Connectedness between sectors: The case of the polish stock market before and during COVID-19

Chirilă, Viorica Article Connectedness between sectors: The case of the polish stock market before and during COVID-19 Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Chirilă, Viorica (2022) : Connectedness between sectors: The case of the polish stock market before and during COVID-19, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 15, Iss. 8, pp. 1-19, https://doi.org/10.3390/jrfm15080322 This Version is available at: https://hdl.handle.net/10419/274844 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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Journal of Risk and Financial Management 15: 322. https://doi.org/10.3390/ jrfm15080322 Academic Editor: Lee A. Smales Received: 23 May 2022 Accepted: 11 July 2022 Published: 22 July 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Journal of Risk and Financial Management Article Connectedness between Sectors: The Case of the Polish Stock Market before and during COVID-19 Viorica Chirilă Department of Accounting, Business Information Systems and Statistics, Faculty of Economics and Business Administration, “Alexandru Ioan Cuza” University of Iasi, 700505 Iasi, Romania; [email protected]o Abstract: This article studies the connectedness between economic sectors of the Polish stock market. The sectors that are considered are the following: banks, basic materials, chemicals, construction, developers, energy, food, and oil and gas. The analysis of the connectedness among sectors is conducted from a statistical and dynamic perspective. Using the time-varying parameter vector autoregression (TVP-VAR) method, the intensity, direction and variation of volatility spillover between the economic sectors are studied. Two samples are analysed, the first one being from 1 January 2013 to 12 December 2019, which corresponds to the period before the pandemic caused by COVID-19, and the second one being from 1 January 2020 to 2 December 2021, which corresponds to the period during the pandemic. A series of results are obtained. First, the connectedness between the economic sectors varies depends on the time. Second, the connectedness between the sectors was stronger during the crisis caused by the outbreak of COVID-19 rather than before the crisis. The volatility of each sector was also primarily due to their own volatility. Thirdly, the banking sector was the main sector with respect to volatility spillover. The results that are obtained are important for making the right decisions regarding financial stability under crisis circumstances, when considering development strategies for some economic sectors but also in portfolio management for performing diversification and risk-mitigation strategies. Keywords: spillover volatility; sector connectedness; stock market; TVP-VAR 1. Introduction The global financial crisis of 2008 led to increased volatility in financial markets. Economic and financial integration, as well as financial liberalization, are some of the factors that have led to an increase in return and volatility spillover in financial markets (Mensi et al. 2021). In addition, financial difficulties caused by political instability, sovereign debt insolvency and recessions are spreading very quickly to other countries (Andrie s , and Galasan 2020;Bo t , oc and Anton 2020). Return and volatility spillover in stock markets is a complex topic that has attracted the attention of researchers and allows for studies of the connectedness between economic sectors (Chakrabarty et al. 2015;Chirilăet al. 2015; Lupu and Lupu 2009;Lupu et al. 2021). Volatility spillovers between different categories of financial markets (Antonakakis et al. 2018;Yao et al. 2022;Gabauer 2021), from the same financial markets in different geographical areas (Škrinjari´c 2019;Škrinjari´c and Šego 2020) or from different categories of economies (Spulbar et al. 2020) are being studied. In the above-mentioned research, special attention is given to the study of volatility spillover or to the connectedness between different sectors of a stock market (Fasanya et al. 2021;Hassan and Malik 2007;Kouki et al. 2011;Shahzad et al. 2021a;Ngene 2021). Knowledge of sectoral connectedness within stock markets is of real interest for portfolio management, macroeconomic analysis and policy makers. Identifying volatility spillover patterns between stocks from different economic sectors allows the portfolio manager to make portfolio diversification decisions in a timely manner for efficient management. In addition, identifying the main sectors with volatility spillover strengthens J. Risk Financial Manag. 2022,15, 322. https://doi.org/10.3390/jrfm15080322 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2022,15, 322 2 of 19 policy makers’ decisions to reduce overall market risk and helps develop specific economic sectors by providing knowledge about which sectors influence the targeted sector. Thus, this study fits into the broader framework of the sustainable development of an economy to the extent that the development of some economic sectors of a country must consider the influence of other economic sectors of the same country. This study allows for the identification of the connectedness between the economic sectors of Poland; therefore, these results can be used to strengthen economic development policies. The analysis of spillovers across markets has acquired a new dimension through the methodology of Diebold and Yilmaz (2008,2012). In addition to identifying variations over time of the return spillover and risk, this methodology allows for the identification of the extent to which this spillover is achieved. The results that were obtained