Working Papers

The WNE Working Papers series has been published by the Faculty of Economic Sciences at the University of Warsaw since 2008.

The WNE Working Papers series provides a fast, open channel for disseminating research conducted at the Faculty of Economic Sciences, University of Warsaw. The papers hosted here are working versions (pre-prints) and may evolve as authors refine their analyses, incorporate feedback, or progress through formal peer-review. What you read is the current version released by the authors, timestamped and assigned DOI/ISSN identifiers to ensure precise citation and version tracking. Copyright remains with the authors, who may, at any time, upload a revised file or add a note directing readers to a later, peer-reviewed publication.

The Working Papers series accepts articles by research employees of the Faculty and publications from conferences organised at the Faculty of Economic Sciences at the University of Warsaw. Articles should be original research papers which have not been previously published, on the subject of economics.

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(1) the main text without the title of the article and the authors (DOC/DOCX file) and

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Number of Results 16

WP(14/2025)477. Can Artificial Intelligence Trade the Stock Market?

Authors: Jędrzej Maskiewicz, Sakowski Paweł
The paper explores the use of Deep Reinforcement Learning (DRL) in stock market trading, focusing on two algorithms: Double Deep Q-Network (DDQN) and Proximal Policy Optimization (PPO) and compares them with Buy and Hold benchmark. It evaluates these…

WP477. Can Artificial Intelligence Trade the Stock Market?

The paper explores the use of Deep Reinforcement Learning (DRL) in stock market trading, focusing on two algorithms: Double Deep Q-Network (DDQN) and Proximal Policy Optimization (PPO) and compares them with Buy and Hold benchmark. It evaluates these algorithms across three currency pairs, the S&P 500 index and Bitcoin, on the daily data in the period of 2019-2023. The results demonstrate DRL's effectiveness in trading and its ability to manage risk by strategically avoiding trades in unfavorable conditions, providing a substantial edge over classical approaches, based on supervised learning in terms of risk-adjusted returns.


DOI: https://doi.org/10.33138/2957-0506.2025.14.477
Jędrzej Maskiewicz, Sakowski Paweł
Reinforcement Learning Deep Learning stock market algorithmic trading Double Deep Q-Network Proximal Policy Optimization

WP(10/2024)446. Predictive modeling of foreign exchange trading signals using machine learning techniques

Authors: Sugarbayar Enkhbayar, Ślepaczuk Robert
This study aimed to apply the algorithmic trading strategy on major foreign exchange pairs and compare the performances of machine learning-based strategies and traditional trend-following strategies with benchmark strategies. It differs from other s…

WP446. Predictive modeling of foreign exchange trading signals using machine learning techniques

This study aimed to apply the algorithmic trading strategy on major foreign exchange pairs and compare the performances of machine learning-based strategies and traditional trend-following strategies with benchmark strategies. It differs from other studies in that it considered a wide variety of cases including different foreign exchange pairs, return methods, data frequency, and individual and integrated trading strategies. Ridge regression, KNN, RF, XGBoost, GBDT, ANN, LSTM, and GRU models were used for the machine learning-based strategy, while the MA cross strategy was employed for the trend-following strategy. Backtests were performed on 6 major pairs in the period from January 1, 2000, to June 30, 2023, and daily, and intraday data were used. The Sharpe ratio was considered as a metric used to refer to economic significance, and the independent t-test was used to determine statistical significance. The general findings of the study suggested that the currency market has become more efficient. The rise in efficiency is probably caused by the fact that more algorithms are being used in this market, and information spreads much faster. Instead of finding one trading strategy that works well on all major foreign exchange pairs, our study showed it’s possible to find an effective algorithmic trading strategy that generates a more effective trading signal in each specific case.


