Deep learning in factor investing: an application to Indonesian Islamic and conventional equities

The efficient market hypothesis (EMH), which posits that no economic agent can consistently achieve superior returns relative to the market, remains a foundational theoretical construct in financial economics. Under the assumption of market efficiency, asset pricing frameworks have been developed to elucidate price dynamics and account for the heterogeneity in average returns across diverse asset classes (Cochrane, 2011). Within these pricing models, the expected return of an asset is defined by a linear combination of factor risk premiums, representing the compensation required by investors for exposure to specific systematic risks. Consequently, a vast body of literature has proposed an extensive array of factors, ranging from macroeconomic and fundamental variables to technical indicators and sentiment measures, to predict expected returns and investigate potential market inefficiencies (e.g. de Oliveira et al., 2013; Feng, Giglio, and Xiu, 2020; Hwang and Rubesam, 2019; Peng et al., 2021; Srijiranon et al., 2022). The EMH also evolved to AMF or adaptive markets hypothesis, whereby the markets are governed by competition, adaptation and natural selection. The implication is that the risk premium of an asset changes over time based on market conditions and the composition of market participants, emphasizing the importance of active risk management and dynamic adaptation in portfolio management (Lo, 2004).

Recent advancements in the field also highlight a transition toward advanced methodologies that transcend linear modeling to enhance the predictive accuracy of expected asset returns. The adoption of machine learning (ML) techniques facilitates the modeling of intricate, nonlinear relationships through optimized functions and hyperparameters. Accordingly, an expansive literature now examines the application of ML specifically for equity price forecasting. While certain studies prioritize technical indicator factors and investor sentiment factors (Peng et al., 2021; Zhen et al., 2025), others leverage broad sets of macroeconomic and fundamental factors (Gu, Kelly, and Xiu, 2020; Qiu, Song, and Akagi, 2016). These studies frequently use artificial neural networks (ANN) and support vector machines (SVM), often integrated with feature selection protocols – such as wrapper and embedded techniques – to ensure that model training is restricted to the most informative predictors.

Parallel to these developments, a substantial body of empirical research advocates for factor investing as a central component of active portfolio construction, highlighting three predominant investment styles: momentum, value and quality. For example, Fama and French (1996), and Lakonishok, Shleifer, and Vishny (1994) used value factors to capture value premiums within the stocks’ expected returns. While Jegadeesh and Titman (1993) used factors that capitalize on the persistence of historical price trends as momentum, Novy-Marx (2013) used quality factors that represent earnings power of the companies. Other studies focused on multi-factors to observe returns predictability (Dewandaru et al., 2015; Cakici et al., 2013; Asness, Moskowitz, and Pedersen, 2013).

However, the research gap exists whereby despite the progress in using ML for general return prediction, empirical research applying the ML techniques specific to the context of factor investing remains sparse. First, most research in factor investing used multilinear regression setup to capture risk premiums to predict stocks’ excess returns. The multilinear models are systematically deployed to generate consistent excess returns relative to established benchmarks. The efficacy of these active mandates is traditionally evaluated via the information ratio (IR), which scales the realized alpha (residual return) against the tracking error (residual volatility). Second, there is no research that used ML techniques specific to Islamic equities within the context of factor investing.

Our research objective is to bridge this gap by using ML as nonlinear techniques, integrated with feature selection methods, in the context of factor investing that captures momentum, value and quality risk premiums for both conventional as well as Islamic equities. There are two main research questions as the main incremental contributions of this research. The first is to investigate on how the predictive performance of factor investing specific to momentum, value and quality factors in the context of ML utilization. The second is to observe the differences in predictive performance of using ML in factor investing between those of conventional equities and Islamic equities.

Our methodological approach involves sequential feature selection (SeFS) and ANN for modeling, complemented by the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) technique to generate denoised price series with heightened predictability. The empirical analysis is conducted on a sample of 954 equities constituting the Jakarta Stock Exchange Composite Index (JKSE), as well as 621 equities of the Indonesia Sharia Stock Index (ISSE). In this case, our research also aims to compare the forecasting performance of our methods between those of conventional and Islamic equities. The data set comprises monthly observations of stock returns and factor variables from January 2015 through December 2025.