allow for comparisons to be made. In addition, the outbreak of an economic and financial crisis led to an increase in research on returns and volatility spillover between different markets, because an increase in spillover has been identified during these periods. The health crisis, caused by the outbreak of COVID-19, also grounded this research. The results that were obtained following the study of volatility spillover are not similar. There are several studies that confirm the financial sector to be the main sector with volatility spillover. An analysis of sectoral connectedness was conducted on the US stock market by Costa et al. (2021) before and during the crisis caused by the outbreak of COVID-19. Through their results, they confirmed an increase in volatility spillover across sectors during the crisis. The energy sector was a net receiver both before and during the COVID-19 crisis, but it was the most connected in the system of studied sectors. The main sector with volatility spillover was the financial sector. The connectedness between six industry sectors in the US stock market was also studied by Liu et al. (2021). The results that were obtained show that the financial sector and the technology sector were the main sectors with volatility spillover. In many situations, the net volatility spillover also changes its direction during financial crises and recession periods. Shahzad et al. (2021a) studied the impact of quantile return spillovers on equity sectors. This method allows for the study of extreme returns, which indicate critical periods that the stock market undergoes. The results that were obtained confirm that the pandemic caused by COVID-19 determined that the restructuring of the connectedness between sectors was stronger in the bulk of the distribution in comparison with the tails of the distribution, where there were extreme returns. A difference compared to the previous financial and economic crises was also noticed for the financial sector, which became an information receiver. Tail-dependency networks were tackled by Le et al. (2021) in a study of 51 international assets (spot exchange, commodities, equity indices, UST bonds and Bitcoin). In this study, conducted for the period of 1 January 2019–30 April 2020, a stronger asymmetry effect was observed for left tails for equities and commodities. In one study, Bouri et al. (2021b) discussed the connectedness between the returns for gold, crude oil, MSCI World, the USD index and the bond index for the period before the pandemic (19 August 2011–13 January 2020) and during the pandemic 13 January 2020–12 May 2020. Before the pandemic, if MSCI World and the USD index (stock indexes) had the most important volatility spillovers, then during the COVID-19 pandemic, bonds became the main assets with a volatility spillover effect. The financial sector was identified as being the main sector with volatility spillover, alongside the energy sector, in the network of eleven sectors of the Australian stock market (Choi et al. 2021). The technology and telecommunication service sectors were the main recipients of volatility. Wu et al. (2019) studied the volatility spillover across stock market sectors in China from 7 January 2000 to 10 May 2018. The results were based on both graph theory and Diebold and Yilmaz’s (2014) methodology, confirming that the industrial sector was the main sector with volatility spillover. This study also confirmed the time-varying volatility spillover. Shahzad et al. (2021b) also studied volatility spillover between the Chinese stock sectors during the COVID-19 pandemic by taking into account the period of J. Risk Financial Manag. 2022,15, 322 3 of 19 2 January 2019–30 September 2020. The 1-min sampling frequency allowed the study of the downside semivariance and upside semivariance. The results confirm the variance in time and the asymmetry of volatility spillover. Chatziantoniou et al. (2020) studied volatility spillover across sectors in the Indian stock market. The authors concluded that volatility spillover increases during periods of economic, financial and health crises, but also during the 2014 Indian elections and the 2016 demonetization period. They also found that shocks start mostly from the cyclical sectors and reach non-cyclical sectors. Thus, the sectors with net volatility spillover are basic materials, industry, finance, and consumer spending and the sectors receiving net volatility are telecommunications, information technology, healthcare and consumer goods. The importance of studying the economic sectors of the stock exchanges is highlighted by the study performed by Bouri et al. (2021a). The authors studied the impact of three governmental decisions for reducing the pandemic’s effects in New Zealand: the stimulus package, lockdown and the travel ban. These governmental policies determined a different response on the stock market depending on each sector. Considering previous research, we can formulate the following research hypotheses: H1. The intensity and direction of connectedness between economic sectors vary over time. H2. The connectedness between economic sectors is stronger during the health crisis caused by the outbreak of COVID-19. H3. The financial sector is the main sector with volatility spillover to other economic sectors, thus influencing the development of most economic sectors. Identifying a deficiency in volatility spillover research in Central and Eastern European stock markets prompted this research. Therefore, this study addresses sectoral connectedness in one of the most developed stock markets in Central and Eastern Europe: Poland. The study provides new insights into the independence of an economic activity sector by adding