Prediction-Driven Downside-Risk Portfolio Optimization Using Forecast Error-Based Mean Semi-Absolute Deviation

Introduction

Portfolio optimization remains a core and evolving problem in finance, with growing interest in AI-driven methods (Gunjan and Bhattacharyya, 2023). Classical risk models commonly rely on symmetric measures of dispersion that treat positive and negative deviations similarly, despite investors’ greater concern with losses. This limitation has motivated downside-risk approaches that focus specifically on unfavorable deviations below a target or benchmark (Landsman et al., 2022). In prediction-driven portfolio settings, however, risk arises not only from realized return variability but also from uncertainty in the forecasts supplied to the allocation model.

Mean–variance optimization is highly sensitive to estimation errors in expected returns, which can substantially degrade out-of-sample portfolio performance and motivate robust optimization methods (Michaud, 1989; Bauder et al., 2021; Georgantas et al., 2024). Estimation risk may also destabilize optimal portfolio weights, leading to excessive turnover and higher transaction costs (Gârleanu and Pedersen, 2013). These concerns become more pronounced when forecasts enter portfolio allocation directly.

Financial time series are characterized by complex, nonlinear, and noisy behavior, which can limit the effectiveness of conventional statistical forecasting techniques. Karimi Dastgerdi and Zamani Boroujeni (2020) emphasize that deep learning methods are particularly suitable for identifying nonlinear dependencies and temporal relationships in financial data, and show that architectures such as recurrent neural networks (RNNs), long short-term memory networks (LSTMs), convolutional neural networks (CNNs), and hybrid models have considerable potential for forecasting stock prices, market indices, and other financial indicators. At the same time, the quality of financial data itself is important. Mohammadi and Mansourfar (2022) demonstrate that noise in financial time series can materially influence market analysis and that denoised series may provide a clearer representation of underlying long-term market relationships. These findings highlight the importance of both predictive modeling and data-related uncertainty in financial decision-making.

Accordingly, the financial forecasting literature has increasingly adopted deep learning techniques for return and price prediction, with LSTM networks becoming particularly prominent because of their ability to capture temporal dependencies in sequential financial data (Tang et al., 2022; Fischer and Krauss, 2018; Karimi Dastgerdi and Zamani Boroujeni, 2020). Evidence across this literature also indicates that architecture, data quality, and evaluation design materially affect reported forecasting performance.

Despite these advances in forecasting, most financial decision pipelines remain based on a conventional “predict-then-optimize” structure, in which prediction models are trained primarily to minimize statistical forecasting error rather than directly improve subsequent portfolio allocation decisions (Butler and Kwon, 2023). This separation is potentially important because even a statistically accurate forecast may generate inefficient or unstable allocations when prediction errors are not incorporated into the optimization objective.

Variance-based risk measures further complicate this issue because they penalize gains and losses symmetrically, although investors are generally more concerned with unfavorable outcomes. Downside-oriented alternatives such as semi-absolute deviation have therefore received increasing attention and can perform favorably in portfolio construction (Lorimer et al., 2024). The problem is compounded by evolving and non-static uncertainty (Borovička, 2022) and by limited out-of-sample generalization in complex forecasting models.

These strands of research point to the broader importance of connecting market information and predictive signals with portfolio-level decision making rather than evaluating forecasts in isolation.

Building on these streams of research, this paper introduces a prediction-driven downside-risk portfolio framework that directly links predictive uncertainty to asset allocation. Deep learning models are first used to generate return forecasts, after which downside risk is quantified using the mean semi-absolute deviation (MSAD) of portfolio-level forecast errors. This risk measure is subsequently embedded within a linear and implementable portfolio optimization framework and evaluated through a walk-forward rolling design using data from the Abu Dhabi Securities Exchange.

The paper makes four primary contributions. First, it introduces a novel downside forecast error (DSFE) measure designed to capture losses associated specifically with systematic over-prediction. Second, the DSFE measure is embedded within an MSAD optimization framework to provide a tractable and prediction-consistent approach to portfolio construction. Third, the study employs a walk-forward evaluation design and benchmarks the proposed portfolios against mean–variance, MAD, CVaR, and equal-weight strategies. Finally, empirical evidence from the Abu Dhabi Securities Exchange is used to assess the economic value of the proposed approach under realistic conditions, including transaction costs, while avoiding claims of universal dominance over conventional portfolio strategies.

Literature Review

Classical mean–variance optimization penalizes upside and downside deviations equally, which is inconsistent with the asymmetric way in which many investors perceive financial risk. This limitation motivated the development of downside-risk models that measure only unfavorable deviations below a target or benchmark. The mean–semivariance approach is among the most influential of these methods (Ballestero, 2005), and subsequent research has shown that semivariance-based efficient frontiers can differ meaningfully from traditional Markowitz portfolios because of their greater emphasis on downside protection (Pla-Santamaria and Bravo, 2013).

Lower partial moments provide a broader framework connecting downside-risk measures with tail-risk concepts (Yao et al., 2021), while Value-at-Risk and Conditional Value-at-Risk (CVaR) are widely used to describe extreme losses. Because semivariance and tail-based measures may become computationally demanding, semi-absolute deviation and mean semi-absolute deviation provide downside-oriented alternatives that can be formulated through linear programming, making them attractive for dynamic portfolios that require frequent re-estimation (Liu and Qin, 2012). Empirical evidence has further supported deviation-based portfolio models relative to conventional variance-based optimization (Lorimer et al., 2024), including extensions designed to accommodate non-normal and asymmetric return distributions (Yue et al., 2019).

A persistent challenge across these portfolio models is estimation risk. Expected returns and risk parameters are not directly observable and therefore must be estimated from historical data. Errors in these estimates can substantially affect portfolio weights and realized performance, motivating robust optimization methods based on uncertainty sets (Georgantas et al., 2024). Deviation-based formulations may provide additional tractability and reduced sensitivity to model misspecification (Ararat et al., 2024). Nevertheless, much of the existing literature continues to treat forecasting and portfolio optimization as separate stages (Butler and Kwon, 2023).

Parallel to developments in portfolio optimization, machine learning and deep learning have become increasingly important in financial forecasting because of their ability to model complex nonlinear relationships in financial time series. Karimi Dastgerdi and Zamani Boroujeni (2020) reviewed major deep learning architectures used for financial market prediction, including RNNs, LSTMs, CNNs, and hybrid architectures, and concluded that these approaches offer considerable capability for capturing nonlinear dependencies and temporal correlations in financial data. Their review also indicates that combinations of recurrent and convolutional structures can improve predictive accuracy and robustness compared with relying exclusively on individual network architectures.

Evidence from individual neural-network applications provides additional support for the use of such methods in stock forecasting. Across the broader literature, model architecture and data availability materially affect forecast quality; this reinforces the need for common information sets and strictly out-of-sample comparisons when alternative architectures are evaluated.

The reliability of such forecasts also depends on the characteristics and quality of financial time-series data. Financial observations commonly contain noise that can obscure their underlying economic structure. Mohammadi and Mansourfar (2022), using wavelet denoising in an analysis of 16 capital market indices, found stronger long-term co-integration among denoised series than among their noisy counterparts. Their findings suggest that noise can materially influence conclusions drawn from financial time-series analysis and reinforce the need to account for data quality when developing predictive financial models.

More recent research has continued to emphasize LSTM-based and hybrid deep architectures for modeling temporal return dynamics (Tang et al., 2022), while Transformers and generative approaches are increasingly being investigated as emerging forecasting tools (Zhang et al., 2024). Deep recurrent and temporal models have demonstrated statistically evaluated predictive performance (Yilmaz and Yildiztepe, 2024), and LSTM-based approaches have improved trend and index forecasting accuracy relative to classical benchmarks in several settings (Al-Khasawneh et al., 2025). However, forecast usefulness depends not only on average predictive accuracy but also on the behavior of forecast errors across market regimes, because errors during turbulent periods may have particularly severe implications for portfolio risk management (Petrozziello et al., 2022).

