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 20

WP(9/2024)445. Statistical arbitrage in multi-pair trading strategy based on graph clustering algorithms in US equities market

Authors: Korniejczuk Adam, Ślepaczuk Robert
The study seeks to develop an effective strategy based on the novel framework of statistical arbitrage based on graph clustering algorithms. Amalgamation of quantitative and machine learning methods, including the Kelly criterion, and an ensemble of …

WP445. Statistical arbitrage in multi-pair trading strategy based on graph clustering algorithms in US equities market

The study seeks to develop an effective strategy based on the novel framework of statistical arbitrage based on graph clustering algorithms. Amalgamation of quantitative and machine learning methods, including the Kelly criterion, and an ensemble of machine learning classifiers have been used to improve risk-adjusted returns and increase the immunity to transaction costs over existing approaches.  The study seeks to provide an integrated approach to optimal signal detection and risk management. As a part of this approach, innovative ways of optimizing take profit and stop loss functions for daily frequency trading strategies have been proposed and tested. All of the tested approaches outperformed appropriate benchmarks. The best combinations of the techniques and parameters demonstrated significantly better performance metrics than the relevant benchmarks. The results have been obtained under the assumption of realistic transaction costs, but are sensitive to the changes of some key parameters


DOI: https://doi.org/10.33138/2957-0506.2024.9.445
Korniejczuk Adam, Ślepaczuk Robert
graph clustering algorithms statistical arbitrage algorithmic investment strategies pair trading strategy Kelly criterion machine learning risk adjusted returns

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(20/2023)427. Ensembling ARIMAX Model in Algorithmic Investment Strategies on Commodities Market

Authors: Jakubowski Paweł, Ślepaczuk Robert, Windorbski Franciszek
This paper presents the results of investment strategies based on predictions from an ARIMA with exogenous variables (ARIMAX/ARIMAX-Garch) model, using the prices of selected commodities and companies from the DJIA index as explanatory variables. The…

WP427. Ensembling ARIMAX Model in Algorithmic Investment Strategies on Commodities Market

This paper presents the results of investment strategies based on predictions from an ARIMA with exogenous variables (ARIMAX/ARIMAX-Garch) model, using the prices of selected commodities and companies from the DJIA index as explanatory variables. The explained variables are four Invesco ETF funds (DBE, DBA, DBP, DBB) corresponding to baskets of energy, agricultural, precious, and industrial metals. The models are optimized using the Walk-Forward technique, and the selection of exogenous variables is based on Granger causality tests. By analyzing the results, we conclude that ARIMAX/ARIMAX-Garch models are not useful tools for making buy or sell decisions for the selected commodity baskets. Out of the 80 estimated models, 44 outperform the Buy & Hold strategy, however, none achieved statistically significant results. Combining individual models into an investment portfolio reduced the risk without significantly reducing the profit, enabling us to consistently beat the benchmark. We also observe that using returns of commodities listed on stock exchanges is more effective than using stock returns. Sensitivity analysis shows instability in results with changes in the length of the training and testing windows. The highest annual return rate of 15.37% from 02.01.2008 to 01.12.2022 was characterized by an ARIMAX model with one commodity exogenous variable.


Jakubowski Paweł, Ślepaczuk Robert, Windorbski Franciszek
ARIMA(X) GARCH ARIMA(X)/GARCH Algorithmic Investment Strategies Granger Causality Investment Performance Evaluation Trading Systems Forecasting Models

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(29/2022)405. The efficiency of various types of input layers of LSTM model in investment strategies on S&P500 index

Authors: Nguyen Thi Thu Giang, Ślepaczuk Robert
The study compares the use of various Long Short-Term Memory (LSTM) variants to conventional technical indicators for trading the S&P 500 index between 2011 and 2022. Two methods were used to test each strategy: a fixed training data set from 200…

WP405. The efficiency of various types of input layers of LSTM model in investment strategies on S&P500 index

The study compares the use of various Long Short-Term Memory (LSTM) variants to conventional technical indicators for trading the S&P 500 index between 2011 and 2022. Two methods were used to test each strategy: a fixed training data set from 2001–2010 and a rolling train–test window. Due to the input sensitivity of LSTM models, we concentrated on data processing and hyperparameter tuning to find the best model. Instead of using the traditional MSE function, we used the Mean Absolute Directional Loss (MADL) function based on recent research to enhance model performance. The models were assessed using the Information Ratio and the Modified Information Ratio, which considers the maximum drawdown and the sign of the annualized return compounded (ARC). LSTM models' performance was compared to benchmark strategies using the SMA, MACD, RSI, and Buy&Hold strategies. We rejected the hypothesis that algorithmic investment strategy using signals from LSTM model consisting only from daily returns in its input layer is more efficient. However, we could not reject the hypothesis that signals generated by LSTM model combining daily returns and technical indicators in its input layer are more efficient. The LSTM Extended model that combined daily returns with MACD and RSI in the input layer generated a better result than Buy&Hold and other strategies using a single technical indicator. The results of the sensitivity analysis show how sensitive this model is to inputs like sequence length, batch size, technical indicators, and the length of the rolling train - test window.


Nguyen Thi Thu Giang, Ślepaczuk Robert
algorithmic investment strategies machine learning testing architecture deep learning recurrent neural networks LSTM technical indicators forecasting financial-time series technical indicators hyperparameter tuning S&P 500 Index

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(25/2021)373. Applying Hybrid ARIMA-SGARCH in Algorithmic Investment Strategies on S&P500 Index

Authors: Nguyen Vo, Ślepaczuk Robert
This research aims to compare the performance of ARIMA as linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We use the …

WP373. Applying Hybrid ARIMA-SGARCH in Algorithmic Investment Strategies on S&P500 Index

This research aims to compare the performance of ARIMA as linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We use the data collected from Yahoo Finance. The dataset has daily frequency and covers the period from 01/01/2000 to 31/12/2019. By using rolling window approach, we compare ARIMA with the hybrid models to examine whether hybrid ARIMA-SGARCH and ARIMA-EGARCH can really reflect the specific time-series characteristics and have better predictive power than simple ARIMA model. In order to assess the precision and quality of these models in forecasting, we decide to compare their equity lines, their forecasting error metrics (MAE, MAPE, RMSE, MAPE) as well as their performance metrics (annualized return compounded, annualized standard deviation, maximum drawdown, information ratio and adjusted information ratio). The results show that the hybrid models outperform ARIMA and the benchmark (Buy&Hold strategy on S&P500 index). These results are not sensitive to varying window sizes, the type of distribution and the type of the GARCH model.


Nguyen Vo, Ślepaczuk Robert
algorithmic investment strategies ARIMA ARIMA-SGARCH ARIMA-EGARCH hybrid model forecast stock returns model robustness
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