The structure of the paper is as follows: Section 2 provides a concise review of the literature; Section 3 describes the data and methodology; Section 4 elaborates on the empirical findings; and Section 5 concludes the study.

This section elaborates the literature review in order on returns predictability, factor investing and forecasting asset returns through the application of ML and decomposition techniques.

Under the assumption of market efficiency, asset pricing frameworks have been developed to elucidate price dynamics and account for the heterogeneity in average returns across diverse asset classes (Cochrane, 2011). Within these pricing models, the expected return of an asset is defined by a linear combination of factor risk premiums, representing the compensation required by investors for exposure to specific systematic risks. Consequently, a vast body of literature has proposed an extensive array of factors, ranging from macroeconomic and fundamental variables to technical indicators and sentiment measures, to predict expected returns and investigate potential market inefficiencies (e.g. de Oliveira et al., 2013; Feng, Giglio, and Xiu, 2020; Hwang and Rubesam, 2019; Peng et al., 2021; Srijiranon et al., 2022). The EMH also evolved to AMF or Adaptive Markets Hypothesis, whereby the markets are governed by competition, adaptation and natural selection. The implication is that the risk premium of an asset changes over time based on market conditions and the composition of market participants, emphasizing the importance of active risk management and dynamic adaptation in portfolio management (Lo, 2004).

Within the domain of active equity management, factor-based investment strategies are systematically deployed to generate consistent excess returns relative to established benchmarks. The efficacy of these active mandates is traditionally evaluated via the IR, which scales the realized alpha (residual return) against the tracking error (residual volatility). A substantial body of academic literature advocates extensive empirical evidence highlighting three predominant investment styles central to active portfolio construction.

The initial two styles consist of momentum and value investing, both of which are extensively documented in the literature (Dewandaru et al., 2015; Cakici et al., 2013; Asness, Moskowitz, and Pedersen, 2013). Momentum strategies use factors that capitalize on the persistence of historical price trends, where securities with high cumulative past returns tend to exhibit continued outperformance (Jegadeesh and Titman, 1993). On the other hand, value-oriented strategies use factors related to fundamental-to-price multiples to identify undervalued securities, predicated on the value effect (Fama and French, 1996; Lakonishok, Shleifer, and Vishny, 1994). The third style involves the integration of quality factors, encompassing dimensions such as accruals-based earnings quality (Sloan, 1996), financial robustness (Piotroski and So, 2012) and gross profitability (Novy-Marx, 2013).

Cochrane (2011) described the recent development of identified asset pricing determinants expanding to a vast array of features far exceeds the factors used in classical models of Fama and French (1993, 1996). Since estimating all possible combination of these factors or features is computationally unfeasible, feature selection is essential for identifying the subset of factors with optimal predictive performance. Furthermore, when using nonlinear models to identify complex patterns, a high volume of features can introduce significant noise. In this case, feature selection is a necessary preprocessing step to ensure only the most informative features are used during model training. Literature suggests that a vast array of factors can be condensed into a smaller group of relevant factors without compromising a model’s explanatory power.

Some research papers investigate macroeconomic and firm fundamental factors. For example, de Oliveira et al. (2013) evaluated 46 factors, including macroeconomic, firm fundamentals, historical prices and technical indicators, to predict the stock price direction of a Brazilian company. By applying a filter-based feature selection method using a correlation criterion, the authors reduced the original set to 18 key factors. Feng, Giglio, and Xiu (2020) evaluated 99 risk factors from companies listed on the NYSE, NASDAQ and AMEX using a Two-Pass Regression approach combined with Double Selection LASSO and Monte Carlo simulations. Their results indicated that most recently proposed factors are statistically redundant, with only a small number demonstrating significant explanatory power. Hwang and Rubesam (2019) evaluated 83 factors from the asset pricing literature using linear models and a Bayesian estimation approach for seemingly unrelated regressions. Testing these models on US stocks, they found that their method selected only ten factors as significant, further highlighting the high level of redundancy within the broader set of variables. Literature also revealed that the excess market return was the only factor that was consistently significant throughout the periods (for example, Nobi, Maeng, Ha, and Lee, 2013; Sensoy, Yuksel, and Erturk, 2013).