The distinction between forecast accuracy and decision quality is therefore critical. Because separating prediction from optimization can yield suboptimal portfolio decisions, decision-oriented approaches have increasingly been advocated (Butler and Kwon, 2023), alongside robust and uncertainty-aware optimization frameworks (Georgantas et al., 2024) and models incorporating downside risk (Barro et al., 2019). Decision-focused learning extends this idea by training predictive models according to the quality of the downstream decision rather than forecast accuracy alone. Ignoring the interaction between forecasting and optimization may result in unstable portfolio allocations even when the underlying mean–variance framework is otherwise correctly specified (Bae et al., 2026).

Related portfolio studies likewise illustrate the importance of transforming financial information into actionable portfolio weights. This broader evidence supports integrating information-processing mechanisms with portfolio selection rather than treating financial prediction as an isolated objective.

Nevertheless, most integrated prediction and optimization approaches continue to rely primarily on symmetric forecasting loss functions and variance-based risk measures. Consequently, the downside consequences of systematic forecast over-prediction remain comparatively underexplored. This issue is especially relevant when portfolio allocation responds directly to predicted returns, because systematic optimism in return forecasts may lead the optimizer to overweight assets whose realized performance subsequently falls below predicted levels.

Expected returns and other portfolio inputs remain vulnerable to estimation error, and even small inaccuracies may generate disproportionately large distortions in optimal portfolio weights and persistent out-of-sample underperformance (Michaud, 1989; DeMiguel et al., 2009; Bauder et al., 2021). Risk parameters themselves are also estimated and therefore subject to forecasting errors (Berger and Fieberg, 2016). Yet the specific role of downside forecast errors in portfolio construction has received substantially less attention.

Methodological design introduces additional concerns. Simplistic training and testing procedures may generate look-ahead bias or data leakage (Zhou et al., 2025). Walk-forward and rolling-window evaluation methods, in which models are repeatedly re-estimated using only information available at each decision point, are more appropriate for non-stationary financial markets (Law and Shawe-Taylor, 2017), but remain underused in machine-learning-based portfolio studies.

Transaction costs represent another important source of divergence between theoretical and realized portfolio performance. Ignoring such costs can systematically overstate investment performance because frequent rebalancing generates trading frictions that reduce realized returns. Dynamic and machine-learning-driven strategies can be particularly vulnerable because they may generate high portfolio turnover (Li et al., 2018; Gârleanu and Pedersen, 2013). Incorporating transaction costs into portfolio evaluation is therefore essential for determining whether forecast-responsive strategies remain economically meaningful in practice.

Finally, conclusions regarding portfolio effectiveness can be sensitive to the selected evaluation metric. The Sharpe ratio, drawdown measures, and downside-sensitive indicators respond differently to extreme observations and asymmetric return distributions, meaning that reliance on a single performance measure may yield misleading conclusions (Arcidiacono and Rossello, 2022). Credible evaluation consequently requires comparisons against appropriate benchmarks together with robustness checks across alternative sample periods and model settings (Tu and Li, 2024).

Overall, the literature reveals several unresolved issues. First, downside risk generated specifically by systematic forecast over-prediction is rarely modeled explicitly. Second, forecasting and portfolio optimization are still commonly treated as separate processes. Third, walk-forward, point-in-time evaluation remains underutilized in machine-learning-based portfolio research. Fourth, transaction costs and turnover are frequently ignored or incorporated only after portfolio construction. Fifth, empirical conclusions are often based on a narrow range of performance metrics. Motivated by these gaps, the present study combines walk-forward deep-learning forecasts, downside-focused forecast errors, and MSAD-based portfolio optimization while explicitly considering transaction costs, benchmark comparisons, and robustness across alternative settings.

Methodology

Data and preprocessing

Data description

This study employs daily equity market data from the Abu Dhabi Securities Exchange (ADX) covering January 2014 to December 2023. The empirical investment universe contains 25 firms selected to represent the main sectors of the Abu Dhabi equity market and to support repeated portfolio formation and rolling out-of-sample evaluation.

The final sample consists of 25 sector-representative equities. Where an index firm lacks sufficiently long or continuous historical observations, a replacement firm from the same sector is used to maintain a stable panel for rolling estimation. Because the resulting fixed universe may introduce survivorship and selection bias, findings should be interpreted as evidence for this empirical sample rather than for the full historical index membership.

The selected firms span banking, telecommunications, energy, industrials, healthcare, consumer services, and real estate, providing cross-sector coverage within the chosen sample.

Daily observations include opening price, highest price, lowest price, closing price, and trading volume for each stock. The data are collected from publicly available financial databases, including the official ADX platform and Investing.com. Prior to model estimation, all observations are aligned by trading date and screened for incomplete records, stale prices, and inconsistent entries.

Return construction and target definition

Let ​ denote the adjusted closing price of asset i on trading day t. The realized one-period simple return is computed as

More generally, the h-period simple return from decision date t to realization date t+h is defined as

where h denotes the forecasting horizon. This definition ensures that the forecasting target is aligned with the investment horizon and that all returns are measured relative to the information available at the portfolio decision date t. The primary empirical analysis uses h=1, while additional robustness analyses later examine medium-horizon forecasts using h=5 and h=10.

Forecasting targets are indexed by their decision and realization dates so that only information available at time t enters the model fitted at that decision date.

Feature engineering and leakage control

The predictive framework utilizes multivariate market information derived from daily OHLCV observations, including opening price, highest price, lowest price, closing price, and trading volume. For each asset i, the raw feature vector at time t is represented as

In addition to raw market variables, OHLCV-derived features are constructed to capture short-term price dynamics, intraday volatility, and changes in trading activity commonly used in deep learning-based financial forecasting (Tang et al., 2022). The following variables are included in the feature set:

The variable ​ represents the lagged daily return of asset i and captures short-term price momentum. The variable ​ measures the normalized intraday high–low price range and serves as a proxy for intraday volatility and price dispersion. The variable denotes the normalized open-to-close price movement and reflects intraday directional changes in market sentiment. Finally, ​ represents the relative variation in trading volume and is included to capture fluctuations in market activity and liquidity conditions.

Together, these variables provide complementary information regarding return dynamics, intraday volatility, directional price behavior, and trading intensity. The inclusion of both price-based and volume-based indicators allows the forecasting models to capture nonlinear temporal dependencies and evolving market conditions more effectively than relying solely on raw closing prices.

To incorporate temporal information into the predictive framework, model inputs are constructed using a rolling lookback window of length L. The empirical analysis sets the deep learning lookback length to L=20 trading days, corresponding approximately to one trading month. Consequently, the sequential input structure for asset i at time t is defined as

where each input vector contains the historical OHLCV observations used for next-period market forecasting.

This structure enables sequential forecasting models, particularly the LSTM architecture, to exploit temporal dependencies embedded in historical financial time-series observations (Fischer and Krauss, 2018).

Data preprocessing and leakage prevention

Reliable rolling estimation requires sufficiently continuous historical observations within each estimation window. Accordingly, an asset is considered eligible for inclusion at rebalancing date t only if the proportion of available observations within the rolling estimation window exceeds a predefined threshold. Let:

Asset i is included in the investable universe at time t only if

.

This filtering procedure reduces distortions arising from insufficient historical observations and supports stable rolling-window estimation under varying market conditions.

Isolated missing observations within otherwise valid windows are handled using forward filling restricted to the corresponding training window. No information from future periods is used during preprocessing or feature construction. Observations associated with stale prices, zero-volume trading days, or obvious recording inconsistencies are removed prior to model estimation. To reduce the influence of extreme observations while preserving genuine market dynamics, return variables are winsorized at the 1st and 99th percentiles within each rolling estimation window.