DOI: https://doi.org/10.33138/2957-0506.2024.10.446
Sugarbayar Enkhbayar, Ślepaczuk Robert
machine learning algorithmic trading foreign exchange market rolling walk-forward optimization technical indicators

WP(25/2023)432. Hedging Properties of Algorithmic Investment Strategies using Long Short-Term Memory and Time Series models for Equity Indices

Authors: Michańków Jakub, Sakowski Paweł, Ślepaczuk Robert
This paper proposes a novel approach to hedging portfolios of risky assets when financial markets are affected by financial turmoils. We introduce a completely novel approach to diversification activity not on the level of single assets but on the le…

WP432. Hedging Properties of Algorithmic Investment Strategies using Long Short-Term Memory and Time Series models for Equity Indices

This paper proposes a novel approach to hedging portfolios of risky assets when financial markets are affected by financial turmoils. We introduce a completely novel approach to diversification activity not on the level of single assets but on the level of ensemble algorithmic investment strategies (AIS) built based on the prices of these assets. We employ four types of diverse theoretical models (LSTM - Long Short-Term Memory, ARIMA-GARCH - Autoregressive Integrated Moving Average - Generalized Autoregressive Conditional Heteroskedasticity, momentum, and contrarian) to generate price forecasts, which are then used to produce investment signals in single and complex AIS. In such a way, we are able to verify the diversification potential of different types of investment strategies consisting of various assets (energy commodities, precious metals, cryptocurrencies, or soft commodities) in hedging ensemble AIS built for equity indices (S&P 500 index). Empirical data used in this study cover the period between 2004 and 2022. Our main conclusion is that LSTM-based strategies outperform the other models and that the best diversifier for the AIS built for the S&P 500 index is the AIS built for Bitcoin. Finally, we test the LSTM model for a higher frequency of data (1 hour). We conclude that it outperforms the results obtained using daily data.


Michańków Jakub, Sakowski Paweł, Ślepaczuk Robert
machine learning recurrent neural networks long short-term memory algorithmic investment strategies testing architecture loss function walk-forward optimization over-optimization

WP(23/2023)430. Mean Absolute Directional Loss as a New Loss Function for Machine Learning Problems in Algorithmic Investment Strategies

Authors: Michańków Jakub, Sakowski Paweł, Ślepaczuk Robert
This paper investigates the issue of an adequate loss function in the optimization of machine learning models used in the forecasting of financial time series for the purpose of algorithmic investment strategies (AIS) construction. We propose the Mea…

WP430. Mean Absolute Directional Loss as a New Loss Function for Machine Learning Problems in Algorithmic Investment Strategies

This paper investigates the issue of an adequate loss function in the optimization of machine learning models used in the forecasting of financial time series for the purpose of algorithmic investment strategies (AIS) construction. We propose the Mean Absolute Directional Loss (MADL) function, solving important problems of classical forecast error functions in extracting information from forecasts to create efficient buy/sell signals in algorithmic investment strategies. Finally, based on the data from two different asset classes (cryptocurrencies: Bitcoin and commodities: Crude Oil), we show that the new loss function enables us to select better hyperparameters for the LSTM model and obtain more efficient investment strategies, regarding risk-adjusted return metrics on the out-of-sample data.


Michańków Jakub, Sakowski Paweł, Ślepaczuk Robert
machine learning recurrent neural networks long short-term memory algorithmic investment strategies testing architecture loss function walk-forward optimization over-optimization

WP(17/2023)424. Optimal Markowitz Portfolio Using Returns Forecasted with Time Series and Machine Learning Models

Authors: Ślusarczyk Damian, Ślepaczuk Robert
We aim to answer the question of whether using forecasted stock returns based on machine learning and time series models in a mean-variance portfolio framework yields better results than relying on historical returns. Nevertheless, the problem of the…

WP424. Optimal Markowitz Portfolio Using Returns Forecasted with Time Series and Machine Learning Models

We aim to answer the question of whether using forecasted stock returns based on machine learning and time series models in a mean-variance portfolio framework yields better results than relying on historical returns. Nevertheless, the problem of the efficient stock selection has been tested for more than 50 years, the issue of adequate construction of mean-variance portfolio framework and incorporating forecasts of returns in it has not been solved yet. Stock returns portfolios were created using ’raw’ historical returns and forecasted return based on ARIMA-GARCH and the XGBoost models. Two optimization problems were concerned: global maximum information ratio and global mini-mum variance. Then strategies were compared with two benchmarks – an equally weighted portfolio and buy and hold on the DJIA index. Strategies were tested on Dow Jones Industrial Average stocks in the period from 2007-01-01 to 2022-12-31 and daily data was used. The main portfolio performance metrics were information ratio* and information ratio**. The results showed that using forecasted returns we can enhance our portfolio selection based on Markowitz framework, but it is not a universal solution, and we have to control all the parameters and hyperparameters of selected models.


