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 3

WP(10/2016)201. Applying Exogenous Variables and Regime Switching to Multifactor Models on Equity Indices

Authors: Sakowski Paweł, Ślepaczuk Robert, Wywiał Mateusz
This article aims to extend the evaluation of classic multifactor models of Carhart(1997) for the case of global equity indices and to expand analysis performed in Sakowski, Slepaczuk, and Wywial (2015). Our intention is to test several modifications…

WP201. Applying Exogenous Variables and Regime Switching to Multifactor Models on Equity Indices

This article aims to extend the evaluation of classic multifactor models of Carhart(1997) for the case of global equity indices and to expand analysis performed in Sakowski, Slepaczuk, and Wywial (2015). Our intention is to test several modifications of these models to take into account different dynamics of equity excess returns between emerging and developed equity indices. Proposed extensions include volatility regime switching mechanism (using dummy variables and the Markov approach) and three new risk factors based on realized volatility of index returns, percentage deviation from nominal GDP trend and capitalisation relative to GDP factor. Additional modifications include introduction of common and country specific variables in order to control for global risk where fluctuations of volatility of various assets, prices of commodities, currencies and rates is really important. Moreover, instead of using data for individual stocks (which is a common approach in the literature), we evaluate the performance of these models for weekly data of 81 world investable equity indices in the period of 2000-2015. Such approach is proposed to estimate equity risk premium for a single country. Empirical evidence from the first part reveals important differences between results for classical models estimated on single stocks (either in international or US-only frame work) and models evaluated for equity indices. Additionally, we observe substantial discrepancies between results for developed countries and emerging markets. The last part of this research helps us to understand results revealed in the first part. Thanks to introduction of new risk factors, and additional common and country specific variables we were able to increase explanatory power of our factor models especially in case of emerging market indices. Finally, using weekly data for the last 15 years we illustrate importance of model risk and data overfitting effects when drawing conclusions upon results of multifactor models.


Sakowski Paweł, Ślepaczuk Robert, Wywiał Mateusz
multi-factor models asset pricing models equity risk premia equity indices new risk factors sensitivity analysis book to market momentum market price of risk emerging and developed equity indices

WP(9/2016)200. Can We Invest Based on Equity Risk Premia and Risk Factors from Multi-Factor Models?

Authors: Sakowski Paweł, Ślepaczuk Robert, Wywiał Mateusz
We find that detailed analysis of multi-factor models makes it possible to propose investment strategies based on equity risk premium disequlibrium. We examine two investment algorithms built on weekly data of world equity indices for emerging and de…

WP200. Can We Invest Based on Equity Risk Premia and Risk Factors from Multi-Factor Models?

We find that detailed analysis of multi-factor models makes it possible to propose investment strategies based on equity risk premium disequlibrium. We examine two investment algorithms built on weekly data of world equity indices for emerging and developed countries in the period of 2000-2015. We create seven risk factors using additional data about market capitalisation, book value, country GDP and betas of equity indices. The first strategy utilises theoretical value of equity risk premium from seven-factor Markov-switching model with variables common for all countries and variables specific to developed/emerging countries. We compare theoretical with realised equity risk premium for a given index to undertake the buy/sell decisions. The second algorithm works only on eight risk factors and applies them as input variables to Markowitz models with alternative optimisation criteria (target risk, target return, maximum Sharpe ratio, minimum variance and equally weighted assets). Finally, we notice that the impact of risk factors on final results of investment strategy is much more important than the selection of a particular econometric model in order to correctly evaluate equity risk premium.


Sakowski Paweł, Ślepaczuk Robert, Wywiał Mateusz
investment algorithms multi-factor models Markov switching model asset pricing models equity risk premia risk factors Markowitz model

WP(8/2016)199. Do Multi-Factor Models Produce Robust Results? Econometric and Diagnostic Issues in Equity Risk Premia Study

Authors: Sakowski Paweł, Ślepaczuk Robert, Wywiał Mateusz
In recent decades numerous studies verified empirical validity of the CAPM model. Many of them showed that CAPM alone is not able to explain cross-sectional variation of stock returns. Researchers revealed various risk factors which explained outperf…

WP199. Do Multi-Factor Models Produce Robust Results? Econometric and Diagnostic Issues in Equity Risk Premia Study

In recent decades numerous studies verified empirical validity of the CAPM model. Many of them showed that CAPM alone is not able to explain cross-sectional variation of stock returns. Researchers revealed various risk factors which explained outperformance of given groups of stocks or proposed modifcations to existing multi-factor models. 
Surprisingly, we hardly find any discussion in financial literature about potential drawbacks of applying standard OLS method to estimate parameters of such models. Yet, the question of robustness of OLS results to invalid assumptions shouldn't be ignored. This article aims to address diagnostic and econometric issues which can influence results of a time-series multifactor model. 
Based on the preliminary results of a five-factor model for 81 emerging and developed equity indices (Sakowski, Slepaczuk and Wywial, 2016a) obtained with OLS we check the robustness of these results to popular violations of OLS assumptions. We find autocorrelation of error term, heteroscedasticity and ARCH effects for most of 81 regressions and apply an AR-GARCH model using MLE to remove them. We also identify outliers and diagnose collinearity problems. Additionally, we apply GMM to avoid strong assumption of IID error term. 
Finally, we present comparison of parameters estimates and Rsquared values obtained by three different methods of estimation: OLS, MLE and GMM. We find that results do not differ substantially between these three methods and allow to draw the same conclusions from the investigated five-factor model.


Sakowski Paweł, Ślepaczuk Robert, Wywiał Mateusz
multi-factor models asset prising models equity risk premia OLS MLE GMM autocorrelation heteroscedasticity outliers collinearity normality econometric diagnostics
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