All continuous input variables are normalized separately within each rolling training window using Min–Max scaling. Let ​ denote a generic feature variable. The normalized feature is computed as

The scaling parameters estimated from the training window are subsequently applied unchanged to the associated validation and test observations. This procedure reduces the risk of future-informed normalization within the walk-forward evaluation (Zhou et al., 2025).

Walk-forward structure and portfolio rebalancing

To approximate realistic portfolio management conditions, the empirical analysis is implemented within a walk-forward rolling retraining framework. At each rebalancing date, forecasting models are estimated using the most recent 252 trading days. Portfolio weights are then constructed from forecasts generated by the updated models, after which the estimation window moves forward and the procedure is repeated (Law and Shawe-Taylor, 2017).

Portfolio rebalancing is conducted every 60 trading days, approximately quarterly. This schedule limits turnover relative to high-frequency rebalancing (Gârleanu and Pedersen, 2013). In the baseline specification, the one-day-ahead forecast is used as a cross-sectional allocation signal at each rebalancing date, and the resulting weights are held until the next scheduled rebalance; it is not interpreted as a 60-day expected return. At each rebalancing date t, the available information set is represented by

.

All preprocessing procedures, feature transformations, scaling parameters, model estimation processes, and portfolio optimization inputs are computed exclusively using information contained in ​. Consequently, no future observations enter the forecasting or portfolio construction pipeline at any stage of the empirical analysis.

Forecasting Models

The forecasting stage is formulated as a multivariate OHLCV prediction problem. Each deep learning model generates forecasts for the future Open, High, Low, Close, and Volume values of each asset. Expected returns are subsequently derived from the forecasted closing prices and supplied to the portfolio optimization stage.

Forecasting objective

The forecasting component of the proposed framework is designed to generate forward-looking market forecasts that subsequently serve as inputs to the portfolio optimization stage. Rather than predicting future returns directly, the deep learning models forecast future market observations represented by the OHLCV (Open, High, Low, Close, and Volume) variables. Expected returns used in portfolio construction are then derived from the forecasted future closing prices. Let:

denote the realized OHLCV vector of asset i observed at time t+h, and let

denote the corresponding forecast generated using information available at decision date t. The predictive objective of the deep learning models is therefore defined as

where denotes the forecasting model parameterized by θ, and represents the rolling input sequence constructed from historical market observations over the lookback window of length L. The baseline empirical specification focuses on one-day-ahead return prediction (h=1), while additional robustness analyses later examine medium-horizon forecasts using h=5 and h=10. At each rebalancing date, the forecasting models generate cross-sectional return expectations for all assets included in the investable universe. These predicted returns are subsequently incorporated into the downside-risk portfolio optimization framework described in the following sections.

Following model estimation, return forecasts are derived from the predicted future closing prices. Let ​ denote the observed closing price available at the portfolio decision date and let ​ denote the corresponding forecasted future closing price. The expected return forecast used in portfolio optimization is computed as

for a forecasting horizon of length h. These forecast-derived expected returns provide the forward-looking return inputs required for the portfolio optimization stage while preserving consistency with the underlying OHLCV forecasting framework. Model estimation is conducted by minimizing the mean absolute forecasting error (MAE) between the predicted and realized OHLCV vectors over the corresponding rolling training sample. The optimization objective is defined as

where k indexes the five forecasted OHLCV variables and T denotes the number of observations in the corresponding rolling training sample. Mean absolute error is used to reduce the influence of very large residuals relative to a quadratic loss.

Forecast generation and model estimation are implemented exclusively within the rolling walk-forward framework. All forecasts are generated using information available at the corresponding decision date, consistent with point-in-time evaluation (Law and Shawe-Taylor, 2017).

Deep learning architectures

To generate forward-looking market forecasts for the portfolio optimization stage, the empirical framework employs three alternative deep learning architectures: Deep Multilayer Perceptron (DMLP), Long Short-Term Memory (LSTM), and Convolutional Neural Network (CNN). The use of multiple forecasting architectures allows the analysis to evaluate the robustness of the proposed downside-risk optimization framework under different nonlinear forecasting structures rather than relying on a single predictive specification.

All forecasting models are trained to predict future OHLCV observations, consisting of opening price, highest price, lowest price, closing price, and trading volume. Expected return forecasts are subsequently derived from the forecasted closing prices and supplied to the portfolio optimization stage. Although all models receive the same historical information set, each architecture processes the sequential data according to its own structural design.

All forecasting models receive the same rolling input tensor

constructed from historical OHLCV-based observations over the lookback horizon L. While the information set remains identical across models, each architecture extracts nonlinear patterns and temporal dependencies using different computational mechanisms.

Deep Multi-Layer Perceptron (DMLP)

The baseline forecasting architecture is a Deep Multilayer Perceptron (DMLP). The rolling input tensor is first flattened into a vector, with L denoting the lookback length and the input channels corresponding to the model features. The flattened input is subsequently processed through two fully connected hidden layers with Rectified Linear Unit (ReLU) activation functions. Consistent with the common forecasting objective, the output layer contains five neurons that generate the predicted future OHLCV vector. Formally, the hidden-layer transformation is represented as

where the weight matrices and bias vectors parameterize the hidden layers and ReLU denotes the activation function. The DMLP serves as a nonlinear feedforward benchmark because it processes the same rolling information set without an explicit recurrent state (Tang et al., 2022).

Long Short-Term Memory (LSTM)

To capture temporal dependencies and persistent sequential structures in financial time series, the empirical framework additionally employs a Long Short-Term Memory (LSTM) network. Unlike feedforward neural networks, the LSTM architecture processes sequential observations directly without flattening the rolling input tensor. The LSTM network updates the hidden representation recursively through memory cells and gating mechanisms. Let ​ denote the cell state and ​ denote the hidden state at time t. The update equations are defined as

,

,

,

,

where ​, ​, and ​ denote the forget, input, and output gates, respectively. The implemented LSTM specification consists of 50 hidden units with a dropout rate of 0.2 and a recurrent dropout rate of 0.2. Model estimation is conducted using the Adam optimizer with a learning rate of 0.01 and a batch size of 32 observations. The loss function is specified as mean absolute error (MAE).

The LSTM architecture is designed for financial forecasting settings characterized by nonlinear temporal interactions and evolving market dynamics (Fischer and Krauss, 2018).

Convolutional Neural Network (CNN)

The empirical framework further incorporates a one-dimensional Convolutional Neural Network (CNN) to capture localized temporal patterns and short-term dependencies embedded in OHLCV sequences. Convolutional filters are applied directly to sequential market observations to extract local price–volume interactions (Tang et al., 2022).

Let ​ denote the sequential input and let k denote a convolutional kernel. The convolutional transformation is represented as

where ∗ denotes the convolution operator and b denotes the bias term.

The implemented CNN specification contains one convolutional layer with 64 filters followed by a max-pooling layer with pooling size equal to 2. The extracted feature maps are subsequently processed through two fully connected dense layers containing 32 and 64 neurons, respectively. ReLU activation functions are applied throughout the hidden layers, while optimization is performed using the Adam optimizer under the mean absolute error (MAE) loss function with a batch size of 32 observations.

The CNN architecture is included to capture local trend structures and short-horizon nonlinear dependencies that may not be fully represented within feedforward forecasting structures.

To support comparison, all architectures use the same rolling estimation windows, forecasting horizons, preprocessing procedures, and out-of-sample evaluation protocol. The design therefore holds the information set and data construction constant across models, although stochastic estimation and model tuning may also contribute to observed performance differences.

Model training and optimization

All forecasting architectures are estimated within a rolling walk-forward framework using only information available at the corresponding estimation date. At each rebalancing step, the models are retrained using the most recent rolling estimation window in order to accommodate evolving market dynamics and time-varying return structures.