Other research focuses on sentiment and technical indicator factors. For example, Srijiranon et al. (2022) developed a hybrid computational framework for stock market forecasting by integrating Principal Component Analysis for factors reduction with long short-term memory (LSTM) architectures. Specific to technical indicator factors, Peng et al. (2021) investigated a set of 124 technical analysis indicators as factors, applying three feature selection algorithms to shrink the feature set. The findings revealed that the factors were not uniformly selected by the feature selection methods. Kumari and Swarnkar (2023) used multiple feature selection techniques, including FFS and LASSO, for 83 technical indicators using day-to-day stock data of six stock indices, before incorporating into ML techniques such as Support Vector Machine, K-Nearest Neighbour and ANN.

ML has become a prominent research focus in finance in recent years. These methods offer significant flexibility because they do not rely on restrictive assumptions regarding data distribution or functional forms. Instead, ML aims to identify non-intuitive patterns within the data to improve forecasting accuracy. These techniques encompass a variety of linear and nonlinear approaches, enabling the modelling of complex relationships through a streamlined set of functions and hyperparameters. Consequently, an extensive body of literature now explores the application of ML specifically for stock price prediction.

For example, Gu, Kelly, and Xiu (2020) compared several ML techniques, including ANNs, random forests and boosted regression trees against traditional linear models. Using a data set of nearly 30,000 financial assets from the NYSE and NASDAQ, the study measured risk premiums and found that ML methods significantly improved predictive performance. Nayak, Pai, and Pai (2016) used Boosted Decision Trees, Logistic Regression and SVMs to forecast trends in the Indian stock market. The research integrated historical price data with market sentiment analysis derived from social media.

Specific to the application of neural networks, Zhen et al. (2025) used LSTM-CNN-Attention model for stock price prediction of Chinese A-share market from 2018 to 2022, supported by the sentiment indicator extracted from the principal component. Srijiranon et al. (2022) used LSTM networks to refine market forecasting, operationalizing a dual-input approach that incorporates both historical price data and sentiment metrics. Qiu, Song, and Akagi (2016) used ANNs to forecast Nikkei 225 Index returns. Their model incorporated several macroeconomic variables as inputs, while integrating genetic algorithms with the neural networks to enhance overall predictive accuracy. Moghaddam, Moghaddam, and Esfandyari (2016) used ANNs to forecast daily returns for the NASDAQ stock exchange. Their model incorporated historical prices and the specific day of the week as key input variables. On the other hand, many recent studies have explored the use of deep neural networks due to their ability to extract abstract data representations through increasing the number of hidden layers. Comprehensive reviews of research in finance applying these deep learning models with more hidden layers were documented in systematic survey papers by Ozbayoglu et al. (2020) and Sezer, Gudelek, and Ozbayoglu (2020).

The most recent study used Support Vector Regression (SVR) with lagged inflation and output gap in a Taylor-rule framework (1964–2024) to forecast 1-year-ahead U.S. excess stock returns, explaining about 40% of their variation and revealing nonlinear, time-varying links between monetary policy conditions and equity risk premia (Roumani, AlSalman, and Murphy, 2026). Feng, Shi, and Kutan (2026) used dynamic automated ML on high-frequency data (2015–2024) for six major and emerging markets to show that local volatility indexes are the strongest predictors of local stock market volatility, VIX has weaker spillover power in China and India than in developed markets, COVID-19 reduced US but increased Chinese market predictability, and cross-market volatility spillovers are asymmetric and much stronger during turbulence.

As financial time series are inherently noisy and nonstationary, predicting their behavior remains a significant challenge for researchers. Due to the complex and chaotic nature of stock prices, individual ML algorithms often fail to produce stable results. To address this, data decomposition techniques, such as empirical mode decomposition (EMD), are integrated with ML to create hybrid models that better capture these complexities. EMD is a flexible, data-driven method designed to analyze nonlinear and nonstationary signals. Research indicates that EMD often outperforms traditional Wavelet and Fourier transforms in processing complex time-series data (Huang et al., 1999). By extracting intrinsic mode functions (IMFs), this technique allows researchers to isolate meaningful economic trends from residual noise within timeseries of prices.