to and extending the existing research literature. The volatility of stock prices in an economic sector expresses the way in which a shock, or new information, is integrated into stock prices, thus providing the possibility of identifying useful patterns in studying the characteristics and evolution of stock market sectors. The results will also provide important information when identifying the vulnerability of economic sectors. The context of the health crisis caused by the outbreak of COVID-19 allowed for a comparative study of some changes that appeared in the connectedness between listed shares from different economic sectors before and during the crisis. Therefore, this study compares the situation of the volatility connectedness between sectoral indices before the outbreak of the health crisis and during it. The methodology proposed by Diebold and Yilmaz (2008), with subsequent additions made by Diebold and Yilmaz (2012,2014), enables the quantification of volatility spillover, thus ensuring the possibility to make the comparisons. In this study, we will use the time-varying parameter vector autoregressions (TVP-VAR) methodology of Antonakakis et al. (2020), which is an improved version of the one proposed by Diebold and Yilmaz (2014). The rest of the paper is organized as follows: Section 2presents the Polish stock market; Section 3covers the econometric methodology; and Section 4presents the used data and the empirical steps. These are followed by the empirical results and conclusions. 2. Polish Stock Market In the year 2004, major CE states such as Poland, Hungary, the Czech Republic and Slovakia, became EU members. It is for this reason that the Polish stock market is studied alongside that of Hungary and the Czech Republic whenever the emerging CE markets are analysed (Scheicher 2001;Li and Majerowska 2008;Syriopoulos 2007). The stock markets from these countries registered much more rapid development than the average of the developed countries in the EU, even if their economic situation was not a favorable one (Havlik 2003). We considered the stock market from Poland because it is one of the most J. Risk Financial Manag. 2022,15, 322 4 of 19 representative emerging markets for Central and Eastern Europe. This is also proved by the fact that it is the only country in this area for which sectoral indices are calculated. Malinowska (2021) studied 238 companies listed on the Warsaw Stock Exchange, the stock market from Poland, during 2007–2015. The conclusion was that the effects of the economic and financial crisis were noticed in the companies’ policies for future investments. The corporations’ profits were not affected but during the period analysed, both the stock return and the future growth of companies decreased. Even if the crisis did not affect the Polish market, the result confirms the lack of adequacy of the local banking sector. Chirilăet al. (2015) studied the volatility spillover between the stock markets from Central and Eastern Europe. The Polish stock market is more influenced by the shocks of its own market than by the shocks of the Euro zone market. This result is also confirmed by the study performed by Sucháˇcek et al. (2021), who analysed the effect of the 2007–2009 economic and financial crisis on the integration of CE stock markets. The authors reached the conclusion that the volatility of the Polish stock market was more influenced by local factors than by external ones. The crisis did not significantly influence the integration of the Polish stock market into the USA and European stock markets. On the Polish stock market, the number of listed companies registered a continuous decrease since 2015. As shown in Figure 1, the highest descending slope was recorded during 2016–2020, when 54 companies disappeared. The decrease in the number of listed companies in the year 2021, in comparison with 2020, is very low, with a decrease of only three companies. The decrease in the capitalization of the Polish stock market can be noticed continuously during 2017–2020, with a decrease of 95,000 million Euros. In the year 2021, the capitalization of the market increased by approximately 50,000 million Euros. J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 4 of 19 2. Polish Stock Market In the year 2004, major CE states such as Poland, Hungary, the Czech Republic and Slovakia, became EU members. It is for this reason that the Polish stock market is studied alongside that of Hungary and the Czech Republic whenever the emerging CE markets are analysed (Scheicher 2001; Li and Majerowska 2008; Syriopoulos 2007). The stock markets from these countries registered much more rapid development than the average of the developed countries in the EU, even if their economic situation was not a favorable one (Havlik 2003). We considered the stock market from Poland because it is one of the most representative emerging markets for Central and Eastern Europe. This is also proved by the fact that it is the only country in this area for which sectoral indices are calculated. Malinowska (2021) studied 238 companies listed on the Warsaw Stock Exchange, the stock market from Poland, during 2007–2015. The conclusion was that the effects of the economic and financial crisis were noticed in the companies’ policies for future investments. The corporations’ profits were not affected but during the period analysed, both the stock return and the future growth of companies decreased. Even if the crisis did not affect the Polish market, the result confirms the lack of adequacy of the local banking sector. Chirilă et al. (2015) studied the volatility spillover between the stock markets from Central and Eastern Europe. The Polish stock market is more influenced