The deep learning input sequence uses a lookback length of L=20 trading days, while the rolling estimation window used for model training and DSFE estimation contains W=252 trading days. All input variables are normalized using Min–Max scaling fitted exclusively on the rolling training sample, and those parameters are applied unchanged to validation and subsequent forecast observations. This point-in-time treatment reduces leakage risk (Zhou et al., 2025).

The MAE loss is adopted because it is less sensitive to large forecasting errors than a quadratic loss, a useful property for financial series that may contain extreme observations.

Model optimization is conducted using the Adam optimization algorithm. The Adam optimizer is selected because of its computational efficiency and stable convergence properties in nonlinear optimization environments involving noisy gradient updates and high-dimensional parameter spaces (Kingma and Ba, 2015).

To reduce overfitting and improve generalization performance, regularization mechanisms are incorporated during model estimation. In the LSTM specification, dropout and recurrent dropout rates of 0.2 are applied to the hidden layers. In addition, early stopping is implemented using validation loss monitoring in order to terminate training once predictive performance ceases to improve over consecutive epochs.

For each rolling estimation window, the available observations are partitioned into training and validation subsets prior to out-of-sample forecasting. The validation subset is used exclusively for hyperparameter tuning and early stopping, while the test observations remain fully unseen during model estimation and model selection stages.

All models use identical rolling estimation windows, forecasting horizons, preprocessing procedures, and evaluation protocols. This standardization supports an architecture comparison while recognizing that training stochasticity and hyperparameter choices may also influence downstream portfolio performance.

Model Role in Portfolio Construction

To approximate realistic forecasting and portfolio management conditions, all predictive models are implemented within a rolling walk-forward retraining framework. Rather than estimating the forecasting architectures once over a fixed training sample, the models are recursively re-estimated throughout the sample horizon using updated historical information.

At each rebalancing date t, the forecasting architectures are trained using the most recent rolling estimation window containing W=252 trading days. Within each window, the models receive sequential inputs with a lookback length of L=20 trading days. In the baseline analysis, a one-step-ahead forecast is generated for each investable asset and used as a cross-sectional allocation signal. Portfolio weights are then held until the next 60-day rebalance; consequently, the forecast horizon and holding period are distinct.

Formally, let

denote the rolling estimation window available at decision date t. The forecasting model is estimated using observations contained in ​, and the resulting forecasts are used to predict future returns over the subsequent investment horizon.

After the realization of the next observation period, the estimation window moves forward according to

This recursive estimation mechanism allows the forecasting models to update as new observations become available.

Portfolio rebalancing is conducted every 60 trading days, approximately quarterly. At each rebalancing date, portfolio weights are reconstructed using forecasts from models estimated with the latest rolling window. This schedule follows a deliberate turnover-control choice rather than a claim that the one-day forecast remains valid throughout the 60-day holding period (Bağcı and Soylu, 2024).

The walk-forward framework additionally mitigates look-ahead bias by ensuring that all forecasting models, preprocessing procedures, scaling parameters, and portfolio optimization inputs are estimated exclusively using information available at the corresponding decision date. Consequently, no future observations enter either the forecasting or portfolio construction stages at any point in the empirical analysis.

Identical rolling windows, forecasting horizons, preprocessing procedures, and rebalancing schedules are applied across architectures. This design improves comparability, but it does not by itself establish that every portfolio-performance difference is caused solely by architecture.

Downside Forecast Error (DSFE): A Prediction-Driven Downside Risk Measure

Economic rationale and downside forecast error definition

Traditional forecasting error measures penalize positive and negative prediction errors symmetrically. However, in portfolio allocation, overestimation of future returns is generally more harmful than underestimation because it may induce excessive capital allocation to assets that subsequently underperform. In contrast, underestimation primarily leads to missed investment opportunities rather than realized portfolio losses.

To explicitly capture this asymmetric investment risk, we define the Downside-Sensitive Forecast Error (DSFE) as the positive part of the forecasting error. Let

denote the forecast error associated with asset iii over forecasting horizon h, where denotes the return forecast generated at decision date t, and ​ denotes the subsequently realized return.

The downside forecast error component is then defined as

The proposed downside forecast error penalizes only optimistic prediction errors ( > r), which are more likely to generate adverse portfolio allocation decisions. Such overestimation errors are particularly harmful because they may induce excessive portfolio exposure to assets whose subsequent realized performance fails to meet expectations. In contrast, underestimation errors primarily result in missed investment opportunities rather than realized investment losses.

Unlike symmetric forecasting losses, the proposed measure links predictive uncertainty to an economically adverse outcome by focusing on optimistic return forecasts that are followed by lower realized returns.

Rolling estimation and point-in-time information structure

To ensure a strictly out-of-sample and point-in-time portfolio construction framework, portfolio weights are determined at each rebalancing date t using only the information set ​, which contains exclusively the information available up to the corresponding decision date.

At each rebalancing date, the forecasting models generate return forecasts sequentially within a rolling estimation window of length W. Let

denote the h-step-ahead forecast for asset i generated at time τ, where

.

After the forecast horizon elapses, the corresponding realized return

becomes observable. The historical forecast error is therefore defined as

Because each forecast is generated before its realization, the historical error series consists of prior rolling-origin out-of-sample errors observed before the current portfolio decision date; contemporaneous fitted residuals are not used as substitutes for these errors.

Rather than evaluating downside forecast errors independently for each asset, the proposed framework measures downside predictive uncertainty directly at the portfolio level. Let

denote the portfolio weight vector determined at rebalancing date t.

The predicted portfolio return and the subsequently realized portfolio return associated with a historical forecast origin τ are respectively defined as

and

The portfolio-level downside forecast loss is then defined as

Accordingly, the proposed downside forecast error mean semi-absolute deviation (DSFE-MSAD) risk measure is defined as

or equivalently,

Unlike asset-level aggregation schemes, this portfolio-based formulation preserves diversification effects and measures predictive downside risk directly at the level where investment decisions are made. Consequently, the resulting risk measure remains fully consistent with the portfolio optimization objective.

Furthermore, all forecasts, realized forecast errors, and DSFE-MSAD estimates are computed using only information available up to the corresponding portfolio decision date. Therefore, the proposed framework eliminates look-ahead bias and maintains the integrity of the rolling walk-forward evaluation design. The rolling estimation mechanism also enables the framework to adapt continuously to changing market conditions, structural breaks, and evolving return dynamics.

Portfolio optimization framework

The proposed portfolio construction framework integrates forward-looking return forecasts with downside forecast-error risk estimation within a unified prediction-driven allocation procedure.

At each portfolio rebalancing date t, the optimal portfolio weight vector is determined conditionally on the information set ​. Unlike conventional mean–variance portfolio optimization frameworks that rely on symmetric historical return dispersion as the primary measure of risk, the proposed approach defines portfolio risk using the downside-sensitive DSFE-MSAD functional introduced in the previous section.

Consequently, the optimization procedure directly links predictive uncertainty to portfolio allocation decisions.

DSFE-based portfolio optimization model

At each portfolio rebalancing date t, the optimal portfolio weight vector is determined conditionally on the information set Unlike conventional mean–variance portfolio optimization frameworks that rely on symmetric historical return dispersion as the primary measure of risk, the proposed approach defines portfolio risk using the downside forecast error mean semi-absolute deviation (DSFE-MSAD) measure introduced in the previous section.

Let

denote the portfolio weight vector at decision date t, and let

denote the vector of forecasted asset returns generated by the forecasting model.

The proposed portfolio construction framework seeks to maximize expected portfolio return while controlling downside predictive risk arising from systematic return overestimation. The resulting mean–risk optimization problem is given by:

where

denotes the portfolio-level downside forecast-error risk measure and

λ≥0

represents the downside forecast-risk aversion parameter.