Previous research adopted EMD to various forecasting areas in financial markets. For instance, Metwally et al. (2025) forecasted the KSE-100 index by combining SVM with CEEMDAN for data decomposition, finding that this hybrid approach significantly improved accuracy metrics. Similarly, Yang and Dai (2012) predicted the Shanghai and Shenzhen 300 index by applying EMD prior to an SVM model; the resulting high- and low-frequency IMFs and residual components enabled the SVM to achieve superior performance rankings. In addition, Lin et al. (2012) used Least Squares Support Vector Regression (LSSVR) to forecast foreign exchange rates by modeling each IMF and residual component individually, demonstrating that this approach outperformed traditional forecasting methods.

Islamic asset classes exhibit a distinct risk-return profile shaped by specific Shariah compliance requirements. In the equity sector, Shariah screening involves two primary stages: a qualitative assessment that excludes firms involved in prohibited industries (such as alcohol, gambling and conventional finance) and a quantitative assessment that restricts interest-bearing debt (Derigs and Marzban, 2008). As a result, Islamic equities typically maintain lower financial leverage, potentially reducing leverage effect during economic crises (Hamada, 1972). In addition, these screening processes also limit the number of eligible stocks and lead to higher concentration in certain sectors. Consequently, investing in Islamic equities may generate a distinctive risk-return profile relative to their conventional equities.

This section elaborates methodology used for estimation, as well as the samples and variables representing the factors.

To improve the predictive performance of traditional factor-based investing, our forecasting framework consists of two stages. First, we use ML techniques for feature selection, which include Sequential Forward Selection (SFS) and Least Absolute Shrinkage and Selection Operator (LASSO). The aim of this stage is to select the main predictors that have strong predictive power within our forecasting model. Second, we use ML technique for forecasting equity returns, which is ANNs. Our forecasting model uses the predictors that are selected in the first stage. In addition, our research also performs our two-stage forecasting framework on the denoised equity returns to observe whether the forecasting performance is improved. In this case, we use Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) to denoise the price returns of each equity.

Our research uses two approaches for selecting factors to be used for prediction. The first one is Information Coefficient (IC), whereby the fundamental law of active investment management defines IC as skills to produce alpha or value added in the active portfolio (Grinold, 1989; Qian and Hua, 2003). The IC is obtained from computing correlation between cross-sectional factors at time t and cross-sectional stock excess returns at time t + 1.

The second approach is feature selection, whereby literature has classified feature selection methods into filter methods, wrapper methods and embedded methods. Peng et al. (2021) argue that filter methods, such as those based on covariance or mutual information, often fail to account for complex, nonlinear dependencies between variables. In addition, wrapper methods produce more efficient and streamlined classification models than filter-based approaches (John, Kohavi, and Pfleger, 1994). Given that our research uses ANNs, which are specifically designed to capture nonlinear patterns and abstract feature relationships, filter methods were excluded in favor of wrapper and embedded selection techniques. Hence, our research uses Sequential Forward Selection (SFS) and LASSO for feature selection. Recent research used these selection techniques, combined with ANN for prediction (for instance, Peng et al., 2021; Kumari and Swarnkar, 2023).

Sequential Forward Selection (SFS) is an iterative search algorithm that builds a feature subset by progressively adding variables that maximize classification performance. Starting with an empty set, the process follows four primary steps:

1. initializing an empty subset S;

2. identifying and selecting the individual feature that yields the optimal evaluation score;

3. recursively adding subsequent features that provide the greatest incremental improvement; and

4. terminating the process once a predefined number of features d is reached or when further additions no longer enhance model accuracy.

On the other hand, LASSO is a regularization technique that incorporates a penalty term into the linear regression objective function (Tibshirani, 1996). The resulting coefficients are determined by solving the following constrained optimization problem:

This is similar to:

The parameter $λ$ serves as a regularization constant that dictates the extent of coefficient shrinkage. As increases, it penalizes the magnitude of the regression coefficients, effectively forcing nonessential variables to zero to generate a sparse model. Typically, the optimal value for$λ$ is determined through K-fold cross-validation to minimize out-of-sample error. In classification tasks, regularization is applied to the logistic regression likelihood function in a similar manner. This process results in LASSO logistic regression, where the model coefficients are determined by solving the following optimization problem:

whereby the likelihood function optimized to obtain the beta coefficients is:

Our research uses ANN as the ML technique for prediction. Henrique, Sobreiro, and Kimura (2019) conducted a mapping of 57 high-impact journal papers focused on ML applications in financial stock price prediction. Their findings identified ANNs and SVMs as the most prominent techniques used in the field. In addition, Nazário et al. (2017) reviewed 85 articles published between 1959 and 2016, classifying them by market types, methodologies, risk considerations and operational tools. This analysis highlighted the widespread use of ANNs, primarily citing their consistent performance when dealing with smaller data sets. There are some advantages of ANN as compared other ML techniques such as LSTM networks, SVR, LightGBM, XGboost and Random Forest (Ouf, El Hawary, Aboutabl, and Adel, 2025). ANN features less complexity without heavy sequence machinery that is hard to train and prone to overfitting noisy temporal patterns of LSTM, handling large data sets and high-dimensional feature spaces better without the kernel and support-vector scaling issues of SVR, as well as learning smooth and continuous response surfaces without piecewise-constant functions of tree-based models (XGboost, Random Forest). ANN is expressed as:

where y is a vector of stock returns as a dependent variable, X is a matrix of factors as observed independent variables, w is a vector of parameters to be estimated. W1, …, WN are the parameters for each hidden layer, wo are the parameters of the output layer, N is the number of hidden layers, and $ψi$ are activation functions, with the incorporation of nonlinearity. Our research uses ANN with more hidden layers.

EMD produces IMFs with decreasing frequency and energy as their order increases, with the first IMF containing the majority of the noise (Li et al., 2024; Bao et al., 2010; Rilling et al., 2003). Hence, the first IMF is eliminated and then sum up the remaining IMF components to reconstruct denoised series of prices data with higher predictability.

A significant limitation of the standard EMD technique is mode mixing, which can obscure the underlying signal (Vapnik and Vapnik, 1998). While Ensemble Empirical Mode Decomposition (EEMD) was developed to mitigate this by introducing Gaussian noise, it often fails to fully eliminate the added noise during reconstruction, leading to significant reconstruction errors (Vapnik and Vapnik, 1998). To address both the mode mixing in EMD and the residual noise issues in EEMD, Huang et al. (1998) introduced CEEMDAN, a more robust variation that ensures a more precise and efficient signal decomposition.

The first step for CEEMDAN is that the signal augmented with Gaussian noise is processed using standard EMD. This procedure yields the primary IMF component, which is characterized by the following mathematical expression:

The first residual component is calculated as:

The next step is to decompose residue $r1t+γ1Ewit$ to compute the second mode as:

The last flat residue component can be computed by repeating all the steps for every IMF as follows:

On momentum investing, the methodology uses price momentum, operationalized as the compounded return realized over a retrospective horizon denoted as J (Leivo and Pätäri, 2011). This parameter J represents the formation period, which is the temporal window used to quantify historical performance (Rey and Schmid, 2007). Such metrics constitute a standard approach within the literature, with common empirical applications using lag specifications ranging from one to twelve months to capture various look-back sensitivities.

Within the framework of quality investing, the analysis centers on franchise value, financial robustness and accruals-based earnings quality. To quantify franchise value, the methodology uses profitability metrics such as return on assets, return on equity (ROE) and return on capital (ROC) (Greenblatt, 2010), alongside the ratio of gross profits to total assets as an alternative proxy for economic rents (Novy-Marx, 2013). Finally, earnings quality is evaluated using Sloan’s (1996) accrual measures, which serve to identify potential earnings manipulation or capital overinvestment.

For value investing, Gray and Carlisle (2013) provide a comprehensive synthesis of variables validated by extensive empirical research to capture value and quality premiums. The primary metric identified is earnings yield, the reciprocal of the price-to-earnings (P/E) ratio. A secondary measure is enterprise yield (EBITDA/EV), colloquially termed the acquirer’s multiple. A tertiary iteration substitutes EBIT for EBITDA, a core component of the magic formula framework that integrates value metrics with quality indicators (Greenblatt, 2010); alternative specifications further refine this yield by using free cash flow or gross profit as the numerator. Finally, the book-to-market ratio is included as a foundational benchmark for identifying valuation anomalies (Fama and French, 1992).

