Predicting stock returns with machine learning: Global versus sector models

Witter, Johannes Article Predicting stock returns with machine learning: Global versus sector models Junior Management Science (JUMS) Provided in Cooperation with: Junior Management Science e. V. Suggested Citation: Witter, Johannes (2025) : Predicting stock returns with machine learning: Global versus sector models, Junior Management Science (JUMS), ISSN 2942-1861, Junior Management Science e. V., Planegg, Vol. 10, Iss. 3, pp. 561-581, https://doi.org/10.5282/jums/v10i3pp561-581 This Version is available at: https://hdl.handle.net/10419/326965 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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WELPE HANNES WINNER THOMAS WRONA THOMAS ZWICK Volume 10, Issue 3, September 2025 JUNIOR MANAGEMENT SCIENCE Johannes Witter,Predicting Stock Returns With Machine Learning: Global Versus Sector Models Robin Roskosch, Beware of Bullshit –A Qualitative Study on Young Adults’ Sustainability Awareness of Online Services Nadhilla Mazaya,Board Gender Diversity: Evidence From Indonesia Alexander Sake, Value Creation Opportunities of Generative AI –A Case Study Justus Olbrich, The Effect of Changes in Internal Control Systems on Audit Risk Jan Oliver Horstmann, Mandatory ESG Disclosure and Firm Value –A Quantitative Analysis of the Effect of Directive 2014/95/EU on Firm Value Meret Anna Gläser, Government Interventions During the COVID-19 Pandemic, Culture, and Corporate Cost Behaviour Zewei Shi, Modeling the Impact of Emission Credit Systems on Automotive Product Portfolios: A Mathematical Analysis of Policy Effects in Europe, China, and the U.S. Under Different Demand Scenarios Hagen Alexander Hönerloh, Numerical Studies for the Scheduling of Continuous Annealing Lines Lea Wedel, KPIs for Sustainability: Defining the Strategy for a Sustainable Future in the Insurance Industry 561 582 609 631 657 677 715 748 781 810 Published by Junior Management Science e.V. This is an Open Access article distributed under the terms of the CC-BY-4.0 (Attribution 4.0 International). Open Access funding provided by ZBW. ISSN: 2942-1861 Predicting Stock Returns With Machine Learning: Global Versus Sector Models Johannes Witter Technical University of Munich Abstract Recent studies highlight the superior performance of non-linear machine learning models, such as neural networks, over traditional linear models in predicting cross-sectional stock returns. These models are capable of capturing complex non-linear interactions between predictive signals and future returns. This thesis researches whether sector-specific neural networks can detect sector-related relationships to outperform a global neural network. It evaluates the predictive power of these models at the stock level and in portfolios based on return forecasts, constructing long-short portfolios from the networks’ sorted predictions. A global neural network model trained on the full sample of stocks dominates neural networks trained on individual GICS sectors in predicting the cross-section of US stock returns. Sector-specific neural networks fail to gain an advantage by capturing complex sector-specific interactions. They underperform the global neural network especially in the early out-of-sample period. The smaller sample size for each GICS sector requires a trade-off between model complexity and robust model estimation. Pooling the data for the global model solves this problem and supports the predictive power of neural networks for stock returns. Keywords: cross-section of stock returns; machine learning; neural networks; return prediction; sector models 1. Introduction I compare a global neural network with sector-specific neural networks to predict the cross-section of US stock returns. Therefore, I evaluate the predictive power of the two different models at the stock level and in portfolios constructed based on return forecasts. Recent research demonstrates the ability of non-linear machine learning models such as neural networks to outperform traditional linear models in predicting the cross-section of returns. I show how these neural networks perform better when trained on pooled data across sectors than on sector-specific data from GICS sectors. My data sample covers the sample period from July 1963 to December 2022, with an out-of-sample period from January 1994 to December 2022. The global neural I would like to express my gratitude to all the people who have supported me in the realization of this thesis. In particular, I would like to thank my supervisor, Dr. Matthias Hanauer, for giving me the opportunity to work on this interesting topic and for his guidance and inspiration throughout the work on my thesis. network achieves a higher positive out-of-sample R2 OOS than the sector models, which underperform a naive forecast of zero. For long-short portfolios based on the sorted predictions of the neural networks, the global model outperforms the sector models in terms of generated monthly returns and Sharpe ratio. The comparison of sector neural networks with simple OLS models highlights the necessary trade-off between estimating a stable model without overfitting and capturing complex sector-specific interactions. I follow the machine learning training approach of Gu et al. (2020). I train neural networks with three hidden layers on 212 stock-specific signals from prior literature to predict the cross-section of returns for the US stock market. The neural networks are trained using a recursive scheme with increasing training samples and a fixed size rolling sample for validation. I refit all models once per year in December and predict monthly out-of-sample returns over the following year. In total, I train eleven different neural network models. A global model is trained on the full sample of stocks. The DOI: https://doi.org/10.5282/jums/v10i3pp561-581 © The Author(s) 2025. Published by Junior Management Science. This is an Open Access article distributed under the terms of the CC-BY-4.0 (Attribution 4.0 International). Open Access funding provided by ZBW. J. Witter /Junior Management Science 10(3) (2025) 561-581562 sector model consists of ten sector-specific neural networks trained on subsets of the sample data filtered for each of the ten sectors defined by the Global Industry Classification Standard (GICS). To assign stocks to sectors, I use existing data on GICS classifications and a custom mapping from the Standard Industrial Classification (SIC) system to GICS sectors. First, I evaluate the two models on their the out-of-sample predictive performance for individual stock return forecasts. The global model outperforms the sector models in all individual GICS sectors and in the full sample. The global neural network produces a monthly R2 OOS of 3.37% in the full sample and a positive R2 OOS for each of the ten sectors. The sector models achieve a monthly R2 OOS of -6.06% in the full sample, so they underperform a naive forecast of zero for all monthly stock returns. Sector models perform particularly poorly in predicting stock returns in sectors with small sample sizes. To understand the differences in predictive performance, I examine the importance of each input variable in predicting returns with the neural network models. Variable importance is determined by the reduction in R2 OOS that results from setting all values of a particular signal to zero while holding all other model estimates fixed. The different models share most of their most important variables. Analogous to Blitz et al. (2023), Size is the most influential signal in predicting returns in the global model and in most sector models. The neural networks tend to perform well in out-of-sample return forecasting when their relative importance is skewed towards Size. Sector models with a broader set of influential characteristics underperform out-of-sample. I compare the profitability of portfolios based on the sorted predictions of the global model with the sector models. At the end of each month, I sort the stocks into decile portfolios and calculate the value-weighted returns of holding the decile portfolios over the next month. A long-short portfolio buys stocks with the highest expected returns and sells those with the lowest. Portfolio strategies based on the out-of-sample predictions of the global model outperform the sector-specific models. A long-short portfolio based on the global model’s forecasts achieves an average monthly out-of-sample return of 2.71% and an annualized Sharpe ratio of 2.07. A long-short portfolio based on the forecasts of the sector models generates an out-of-sample monthly return of 0.99% and an annualized Sharpe ratio of 1.14. The outperformance of the global neural network is particularly strong in the early years of the out-of-sample period. During this period, the