Under this formulation, portfolio optimization jointly balances expected portfolio return against downside predictive uncertainty. Unlike conventional variance-based portfolio optimization models, the proposed framework penalizes only economically adverse forecasting errors associated with optimistic return predictions. Consequently, the optimization process directly incorporates forecast-induced downside risk into portfolio allocation decisions.

The parameter λ governs the trade-off between expected return maximization and downside forecast-risk control. Larger values of λ place greater emphasis on downside predictive risk reduction, whereas smaller values increase the relative importance of return generation.

The parameter λ is examined over a predefined grid, with the Sortino ratio used as the primary sensitivity criterion. Because selecting λ on the reported evaluation path can introduce specification-search bias, the resulting comparison should be interpreted as exploratory unless the choice is confirmed in an independent validation period.

For computational implementation, the optimization problem is transformed into an equivalent linear programming representation described in the following subsection.

Linear Programming Reformulation

Although the DSFE-MSAD risk measure provides a natural representation of downside predictive uncertainty, the optimization problem contains the non-smooth operator

max(0,⋅),

which must be reformulated to obtain a tractable optimization model.

Recall that the portfolio-level DSFE-MSAD risk measure is defined as

To linearize this expression, an auxiliary variable

Under these constraints, the auxiliary variable ​ assumes the value of the positive part of the portfolio forecast error at each observation within the rolling estimation window.

Consequently, the DSFE-MSAD risk measure can be written as

This reformulation eliminates the non-smooth maximum operator and converts the downside forecast-error risk measure into a linear function of the auxiliary variables.

As a result, the proposed portfolio optimization problem can be expressed as a standard linear programming problem. The linear structure substantially improves computational tractability and facilitates repeated portfolio re-optimization within the rolling walk-forward framework. Similar advantages have been documented in the literature on mean semi-absolute deviation portfolio optimization, where linear reformulations allow efficient implementation in dynamic portfolio management environments (Liu and Qin, 2012).

Complete Linear Programming Formulation

Substituting the linearized representation of the DSFE-MSAD risk measure into the portfolio optimization problem yields the complete linear programming formulation of the proposed prediction-driven portfolio allocation model.

At each portfolio rebalancing date t, the optimal portfolio weights are obtained by solving

subject to

denotes the minimum acceptable expected portfolio return determined from the cross-sectional distribution of forecasted asset returns at the corresponding rebalancing date.

The objective function simultaneously maximizes expected portfolio return and minimizes downside predictive risk arising from systematic return overestimation. The first term rewards assets with higher forecasted returns, whereas the second term penalizes historical downside forecast errors observed within the rolling estimation window.

The constraints in Equations (1)–(2) ensure that the auxiliary variables correctly represent the positive part of portfolio forecast errors. Equations (3)–(5) guarantee full investment, prohibit short-selling, and limit portfolio concentration. Equation (6) imposes a minimum expected return requirement and prevents excessively conservative allocations.

Because both the objective function and all constraints are linear in the decision variables , the resulting optimization problem constitutes a standard linear programming model. Consequently, the proposed DSFE-MSAD framework can be solved efficiently using conventional linear programming algorithms at each rebalancing date within the rolling walk-forward portfolio construction process.

The linear structure of the model is particularly advantageous in dynamic portfolio management settings, where portfolio weights must be re-estimated repeatedly over time. By preserving computational tractability while incorporating forecast-induced downside risk, the proposed framework provides a practical and scalable approach to prediction-driven portfolio optimization.

Portfolio turnover and transaction costs

To improve the economic realism of the empirical evaluation, portfolio performance is assessed after accounting for proportional transaction costs associated with portfolio rebalancing.

Portfolio turnover at rebalancing date t is defined as

The corresponding transaction cost incurred at time t is computed as

Where

c=0.001

represents the proportional transaction cost rate corresponding to 0.1% per trade.

Net portfolio return after transaction costs is therefore defined as

Incorporating transaction costs into portfolio evaluation reduces overstatement caused by rebalancing activity and improves the practical interpretation of the strategies (Bağcı and Soylu, 2024).

Because dynamic forecasting models may induce unstable portfolio weights and elevated trading activity, turnover is particularly important in prediction-driven portfolio management (Gârleanu and Pedersen, 2013).

Benchmark portfolio strategies

To evaluate the economic value of the proposed DSFE-based optimization framework, portfolio performance is compared against four widely used benchmark allocation strategies.

The benchmark portfolios include:

• Equal-weighted (EW) portfolio
• Mean–variance (MV) portfolio
• Mean absolute deviation (MAD) portfolio
• Conditional Value-at-Risk (CVaR) portfolio

The equal-weighted portfolio serves as a naïve diversification benchmark that avoids estimation risk associated with optimized portfolio weights (DeMiguel et al., 2009). The mean–variance portfolio represents the classical Markowitz allocation framework based on expected return and return variance (Markowitz, 1952). The MAD portfolio replaces variance with mean absolute deviation in a linear formulation (Konno and Yamazaki, 1991), while CVaR captures expected loss in the tail beyond a selected quantile (Rockafellar and Uryasev, 2000).

All benchmark portfolios use the same rolling estimation windows, transaction-cost assumption, and rebalancing frequency. The comparison therefore uses a common evaluation schedule, but it should be interpreted as a comparison of complete strategies rather than as a causal isolation of the DSFE risk measure.

Optimization implementation within the walk-forward framework

Portfolio optimization is conducted sequentially throughout the out-of-sample evaluation horizon. At each 60-trading-day rebalancing date, the following procedure is implemented:

1. Forecasting architectures are retrained using the most recent rolling estimation window;
2. Forward-looking return forecasts are generated for all eligible assets using the specified forecasting horizon;
3. Downside forecast errors are estimated using rolling historical prediction errors;
4. Portfolio weights are optimized through the proposed DSFE-MSAD allocation framework;
5. The resulting weights are held over the following 60-trading-day rebalancing interval, and transaction costs are deducted when the portfolio is rebalanced.

For the baseline analysis, one-step-ahead forecasts (h=1) are used as cross-sectional signals at rebalancing dates. Additional analyses use h=5 and h=10 forecasts. These horizons remain shorter than the 60-day holding interval and therefore constitute a robustness check on the allocation signal, not a fully horizon-matched investment design.

After each rebalancing step, the rolling estimation window advances forward and the entire forecasting–optimization process is repeated.

By construction, all portfolio decisions are generated exclusively using information available at the corresponding decision date. Consequently, no future information enters either the forecasting stage or the optimization stage at any point during the empirical analysis.

Figure 2. DSFE-based prediction-driven portfolio optimization procedure

Portfolio Performance Evaluation and Statistical Testing

Portfolio performance evaluation metrics

Several complementary measures are used to evaluate portfolio performance because raw returns alone do not describe volatility, downside risk, drawdown, and trading intensity.

Average portfolio return

The average portfolio return over the out-of-sample evaluation horizon is computed as

where ​ denotes the realized portfolio return at time t.

Sharpe ratio

The Sharpe ratio evaluates excess portfolio return relative to total return volatility and is defined as

where ​ denotes the risk-free rate and ​ denotes the standard deviation of portfolio returns.

The Sharpe ratio does not distinguish upside from downside volatility and therefore complements, rather than replaces, downside-sensitive measures.

Sortino ratio

To account explicitly for downside risk exposure, the empirical analysis additionally employs the Sortino ratio, defined as

where denotes downside return deviation computed using only negative portfolio returns.

Because the DSFE framework is downside-oriented, the Sortino ratio is particularly relevant because its denominator focuses on downside deviation.

Maximum drawdown

Portfolio downside vulnerability is further evaluated using maximum drawdown (MDD), which measures the largest cumulative portfolio loss relative to the previous portfolio peak:

Maximum drawdown is particularly relevant for downside-sensitive strategies because it records the largest peak-to-trough cumulative loss.