by the shocks of its own market than by the shocks of the Euro zone market. This result is also confirmed by the study performed by Sucháček et al. (2021), who analysed the effect of the 2007–2009 economic and financial crisis on the integration of CE stock markets. The authors reached the conclusion that the volatility of the Polish stock market was more influenced by local factors than by external ones. The crisis did not significantly influence the integration of the Polish stock market into the USA and European stock markets. On the Polish stock market, the number of listed companies registered a continuous decrease since 2015. As shown in Figure 1, the highest descending slope was recorded during 2016–2020, when 54 companies disappeared. The decrease in the number of listed companies in the year 2021, in comparison with 2020, is very low, with a decrease of only three companies. The decrease in the capitalization of the Polish stock market can be noticed continuously during 2017–2020, with a decrease of 95,000 million Euros. In the year 2021, the capitalization of the market increased by approximately 50,000 million Euros. 220,000 240,000 260,000 280,000 300,000 320,000 340,000 420 440 460 480 500 2014 2015 2016 2017 2018 2019 2020 2021 MARKET_CAPITALISATION NO_OF_LISTED_COMPANIES Figure 1. The evolution of the number of listed stocks and the capitalization of the stock market in Poland. Note: Performed by the authors based on the data from the Polish stock market (www.gpw.pl, accessed on 14 June 2022). Figure 1. The evolution of the number of listed stocks and the capitalization of the stock market in Poland. Note: Performed by the authors based on the data from the Polish stock market (www.gpw.pl, accessed on 14 June 2022). In order to determine the structure of the capitalization of the stock market according to different economic sectors, we took into consideration the capitalization of each stock composing the sectoral indices. The data were taken from the website www.investing.com, accessed on 14 June 2022. The results obtained are presented in Figure 2below. J. Risk Financial Manag. 2022,15, 322 5 of 19 J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 5 of 19 In order to determine the structure of the capitalization of the stock market according to different economic sectors, we took into consideration the capitalization of each stock composing the sectoral indices. The data were taken from the website www.investing.com on 14 June 2022. The results obtained are presented in Figure 2 below. Figure 2. The structure of the market capitalization of the Polish stock market according to different sectors. Source: Data processed by the authors are from www.investing.com (accessed on 14 June 2022). Based on these data, it can be noticed that the banking sector has a very high weight of 50.79%, followed by the energy sector (18.55%) and the oil and gas sector (11.33%). 3. Methods The spillover assessment using the methodology proposed by Diebold and Yilmaz (2008, 2012, 2014) is widely used for estimating volatility spillover. However, the spillover dynamics based on a VAR model are influenced by the chosen size for the rollingwindow, extreme values, mismatch for high-frequency data and information loss caused by the rolling-window. The removal of these disadvantages was achieved by using TVPVAR presented by Antonakakis et al. (2020). This study uses the latter methodology. We will go through several stages: (a) identifying the descriptive characteristics of the volatility indices of the Polish stock market’s sectors, (b) testing the stationarity of the sectors’ volatility series, (c) estimating the vector autoregressive (VAR) model, and d) forecasting the error variance decomposition for the quantification of volatility spillover (TVP-VAR). A vector-autoregressive model, VAR, is estimated and the variance decomposition matrix is determined. This allows the quantification of directional and net spillovers (connectedness) between stock market sectors. The estimated VAR model can be written as follows: 𝑥=∑𝜑𝑥𝜀   , (1) where 𝑥 is the vector of endogenous variables, 𝜑 is the autoregressive coefficient matrix, and 𝜀 is the vector of error terms. Relation (1) can be written as a moving average as follows: 𝑥=∑ 𝐴 𝜀   , (2) 𝐴 =𝜑 𝐴 𝜑 𝐴 ⋯𝜑 𝐴 , where 𝐴 is the coefficient matrix, 𝐴 is the identity matrix and 𝐴 = 0 for j < 0. Figure 2. The structure of the market capitalization of the Polish stock market according to different sectors. Source: Data processed by the authors are from www.investing.com (accessed on 14 June 2022). Based on these data, it can be noticed that the banking sector has a very high weight of 50.79%, followed by the energy sector (18.55%) and the oil and gas sector (11.33%). 3. Methods The spillover assessment using the methodology proposed by Diebold and Yilmaz (2008,2012,2014) is widely used for estimating volatility spillover. However, the spillover dynamics based on a VAR model are influenced by the chosen size for the rolling-window, extreme values, mismatch for high-frequency data and information loss caused by the rolling-window. The removal of these disadvantages was achieved by using TVP-VAR presented by Antonakakis et al. (2020). This study uses the latter methodology. We will go through several stages: (a) identifying the descriptive characteristics of the volatility indices of the Polish stock market’s sectors, (b) testing the stationarity of the sectors’ volatility series, (c) estimating the vector autoregressive (VAR) model, and (d) forecasting the error variance decomposition for the quantification of volatility spillover (TVP-VAR). A vector-autoregressive model, VAR, is estimated and the variance decomposition matrix is determined. This allows the quantification of directional and net spillovers (connectedness) between stock market sectors. The estimated VAR model can be written as follows: xt=∑p i=1ϕixt−1+εt, (1) where xt is the vector of endogenous variables, ϕi is the autoregressive coefficient matrix, and εtis the vector of error terms. Relation (1) can be written as a moving average as follows: xt=∑∞ i=1Ajεt, (2) Aj=ϕ1Aj−1+ϕ2Aj−2+· · · +ϕpAj−p, where Ajis the coefficient matrix, A0is the identity matrix and A0= 0 for j< 0. The moving average coefficients are used for variance decomposition. The variance of the H-step-ahead forecast error is decomposed into the variances determined by the shocks of the system in the VAR(p) model. J. Risk Financial Manag. 