Our research uses samples of Indonesia equities that are constituents of Indonesian conventional stock market index and Indonesian Islamic stock market index. We use 949 equities that are the constituents of JKSE, which serves as the Indonesian conventional stock market index. On the other hand, we use 621 equities that are the constituents of ISSE, which serves as the Indonesian Islamic stock market index. The samples are monthly data of stock returns and factor variables, ranging from January 2015 until December 2025. In terms of using feature selection techniques and ML methods to minimize overfitting in our forecasting, we use a training-testing proportion of 75% to 25% on the data set. The training data set is used for feature selection and ANN estimation. In addition, Heaton, Polson, and Witte (2017) documented that increasing the number of hidden layers in an ANN enables the algorithm to better capture stylized facts within financial data. In the context of factor models, this structure allows an ANN to generalize complex cross-interactions, effectively functioning as a hierarchical nonlinear factor model. Therefore, our research uses ANN with 3, 5 and 7 hidden layers, using the Sigmoid function σ (⋅) as the activation function and running 400 training epochs, with the aim to minimize overfitting in testing data set.

Peng et al. (2021) and Kumari and Swarnkar (2023) suggest the following metrics to measure the prediction performance:

In this context, TP and TN represent the counts of correctly identified positive and negative cases, respectively. Conversely, FP denotes the number of incorrect positive predictions (Type I error), while FN refers to the number of missed positive cases (Type II error). Precision serves as a performance metric that accounts for Type I errors, specifically identifying instances where assets were predicted to appreciate but actually declined. In contrast, recall captures the impact of Type II errors, representing profitable opportunities that the model failed to identify. Peng et al. (2021) argue that precision is a critical metric for risk-averse investors focused on minimizing capital losses, whereas recall is more relevant for those with a higher risk tolerance who seek to maximize the capture of potential market gains.

Table 1 details the descriptive statistics for momentum, quality and value factors across the constituent equities of the Indonesian equity market. Analysis of momentum indicators reveals positive mean returns that scale monotonically with the look-back horizon, providing empirical evidence of sustained price persistence over the preceding ten-year period. This longitudinal trend is corroborated by quality metrics, specifically ROE, which exhibit robust average values, suggesting that the observed market momentum is fundamentally underpinned by strong corporate profitability. Concurrently, the sample is characterized by compressed valuation multiples; the preponderance of value factors, most notably the book-to-market ratio, report low mean values, indicating a market environment defined by attractive fundamental pricing.

Given the substantial cross-sectional volatility evidenced by the high standard deviations of the factors, we use a z-score transformation across the entire factor suite. This normalization procedure adheres to rigorous factor investing conventions, mitigating the influence of outliers and ensuring a standardized scale. Furthermore, this adjustment is essential to enhance the efficiency and consistency of the estimators within our predictive modeling framework.

Our research executes a feature selection protocol on the training data set, encompassing the momentum, quality and value factor dimensions. Table 2 details the calculated ICs for the factor suite across both conventional and Islamic equity universes. The computation of ICs aims to quantify the cross-sectional predictive efficacy of each factor. This metric serves as a direct proxy for forecasting skill, consistent with the theoretical framework of the Fundamental Law of Active Management. The results indicate that momentum factors possess superior predictive efficacy relative to quality and value dimensions, with one-month momentum exhibiting the highest information content. A comparative analysis reveals that conventional and Islamic equities share broadly similar IC magnitudes across most factors, suggesting a high degree of commonality in factor risk premia between the two segments. However, idiosyncratic differences emerge within the value and quality clusters: the earnings-to-price ratio demonstrates higher predictive power for conventional stocks, whereas the book-to-market ratio serves as a more robust signal for Islamic equities. Regarding quality metrics, gross profit-to-total assets yields higher predictive utility within the conventional equity sample.

