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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Number of Results 6

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(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

WP(14/2019)299. Does the inclusion of exposure to volatility into diversified portfolio improve the investment results? Portfolio construction from the perspective of a Polish investor.

Authors: Latoszek Michał, Ślepaczuk Robert
The main goal of this research is to analyse the investment benefits from an incorporation of the volatility exposure to the diversified portfolio from the perspective of a Polish investor. Volatility, treated as a new asset class, may improve the pe…

WP299. Does the inclusion of exposure to volatility into diversified portfolio improve the investment results? Portfolio construction from the perspective of a Polish investor.

The main goal of this research is to analyse the investment benefits from an incorporation of the volatility exposure to the diversified portfolio from the perspective of a Polish investor. Volatility, treated as a new asset class, may improve the performance of the portfolio due to its negative correlation with most types of assets. This topic has been widely investigated for the United States and Europe whereas Polish market appears to be not heavily researched and this study may fill this gap. The research covers the period from October 2010 to July 2018 and is performed on the daily close prices. To construct the portfolios, the analysis uses the mean-variance framework and the naïve diversification approach. The comparison of risk-adjusted returns between investments with and without volatility exposure enables to answer the research question about an improvement of the results by the addition of a non-standard asset to the diversified portfolios. The VXX is considered as the proxy for volatility as it is the most popular ETN which follows the volatility index derivatives with the given maturity. To test the robustness of the results, the portfolios are constructed with a broad range of different parameters and assumptions imposed on the optimization procedure.


Latoszek Michał, Ślepaczuk Robert
Volatility asset class portfolio optimization Polish market Markowitz portfolio naïve diversification

WP(11/2009)21. Emerging versus developed volatility indices. The comparison of VIW20 and VIX indices.

Authors: Ślepaczuk Robert, Zakrzewski Grzegorz
Modeling of financial markets volatility is one of the most significant issues of contemporary finance, especially with regard to analyzing high-frequency data. Accurate quantification and forecast of volatility are of immense importance in risk mana…

WP21. Emerging versus developed volatility indices. The comparison of VIW20 and VIX indices.

Modeling of financial markets volatility is one of the most significant issues of contemporary finance, especially with regard to analyzing high-frequency data. Accurate quantification and forecast of volatility are of immense importance in risk management (VaR models, stress testing and worst-case scenario), models of capital market and options valuation techniques. What we show in this paper is the methodology for calculating volatility index for Polish capital market (VIW20 - index anticipating expected volatility of WIG20 index). The methods presented are based on VIX index (VIX White Paper, 2003) and enriched with necessary modifications corresponding to the character of Polish options market. Quoted on CBOE, VIX index is currently known as the best measure of capital investment risk perfectly illustrating the level of fear and emotions of market participants. The conception of volatility index is based on the combination of realized volatility and implied volatility which, using methodology of Derman et al. (1999) and reconstructing volatility surface, reflects both volatility smile as well as its term structure. The research is carried out using high-frequency data (i.e. tick data) for index options on WIG20 index for the period November 2003 - May 2007, in other words, starting with the introduction of options by Warsaw Stock Exchange. All additional simulations are carried out using data gathered in years 1998-2008. Having analyzed VIW20 index in detail, we observed its characteristic behavior during the periods of strong market turmoils. What we also present is the analysis of the influence of VIW20 and VIX index-based instruments both on construction of minimum risk portfolio and on the quality of derivatives portfolio management in which volatility risk and liquidity risk play a key role. The main objective of this paper is to provide foundations for introducing appropriate volatility indices and volatility-based derivatives. This is done with paying attention to crucial methodology changes, necessary if one considers strong markets inefficiencies in emerging countries. As the introduction of appropriate instruments will enable active management of risks that are unhedgable nowadays it will significantly contribute to the development of the given markets in the course of time. In the summary we additionally point to the benefits Warsaw Stock Exchange might obtain from, being one of the few emerging markets possessing appropriately quantified investment risk as well as derivatives to manage it.


Ślepaczuk Robert, Zakrzewski Grzegorz
financial market volatility high-frequency data realized volatility realized range implied and historical volatility volatility forecasting option pricing models investment strategies portfolio optimization
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