2022,15, 322 6 of 19 The contribution of variable x to the H-step-ahead generalized forecasting error variance for variable i, based on the generalized VAR of Koop et al. (1996) and Pesaran and Shin (1998), can be calculated as follows: θg ij(H) = σ−1 jj ∑H−1 h=0(e0 iAh∑ej)2 ∑H−1 h=0(e0 iAh∑A0 hej), (3) where σjj is the standard deviation of the error variable in equation j, and ei is the vector taking the value 1 for element iand zero otherwise. The generalized forecast error variance shares are thus obtained by normalization: e θg ij(H) = θij(H) ∑n j=1θij(H), (4) thus, ∑n j=1e θij(H) = 1 and ∑n i,j=1e θij(H) = N. The measurement of pairwise directional connectedness, at horizon H, from jto iis achieved based on the following formula: Si←j(H) = e θij(H)(5) The measurement of net pairwise directional connectedness is achieved based on the following formula: Sij(H) = Si←j(H)−Sj→i(H)(6) The directional volatility connectedness received by sector ifrom all other sectors j(FROM): Si←·(H) = ∑N j=1, j6=ie θij(H) ∑N i,j=1e θij(H)·100 =∑N j=1, j6=ie θij(H) N·100 (7) The directional volatility connectedness transmitted by sector ito all other sectors j(TO): S·←i(H) = ∑N i=1, j6=ie θij(H) ∑N i,j=1e θij(H)·100 =∑N i=1, j6=ie θij(H) N·100, (8) The net total directional spillover for sector i: Si(H) = S·←i(H)−Si←·(H), (9) The total spillover index: S(H) = S·←i(H) N=Si←·(H) N, (10) 4. Data and Empirical Steps For the study of the volatility spillover between shares of different economic sectors traded on the Polish stock exchange, the period from 1 January 2013 to 2 December 2021 is considered. This time frame allows studying volatility spillover before the outbreak of the health crisis caused by COVID-19 (without taking into consideration the period of the global financial crisis of 2008–2009 and the European sovereign debt crisis, 2010–2012) and also allows us to study the volatility spillover between sectors during the health crisis. The period considered is based on the research conducted by Costa et al. (2021), which had the same start date for the sample, and the sample stops earlier, on 31 December 2020. Daily returns determined based on sectoral indices will allow the performance quantification of each of the economic sectors we analysed. J. Risk Financial Manag. 2022,15, 322 7 of 19 The data used are the daily values of the sectoral stock indices calculated on this stock market including banks, basic materials, chemicals, construction, developers, energy, food, and oil and gas. They are considered high-frequency, daily data for several reasons. First, financial markets are known to immediately incorporate the information that emerges in the market into asset prices. Thus, the closing prices of the sectoral indices will reflect all the news or changes that occur during the day in the economic sector. Secondly, the daily closing prices of the sectoral indices also reflect the expectations regarding the evolution of the business sector. The return rate for each business sector is calculated based on the following formula: ri,t=lnIi,t Ii,t−1·100, (11) where ri,t is the log-return for the economic sector iat time t. Ii,t and Ii,t−1 are the values of the sectoral index i, at time tand t−1, respectively. Consistent with the studies of Antonakakis et al. (2018), Corbet et al. (2020) and Costa et al. (2021) for determining the volatility of the i-index price, we will use the following formula: Vi,t=|ln Ii,t−ln Ii,t−1|, (12) For each index, 2327 daily returns and volatilities were determined. This study carries out a comparison between the volatility spillover situation before and after the outbreak of COVID-19. Therefore, two sampling units are considered: the first sample unit covers the period from 1 January 2013 to 31 December 2019 (here, we also determined 1825 values for returns and volatility) and the second sample unit covers the period from 1 January 2020 to 2 December 2021 (502 values for returns and volatility). The samples are in compliance with the choice of samples performed by Costa et al. (2021) and Akhtaruzzaman et al. (2020). The stages that we will go through in achieving the proposed general objective are the following: (a) performing a descriptive analysis of the variables studied, (b) testing the stationarity of the variables to allow moving onto the next stage, (c) estimating the TVP-VAR model, and (d) conducting error variance decomposition. The results will allow for the prediction of the components according to the shocks of the studied component and the other components. 