For the feature selection methodology, we implement a dual-optimization approach using SeFS and LASSO regression. These methodologies are used to isolate the most parsimonious and statistically significant predictors from the factor pool, thereby mitigating the curse of dimensionality and enhancing the generalization capabilities of the neural network architectures. Table 3 delineates the subset of factors identified through SeFS and LASSO regularization for both conventional and Islamic equity cohorts. Within the conventional universe, a consensus emerges across both selection methodologies, pinpointing one-month momentum, earnings-to-price and gross profit-to-total assets as the primary predictors. These empirical results suggest that the one-month look-back period serves as the most potent proxy for capturing the momentum risk premium. While the earnings-to-price ratio, a fundamental metric in value-based strategies, is confirmed as a significant driver of the value premium, our findings highlight the gross profit ratio as the preeminent signal for quality. This observation aligns with the research demonstrated by Novy-Marx (2013), which posits that the gross profit-to-total assets ratio is a powerful metric that captures the “franchise value” or economic profitability of a firm, often outperforming traditional accounting measures like ROE or earnings. Specifically, it underscores a company’s capacity to generate high-margin operational returns relative to its asset base, a quintessential characteristic of sustained competitive advantage and brand equity.

The convergence of these three primary predictors is similarly evidenced within the Islamic equity universe. However, a distinct divergence occurs in Islamic equities, where both feature selection methods also incorporate EBIT-to-Enterprise Value (EBIT/EV) and gross profit-to-Enterprise Value (GP/EV) as significant value-based predictors. This suggests that Islamic equities may exhibit a more pronounced sensitivity to valuation anomalies, as a broader array of value metrics demonstrates the requisite predictive efficacy to capture the value premium within this specific asset class. This is understandable since Islamic equities are extracted from Shari’ah screening. The screening criteria impose a certain limit of interest-based debt in the balance sheets of the companies using debt-to-equity ratio. Consequently, Islamic equities are exposed to lesser financial leverage effect relative to that of conventional equities. Specifically, the equities with smaller leverage portray lower market to book values, along with lesser volatility in earnings and excess returns, which is in line with the main characteristics of undervalued stocks.

Our study uses the selected factors in our forecasting model. Table 4 details the empirical results of the ANN estimation, using a standard 75 / 25 training-to-testing data set partition. The predictive framework was evaluated across multiple specifications, incorporating various feature selection regimes and varying depths of hidden layers to assess the efficacy of deep learning architectures. The model demonstrates predictive power, with forecasting performance metrics – including accuracy, precision, recall and the F-score – consistently oscillating within the 70% to 85% range. Specifically, Table 4 shows that the Recall and F-score demonstrate the forecasting performance within the 70% to 80% range, whereas the Accuracy and Precision reveals the performance between 80% to 85% range. Interestingly, the results exhibit relative insensitivity to the specific feature selection methodology or the expansion of hidden layers. This lack of significant variance suggests that the factor risk premia derived from classical asset pricing models possess an inherent structural stability that is not materially enhanced by increasing model complexity or architectural depth. A cross-segment comparison reveals that Islamic equities yield marginally superior forecasting performance relative to conventional equities. This discrepancy is likely rooted in the fundamental composition of the Shariah-compliant universe; as identified in our feature selection analysis, Islamic equities exhibit a more pronounced orientation toward value factors. Consequently, the increased stability and persistence of the value premium over the long-term horizon facilitate more robust empirical estimation and higher predictive accuracy within this asset class.

To further refine the robustness of our results, we apply our methodology to equity prices processed via CEEMDAN. Following the literature (Li et al., 2024; Bao et al., 2010; Rilling et al., 2003), which identifies the first IMF as containing the preponderance of stochastic noise, we reconstruct the price series by aggregating the remaining IMF components. This denoising procedure aims to isolate the underlying signal, thereby enhancing the predictability of the data. Figure 1 presents the sample result of an Indonesia-listed equity in terms of decomposing equity prices, along with all the related IMFs.

Table 5 delineates the ICs, while Table 6 summarizes the feature selection outcomes for the denoised series. Consistent with our prior findings, momentum factors maintain superior predictive efficacy, with the one-month and three-month horizons demonstrating the highest information content. As evidenced in Table 6, short-term momentum factors (1, 3 and 6-month horizons) are consistently identified as primary predictors for both conventional and Islamic cohorts. This suggests that the denoised returns exhibit a smoother risk-return profile, which is more effectively captured by short-range momentum signals. Furthermore, the persistent selection of multiple value factors within the Islamic equity sample reinforces our earlier conclusion that Islamic stocks are fundamentally characterized by a pronounced and predictable value risk premium orientation.