Calmar ratio

The Calmar ratio evaluates portfolio return relative to maximum drawdown and is defined as

The Calmar ratio relates return to maximum drawdown and therefore provides a drawdown-based complement to volatility-based ratios.

Portfolio turnover

Portfolio turnover is also evaluated to assess trading intensity and implementation stability; lower turnover indicates greater stability and reduced transaction-cost exposure (computed as in Section 3.4.3).

All performance measures are computed using net portfolio returns after transaction costs throughout the entire out-of-sample evaluation horizon.

Statistical significance tests

Forecast-accuracy differences are evaluated using the Diebold–Mariano test, and sampling uncertainty in selected portfolio metrics is summarized with bootstrap confidence intervals.

Diebold–Mariano test

Differences in forecasting performance across alternative predictive models are evaluated using the Diebold–Mariano (DM) test. The DM statistic examines whether the expected loss differential between two competing forecasting models is statistically distinguishable from zero.

Let

denote the loss differential between forecasting models 1 and 2 at time t, where L(⋅) denotes the forecasting loss function. The null hypothesis of equal predictive accuracy is defined as

The DM test is particularly appropriate in rolling forecasting environments involving sequential out-of-sample predictions.

Bootstrap inference

Because financial return distributions may exhibit non-normality, volatility clustering, and heavy tails, statistical robustness is further evaluated using bootstrap resampling procedures. Bootstrap confidence intervals are constructed for key portfolio performance measures in order to reduce sensitivity to distributional assumptions.

These procedures provide complementary evidence, but non-rejection in a pairwise test should not be interpreted as proof that two models have identical predictive ability.

Robustness analysis

To evaluate the stability and reliability of the proposed DSFE-MSAD portfolio optimization framework, two complementary robustness analyses are conducted.

Alternative forecasting horizons

The baseline empirical specification focuses on one-step-ahead return prediction. To assess the sensitivity of the proposed framework to forecast horizon selection, additional analyses are performed using medium-horizon forecasting windows corresponding to:

• ( h = 5 ) trading days
• ( h = 10 ) trading days

This robustness exercise evaluates whether the economic value of downside forecast-error-aware portfolio optimization remains stable when prediction uncertainty increases over longer forecasting horizons.

Bootstrap inference

To assess the statistical reliability of the portfolio performance results, a bootstrap resampling procedure is applied to the out-of-sample portfolio return series. Confidence intervals are constructed for annualized returns and Sharpe ratios using repeated bootstrap samples.

Unlike conventional parametric inference methods, bootstrap inference does not require restrictive assumptions regarding the underlying return distribution and therefore provides a flexible assessment of estimation uncertainty. The resulting confidence intervals are used to evaluate the stability of the reported portfolio performance measures and the robustness of the main empirical findings.

Figure 3. Empirical evaluation, statistical testing, and robustness analysis framework

Empirical Implementation Details

To ensure transparency and reproducibility, all forecasting, optimization, and evaluation procedures are implemented within a strict rolling walk-forward framework designed to replicate realistic portfolio management while preventing information leakage.

The dataset spans January 2014 through December 2023 for all FADXSI constituent firms. The initial estimation sample begins in January 2014, with sequential out-of-sample portfolio evaluation conducted from January 2019 through December 2023.

At each rolling iteration, forecasting models are retrained using the most recent 252-trading-day window (approximately one year); forward-looking forecasts are then generated and used in the DSFE-based optimization, and the window advances sequentially throughout the evaluation horizon.

Portfolio weights are rebalanced every 60 trading days (approximately quarterly) to reduce excessive trading activity, limit turnover-induced costs, and improve implementation realism.

To eliminate look-ahead bias, preprocessing and normalization are implemented exclusively within each rolling estimation window, using only information observable up to the corresponding decision date, so no future information enters either the forecasting or optimization stage.

The downside forecast-risk aversion parameter λ is examined over a predefined grid using the Sortino ratio as the primary sensitivity criterion. This tuning step is reported as exploratory because an independent validation period is not documented.

The DSFE-MSAD, MAD, and CVaR portfolio optimization problems are solved using linear programming routines implemented in Python through SciPy. The mean–variance benchmark is solved using constrained nonlinear optimization.

The forecasting and optimization pipeline runs sequentially throughout the evaluation horizon: at each 60-day rebalancing date, forecasting architectures are retrained, downside forecast errors updated, portfolio weights re-optimized, and performance evaluated over the following period—ensuring all results correspond to implementable real-time decisions.

Figure 4. Empirical implementation protocol under the rolling walk-forward portfolio optimization framework

Empirical Results and Discussion

The empirical findings are presented in this section, using out-of-sample portfolio returns from the Abu Dhabi Securities Exchange within a rolling walk-forward framework. The evaluation proceeds in stages: predictive performance of the deep learning architectures (via forecasting accuracy measures and Diebold–Mariano tests), DSFE-MSAD portfolio performance relative to benchmark strategies under transaction-cost-adjusted conditions, the comparative role of forecasting architecture, and finally transaction-cost, turnover, and economic interpretation.

Forecasting Performance of Deep Learning Architectures

The forecasting performance of the proposed deep learning architectures is evaluated within the rolling walk-forward framework using out-of-sample one-step-ahead return predictions generated throughout the empirical evaluation horizon. Forecasting accuracy is assessed using mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and directional forecasting accuracy measured by the hit ratio. The results are reported in Table 5.

Table 5 reports average forecasting performance; predictive accuracy is broadly similar across models, with only modest differences observed.

Among the evaluated specifications, CNN has the lowest average MAE (0.1094) and RMSE (0.1196) and the highest reported hit ratio (0.4008). These are descriptive differences only: the hit ratio remains below 0.5, no naïve directional benchmark is reported, and the pairwise Diebold–Mariano tests do not establish statistically significant superiority.

DMLP records the lowest average MSE (0.0283), while its other reported error measures are close to those of CNN and LSTM. Given the non-significant pairwise Diebold–Mariano results, these small metric differences should not be interpreted as a stable ranking of predictive skill.

LSTM produces forecast errors broadly comparable to the other models. Its recurrent structure may capture temporal relationships, but the aggregate forecasting results reported here do not demonstrate a predictive-accuracy advantage.

To further evaluate the statistical significance of predictive accuracy differences across architectures, Diebold–Mariano pairwise predictive accuracy tests are conducted using the out-of-sample forecasting error series.

The results reported in Table 6 indicate that none of the pairwise forecasting comparisons are statistically significant at conventional confidence levels. All reported p-values exceed 0.10, implying that the null hypothesis of equal predictive accuracy cannot be rejected for any pair of forecasting architectures.

Although Table 5 suggests modest differences across models, the DM tests indicate these are not statistically distinguishable from random variation, so no architecture consistently outperforms in predictive accuracy.

This is economically relevant: subsequent portfolio-performance differences may reflect the interaction between forecast characteristics and the optimization framework rather than forecasting accuracy itself, so portfolio-level results should be read as evidence on the economic value of forecast-driven allocation.

• 1. Portfolio Performance Comparison

This section evaluates out-of-sample DSFE-MSAD performance relative to four benchmarks—equal-weighted (EW), mean–variance (MV), MAD, and CVaR—separately across the DMLP, CNN, and LSTM forecasting architectures within the rolling walk-forward framework, with all statistics net of 0.1% transaction costs.

The DSFE penalty parameter was calibrated via grid-search using the DMLP framework as a representative environment, testing λ∈{0.15,0.25,0.35,0.45} against out-of-sample downside-risk-adjusted performance (Sortino ratio, drawdown stability, turnover). Table 7 shows λ=0.45 provides the most balanced trade-off between cumulative growth and downside forecast-risk control, so it is adopted throughout.

Lower λ values under-control downside forecast risk, while larger values produce excessively conservative allocations with weaker growth; λ=0.45 is used throughout.

The overall out-of-sample portfolio performance results are summarized in Table 8.