5. Empirical Results 5.1. Preliminary Analysis Figure 3shows the evolution of the return and of the value of the sectoral indices during the analysed period. A different evolution of these economic sectors can be observed, which suggests the possibility of diversifying a portfolio by buying stocks with different fields of activity. We also note an increase in stock market volatility from all sectors at the end of 2019 at the same time as the outbreak of COVID-19. The estimation of descriptive statistical indicators for the volatility of sectoral indices, presented in Table 1, shows that the basic materials and chemicals sectors had the highest average risk before the health crisis. However, after the outbreak of COVID-19, the highest level of average risk appears to be in the basic materials and energy sectors as shown in Table 2. The distributions of the volatilities of all sectors also show asymmetry and skews that deviate from a normal distribution, a result confirmed by the Jarque-Berra test. J. Risk Financial Manag. 2022,15, 322 8 of 19 J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 7 of 19 The data used are the daily values of the sectoral stock indices calculated on this stock market including banks, basic materials, chemicals, construction, developers, energy, food, and oil and gas. They are considered high-frequency, daily data for several reasons. First, financial markets are known to immediately incorporate the information that emerges in the market into asset prices. Thus, the closing prices of the sectoral indices will reflect all the news or changes that occur during the day in the economic sector. Secondly, the daily closing prices of the sectoral indices also reflect the expectations regarding the evolution of the business sector. The return rate for each business sector is calculated based on the following formula: 𝑟, =ln 󰇧𝐼, 𝐼,󰇨∙100, (11) where 𝑟, is the log-return for the economic sector i at time t. 𝐼, and 𝐼,are the values of the sectoral index i, at time t and t − 1, respectively. Consistent with the studies of Antonakakis et al. (2018), Corbet et al. (2020) and Costa et al. (2021) for determining the volatility of the i-index price, we will use the following formula: 𝑉,=ln𝐼,−𝑙𝑛𝐼,, (12) For each index, 2327 daily returns and volatilities were determined. This study carries out a comparison between the volatility spillover situation before and after the outbreak of COVID-19. Therefore, two sampling units are considered: the first sample unit covers the period from 1 January 2013 to 31 December 2019 (here, we also determined 1825 values for returns and volatility) and the second sample unit covers the period from 1 January 2020 to 2 December 2021 (502 values for returns and volatility). The samples are in compliance with the choice of samples performed by Costa et al. (2021) and Akhtaruzzaman et al. (2020). The stages that we will go through in achieving the proposed general objective are the following: (a) performing a descriptive analysis of the variables studied, (b) testing the stationarity of the variables to allow moving onto the next stage, (c) estimating the TVPVAR model, and d) conducting error variance decomposition. The results will allow for the prediction of the components according to the shocks of the studied component and the other components. 5. Empirical Results 5.1. Preliminary Analysis Figure 3 shows the evolution of the return and of the value of the sectoral indices during the analysed period. A different evolution of these economic sectors can be observed, which suggests the possibility of diversifying a portfolio by buying stocks with different fields of activity. We also note an increase in stock market volatility from all sectors at the end of 2019 at the same time as the outbreak of COVID-19. - 15 - 10 -5 0 5 10 15 2,000 4,000 6,000 8,000 10,000 2013 2014 2015 2016 2017 2018 2019 2020 2021 LR_BK P_BK -20 -15 -10 -5 0 5 10 15 1,000 2,000 3,000 4,000 5,000 6,000 7,000 2013 2014 2015 2016 2017 2018 2019 2020 2021 LR_BM P_BM (a) (b) J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 8 of 19 - 15 - 10 -5 0 5 10 15 4,000 8,000 12,000 16,000 20,000 2013 2014 2015 2016 2017 2018 2019 2020 2021 LR_CHE P_CHE -15 -10 -5 0 5 10 15 1,000 2,000 3,000 4,000 5,000 2013 2014 2015 2016 2017 2018 2019 2020 2021 LR_CO P_CO (c) (d) -15 -10 -5 0 5 10 15 1,000 1,500 2,000 2,500 3,000 3,500 2013 2014 2015 2016 2017 2018 2019 2020 2021 LR_DE P_DE -15 -10 -5 0 5 10 15 0 1,000 2,000 3,000 4,000 5,000 2013 2014 2015 2016 2017 2018 2019 2020 2021 LR_EN P_EN (e) (f) -15 -10 -5 0 5 10 15 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 11 12 13 14 15 16 17 18 19 20 21 LR_FOOD P_FOOD - 10 -5 0 5 10 15 2,000 4,000 6,000 8,000 10,000 2013 2014 2015 2016 2017 2018 2019 2020 2021 LR_OG P_OG (g) (h) Figure 3. Return and volatility evolution of equity sectors on the Polish stock market from 1 January 2013 to 2 December 2021. Note: (a) LR_BK, P_BK (b) LR_BM, P_BM (c) LR_CHE, P_CHE (d) LR_CO, P_CO (e) LR_DE, P_DE (f) LR_EN, P_EN (g) LR_FOOD, P_FOOD (h) LR_OG, P_OG represent the returns as well as the values of the sectoral indices of banks, basic materials, chemicals, construction, developers, energy, food, and oil and gas, respectively. The estimation of descriptive statistical indicators for the volatility of sectoral indices, presented in Table 1, shows that the basic materials and chemicals sectors had the highest average risk before the health crisis. However, after the outbreak of COVID-19, the highest level of average risk appears to be in the basic materials and energy sectors as shown in Table 2. The distributions of the volatilities of all sectors also show asymmetry and skews that deviate from a normal distribution, a result confirmed by the Jarque-Berra test. For the estimation of the TVP-VAR model, the variables considered must comply with the stationarity condition. To test the unit root, several tests were used in order to guarantee the validity of the results: the augmented Dickey–Fuller test (ADF) (Dickey and Fuller 1979), the Phillips–Perron test (Phillips and Perron 1988), the augmented Dickey– Fuller breakpoint unit root test (Perron 