is obtained (where some coefficients are zero while others remain active). To determine the optimal value of ζ, we employed cross-validation with a grid search approach to minimize out-of-sample prediction error. In this study, we set the regularization parameter ζ to 0.01. Also, the multicollinearity diagnostics showed no evidence of coefficient-sign instability due to collinear predictors.
As returns fluctuate, the system recalculates and re-optimizes portfolio weights based on model predictions. These updated weights are reintegrated into the training loop, allowing the model to adapt and improve continuously. If no significant market shift is detected, the model transitions to performance evaluation, where key metrics are computed to assess its effectiveness. This adaptive process ensures the system not only learns from historical patterns but also responds dynamically to market changes. The trained PALR scheme can predict the probability of positive or negative returns. It is also worth mentioning that other machine-learning techniques, such as Support Vector Machine (SVM), Discriminant, Random Forest (RF), and Decision Tree (DT), have been used to compare and evaluate the proficiency of the proposed scheme.
Dynamic portfolio return classification adapts to shifting financial markets by continuously updating its models and input features based on recent market conditions (return and volatility). These features are time-sensitive variables that capture the changing behavior of market participants. Observing shifts in volatility and return trends supports real-time reclassification of portfolio returns. This responsiveness ensures that the classification remains accurate even during sudden market shifts.
Finally, the performance of the scheme was evaluated using metrics such as accuracy, precision, recall, F1-score, and area under the ROC curve (AUC), along with other additional financial performance tools. These measures helped assess both the predictive capability of the model and its practical effectiveness in guiding dynamic portfolio decisions.
6. Conclusions
In this paper, we proposed a PALR scheme that adapts to changing market conditions and improves prediction accuracy compared to conventional methods. More importantly, the proposed dynamic portfolio-based return prediction algorithm offers a robust solution for return prediction in uncertain financial markets. It dynamically adjusts portfolio weights in response to changing market conditions, effectively addressing the challenges posed by market volatility. This algorithm enhances predictive accuracy and reduces risk exposure. The integration of machine learning enables continuous refinement of the PALR model, helping investors make more informed decisions. Ultimately, this demonstrated the capability of the proposed model in terms of accuracy, precision, and robustness. Also, it is worth mentioning that the scheme adapts to various financial market conditions, thereby enhancing the practical applicability of the proposed scheme in real-time. The experimental results showed that the PALR scheme outperformed RF, SVM, DT, and Discriminant in terms of accuracy, precision, recall, MSE, F-score, AUC, and PR curve.
This study presents a method for classifying dynamic portfolio returns, applicable to portfolio optimization and management. Both theoretically and practically, the proposed approach has shown promising results with negligible classification errors when tested on the DJIA and HSI datasets. More importantly, the proposed PALR scheme will ultimately support investors, asset and portfolio managers, and financial institutions in developing investment strategies and making effective investment decisions. Consequently, this will significantly reduce the time and resources required by investors and managers to make informed decisions.
To address the issue of potential overfitting, which is critical in financial modeling, both train–test splitting with temporal separation and L1 (Lasso) regularization were employed. The temporal split was used to simulate out-of-sample prediction, ensuring that future data did not leak into the training process. Additionally, L1 regularization was incorporated into the logistic regression framework to penalize model complexity and further mitigate overfitting.
The integration of PALR into real-time trading systems enables adaptive portfolio decision-making by dynamically responding to market fluctuations using price-sensitive features. This real-time capability enhances execution timing and risk-adjusted returns. From a regulatory perspective, PALR can support transparent and explainable AI-driven trading decisions, aligning with growing compliance demands for model interpretability and auditability. It can also help regulators by spotting unusual trading patterns or market problems. This supports better monitoring and policy decisions. Moreover, PALR is grounded in economic theory by incorporating rational market signals and aligns with observed investor behavior, such as trend-following and risk aversion, thereby bridging data-driven models with behavioral finance insights.
To implement PALR in an operational setting, the model can be embedded within an automated trading system consisting of four core modules: (1) real-time data ingestion, where live financial data streams (prices, volume, news sentiment) are collected via APIs; (2) a feature engineering layer, which computes rolling volatility, momentum indicators, and adjusted price signals; (3) an inference engine, where the trained PALR model classifies current portfolio positions based on real-time features; and (4) execution and feedback, where trades are placed via brokerage APIs and outcomes are logged for continual model refinement. The model’s probabilistic outputs can also be integrated into risk-weighted decision thresholds, allowing for flexibility depending on market volatility. This end-to-end setup ensures PALR can adapt dynamically and provide timely, data-driven decisions within live financial systems.
While the PALR model improves responsiveness to market dynamics, it also presents certain limitations. Its performance is highly dependent on preprocessing decisions—such as normalization techniques, window size, and cross-validation—which can greatly affect both predictive accuracy and model stability. Inconsistent or suboptimal preprocessing may introduce bias or generate misleading trading signals. Additionally, applying PALR in less liquid or emerging markets poses challenges. These markets often display irregular price movements, lower trading volumes, and heightened volatility, all of which can undermine the model’s effectiveness and may necessitate further calibration or alternative modeling strategies.
PALR is built on logistic regression, which is inherently interpretable. Each feature’s impact on decision-making (e.g., volatility, return, price movement) can be quantified. This allows for clear explanations to stakeholders, auditors, and clients. This eventually fulfils the MiFID II requirements for algorithmic transparency and investor protection. In addition, the model integrates real-time price signals, which can be updated periodically, allowing for responsive risk management. The ability to dynamically classify portfolios based on volatility and return helps in the early detection of excessive risk exposure. This aligns with risk governance standards under MiFID II and Basel III. Since PALR is statistically grounded, it will enable full audit trails needed by regulators. In advisory settings, PALR can be adapted to consider investor-specific constraints (e.g., risk tolerance, investment horizon), ensuring portfolio recommendations remain suitable and compliant with client profiling requirements.
It is evident that there is a pressing need to explore the capabilities of PALR as a tool for classifying smaller, emerging, or less liquid markets. These markets often exhibit unique structural characteristics, such as heightened volatility, lower liquidity, and irregular trading patterns, which require careful study. While our current study primarily focuses on large, liquid markets to establish the core performance of PALR, the model is inherently designed with flexibility. Its dynamic adjustment mechanism is driven by price movements and returns. It can be calibrated for alternative market environments through tailored feature selection, threshold tuning, and regularization adjustments. Therefore, it is crucial to empirically validate the performance of PALR in emerging or less liquid markets in our future research. More importantly, future research will explore the effects of alternative data preparation strategies, return definitions, and prediction horizons.
In our future research, we will incorporate more diverse data sources, including macroeconomic indicators, sentiment analysis, and technical indicators. Hence, these will provide a more comprehensive view of the market dynamics, enabling investors and traders to make informed decisions with greater confidence. Essentially, this will explore potential trading opportunities that adapt to the portfolio dynamics in a rapidly changing market environment. In future extensions, we also plan to explore online learning strategies or retraining at fixed intervals to enhance adaptability in real-time applications. Furthermore, to enhance the risk assessment of the dynamic portfolio, we will incorporate additional robust risk measures, such as value at risk (VaR), to better capture tail risk. Ultimately, this would provide a more comprehensive understanding of downside risk, especially under non-normal return distributions.