Ślusarczyk Damian, Ślepaczuk Robert
Algorithmic Investment Strategies Markowitz framework portfolio optimization forecasting ARIMA GARCH XGBoost minimum variance

WP(15/2023)422. Ensembled LSTM with Walk Forward Optimization in Algorithmic Trading

Authors: Chojnacki Karol, Ślepaczuk Robert
This study compares well-known tools of technical analysis (Moving Average Crossover MAC) with Machine Learning based strategies (LSTM and XGBoost) and Ensembled Machine Learning Strategies (LSTM ensembled with XGBoost and MAC). All models were …

WP422. Ensembled LSTM with Walk Forward Optimization in Algorithmic Trading

This study compares well-known tools of technical analysis (Moving Average Crossover MAC) with Machine Learning based strategies (LSTM and XGBoost) and Ensembled Machine Learning Strategies (LSTM ensembled with XGBoost and MAC). All models were compared to Buy and Hold benchmark and evaluated using Performance Metrics, that is Annualized Return Compounded, Maximum Drawdown, Maximum Loss Duration, and three types of Information Ratio. This research uses daily S&P 500 index data ranging from 2000 to 2023. Every strategy was optimized with novel walk forward approach consisting of numerous in sample and out of sample periods. MAC and best performing ML methods were subjected to sensitivity analysis. The results show that LSTM ensembled with XGBoost and MAC yields the most promising results in terms of risk-adjusted returns which suggest further research focused on ensembling of individual ML strategies. Finally, we show that classical methods of technical analysis (that is, MAC) are much less robust and indifferent to change in hyperparameters than machine learning based algorithms, especially LSTM.


Chojnacki Karol, Ślepaczuk Robert
Algorithmic Investment Strategies Machine Learning Recurrent Neural Networks Long Short-Term Memory XGBoost Walk Forward Optimization Trading algorithms Technical Analysis Indicators

WP(5/2023)412. The performance of time series forecasting based on classical and machine learning methods for S&P 500 index

Authors: Uzzal Maudud Hassan, Ślepaczuk Robert
Based on one step ahead forecasts, this study compares the forecasting abilities of the traditional technique (ARIMA) with recurrent neural network (LSTM). In order to check the possible use of these forecasts in different asset management methods, t…

WP412. The performance of time series forecasting based on classical and machine learning methods for S&P 500 index

Based on one step ahead forecasts, this study compares the forecasting abilities of the traditional technique (ARIMA) with recurrent neural network (LSTM). In order to check the possible use of these forecasts in different asset management methods, these forecasts are afterwards included into trading signals of investment strategies. As a benchmark method, the Random Walk model producing naive forecasts has been utilized. This research examines daily data from the S&P 500 index for 20 years, from 2000 to 2020, and it includes information on some significant market turbulence. The methods were tested in terms of robustness to changes in parameters and hyperparameters and evaluated based on various error metrics (MAE, MAPE, RMSE MSE). The results show that ARIMA outperforms LSTM in terms of one step ahead forecasts. Finally, LSTM model with a variety of hyperparameters - including a number of epochs, a loss function, an optimizer, activation functions, a number of units, a batch size, and a learning rate - was tested in order to check its robustness.