global model achieves its highest returns while the sector models struggle to remain profitable. The sector-specific neural networks continue to underperform when compared to simple ordinary least squares (OLS) models. A long-short portfolio based on the sorted predictions of the OLS sector models generates a higher valueweighted return than the sector neural networks. However, the OLS outperformance comes only from the first half of the out-of-sample period when less training data is available. Small sector sample sizes require a trade-off between stable model estimation and capturing complex sector-specific interactions. The global neural network trained on pooled data significantly outperforms the OLS models. The global neural network shows some out-of-sample sector allocation power. In the cross-section of sectors, it correctly predicts higher relative returns for the most profitable sectors and lower returns for the least profitable sectors. As a result, the returns generated by the global model are lower with sector-neutral portfolios. Section 2reviews the recent literature on machine learning for return forecasting and global versus industry-specific models. Section 3presents the sources of stock data and input signals for return prediction and explains the sector classifications. Section 4describes the methodology used to train neural networks for return prediction and to construct portfolios based on these predictions. Section 5presents the results of comparing the forecasting performance of the global model with the sector models. Section 6concludes. 2. Literature review The past decades produced a variety of literature focusing on predicting the cross-section of stock returns. Authors explore a variety of variables in linear models, but there is still a lack of consensus regarding which variables are related to expected stock returns. This problem is often referred to as factor zoo. Linear models cannot deal with many variables and their potential nonlinearities and interactions. Therefore, recent research focuses on more complex machine learning models to handle the high dimensionality in the factor zoo. Early literature focuses on single machine learning models and their ability to outperform traditional methods. Moritz and Zimmermann (2016) propose tree-based conditional portfolio sorts as a machine learning approach. In their models, recent past returns within the last six months predict future returns and outperform linear models like Fama-MacBeth regressions. Excess returns persist even after accounting for transaction costs and common risk factors. Traditional methodologies with linear assumptions fail to capture a nonlinear relationship between past and future returns. A nonparametric model using adaptive group least absolute shrinkage and selection operation (LASSO) isolates relevant predictors in a high-dimensional setting in Freyberger et al. (2020). A small subset of variables, including size, total volatility, and recent return-based metrics, provide unique predictive power. Their model significantly outperforms linear approaches like those of Lewellen (2015) with higher out-of-sample Sharpe ratios. The nonparametric model selects fewer variables in-sample than the linear models but captures nonlinear interactions. Gu et al. (2020) are among the first to present a comparative analysis of machine learning models for predicting stock returns. Their models agree on a small set of dominant variables, with price trends, liquidity, and volatility as the most influential predictors. Neural networks perform the best among all machine learning models, and portfolios sorted on neural network return predictions double the J. Witter /Junior Management Science 10(3) (2025) 561-581 563 Sharpe ratios of linear models. Shallow neural networks outperform deeper ones due to the limited data and low signalto-noise ratio in empirical asset pricing. Interactions and nonlinear relations between variables drive the outperformance of machine learning methods. Azevedo and Hoegner (2023) report similar results with tree-based and neural network approaches. Their machine learning methods uncover interaction effects challenging traditional risk-based explanations in asset pricing. Neural network models utilize 299 stock market anomalies to achieve monthly out-of-sample returns 1% higher than a linear benchmark. Linear regressions are easy to interpret but underperform their machine learning models using statistical significances and returns. Most recent literature uses technically more advanced machine learning strategies. Azevedo et al. (2024) examine the expected returns of deep learning strategies. Their long short-term memory (LSTM) models yield net returns of up to 1.42% per month, even after accounting for the recent era of high liquidity, transaction costs, and post-publication decay. Strategies combining several machine learning models constantly achieve significant returns after cost. Cost mitigation techniques reduce turnover and trading costs but do not improve net performance. L. Chen et al. (2024) combine three deep neural network models with no-arbitrage constraints to estimate asset pricing models for US stocks. Incorporating specific domain knowledge into the technical implementation enhances prediction accuracy and out-of-sample performance. Their deep learning strategies with no-arbitrage constraints outperform other machine learning benchmarks in Sharpe ratio and identify the core variables driving asset prices. Other research focuses on using machine learning to predict stock returns not only in the US but globally. Tobek and Hronec (2021) aggregate 153 anomalies across global markets into one mispricing signal using machine learning. Their strategy outperforms linear models out-of-sample in various international markets. Extending the training sample with international data does not improve out-of-sample performance for the US market. However, machine learning models trained on US stocks perform well in markets outside the US. Cakici et al. (2023) investigate machine learning’s cross-sectional return predictability across 46 global stock markets. Combining predictions from multiple machine learning models delivers robust out-of-sample returns across diverse markets. Developed markets show higher profitability than emerging ones. Firm size and idiosyncratic risk are the most important variables for predictions, with higher returns in smaller firms and markets with more idiosyncratic risk. Azevedo et al. (2023) also focus on the out-of-sample performance of different machine learning models across an international data sample. Neural networks and composite predictors perform the best. These models achieve significant monthly long-short returns of around 2%. Portfolio returns remain significant even after transaction costs and outperform linear benchmark models. Drobetz and Otto (2021) use machine learning strategies to predict European stock returns. Like in the US market, machine learning models outperform traditional linear models by capturing nonlinearities and variable interactions. Neural networks and classification-based approaches perform best and generate significant returns even after transaction costs. Support vector machines, which classify stocks into decile portfolios, deliver even higher returns by eliminating the noise of expected returns at the stock level. Leippold et al. (2022) apply machine learning models to the Chinese stock market. In a market dominated by retail investors, liquidity and volatility indicators have predictive power over traditional variables like valuation ratios. Neural networks perform best, particularly for small-cap and non-state-owned firms. They achieve higher predictability in China than in the US due to distinct asset pricing dynamics driven by local investor behavior. Hanauer and Kalsbach (2023) assess various machine learning models for predicting stock returns in a broad sample of emerging markets. Like in developed markets, their models identify nonlinearities and interactions among variables. Tree-based methods and neural networks deliver superior long-short returns and alphas over linear models. Efficient trading rules ensure machine learning predictions outperform even after transaction costs, short-selling constraints, and limiting the sample to big stocks. Despite the strong performance of machine learning models for stock market prediction, there are still problems in implementing them in practice. Rasekhschaffe and Jones (2019) focus on mitigating overfitting in machine learning models. Feature engineering and forecast combinations decrease the risk of overfitting. These techniques increase the signal-to-noise ratio and produce more robust predictions. Avramov et al. (2023) criticize high limits-to-arbitrage environments and exclude stocks like microcaps