The empirical results reveal substantial differences in portfolio behavior across forecasting architectures and optimization methodologies. Among the benchmarks, the CVaR portfolio consistently delivers the strongest overall performance in the main one-step-ahead setting, achieving the highest annualized returns, Sharpe/Sortino ratios, and terminal net wealth across all forecasting environments.

The strong CVaR performance suggests tail-risk control remains highly effective in this market; the mean–variance portfolio is competitive but generally outperformed by CVaR on most indicators.

The evidence should not be read as the DSFE-MSAD framework universally outperforming conventional approaches; its contribution lies in introducing a prediction-consistent downside forecast-risk measure that explicitly incorporates adverse forecast uncertainty into allocation.

By contrast, DSFE-MSAD produces more moderate but comparatively stable out-of-sample growth while explicitly incorporating downside forecasting uncertainty. Unlike approaches relying on historical return dispersion, it directly penalizes downside forecast errors from overly optimistic predictions, yielding more conservative allocation dynamics.

The cumulative net wealth trajectories corresponding to the alternative portfolio construction methodologies are illustrated in Figures 5–7.

Under DMLP, the DSFE-MSAD strategy generates positive out-of-sample growth throughout, but performs below the EW, MAD, MV, and CVaR benchmarks on most metrics (Table 8), with lower annualized return, weaker risk-adjusted performance, lower terminal wealth, and the largest maximum drawdown among DMLP-based portfolios—suggesting the DMLP architecture's relatively weaker forecasts limit the framework's effectiveness here.

The CNN-based implementation outperforms the DMLP-based one but trails the LSTM-based one on the main indicators. Per Table 8, it achieves higher annualized return, Sharpe, Sortino, Calmar, and terminal wealth than DMLP, though it does not beat the benchmarks—suggesting CNN forecasts are useful but yield more limited portfolio-level benefits than LSTM.

The LSTM-based DSFE-MSAD framework produces the strongest out-of-sample performance among the three, achieving the highest cumulative net wealth (Figure 7) with comparatively stable growth—consistent with the recurrent structure's effectiveness at modeling persistent temporal dependencies and sequential market dynamics.

Overall, DSFE-MSAD provides a practically implementable downside-risk-aware allocation mechanism that remains competitive under realistic transaction costs. Although it does not universally dominate all benchmarks in cumulative return, it successfully integrates downside forecast uncertainty while maintaining stable, economically meaningful performance across architectures.

• 1. Comparative Analysis of Forecasting Architectures

This section compares DSFE-MSAD economic performance across the deep learning forecasting architectures, focusing specifically on how architecture selection affects allocation efficiency and long-run out-of-sample performance.

Table 9 shows forecasting architecture exerts a substantial influence on DSFE-MSAD performance. Although all architectures generate viable strategies, meaningful differences emerge in cumulative wealth, downside-risk-adjusted performance, turnover, and stability.

The LSTM-based implementation produces the strongest overall performance, achieving the highest annualized return, Sharpe ratio, Sortino ratio, and terminal wealth among DSFE-MSAD portfolios (Table 9). This is economically consistent with the recurrent structure's capacity to capture persistent nonlinear temporal dependencies and evolving market dynamics, translating into more competitive allocation outcomes.

The CNN-based implementation also performs comparatively well: although it does not match LSTM in cumulative wealth, it produces competitive risk-adjusted performance and stable dynamics, consistent with convolutional filters effectively extracting localized nonlinear temporal patterns from OHLCV sequences.

The DMLP-based implementation generates the weakest overall performance, with lower cumulative growth, weaker risk-adjusted performance, and the highest average turnover among the three—consistent with its inferior forecasting accuracy (Section 4.1). Since DMLP does not model temporal persistence, its forecasts appear less effective for dynamic, forecast-driven allocation.

The comparative cumulative net wealth trajectories associated with the three DSFE-MSAD implementations are illustrated in Figure 8.

As Figure 8 shows, the LSTM specification generates the strongest long-run cumulative growth, the CNN implementation shows smoother evolution in several subperiods, and DMLP displays weaker, less stable growth—supporting the conclusion that architectures modeling sequential temporal dependence produce more effective DSFE-MSAD outcomes.

Overall, forecasting architecture selection is a critical determinant of DSFE-MSAD allocation effectiveness, and improvements in forecasting quality materially enhance downside-risk-aware portfolio performance under realistic transaction costs.

Transaction Cost and Turnover Analysis

This section evaluates the effect of proportional transaction costs and turnover on realized performance of DSFE-MSAD and the benchmark strategies, since forecasting-driven models may require frequent adjustments as return expectations and forecast-risk estimates change.

Table 10 reports gross and net performance after 0.1% transaction costs per trade; costs reduce performance across all strategies, with the magnitude varying by turnover intensity.

As expected, the equal-weighted portfolio has the lowest average turnover (0.1877), so cost impact is minimal: annualized return declines only marginally from 23.66% to 23.57%, and terminal wealth from 2.7495 to 2.7392—reflecting its limited need for rebalancing.

The mean–variance portfolios also show relatively low turnover (0.2160–0.2402), so transaction costs have only a modest effect; MAD and CVaR similarly experience moderate turnover and remain attractive after cost adjustments.

By contrast, DSFE-MSAD generates substantially higher turnover: 1.5575 under DMLP, 1.4154 under LSTM, and 1.4013 under CNN—reflecting active adjustment to evolving forecasts and downside forecast-risk estimates.

The higher turnover of the DSFE-MSAD portfolios results in larger transaction-cost effects. For the DMLP-based implementation, annualized return declines from 15.56% to 14.81%, while terminal wealth decreases from 1.9907 to 1.9301 after transaction-cost adjustments. Under the LSTM forecasting architecture, annualized return decreases from 26.94% to 26.19%, accompanied by a reduction in terminal wealth from 3.1135 to 3.0269. Similarly, the CNN-based implementation experiences a decline in annualized return from 19.24% to 18.55%, while terminal wealth decreases from 2.3121 to 2.2485.

Although costs affect DSFE-MSAD more than benchmarks, the reduction remains moderate relative to overall profitability; all implementations continue to generate positive, economically meaningful net returns.

The turnover results also clarify the framework's economic interpretation: unlike approaches relying on historical risk-return characteristics, DSFE-MSAD continuously updates allocations in response to changing forecasts and downside uncertainty, so higher turnover reflects its adaptive, forecast-responsive nature rather than excessive trading.

Overall, DSFE-MSAD remains implementable under realistic trading conditions, though turnover management—via explicit penalties or transaction-cost-aware constraints—represents an important avenue for improving net-of-cost performance.

Statistical Evaluation and Economic Interpretation

The DSFE-MSAD framework produces economically meaningful allocations in this sample, although it does not uniformly beat all benchmarks. Pairwise Diebold–Mariano tests do not reject equal predictive accuracy among the three forecasting architectures. This non-rejection does not prove identical forecasting skill, and portfolio-level differences may reflect forecasting outputs, optimization sensitivity, and estimation variation. Unlike the historical-dispersion benchmarks, DSFE-MSAD penalizes optimistic forecast errors specifically, thereby embedding an asymmetric form of forecast risk in the allocation rule.

The LSTM-based implementation has the strongest realized performance among the reported DSFE-MSAD variants, with the highest cumulative net wealth. This is an economic ranking within the sample, not evidence that LSTM has statistically superior predictive accuracy. DSFE-MSAD portfolios also have higher turnover than the benchmarks and are therefore more sensitive to transaction costs. Conventional MV and CVaR portfolios achieve higher cumulative wealth or risk-adjusted performance on several reported measures. The principal contribution is the direct integration of downside forecast uncertainty into portfolio construction rather than universal return dominance.