Table 7 provides the empirical findings of the ANN estimation when applied to the denoised equity price series. The model demonstrates significant predictive capacity, with performance indicators – encompassing accuracy, precision, recall and F-score – yielding consistent values between 65% and 75%. Consistent with our preceding analysis, these predictive outcomes exhibit substantial invariance to changes in the feature selection protocol or the number of hidden layers. Notably, the forecasting performance observed with denoised prices is marginally inferior to that achieved with the original price series. The denoised price series mostly contain the trend components, which are captured by all momentum factors presented in Table 6. Nonetheless, removing the short-term components reduce the predictive power of both value and quality factors, thereby decreasing the overall forecasting performance for the denoised series. This suggests that the signal decomposition process may have inadvertently discarded idiosyncratic information related to quality and value risk premiums embedded within the raw data, thereby reinforcing the conclusion that market dynamics are efficiently captured by factor risk premiums within a classical asset pricing framework. Furthermore, the results corroborate our earlier findings that Islamic equities facilitate slightly more accurate forecasting compared to conventional equities.

This study investigates the efficacy of integrating ML architectures and sophisticated feature selection protocols within a traditional asset pricing framework to enhance the predictability of equity returns. While linear factor models remain the cornerstone of financial theory, we contend that nonlinear specifications are essential to capture the latent structural complexities of modern markets. We propose a methodological pipeline that synergizes ANN and SFS with established risk premia – specifically momentum, value and quality. To isolate robust signals, we further augment the data using CEEMDAN to generate denoised price series. The empirical robustness of this approach is tested on a decadal data set (2016–2025) comprising 949 constituents of the JKSE and 621 constituents of the ISSI, providing a unique comparative lens between conventional and Islamic equity universes.

Our empirical results, anchored by ICs, reveal that momentum factors exhibit superior predictive efficacy, with one-month momentum emerging as the most potent signal. The convergence of SeFS and LASSO regularization identifies a parsimonious set of primary predictors: one-month momentum, earnings-to-price and gross profit-to-total assets. Notably, the prominence of the gross profit ratio validates the “franchise value” hypothesis, signaling economic profitability more effectively than traditional accounting metrics. While these predictors are consistent across both cohorts, Islamic equities display a distinct sensitivity to a broader array of valuation anomalies, incorporating EBIT/EV and GP/EV as significant drivers. This suggests that Shariah-compliant assets are characterized by a more multifaceted and pronounced value risk premium.

The predictive performance of our ANN models remains robust, with classification metrics – including accuracy, precision, recall and F-score – consistently ranging between 70% and 85%. Interestingly, the models exhibit a high degree of invariance to architectural depth (the number of hidden layers) or specific feature selection methods, suggesting that the underlying factor risk premia possess an inherent structural stability that transcends algorithmic complexity. In other words, for practical usage to gain structural stability, investors or traders who use nonlinear ML techniques using both training and test data sets for forecasting asset returns should use of prominent risk factors that are derived from vast theoretical and empirical studies. On the other hand, a cross-segment analysis indicates that Islamic equities yield marginally superior forecasting results. This outperformance is likely attributable to their fundamental orientation toward value factors, which appear to offer greater persistence and stability for empirical estimation within this asset class.

Finally, our robustness tests using CEEMDAN-denoised returns corroborate the dominance of short-term momentum signals (1, 3 and 6-month horizons), which effectively capture the smoothed risk-return profiles of the reconstructed series. Although the denoised models maintain significant predictive capacity (65%–75%), they marginally underperform relative to the original price series. This performance delta implies that the decomposition process may discard idiosyncratic but meaningful information, reinforcing the conclusion that classical asset pricing factors, even in their raw state, efficiently capture the primary drivers of market dynamics. Collectively, these findings offer critical insights for investors and scholars navigating the intersection of factor investing and deep learning in emerging markets for both conventional and Islamic equities. The first implication for emerging market investors is that investors can enhance predictive performance of traditional-based factor investing by using ML techniques to capture nonlinearity in relationships. Second, emerging market investors who use ML can gain benefits of structural stability in ML architecture by using prominent risk premiums as a set of predictors, which are derived from theoretical and empirical evidence with respect to asset pricing models. Third, Shari’ah-compliant investors can gain similar forecasting performance relative to that of conventional investors in the context of using ML in factor investing, with Islamic factor investing is driven more by value premiums.