Uzzal Maudud Hassan, Ślepaczuk Robert
deep learning recurrent neural networks ARIMA algorithmic investment strategies trading systems LSTM walk-forward process optimization

WP(12/2022)388. Investment Portfolio Optimization Based on Modern Portfolio Theory and Deep Learning Models

Authors: Wysocki Maciej, Sakowski Paweł
This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. In this study we propose a novel framework for variance-covariance matrix estimation for purposes of the portfolio op…

WP388. Investment Portfolio Optimization Based on Modern Portfolio Theory and Deep Learning Models

This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. In this study we propose a novel framework for variance-covariance matrix estimation for purposes of the portfolio optimization, which is based on deep learning models. We employ the long short-term memory (LSTM) recurrent neural networks (RNN) along with two probabilistic deep learning models: DeepVAR and GPVAR to the task of one-day ahead multivariate forecasting. We then use these forecasts to optimize portfolios that consisted of stocks and cryptocurrencies. Our analysis presents results across different combinations of observation windows and rebalancing periods to compare performances of classical and deep learning variance-covariance estimation methods. The conclusions of the study are that although the strategies (portfolios) performance differed significantly between different combinations of parameters, generally the best results in terms of the information ratio and annualized returns are obtained using the LSTM-RNN models. Moreover, longer observation windows translate into better performance of the deep learning models indicating that these methods require longer windows to be able to efficiently capture the long-term dependencies of the variance-covariance matrix structure. Strategies with less frequent rebalancing typically perform better than these with the shortest rebalancing windows across all considered methods.


Wysocki Maciej, Sakowski Paweł
Portfolio Optimization Deep Learning Variance-Covariance Matrix Forecasting Investment Strategies Recurrent Neural Networks Long Short-Term Memory Neural Networks

WP(42/2020)348. Does Bitcoin Improve Investment Portfolio Efficiency?

Authors: Sakowski Paweł, Turovtseva Daria
The aim of the paper is to check if cryptocurrency Bitcoin – a new investable asset class representative – is able to improve the performance of an optimal portfolio. Using two Markowitz criteria of optimization – expected return ma…

WP348. Does Bitcoin Improve Investment Portfolio Efficiency?

The aim of the paper is to check if cryptocurrency Bitcoin – a new investable asset class representative – is able to improve the performance of an optimal portfolio. Using two Markowitz criteria of optimization – expected return maximization and expected shortfall (CVaR) minimization – we test the investment opportunities after adding Bitcoin to the portfolio of 10 traditional assets (among them equity, fixed income, money, commodities and money market indices). Using daily observations from 1.05.2013 till 24.05.2019, we examine the behavior of the portfolios without and with Bitcoin and check if the return-risk ratio improves for the latter. Discussing the results, we conduct the sensitivity analysis by changing the lookback window (LB) and rebalancing frequency (RB) parameters. Empirical analysis suggests that Bitcoin-inclusive portfolios provide an investor with wider diversification opportunities. Robustness check confirms the findings and also advocates for the cryptocurrency to be added to the portfolio.


Sakowski Paweł, Turovtseva Daria
Portfolio optimization portfolio theory cryptocurrency Bitcoin Markowitz model asset allocation portfolio diversification investment opportunities

WP(21/2020)327. HRP performance comparison in portfolio optimization under various codependence and distance metrics

Authors: Barziy Illya, Chlebus Marcin
Problem of portfolio optimization was formulated almost 70 years ago in the works of Harry Markowitz. However, the studies of possible optimization methods are still being provided in order to obtain better results of asset allocation using the empir…

WP327. HRP performance comparison in portfolio optimization under various codependence and distance metrics

Problem of portfolio optimization was formulated almost 70 years ago in the works of Harry Markowitz. However, the studies of possible optimization methods are still being provided in order to obtain better results of asset allocation using the empirical approximations of codependences between assets. In this work various codependences and metrics are tested in the Hierarchical Risk Parity algorithm to determine whether the results obtained are superior to those of the standard Pearson correlation as a measure of codependence. In order to compare how HRP uses the information from alternative codependence metrics, the MV, IVP, and CLA optimization algorithms were used on the same data. Dataset used for comparison consisted of 32 ETFs representing equity of different regions and sectors as well as bonds and commodities. The time period tested was 01.01.2007-20.12.2019. Results show that alternative codependence metrics show worse results in terms of Sharpe ratios and maximum drawdowns in comparison
to the standard Pearson correlation for each optimization method used. The added value of this work is using alternative codependence and distance metrics on real data, and including transaction costs to determine their impact on the result of each algorithm.


Barziy Illya, Chlebus Marcin
Hierarchical Risk Parity portfolio optimization ETF hierarchical structure clustering backtesting distance metrics risk management machine learning
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