1989) and the ERS test (Elliott et al. 1996). The results obtained and presented in Tables 1 and 2 confirm the lack of unit root for the volatility series in the two periods studied. Table 1. Indicators of the descriptive statistics of volatility for the period of 1 January 2013–31 December 2019. Banks Basic Materials Chemicals Construction Developers Energy Food Oil and Gas Mean 0.009031 0.013779 0.011371 0.007420 0.005962 0.010875 0.008590 0.011226 Median 0.006854 0.010157 0.008710 0.005549 0.004714 0.008481 0.006492 0.008866 Maximum 0.061566 0.160636 0.079919 0.065477 0.056232 0.061967 0.118438 0.086895 Figure 3. Return and volatility evolution of equity sectors on the Polish stock market from 1 January 2013 to 2 December 2021. Note: ( a ) LR_BK, P_BK ( b ) LR_BM, P_BM ( c ) LR_CHE, P_CHE ( d ) LR_CO, P_CO ( e ) LR_DE, P_DE ( f ) LR_EN, P_EN ( g ) LR_FOOD, P_FOOD ( h ) LR_OG, P_OG represent the returns as well as the values of the sectoral indices of banks, basic materials, chemicals, construction, developers, energy, food, and oil and gas, respectively. J. Risk Financial Manag. 2022,15, 322 15 of 19 J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 14 of 19 (a) Banks (b) Basicm, (c) Chemic, (d) Constr, (e) Dev, (f) Energy, (g) Food and (h) Oil_Gas represent the sectors banks, basic materials, chemicals, construction, developers, energy, food, and oil and gas, respectively. The results were obtained by the authors In the other sectors, the periods when they were net receivers alternated with periods when they had net volatility spillovers. During the pandemic period, these sectors were also net receivers of volatility, except for the construction sector for which there was a small period of time in mid-2020 when it had a net spillover. -30 -20 -10 0 10 20 30 2013 2014 2015 2016 2017 2018 2019 2020 2021 NET_BANKS -30 -20 -10 0 10 20 30 2013 2014 2015 2016 2017 2018 2019 2020 2021 NET _ BASICM (a) (b) -30 -20 -10 0 10 20 30 2013 2014 2015 2016 2017 2018 2019 2020 2021 NET_CHEMICALS -30 -20 -10 0 10 20 30 2013 2014 2015 2016 2017 2018 2019 2020 2021 NET_CONSTR (c) (d) -30 -20 -10 0 10 20 30 2013 2014 2015 2016 2017 2018 2019 2020 2021 NET_DEV -30 -20 -10 0 10 20 30 2013 2014 2015 2016 2017 2018 2019 2020 2021 NET_ENERGY (e) (f) -30 -20 -10 0 10 20 30 2013 2014 2015 2016 2017 2018 2019 2020 2021 NET_FOOD -30 -20 -10 0 10 20 30 2013 2014 2015 2016 2017 2018 2019 2020 2021 NET_OIL_GAS (g) (h) Figure 6. Net volatility spillovers for sectors in the Polish stock market in the period 1 January 2013– 2 December 2021. Note: (a) Banks (b) Basicm, (c) Chemic, (d) Constr, (e) Dev, (f) Energy, (g) Food Figure 6. Net volatility spillovers for sectors in the Polish stock market in the period 1 January 2013–2 December 2021. Note: ( a ) Banks ( b ) Basicm, ( c ) Chemic, ( d ) Constr, ( e ) Dev, ( f ) Energy, ( g ) Food and ( h ) Oil_Gas represent the sectors banks, basic materials, chemicals, construction, developers, energy, food, and oil and gas, respectively. The results were obtained by the authors. J. Risk Financial Manag. 2022,15, 322 16 of 19 J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 15 of 19 and (h) Oil_Gas represent the sectors banks, basic materials, chemicals, construction, developers, energy, food, and oil and gas, respectively. The results were obtained by the authors. Figure 7 shows all net pairwise directional connectedness between the eight equity sectors on the Polish stock market. For each sector, the colours of the circles represent the nature of the sector, and the size of the circles represents the size of the spillover. The blue or dark grey colour shows us the sectors with volatility spillovers and the yellow or light grey colour shows us sectors that are net volatility receivers. The direction of the arrows indicates the direction of the volatility spillover and the thickness of the arrows indicates the size of the net spillover. Figure 7a shows the results obtained on the volatility spillovers between sectors before the pandemic and Figure 7b shows the results obtained during the pandemic. (a) (b) Figure 7. Net volatility spillovers between pairs of sectors in the Polish stock market. (a) In the period of 1 January 2013–31 December 2019 (before the crisis caused by the outbreak of COVID-19); (b) in the period of 1 January 2020–2 December 2021 (during the crisis caused by the outbreak of COVID-19). The banking sector had the largest net volatility spillover followed closely by the basic materials sector. This result is in line with the one obtained by Costa et al. (2021), according to which the financial sector was the main sector with volatility spillover in the US during the COVID-19 period. At the same time, Akhtaruzzaman et al. (2020) confirmed a stronger spillover of financial companies in comparison with the non-financial ones. In the same category, for the pre-pandemic period, we can also include the construction and oil and gas sectors but with a much lower net spillover. The net spillover was higher from the banking sector to the energy, developer and chemical sectors. From the basic materials sector, the net spillover was higher than in the food sector. In addition, it can be seen that there were net spillovers from almost all sectors to the food and developer sectors. The largest sector receiving volatility was the developer sector, followed by the food, chemicals and energy sectors. The situation changed during the pandemic during which we observed only two sectors with net volatility spillovers of the same intensity: banks and basic materials. Although there were more sectors receiving volatility compared to the pre-pandemic situation, the developer sector remained a receiver of volatility from most sectors, whereas the food sector received less volatility. There was also an increase in net spillover from the banking sector to the construction and food sectors. The results presented confirm hypothesis H 1, according to which the direction of the connectedness between economic sectors varies over time. Figure 7. Net volatility spillovers between pairs of sectors in the Polish stock market. ( a ) In the period of 1 January 2013–31 December 2019 (before the crisis caused by the outbreak of COVID-19); ( b ) in the period of 1 January 2020–2 December 2021 (during the crisis caused by the outbreak of COVID-19). 