Robustness Analysis

To further evaluate stability, additional robustness analyses use alternative forecasting horizons (h=5, h=10, versus the baseline h=1) and bootstrap-based statistical inference. First, the DSFE-MSAD framework's behavior is examined across horizons to test whether relative architecture performance holds beyond the one-day-ahead setting; second, bootstrap confidence intervals assess sampling uncertainty around the reported results.

Robustness across Alternative Forecasting Horizons

Table 11 reports DSFE-MSAD performance under five- and ten-day forecasting horizons, testing whether the relative performance of the architectures remains stable over longer investment horizons.

The relative ranking of architectures remains broadly stable across horizons: LSTM-based DSFE-MSAD delivers the strongest performance in all scenarios. Although performance declines moderately relative to baseline, LSTM consistently achieves the highest annualized returns, strongest risk-adjusted performance, and largest terminal wealth, reaching 2.605 under h=5 and 2.836 under h=10.

CNN also performs well under both horizons: annualized return rises from 18.55% (baseline) to 21.64% under h=5, then declines to 19.02% under h=10, with terminal wealth of 2.542 and 2.292 respectively—reasonably stable, though still below LSTM.

DMLP shows the largest improvement over its baseline as the horizon increases: annualized return rises from 14.81% (h=1) to 18.42% and 18.91% (h=5, h=10), with terminal wealth rising from 1.930 to 2.237 and 2.282—though it still underperforms LSTM.

Figure 9 confirms these patterns visually: LSTM maintains more stable long-run growth, DMLP shows greater variability in several subperiods, and CNN occupies an intermediate position.

Across the reported alternative horizons, DSFE-MSAD remains economically viable and the LSTM implementation retains the strongest within-sample ranking. Because the forecast horizons are shorter than the 60-day holding interval and the intervals overlap substantially, this evidence should be interpreted as a sensitivity analysis rather than proof of architectural superiority.

Bootstrap Confidence Intervals

To further assess reliability, bootstrap confidence intervals are constructed for annualized return and Sharpe ratio, providing a non-parametric assessment of sampling uncertainty without imposing restrictive distributional assumptions.

Table 12 reports 95% confidence intervals across architectures and horizons. Portfolio performance shows meaningful sampling variability; several return intervals include values near zero or moderately negative, reflecting the uncertainty inherent in out-of-sample evaluation.

The LSTM-based portfolios show the most favorable interval characteristics: at h=1, the annualized-return interval is entirely positive (0.0180–0.5577), with Sharpe ratio ranging 0.1921–1.8858; similar patterns hold at h=10, with both intervals strictly positive—supporting the LSTM implementation's stability.

The CNN- and DMLP-based implementations show wider intervals, with some lower bounds slightly below zero, indicating greater sensitivity to alternative return realizations. Still, the baseline ranking holds broadly, with LSTM generally showing the strongest risk-adjusted characteristics.

The bootstrap intervals overlap substantially and therefore do not support statistical dominance by any architecture. The results are best interpreted as evidence of considerable sampling uncertainty around the economic rankings.

Practical Implications

The findings offer five key insights for portfolio managers and quantitative investors integrating machine learning forecasts into portfolio construction:

Forecast uncertainty as economic risk. Rather than a purely statistical concern, DSFE-MSAD treats downside forecast errors as an economically relevant risk source, relaxing the assumption that forecast errors affect outcomes symmetrically.

Forecasting architecture and allocation outcomes. Although the DM tests do not establish significant accuracy differences, the LSTM-linked portfolio has the strongest realized performance among the DSFE-MSAD variants. This is a within-sample economic result and should not be interpreted as proof that recurrent architectures are generally more reliable.

Turnover-cost trade-off. DSFE-MSAD adapts more actively to evolving forecasts, generating higher turnover than benchmarks. Net performance remains attractive after costs, but turnover management—via explicit penalties or constraints—could improve outcomes further.

Sensitivity across horizons. The LSTM-linked implementation remains best ranked in the reported h=5 and h=10 analyses, although these horizons are still shorter than the 60-day holding period and the bootstrap intervals overlap.

Complementary, not universal, tool. Since CVaR remains a strong performer on several metrics, DSFE-MSAD is best viewed as an additional mechanism for incorporating forecast uncertainty—particularly where forecast reliability and downside prediction risk are central—rather than a replacement for established methods.

Conclusion

This study proposed a prediction-driven portfolio optimization framework based on Downside Forecast Error Mean Semi-Absolute Deviation (DSFE-MSAD), a novel downside-risk measure incorporating adverse forecast uncertainty into allocation. Unlike approaches relying exclusively on expected returns and historical risk, the framework recognizes forecasting errors have asymmetric economic consequences and focuses on portfolio-level downside forecast errors.

Three deep learning architectures—DMLP, LSTM, and CNN—were integrated into portfolio construction and evaluated within a rolling walk-forward framework, compared across Equal Weighting (EW), Mean–Variance (MV), Mean Absolute Deviation (MAD), and Conditional Value-at-Risk (CVaR).

The forecasting results show broadly comparable predictive performance across architectures; Diebold–Mariano tests find no statistically significant superiority for any one, so portfolio-level findings should not be attributed solely to forecasting-accuracy differences.

The portfolio results show that incorporating downside forecast uncertainty materially affects allocation and long-run outcomes. The LSTM-based specification consistently delivers the strongest performance—highest annualized return, Sharpe, Sortino, Calmar, and terminal wealth within the DSFE-MSAD group—while CNN is intermediate and DMLP comparatively weaker and more sensitive to fluctuations.

Across the reported five- and ten-day forecast horizons, the within-sample ranking is largely unchanged, with the LSTM-linked implementation leading the other DSFE-MSAD variants. Bootstrap intervals are wide and overlapping, indicating substantial sampling uncertainty rather than statistical dominance.

The transaction-cost analysis shows DSFE-MSAD requires more frequent rebalancing than several benchmarks, raising turnover and implementation costs, though portfolios remain economically viable net of costs—suggesting turnover-control mechanisms as a useful future refinement.

Several limitations should be acknowledged. The analysis covers one equity market and a fixed 25-stock universe; substitutions made to obtain continuous histories may introduce survivorship or selection bias. The 252-day rolling window is small relative to the capacity of the deep networks and may increase overfitting risk. The baseline one-day forecast is used as a signal for weights held until the next 60-day rebalance, so the forecast and holding horizons are not fully aligned. The study does not report a naïve forecasting benchmark, and the λ sensitivity exercise is not documented as using an independent validation period. Bootstrap dependence settings and formal tests of portfolio-performance differences are also not fully reported. These features limit causal attribution and external generalization. Future work should use historical point-in-time constituents, horizon-matched allocation, larger or pooled training samples, nested validation, dependence-aware resampling, and multiple markets or asset classes.

Overall, downside forecast-error information can be incorporated systematically into portfolio optimization. In this empirical sample, DSFE-MSAD produces economically viable portfolios but does not uniformly outperform conventional approaches. The evidence therefore supports the framework as a complementary allocation mechanism whose broader effectiveness requires independent, horizon-matched validation.

Declarations

Author contributions

All authors contributed to the conception and design of the study, interpretation of the findings, critical revision of the manuscript, and approval of the final version. Naji Khaleef Ajeel prepared the initial draft and conducted the empirical analysis. Ali Souri and Ezatollah Abbasian supervised the research and contributed to the methodological development. Eslam Fakher contributed to data curation, validation, and review of the manuscript. All authors agree to be accountable for the work.

Conflict of interest

The authors declare that they have no competing financial or non-financial interests that could have influenced the work reported in this manuscript.

Ethics approval

This study uses secondary, publicly available financial-market data and does not involve human participants, personal data, animals, clinical interventions, or biological materials. Institutional ethics approval was therefore not required.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Data availability

The study uses publicly available market data obtained from the Abu Dhabi Securities Exchange and Investing.com. The processed dataset and analysis code may be made available by the corresponding author upon reasonable request, subject to the terms of the original data providers.