and distressed firms. Machine learning portfolios often rely on long and short positions that are impossible in practice. The profitability of machine learning strategies is reduced when trading costs are considered due to high turnover. The authors propose including trading costs in machine learning models and imposing economic restrictions. Blitz et al. (2023) report the impact of varying prediction horizons in machine learning models for stock return predictions. While one-month forecasts yield high gross returns, the net returns considering transaction costs are minimal after 2004. Machine learning models with longer prediction horizons provide significant net alpha due to reduced portfolio turnover. One-month forecasts rely on short-term price signals, whereas longer horizon predictions rely more on value-oriented signals. Aligning the design of machine learning models with trading horizons enhances profitability through reduced turnover and better after-cost performance. In this thesis, I focus on sector-specific versus global machine learning models. Therefore, it is appropriate to consider prior research on the relation between industryspecific and market predictions. This includes traditional methods of predicting the cross-section of stock returns, like factor investing and other linear regression models. Kim et al. (2013) enhance the linear residual income model (RIM) with industry-specific factors using the value-to-book (V/B) J. Witter /Junior Management Science 10(3) (2025) 561-581564 ratio. Decomposing V/B into industry-specific components better predicts future abnormal returns and outperforms traditional RIM implementations. Their industry-adjusted RIM model provides superior predictive accuracy for abnormal returns compared to conventional valuation measures. Liu et al. (2014) analyze the predictive power of industry effects in option-implied volatility measures on stock returns. Industry-neutral portfolios outperform full-universe portfolios with higher Sharpe ratios and lower downside risk. Cavaglia et al. (2006) explore region-neutral and industryneutral value portfolios. Industry-neutral portfolios offer more stable returns and higher information ratios due to lower volatility and less cyclicality. They capture the global value premium more effectively and provide a better riskreturn profile. Modern machine learning models also capture economically meaningful interdependencies among industries. Rapach et al. (2019) examine cross-industry return predictability with machine learning models like LASSO. Due to gradual information diffusion, lagged returns from industries like financial and commodity sectors can predict returns in other sectors. An industry-rotation strategy based on these crossindustry signals outperforms linear methods. Ciner (2019) uses a random forest model as a machine learning strategy to predict market returns with industry returns. Industry returns provide significant out-of-sample predictive power for the market index. Random forests outperform traditional linear models due to their capacity to capture both linear and non-linear dynamics. Industry-level information forecasts market movements in a way that linear models fail to capture. This thesis extends the existing literature on machine learning in empirical asset pricing by integrating it with industry-specific strategies. Building upon the work of Gu et al. (2020), I use neural networks as well-performing machine learning models to forecast the cross-section of stock returns for the US market. I compare long-short portfolio returns achieved by sector-specific models with those of a global model. 3. Data 3.1. Stock data My sample includes all US stocks listed on the NYSE, AMEX, and NASDAQ. The sample period runs from July 1963 to December 2022. I source equity returns and other stock market data from CRSP. Accounting data to replicate the Fama and French (2015) five-factor model is from Compustat. I calculate monthly excess returns as the one-month stock return from CRSP over the risk-free rate provided on Kenneth R. French’s homepage.1To predict the cross-section of stock returns, I subtract the monthly cross-sectional median excess 1See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_lib rary.html (2024). return from the monthly excess return for each stock. “Returns” throughout this thesis denote these relative monthly stock returns with the market component already removed. The input variables to the machine learning models come from A. Y. Chen and Zimmermann (2022). I download the August 2023 version of signals from their Open Source Asset Pricing (OSAP) website.2This includes 209 firm-level characteristics replicated from the academic asset pricing literature. I use the terms variables, signals, and characteristics interchangeably throughout this thesis. In addition to the 209 signals from the OSAP data, I define three input variables from CRSP data. Short-term reversal is the prior one-month return, Price is the natural logarithm of the CRSP price data field, and Size is the natural logarithm of the price multiplied by the shares outstanding. All input variables are signed so that higher values correspond to higher expected returns. Following Gu et al. (2020), Blitz et al. (2023) and other recent literature, I rank all input variables cross-sectionally for each month into the interval of [-1,1]. This helps neural network models deal with varying ranges of values and different variances across the signals during training. Missing values are filled with the monthly cross-sectional median rank. I follow Hou et al. (2020) and Blitz et al. (2023) and exclude microcaps from my sample to prevent them from driving my results. I define microcaps as all stocks with a monthly market capitalization below the 20th percentile of the NYSE market capitalization in that month. After excluding microcaps, my full sample from July 1963 to December 2022 includes approximately 1.3 million monthly stock observations with a monthly average of 1842 stocks. 3.2. Sector data To train sector-specific machine learning models, I assign all stocks in my sample to sectors according to the Global Industry Classification Standard (GICS) from MSCI and S&P. I categorize stocks into ten sectors defined by GICS: Energy, Materials, Industrials, Consumer Discretionary, Consumer Staples, Health Care, Financials, Information Technology, Communication Services, and Utilities. Due to the small number of observations, I include the Real Estate sector in the Financials sector. This corresponds to the GICS classification before 2016, better representing the biggest part of my sample period. I prefer the GICS over the Standard Industrial Classification (SIC) system often used in other literature on industry specifics. The GICS is the more modern industry taxonomy with a stronger focus on new industries like the computer, software, and information technology sectors. I source data on SIC industry classification from CRSP and data on GICS sector classification from Compustat. GICS data has weaker coverage than SIC data, particularly from 2See https://www.openassetpricing.com/august-2023-data-release/ (2023). J. Witter /Junior Management Science 10(3) (2025) 561-581 565 the beginning of my sample until 1985. Therefore, I develop a mapping from SIC industries to GICS sectors described in Table 1. If a monthly stock observation is not assigned to a sector under GICS but to a SIC industry, I fill in the missing GICS classification based on the mapping in Table 1. The mapping is based on two different inputs. First, I consider overlaps between the SIC and GICS classifications for stock observations with both data points in my sample. For example, 90% of all stocks classified as Financials in SIC are also classified as Financials in GICS. Similarly, over 80% of all stocks classified as utilities in SIC are also classified as Utilities in GICS. Second, I consider the definitions of the industry taxonomy in both classification systems.3For example, SIC includes transportation, communications, electric, gas, and sanitary services in one Division. GICS classifies Transportation as an industry group in the sector Industrials, communications belong to the sector Communication Services, and electric, gas, and sanitary services belong to the sector Utilities. This enables me to map the corresponding SIC major groups to the GICS sectors. Table 1includes the ten GICS sectors used for sectorspecific machine learning models. It summarizes all SIC digit codes and the corresponding industry description mapped to each GICS sector. For example, I map the SIC codes 12001399 (Major Group Coal Mining and Major Group Oil And Gas Extraction) and 2900-2999 (Major Group Petroleum Refining And Related Industries) to the GICS sector Energy. The SIC industries mapped to a GICS sector can be either entire Divisions (determined by a capital letter) or more detailed Major Groups (determined by the first two digits) and Industry Groups (determined by the first three digits). If I recognize no clear relationship between a SIC industry and GICS sectors, then I don’t include this SIC industry in the mapping. A stock with missing GICS data and a SIC code not contained in the mapping will not be assigned to a GICS sector. The same happens to stocks with missing data for both classification systems. After applying the mapping, 15,239 out of 1.3 million monthly stock observations in the full sample are not assigned to a GICS sector. They are included in the training data for the global neural network but not in the training data for the sector-specific neural networks. 