6. Conclusions, Limits of the Research and Future Directions The plans for the development of a country’s economic sectors must also take into account the connectedness between them. The study of the connectedness between the economic sectors of Poland allows us, on one hand, to strengthen policy makers’ decisions and, on the other hand, to strengthen the management of financial investment portfolios. This research presents new results on the connectedness and volatility spillover between stock market sectors in Poland. To the best of our knowledge, this is the only study with this objective conducted for a Central and Eastern European country. The methodology used is the one proposed by Antonakakis et al. (2020), which has multiple advantages compared to the method originally proposed by Diebold and Yilmaz (2008). For this research, the daily data of the sectoral indices from 1 January 2013 to 2 December 2021 were used. The time interval chosen for the analysis allowed the comparative study of volatility spillover between sectors before the outbreak of the COVID-19 pandemic and during the pandemic. The methodology used allowed a static as well as a dynamic comparative analysis. This methodology also allowed for comparisons to be made in regard to the level of spillover between stock market sectors from other countries. Static analysis of volatility spillover between the sectors of the Polish stock market and thus the connectedness between sectors shows a lower level before the COVID-19 pandemic than during the pandemic. The result suggests both the variation in time of the connectedness, which confirms research hypothesis H1 and also a higher level during the COVID-19 crisis, thus confirming research hypothesis H2. The dynamic analysis also underlines the fact that the sector with the highest volatility spillover is the banking sector, which confirms research hypothesis H3, i.e., that the financial sector has the strongest connectedness with the other economic sectors. The analysis of time-varying volatility spillover confirms the variation in the connectedness between sectors, confirming research hypothesis H1. In addition, the connectedness between sectors changes direction during the pandemic; for example, the chemical sector became a sector with volatility spillover although it was previously a volatility receiver, confirming research hypothesis H1. The results indicate an increase in volatility spillover in the system consisting of the Polish stock market sectors. The implications of these results would be that the advantages of sectoral diversification in times of crisis become smaller. When making practical decisions, risk managers need to take into account the strongest connectedness between sectors and adjust portfolio diversification by considering sectors with weak or very weak connectedness. Thus, investors, based on the knowledge of the dynamics performed following this J. Risk Financial Manag. 2022,15, 322 17 of 19 research, can adjust their transactional decisions in order to mitigate the risks, optimize the returns and ensure diversification during stock exchange turbulences. In this way, policymakers can also identify which sectors are those with the largest volatility spillovers and which are the largest volatility receivers. Identifying these sectors enables the design of macroprudential policies that will have the effect of reducing volatility spillover. Identifying the increase in volatility spillover also makes it possible to anticipate the outbreak of a crisis or a turbulent period; thus, it is a tool that can be used to forecast and monitor the outbreak of financial crises. Therefore, the results of this research highlight the limitations of the advantages of sectoral diversification and the need for risk management and portfolio allocation. In order to ensure the stability of the Polish stock market, it is also necessary to carefully monitor the volatility spillover among the economic sectors. Specifically, follow-up measures are needed in the banking, chemicals as well as in the basic materials sectors for the stability of the Polish stock market. Governmental decisions adapted to each sector, beyond a fiscal approach, are required. This approach is suggested by the research conducted by Bouri et al. (2021a) who indicate different effects on the sectors of the stock markets following the governmental decisions taken in New Zealand. A limitation of this research is the lack of possible comparisons with Central and Eastern European countries. This is partly due to the fact that there is no research on this group of countries and partly because no sectoral indices are available in other Central and Eastern European countries. This research also offers a new research direction, i.e., studying the connectedness of Polish economic sectors with those of EU member countries. The result obtained would allow for identifying the connectedness between the same economic sectors from different countries. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Data Availability Statement: Not applicable. 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