4. Methodology 4.1. Return prediction using machine learning My methodology follows Gu et al. (2020) and Hanauer and Kalsbach (2023), with the difference that I train one global model and one sector-specific model for each of the ten GICS sectors. I aim to predict the cross-section of US stock returns, so I forecast the outperformance of a stock relative to the US stock market. The relative return of a stock is defined as 3See https://www.msci.com/our-solutions/indexes/gics for GICS definitions and https://www.osha.gov/data/sic-manual for SIC definitions. rrel i,t=ri,t−Mktt, (1) where ri,tis the excess return of stock iin month tand Mktt is the cross-sectional median excess return across all stocks in the sample in month t. I describe the one-month-ahead relative return of a stock rrel i,t+1as an additive prediction error model: rrel i,t+1=Etrrel i,t+1|xi,t+εi,t+1. (2) Et[rrel i,t+1|xi,t]is the conditional expected relative return of stock iin month tfor month t+1. It is conditional as it depends on xi,t∈Rp, a vector of stock-specific pinput variables known at month t.εi,t+1is the prediction error term. I estimate the expected relative return with the unknown function f∗,f∗:Rp→R. It estimates the expected return depending only on the vector of pstock-specific input variables available in month t: Etrrel i,t+1|xi,t=f∗(xi,t). (3) In the case of neural networks, the unknown function f∗(x)is approximated by a nonlinear function f(x,θ,ρ). This function is parametrized by a vector of coefficients θ and a set of hyperparameters ρ. When training neural networks, the coefficients θare estimated from the training data with respect to the hyperparameters ρand a predefined loss function L. The hyperparameters ρare optimized concerning the loss function Lbased on the estimated coefficients θ and available data. Neural networks as a form of supervised machine learning outperform linear models in prior literature (Azevedo & Hoegner, 2023; Gu et al., 2020). Therefore, I choose threelayer neural networks as the machine learning model for this thesis. Appendix A4 describes the model architecture and hyperparameters used to train the neural networks. In addition, I later use ordinary least squares (OLS) models as a benchmark for sector-specific neural networks. The global neural network model takes the full sample of 1.3 million monthly stock observations as input. The sectorspecific machine learning models for the ten GICS sectors take all monthly stock observations assigned to the respective GICS sector as input. Therefore, the samples used to train the sector-specific neural networks differ significantly in their number of observations, depending on the sector’s size. To avoid data leakage, I divide all input samples into three disjoint time periods, which always keep the temporal ordering of the data: the training, validation, and testing samples. First, I estimate the neural network coefficients for a range of hyperparameter values on the training sample. The validation sample compares the loss function results for each set of hyperparameters based on the estimated model from the J. Witter /Junior Management Science 10(3) (2025) 561-581566 Table 1: Mapping of SIC to GICS industries This table maps industries classified under the Standard Industrial Classification (SIC) system to sectors classified under the Global Industry Classification Standard (GICS) system used in this thesis. The first column contains the 11 different sectors of the GICS system. Throughout this thesis, the 11th sector, Real Estate, is not considered separately, but is included in the Financials sector. The second and third columns contain the SIC industries mapped to the GICS sector in the first column. The second column contains the SIC digit code, and the third includes the corresponding industry description. The SIC industries mapped to a GICS sector can be either entire Divisions (determined by a capital letter) or more detailed Major Groups (determined by the first two digits) and Industry Groups (determined by the first three digits). This mapping is used to classify individual stocks into sectors when GICS sector information is unavailable in Compustat. If a SIC industry classification is available, the GICS sector is added according to this mapping. If no SIC classification is available either, the GICS sector value is ’Missing’, and the stock is not included in the training data for the sector models. GICS Sector SIC Code SIC Description 10 - Energy 1200–1399 Coal Mining and Oil/Gas Extraction 2900–2999 Petroleum Refining and Related Industries 15 - Materials Division B 1000–1499 (excluding 1200–1399) Mining (excluding Coal Mining and Oil/Gas Extraction) 2400–2499 Lumber and Wood Products, Except Furniture 2600–2699 Paper and Allied Products 3300–3399 Primary Metal Industries 20 - Industrials Division C 1500–1799 Construction Division E 4000–4999 (excluding 4800–4999) Transportation (excluding Communications and Utilities) Division J 9100–9999 (excluding 9900–9999) Public Administration (excluding Nonclassifiable Establishments) 3400–3499 Fabricated Metal Products, Except Machinery and Transportation Equipment 3500–3599 Industrial and Commercial Machinery 7320–7329 Credit Reporting and Collection 7340–7349 Services to Dwellings and Other Buildings 7360–7369 Personnel Supply Services 7390–7399 Miscellaneous Business Services 7500–7599 Automotive Repair Services and Parking 7600–7699 Miscellaneous Repair Services 8710–8719 Engineering Architectural and Surveying Services 8740–8749 Management and Public Relations 8900–8999 Services Not Elsewhere Classified 25 - Consumer Discretionary Division G 5200–5999 (excluding 5400–5499) Retail Trade (excluding Food Stores) Division F 5000–5199 (excluding 5140–5189, 5180–5189) Wholesale Trade (excluding Groceries and Beer, Wine, and Distilled Alcoholic Beverages) 1500–1599 Building Construction General Contractors and Operative Builders 2200–2299 Textile Mill Products 2300–2399 Apparel and Other Finished Products Made from Fabrics and Similar Materials 2500–2599 Furniture and Fixtures 3100–3199 Leather and Leather Products J. Witter /Junior Management Science 10(3) (2025) 561-581 567 Table 1— continued GICS Sector SIC Code SIC Description 25 - Consumer Discretionary 3900–3999 Miscellaneous Manufacturing Industries 7000–7099 Hotels, Rooming Houses, Camps, and Other Lodging Places 7200–7299 Personal Services 7800–7899 Motion Pictures 7900–7999 Amusement and Recreation Services 30 - Consumer Staples Division A 0100–0999 Agriculture, Forestry, and Fishing 2000–2199 Food Products and Tobacco Products 5140–5159 Wholesale Trade - Groceries 5180–5189 Wholesale Trade - Beer, Wine, and Distilled Alcoholic Beverages 5400–5499 Food Stores 35 - Health Care 2800–2899 Chemicals and Allied Products (including Drugs) 3840–3849 Surgical Medical and Dental Instruments and Supplies 3850–3859 Ophthalmic Goods 8000–8099 Health Services 8300–8399 Social Services 8730–8739 Research Development and Testing Services 9900–9999 Nonclassifiable Establishments 40 - Financials Division H 6000–6799 Finance, Insurance, and Real Estate 45 - Information Technology 3570–3579 Computer and Office Equipment 3600–3699 Electronic and Other Electrical Equipment and Components 3820–3829 Laboratory Apparatus and Analytical Optical Measuring and Controlling Instruments 7370–7379 Computer Programming Data Processing 50 - Communication Services 4800–4899 Communications 55 - Utilities 4900–4999 Electric, Gas, and Sanitary Services 60 - Real Estate Included in GICS sector 40 - Financials training sample. The optimal hyperparameter set minimizes the loss function on the validation sample and is then used to retrain five different neural networks on the training sample. I use these five models to predict the monthly returns for the test sample. The final prediction for each stock is the average over the five individual model predictions to reduce the variance in single forecasts. Following the training approach as in Gu et al. (2020) and Blitz et al. (2023), I retrain the models once at the end of every year but predict every month using the latest model and data. The first 18 years of my sample (July 1963 to December 1981) are the first training sample, and the next 12 years (January 1982 to December 1993) the first validation sample. The first one-year test sample is the following 12 months, so the first out-of-sample (OOS) prediction is made for January 1994. To predict the monthly returns from January 1995 to December 1995, I extend the training sample by one year (July 1963 to December 1982) and roll forward the validation sample by one year (January 1983 to December 1994). I repeat this procedure for each year in my sample. No future information is leaked from a previous period. To evaluate the predictive performance for individual stock return forecasts on the test sample, I use the pooled out-of-sample R2 OOS defined by Gu et al. (2020): R2 OOS =1−PT tPN irrel i,t−ˆ rrel i,t2 PT tPN irrel i,t2. (4) This metric compares the out-of-sample forecasts with a naive forecast of zero, better suited to individual return predictions than the typical forecast with mean returns. J. Witter /Junior Management Science 10(3) (2025) 561-581568 4.2. Variable importance As a primary measure to interpret the results of the machine learning models, I rank the respective input variables according to their variable importance. This aims to identify characteristics that influence the cross-section of expected returns. Following Gu et al. (2020) and Blitz et al. (2023), I define variable importance as the reduction in panel predictive out-of-sample R2 OOS. For each annually trained neural network, I iteratively set the values for each input variable to zero while holding the model estimates fixed. In each iteration, I predict new monthly returns for the respective oneyear test sample and calculate the change in out-of-sample R2 OOS. I use the average variable importance across each annually trained model to rank each feature where rank one is the most important characteristic. To determine the relative importance of individual variables for the performance of each model, I normalize variable importance within a model to sum to one. If setting a signal to zero increases the panel predictive out-of-sample R2 OOS, the variable importance measure for that signal is negative. Therefore, the normalized variable importance of other signals within a model can be greater than 1. 4.3. Machine learning portfolios Portfolio performance is my primary metric for evaluating the forecast performance of machine learning models. At the end of each month, each model produces a prediction of a stock’s next month’s relative return ˆ rrel i,t+1. Based on these forecasts, I sort stocks from highest to lowest predicted return and assign them into decile portfolios using NYSE breakpoints.4I reassign and rebalance portfolios at the end of each month. I compute value-weighted returns from holding the decile portfolios over the next month to avoid small stocks driving the results. Finally, I construct a zero-net investment (long-short) portfolio that goes long in the highest decile portfolio (decile 10) and short in the lowest decile portfolio (decile 1). I evaluate the predictive performance of three different machine learning strategies. The first strategy forms decile portfolios based on the predictions of the global neural network model. The second strategy forms decile portfolios with sector-neutral portfolio sorts based on the global neural network model predictions. This means each sector gets individual breakpoints for the decile sorts. The third strategy forms decile portfolios based on the predictions from the sectorspecific neural networks. First, I perform portfolio sorts for each sector individually based on the respective model forecasts. Then, I combine the sector-specific decile portfolios into single decile portfolios. For example, the top decile portfolio for month tcontains all stocks from the ten top decile portfolios across all sectors in month t. 4Breakpoints for the decile sorts are first determined using only stocks listed on the NYSE. All stocks are then sorted into decile portfolios based on these breakpoints, regardless of which exchange they are listed on. As the NYSE contains stocks with larger average market capitalizations, this reduces the influence of small stocks on the portfolio sorts. To compare the results of the three neural network portfolio sorts, I provide each decile portfolio’s average predicted returns, realized returns, and Sharpe ratios. I compute mean returns and associated t-statistics for the long-short portfolios of each machine learning strategy. To benchmark the longshort returns, I consider the adjusted R2-value and alphas from the Capital Asset Pricing Model (CAPM) and Fama and French (2015) five-factor model with their associated Newey and West (1987) adjusted t-statistics using six lags. The factors are based on the same sample of 1.3 million monthly stock observations as the neural network portfolios. Finally, I benchmark the predictive performance of the sector-specific neural networks with OLS models in Section 5.4. The portfolio sorts work similarly but are based on predictions from sector-specific OLS models. All sector models mentioned outside of Section 5.4 always refer to sector-specific neural networks. 5. Empirical results 5.1. Prediction performance The global neural network dominates the sector-specific neural networks in out-of-sample predictive performance for individual stock return forecasts. On the full sample over the out-of-sample period from January 1994 to December 2022, the global model achieves a monthly R2 OOS of 3.37%. The sector models achieve a monthly R2 OOS of -6.06%, so they underperform a naive forecast of zero for all monthly stock returns. Across all ten GICS sectors, the global model outperforms the respective sector model. Sector models perform particularly worse for sectors with only a small sample size. Table 2compares the monthly out-of-sample stock-level prediction performance across all ten GICS sectors between the global model and the ten sector-specific models. The sector performance for the global model is determined by filtering the out-of-sample predictions of the global neural network for the respective sector stocks. In addition, Table 2includes the average monthly observations per sector over the full sample period from July 1963 to December 2022. This demonstrates the sample size for each sector. The global model produces positive R2 OOS statistics across all individual sectors. Taking the full sample of stocks, the global model achieves a R2 OOS of 3.37%. Therefore, the predictions consistently outperform a naive forecast of zero to all stocks in all months over the out-of-sample period. Except for Utilities, the R2 OOS statistics for all sectors are larger than 2%. Over six out of ten sectors the global model produces R2 OOS above 3%, with the highest value at 4.57% for the sector Health Care. Utilities appear to be an outlier with 0.11%, more than an order of magnitude smaller than the R2 OOS for all other sectors. There is no correlation between the sectors’ sample size and the predictive performance of the global neural network. The model achieves a R2 OOS of 3.11% on Communication Services, the sector with the smallest sample size and only an average of 58 stocks per month in the sample. This is more than the 2.26% for Financials, the biggest sector J. Witter /Junior Management Science 10(3) (2025) 561-581 575 Table 4: Statistics of neural network long-short portfolios This table summarizes the out-of-sample statistics of the value-weighted long-short portfolios formed from different neural network model return predictions. All stocks are sorted into decile portfolios based on their predicted relative returns (with the market component removed) for the next month. A long-short portfolio buys the highest expected return stocks (decile 10) and sells the lowest (decile 1). Results are reported for the global model, the global model with sector-neutral portfolio sorts, and the sector models. Panel A presents the average value-weighted monthly full sample mean return and average monthly sub-sample mean returns with associated t-statistics (t-stat). Panel B reports the average CAPM alphas and average Fama and French (2015) five-factor model (FF5) alphas, corresponding Newey and West (1987) adjusted t-statistics with six lags (t-statα), and corresponding R2. The sample consists of US CRSP stocks, excluding microcap stocks with a market capitalization smaller than the 20th percentile of stocks listed on the NYSE. The sample runs from January 1994 to December 2022. Global model Global model + sector-neutral sorts Sector models Panel A: Percentage returns Mean 1994–2022 2.71 2.08 0.99 t-stat 11.16 10.36 6.14 Mean 1994–2008 3.24 2.66 0.70 t-stat 9.55 9.08 3.06 Mean 2009–2022 2.14 1.46 1.29 t-stat 6.24 5.49 5.80 Panel B: Risk-adjusted performance CAPM alpha (%) 2.57 2.00 0.98 t-statα8.80 9.55 5.78 R20.03 0.02 -0.003 FF5 alpha (%) 2.44 1.90 0.85 t-statα8.80 8.78 5.98 R20.14 0.12 0.04 mance is significantly more substantial in the first half of the out-of-sample period, when it earns more than four times as much as the sector neural networks. The global model performs better from 1994 to 2008 with a 3.24% monthly long-short return and an associated t-statistic of 9.55 compared to a 2.14% return from 2009 to 2022 with an associated t-statistic of 6.24. This is analogous to the results of Blitz et al. (2023), who find a weaker outof-sample performance for machine learning models in their later subsample after 2004. They base this result partly on the strength of the Size factor over different time periods. Size is the most important predictor for returns in my global neural network. According to Blitz et al. (2023), the stronger performance of the global model in the earlier subsample can be attributed to the excellent performance of the Size factor in earlier periods. The Size factor starts to perform worse in the last 20 years, which weakens the profitability of the global neural network in the second subsample. The long-short portfolio based on the sorted predictions of the sector models underperforms the global model, particularly in the first half of the out-of-sample period. It achieves a monthly mean return of 0.7% with an associated t-statistic of 3.06. Although still less profitable than the global model, the sector-specific neural networks improve in the second subsample with an average return of 1.29%. Associated tstatistics are not far apart, with 5.80 for the sector models and 6.24 for the global model. Therefore, both strategies are similar in risk-return profile over the second half of the outof-sample period. Two factors can drive the improved performance of the sector models in the later period of the sample. First, not all sector neural networks rely on Size as an essential signal to the same extent as the global model. Therefore, their profitability is not as dependent on the performance of the Size factor. Second, in the earlier part of the sample, the training samples for the sector-specific neural networks are tiny, with a very low observations-to-parameters ratio. This makes it more challenging to estimate coefficients in a neural network without overfitting on the training data. Table A1 in the Appendix reports the out-of-sample performance of individual GICS sector long-short portfolios based on the sorted predictions from the ten sector-specific neural networks. Panel B of Table 4summarizes the risk-adjusted performance of the long-short portfolios for each strategy based on factor pricing models. I report alphas on top of the Capital Asset Pricing Model (CAPM) and the Fama and French (2015) five-factor model (FF5) with associated Newey and J. Witter /Junior Management Science 10(3) (2025) 561-581576 West (1987) adjusted t-statistics with six lags (t-statα) and adjusted R2with respect to each factor model. The risk-adjusted performance yields similar results as the raw long-short returns with a superior global model. All three neural network strategies achieve statistically significant alphas with t-statistics ranging from 5.78 for the sector models on the CAPM to 9.55 for the global model with sector-neutral portfolio sorts on the CAPM. The global model produces the highest alphas, with 2.57% on the CAPM and 2.44% on FF5. The sector-neutral portfolio sorts slightly lower the alphas of the global model to 2.00% on top of the CAPM and 1.90% on top of FF5. The sector-specific models span the lowest alphas, with 0.98% on the CAPM and 0.85% on FF5. The CAPM barely has any explanatory power on the average long-short returns of neural network forecasts, with R2never exceeding 0.03 for the global model. The five-factor model explains as much as 14% of the variation in the longshort portfolio based on the global model’s forecasts. Unsurprisingly, the Size factor is the statistically most significant factor in regressions of portfolio returns on the five-factor model for all neural network strategies. The results of Tables 3and 4are illustrated in Figure 3. It plots the cumulative log returns of the value-weighted long and short sides for the three neural network strategies in the out-of-sample period. The long side buys the stocks in the highest decile portfolio and the short side sells the lowest decile portfolio. Therefore, returns on the short portfolio are the relative returns of the lowest decile stocks multiplied by -1. The cumulative performance is cut off in December 2008 and restarted in January 2009 to present differences in cumulative returns between the two halves of the out-of-sample period. The global model consistently dominates the sector models over time. However, its outperformance is mainly in the first half of the out-of-sample period and tapers off thereafter. The cumulative returns of all three strategies follow similar patterns in the second half of the out-of-sample period. The long-short spreads are still larger for the global neural network after 2008, but the magnitude of the returns relative to the sector models is smaller. Sector-neutral portfolio sorting prevents the global model from outperforming the sector neural networks in the second half of the out-of-sample period. The performance of long-short portfolios for the global model is not predominantly based on the short side, which would raise questions about practical implementation due to shorting frictions. The return series of the global model’s long portfolio is strong initially and starts to shift after 2000. It still delivers positive results, but with higher volatility, the overall magnitude of relative returns is lower. The stocks in the top decile of the global neural network’s forecasts cumulate double the returns in the eight years from 1994 to 2001 than in the following seven years. The second half of the out-of-sample period from 2009 to 2023 accumulates roughly the same returns as the first eight years. Apart from the shift in the return series during the dot-com bubble crash in 2001, global shocks such as the financial crisis of 2008 and 2009 or the COVID-19 pandemic in early 2020 did not cause significant portfolio downturns. The short side of the global model generates positive returns but underperforms the long portfolio in both subsamples. Its positive performance is mainly due to the dotcom bubble crash from 2000 to 2002. Apart from this period, cumulative returns increase only slightly or move sideways over extended periods in the plot. The long and short sides of the portfolios for the global model with sector-neutral portfolios generally follow the same pattern. The magnitude of returns and the long-short spread are smaller. The shift in the return series after 2000 is more pronounced, and the dot-com bubble crash causes a portfolio downturn. The top and bottom decile portfolios based on the sorted predictions of the sector neural networks do not perform well in the first half of the out-of-sample period. The long portfolio generates no significant returns after 1999 and wipes out all accumulated returns in the dot-com bubble crash. The short portfolio benefits from this crisis but otherwise does not generate any substantial returns. It is the only portfolio to accumulate negative returns in parts of the out-of-sample period. After 2008, the cumulative returns of the long and short portfolios recover but never reach the magnitude of the global model. Appendix A2 plots the cumulative log returns of top and bottom decile portfolios sorted on the out-of-sample return forecasts of individual sector-specific neural network models. 5.4. Benchmarking with OLS sector models Sector-specific neural networks underperform a benchmark in the form of sector-specific ordinary least squares (OLS) models in the full sample. A long-short portfolio based on the sorted predictions of OLS sector models generates a higher value-weighted relative return than the sector neural networks. However, the OLS outperformance comes only from the first half of the out-of-sample period. The tradeoff between stable model estimation and capturing sectorspecific complex interactions is particularly relevant for small sector samples. Forecasts from the global neural network on the pooled data across sectors remain more profitable than the OLS models. Sector models underperform the global model regarding stock-level forecasting and long-short portfolio performance, even when sector-specific breakpoints sort the global model predictions. As a first step towards understanding the reasons for this observation, I compare the sector-specific models with another machine learning technique. The sector models used in this thesis build on a neural network architecture with three hidden layers (NN3). I compare these with sector-specific models based on a simple linear predictive regression model estimated by ordinary least squares. The methodology remains the same; only the machine learning model for predicting returns from stock-specific signals changes. Table 5compares the out-of-sample performance of longshort portfolios based on the sorted predictions from the two J. Witter /Junior Management Science 10(3) (2025) 561-581 577 Figure 3: Cumulative performance of top and bottom decile portfolios The figure plots the cumulative log returns of top and bottom decile portfolios sorted on the out-of-sample neural network return forecasts. Each month, stocks are sorted into value-weighted decile portfolios based on the predicted relative returns (with the market component removed) from the three neural network strategies. The solid and dash lines represent long (top decile) and short (bottom decile) positions, respectively. For the short position, the monthly relative returns of the bottom portfolio are multiplied by -1. The figure includes plots for the cumulative returns of the global model, the global model with sector-neutral portfolio sorts, and the sector models. The sample consists of US CRSP stocks, excluding microcap stocks with a market capitalization smaller than the 20th percentile of stocks listed on the NYSE. The sample runs from January 1994 to December 2022. The cumulative performance is cut off in December 2008 and restarted in January 2009 to present differences in cumulative returns between the two sub-samples. J. Witter /Junior Management Science 10(3) (2025) 561-581578 Table 5: Performance of NN3 sector models versus OLS sector models This table compares the out-of-sample performance of the value-weighted long-short portfolios formed from different machine learning sector model return predictions. Results are reported for the NN3 sector models (same sector models as in Table 4and Figure 3) and OLS sector models. All stocks are sorted into decile portfolios based on their predicted relative returns (with the market component removed) for the next month. A long-short portfolio buys the highest expected return stocks (decile 10) and sells the lowest (decile 1). Panel A compares the average value-weighted monthly full sample mean return and average monthly sub-sample mean returns with associated t-statistics (t-stat). Panel B visualizes the cumulative log returns of top and bottom decile portfolios sorted on the out-of-sample return forecasts of the two machine learning strategies. The solid and dash lines represent long (top decile) and short (bottom decile) positions, respectively. The sample consists of US CRSP stocks, excluding microcap stocks with a market capitalization smaller than the 20th percentile of stocks listed on the NYSE. The sample runs from January 1994 to December 2022. Panel A: Percentage returns Sector Models Mean 1994-2022 t-stat Mean 1994-2008 t-stat Mean 2009-2022 t-stat NN3 0.99 6.14 0.70 3.06 1.29 5.80 OLS 1.43 7.80 1.78 6.41 1.05 4.53 Panel B: Cumulative performance of top and bottom decile portfolios different machine learning methods. Panel A reports average monthly value-weighted out-of-sample returns with associated t-statistics (t-stat). The sector neural networks (NN3) returns are the same as in Panel A of Table 4. Panel B visualizes the cumulative out-of-sample log returns of the value-weighted long and short sides for the two machine learning models. The OLS sector models outperform the neural network sector models over the whole out-of-sample period from January 1994 to December 2022. They achieve average monthly long-short portfolio returns of 1.43% with an associated tstatistic of 7.80. However, the results differ for the two different subsamples. The outperformance of the OLS models is based solely on the first half of the out-of-sample period from 1994 to 2008. The OLS sector models generate significantly higher long-short returns than the NN3 sector models during this period. The monthly relative returns of 1.78% for the OLS models are more than double the 0.70% achieved by the sector models. The picture changes when looking at the later subsample from 2009 to 2022. In this period, OLS models underperform NN3 models, with average monthly returns of 1.05% and an associated t-statistic of 4.53. Panel B illustrates these results. The cumulative log returns for the OLS long and short portfolios remain positive throughout the out-ofsample period. They perform more reliably in the early years, with only a tiny long-short spread. As with all other machine J. Witter /Junior Management Science 10(3) (2025) 561-581 579 learning models, the gains for the short portfolio are mainly due to the dotcom bubble crash. The biggest difference between the OLS and NN3 sector models is the long portfolio in the first half of the out-of-sample period. The cumulative returns of the top decile stocks based on OLS forecasts are about an order of magnitude higher than their NN3 counterparts. In the second subsample from 2009 to 2022, the returns of the OLS long and short portfolios follow a similar pattern to the NN3 returns, with a slight underperformance. These results demonstrate a trade-off between robust model estimation and complex model architecture to capture sector-specific nonlinearities and variable interactions. A simple linear regression model such as OLS requires only a single parameter for each of the 212 signals. The parameters for the optimization problem are derived from a closed-form solution. Therefore, OLS models benefit from a higher ratio of observations to parameters and more stable model parameters. Their obvious disadvantage is the inability to capture non-linearities and variable interactions. The number of estimated coefficients in each of my neural network models is 7,489. These numbers result in a low observations-to-parameter ratio on small data sets, such as the individual sector samples, especially at the beginning of my sampling period when the training samples are the smallest. In low signal-to-noise problems like stock return prediction, complex machine learning models such as neural networks tend to overfit noise rather than extract signals. The NN3 sector models cannot exploit their advantage of being able to capture complex sector-specific relationships between signals and future returns. This can lead to the poor predictive performance of neural networks for small sectors and low portfolio returns in the first half of the outof-sample period. The pooling of data across sectors for the global model improves the ratio of observations to parameters. This explains why it does not suffer from the same problems as the sectoral models. The global neural network is still able to capture nonlinearities and variable interactions across sectors and thus significantly outperforms OLS models in the full sample, in line with previous research (e.g., Azevedo and Hoegner (2023), Blitz et al. (2023), and Gu et al. (2020)). Table A3 in the Appendix summarizes the out-of-sample statistics of the value-weighted long-short portfolios formed from different sector-specific OLS model return predictions. 5.5. Sector allocation as a return driver The global neural network demonstrates some out-ofsample sector allocation power. In the cross-section of sectors, it correctly predicts higher relative returns for the most profitable sectors and lower returns for the least profitable sectors. This allows the global model to generate higher returns in the long (top decile) portfolio when portfolio sorting is not sector-neutral. As seen in Table 4, sector-neutral portfolio sorts worsen the profitability of long-short portfolios sorted on the out-ofsample return forecasts of the global neural network. To better understand this difference in performance, I briefly evaluate the global neural network’s potential out-of-sample sector allocation power. Table 6summarizes my results. For each of the ten GICS sectors, Panel A reports the average valueweighted realized monthly relative return compared to the average predicted return from the global model. In addition, I report the average monthly allocation to the respective sector in the top decile portfolio sorted based on forecasts from the global model. I focus on the long portfolio, the stronger driver of the global model’s profitability than the short portfolio. Panel B plots the cumulative value-weighted relative log returns per sector over the out-of-sample period from January 1994 to December 2022. Information Technology (tech) is the best-performing sector over the entire out-of-sample period, with a monthly relative return of 0.23%. Health Care (health) follows in second place with a return of 0.09%, and Energy (energy) is in third place with a return of 0.01%, thanks to solid gains after 2020. All other sectors generate negative value-weighted relative returns out-of-sample.5The worst-performing sectors are Utilities (utilities), with an average monthly return of -0.24%, and Communication Services (comm), with a return of -0.35%. Apart from Information Technology, the global model’s return predictions are not very close to the realized returns, and they overstate expected returns. Still, it performs relatively well in cross-sectionally classifying the sectors into the correct extremes. The global model correctly identifies the two best-performing sectors and predicts Utilities and Communication Services to be among the three worst-performing sectors. As a result, the global model shows some (limited) outof-sample sector allocation power. The long portfolio based on global neural network forecasts has high average allocations to Information Technology (22.93%) and Health Care (15.09%). It has an average allocation of less than 5% to each of the three worst-performing sectors: Materials, Utilities, and Communication Services. The global model generates higher returns than sector-neutral portfolios by overweighting more profitable sectors and underweighting less profitable sectors in the top decile portfolio. 6. Conclusion I examine the difference in predictive power for the crosssection of US stock returns between a global machine learning model and sector-specific models. Based on their strong performance in previous research, I use neural networks as the machine learning models. The global neural network is trained on the full sample of stocks, while the sector neural networks are trained on ten different GICS sectors. The global model consistently outperforms the sector models outof-sample in terms of predictive accuracy and profitability. It 5Equally-weighted results (not reported) show that almost all sectors have positive relative returns. On average, stocks with smaller market capitalization generate higher relative returns. This further demonstrates the strong performance of the Size factor in the sample and justifies the high variable importance of Size in the global neural network. J. Witter /Junior Management Science 10(3) (2025) 561-581580 Table 6: Sector allocation power of global neural network model This table summarizes parts of the out-of-sample sector allocation power of the global neural network model. Panel A compares the average monthly realized relative returns (with the market component removed) per sector to the average monthly predicted relative returns from the global model over the out-of-sample period. The sectors in Panel A are ranked in descending order of realized returns. Panel A additionally reports the average monthly allocation to each sector of the long (top decile) portfolio sorted based on the global model’s return predictions for the next month. Panel B plots the cumulative relative log returns per sector over the out-of-sample period. All returns are value-weighted. The out-of-sample period runs from January 1994 to December 2022. The sample consists of US CRSP stocks, excluding microcap stocks with a market capitalization smaller than the 20th percentile of stocks listed on the NYSE. Panel A: Percentage returns and long portfolio allocation Sector Realized returns Predicted returns Long portfolio allocation Information Technology 0.23 0.26 22.93 Health Care 0.09 0.17 15.09 Energy 0.01 0.06 7.21 Consumer Discretionary -0.10 0.14 14.52 Consumer Staples -0.11 -0.03 3.74 Industrials -0.11 0.12 11.54 Financials -0.13 0.14 12.96 Materials -0.16 0.11 4.50 Utilities -0.24 -0.02 3.96 Communication Services -0.35 0.05 4.36 Panel B: Cumulative relative log returns per sector derives most of its predictive power from Size as an input signal. A long-short portfolio based on the sorted predictions of the global model generates significant returns and Sharpe ratios over the entire out-of-sample period. The sector models generate negative out-of-sample R2 OOS and their long-short portfolio returns are lower, especially in the early out-of-sample period. Complex models such as non-linear neural networks struggle to exploit their advantages on small sector-specific samples and underperform simple OLS models. The results for the global model support the recent literature on the strong predictive power of neural networks for the cross-section of stock returns. References Amihud, Y. (2002). Illiquidity and stock returns: cross-section and timeseries effects. Journal of Financial Markets,5(1), 31–56. Avramov, D., Cheng, S., & Metzker, L. (2023). Machine Learning vs. Economic Restrictions: Evidence from Stock Return Predictability. Management Science,69(5), 2587–2619. Azevedo, V., & Hoegner, C. (2023). Enhancing stock market anomalies with machine learning. Review of Quantitative Finance and Accounting, 60(1), 195–230. Azevedo, V., Hoegner, C., & Velikov, M. (2024). The Expected Returns on Machine-Learning Strategies. SSRN Electronic Journal. Azevedo, V., Kaiser, G. S., & Mueller, S. (2023). Stock market anomalies and machine learning across the globe. Journal of Asset Management, 24(5), 419–441. Blitz, D., Hanauer, M. X., Hoogteijling, T., & Howard, C. (2023). The Term Structure of Machine Learning Alpha. SSRN Electronic Journal, 1– 40. J. Witter /Junior Management Science 10(3) (2025) 561-581 581 Cakici, N., Fieberg, C., Metko, D., & Zaremba, A. (2023). Machine learning goes global: Cross-sectional return predictability in international stock markets. Journal of Economic Dynamics and Control,155, 1–32. Cavaglia, S. M. F. G., Sefton, J., Scowcroft, A., & Smith, B. (2006). Global Style Investing. The Journal of Portfolio Management,32(4), 10– 22. Chen, A. Y., & Zimmermann, T. (2022). Open Source Cross-Sectional Asset Pricing. Critical Finance Review,27(2), 207–264. Chen, L., Pelger, M., & Zhu, J. (2024). Deep Learning in Asset Pricing. Management Science,70(2), 714–750. Ciner, C. (2019). Do industry returns predict the stock market? A reprise using the random forest. Quarterly Review of Economics and Finance, 72, 152–158. Drobetz, W., & Otto, T. (2021). Empirical asset pricing via machine learning: evidence from the European stock market. Journal of Asset Management,22(7), 507–538. Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model. Journal of Financial Economics,116(1), 1–22. French, K. R. (2024). Current Research Returns. Retrieved November 1, 2024, from http://mba.tuck.dartmouth.edu/pages/faculty/k en.french/data_library.html Freyberger, J., Neuhierl, A., & Weber, M. (2020). Dissecting Characteristics Nonparametrically. The Review of Financial Studies,33(5), 2326– 2377. Gu, S., Kelly, B., & Xiu, D. (2020). Empirical Asset Pricing via Machine Learning. The Review of Financial Studies,33(5), 2223–2273. Hanauer, M. X., & Kalsbach, T. (2023). Machine learning and the crosssection of emerging market stock returns. Emerging Markets Review,55, 101022. Hou, K., Xue, C., & Zhang, L. (2020). Replicating Anomalies. The Review of Financial Studies,33(5), 2019–2133. Kim, K. J., Lee, C., & Tiras, S. L. (2013). The effects of adjusting the residual income model for industry and firm-specific factors when predicting future abnormal returns. Asia-Pacific Journal of Financial Studies,42(3), 373–402. Leippold, M., Wang, Q., & Zhou, W. (2022). Machine learning in the Chinese stock market. Journal of Financial Economics,145(2), 64–82. Lewellen, J. (2015). The Cross-section of Expected Stock Returns. Critical Finance Review,4(1), 1–44. Liu, X., Pong, E. S. Y., Shackleton, M. B., & Zhang, Y. (2014). Option-Implied Volatilities and Stock Returns: Evidence from Industry-Neutral Portfolios. The Journal of Portfolio Management,41(1), 65–77. Moritz, B., & Zimmermann, T. (2016). Tree-Based Conditional Portfolio Sorts: The Relation between Past and Future Stock Returns. SSRN Electronic Journal, 1–81. MSCI Inc. (2024). The Global Industry Classification Standard (GICS®). Retrieved November 1, 2024, from https://www.msci.com/our-sol utions/indexes/gics Nagel, S. (2005). Short sales, institutional investors and the cross-section of stock returns. Journal of Financial Economics,78(2), 277–309. Newey, W. K., & West, K. D. (1987). A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. The Econometric Society,55(3), 703–708. Rapach, D. E., Strauss, J. K., Tu, J., & Zhou, G. (2019). Industry Return Predictability: A Machine Learning Approach. The Journal of Financial Data Science,1(3), 9–28. Rasekhschaffe, K. C., & Jones, R. C. (2019). Machine Learning for Stock Selection. Financial Analysts Journal,75(3), 70–88. Tobek, O., & Hronec, M. (2021). Does it pay to follow anomalies research? Machine learning approach with international evidence. Journal of Financial Markets,56. U.S. Department of Labor. (2025). Standard Industrial Classification (SIC) Manual. Retrieved November 1, 2024, from https://www.osha.g ov/data/sic-manual