Climate transition risk and the impact on green bonds

Antoniuk, Yevheniia; Leirvik, Thomas Article Climate transition risk and the impact on green bonds Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Antoniuk, Yevheniia; Leirvik, Thomas (2021) : Climate transition risk and the impact on green bonds, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 14, Iss. 12, pp. 1-19, https://doi.org/10.3390/jrfm14120597 This Version is available at: https://hdl.handle.net/10419/258700 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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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Journal of Risk and Financial Management Article Climate Transition Risk and the Impact on Green Bonds Yevheniia Antoniuk 1,* and Thomas Leirvik 1,2,3   Citation: Antoniuk, Yevheniia, and Thomas Leirvik. 2021. Climate Transition Risk and the Impact on Green Bonds. Journal of Risk and Financial Management 14: 597. https://doi.org/10.3390/jrfm14120597 Academic Editors: Chien-Chiang Lee, Chi-Chuan Lee, Zixiong Xie and Michał Buszko Received: 3 November 2021 Accepted: 7 December 2021 Published: 10 December 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. 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/). 1Nord University Business School, Nord University, 8049 Bodø, Norway; [email protected] 2School of Business and Economics, UiT The Arctic University of Norway, 9037 Tromsø, Norway 3NTNU Business School, Norwegian University of Science and Technology, 8900 Trondheim, Norway *Correspondence: [email protected] Abstract: The green bond market develops rapidly and aims to contribute to climate mitigation and adaptation significantly. Green bonds as any asset are subject to transition climate risk, namely, regulatory risk. This paper investigates the impact of unexpected political events on the risk and returns of green bonds and their correlation with other assets. We apply a traditional and regressionbased event study and find that events related to climate change policy impact green bonds indices. Green bonds indices anticipated the 2015 Paris Agreement on climate change as a favorable event, whereas the 2016 US Presidential Election had a significant negative impact. The negative impact of the US withdrawal from the Paris agreement is more prominent for municipal but not corporate green bonds. All three events also have a similar effect on green bonds performance in the long term. The results imply that, despite the benefits of issuing green bonds, there are substantial risks that are difficult to hedge. This additional risk to green bonds might cause a time-varying premium for green bonds found in previous literature. Keywords: green bonds; event study; climate regulatory risk; sustainable investment 1. Introduction This paper investigates how green bonds are affected by unexpected political events related to climate change. We find that over the period July 2014 and November 2021, green bonds significantly outperform conventional bonds in terms of returns. We further find that the 2016 US presidential election (USPE) has a significant negative impact on bonds in general and green bonds in particular. Other unexpected political events, such as the 2015 Paris Agreement (PA), have a positive and significant impact on green bonds and no significant impact on conventional bonds. Green bonds (GB) were introduced by the European Investment Bank in 2007 as an instrument with a purpose to finance projects with an environmentally friendly profile; see, for example, Horsch and Richter (2017), Zhang et al. (2019) and Nguyen et al. (2020). A GB is a fixed-income instrument specifically earmarked to raise money in the debt markets for climate and environmentally friendly projects. These bonds are typically asset-linked and backed by the issuing entity’s balance sheet, so they usually carry the same credit rating as their issuers’ other debt obligations. GBs are designated bonds intended to encourage sustainability and to support climate adaptation and mitigation. The green bond market has grown in popularity, and not without reason: according to Chambwera et al. (2014), mitigation and adaptation to climate change require significant investments of $70–100 billion per year to ensure sufficient adaptation in major sectors until 2050. Bonds are suitable financial vehicles for these purposes because they have an inter-temporal basis and let the issuer pay back the raised capital over time. This is one reason why climate finance researchers suggested an introduction of a climate bond in the first place. According to Flaherty et al. (2017), easing the investment burden for the current generation while implementing climate-change policy can be more easily carried out using GB. It means that GB has an important role in the transition to a low-carbon economy. J. Risk Financial Manag. 2021,14, 597. https://doi.org/10.3390/jrfm14120597 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2021,14, 597 2 of 19 Longand short-term climatic trends include changes in the distribution of temperature, precipitation, and cloudiness. Observational studies have found that temperature increases over time, with an increase in all regions on Earth and with an increase in the level, variability, and drivers of the level of temperature; see, for example, Storelvmo et al. (2016), Yuan et al. (2021), and Kotz et al. (2021). Precipitation, on the other hand, shows more heterogeneous trends, with dry areas getting dryer and wet areas getting wetter; see Gulev et al. (2021) for a thorough treatment of the matter. The change in climatic trends has, in general, a profound impact on economies and financial markets around the world, see Burke et al. (2015), Campiglio et al. (2018), Sarkodie et al. (2020), and Bartram et al. (2021), and on the banking sector in particular, see Duqi et al. (2021). Moreover, Bolton and Kacperczyk (2021) find that investors are already demanding compensation for carbon emissions. Exposure to climate risk restricts access to finance in general (Ginglinger and Moreau 2019). Higher exposure to such risk leads to higher cost of debt (Kling et al. 2021), lower credit ratings, and higher yield spreads (Seltzer et al. 2021) because such companies are perceived as more likely to default (Capasso et al. 2020). In our paper, we investigate how unexpected political events related to transitioning countries and economies towards lower carbon emissions affect the green bond market. Low-carbon transition is seen as a way to reduce climate change’s impact on the economy and planet. This process is expected to induce transition risks in addition to physical ones stemming from the climate change itself. Although both are important, this paper’s focus is on the former. The reason is that firms feel less exposed to physical risk, which is expected to materialize in the more distant future (Sakhel 2017). Transition climate risks include a regulatory risk that comes with an introduction of and adjustments to climate policy, either global or local. Companies are more concerned about regulatory risk because its impact could lead to additional expenses or changes in expected growth that should be priced. With the strong link that GB has to climate and the environment, we hypothesize that GB’s price is affected by events related to environmentally sensitive issues, such as climate change and political legislation and regulations on the matter. Mitigation and adaption to climate change have been on the political agenda for a few years, though there are few globally recognized regulations and limitations on, for example, greenhouse gas emissions. Often, regulatory changes are long processes with lengthy negotiations. According to the efficient market hypothesis (see Fama 1970;Tran and Leirvik 2019), any regulations that impact a firm or industry are reflected in the asset prices. For this reason, we investigate how abrupt and unexpected political events affect the prices since such events are hard to account for before the event. Building on the previous literature, we focus on three events: the Paris agreement, the 2016 US presidential election, and the US withdrawal from the Paris agreement, and find that all three significantly affect the bond markets. The green label attracts investors interested in or focused on socially responsible investments (SRI) and investors who want to diversify portfolios, as highlighted in Nguyen et al. (2020). Green bonds widen the choice for SRI investors since they can invest in a project and not in the company itself (Shishlov et al. 2016). The demand for green bonds is high, increases every year, and continues to rise, according to Banga (2019). Thus, green bond investors must understand the risks inherent in the prices. We argue that green bonds might have an uncompensated advantage since they offer higher returns with lower volatility. However, as we show, there is significant political risk tied up in the prices of GBs, which might be the reason why the premiums found by Zerbib (2019) changes over time. So far, the impact of climate risk has been mostly studied on the stock market with an emphasis on carbon risks (Bolton and Kacperczyk 2021;In et al. 2019;Kumar et al. 2019) and attention paid to climate-related policies events (Antoniuk and Leirvik 2021;Birindelli and Chiappini 2021;Diaz-Rainey et al. 2021;Koch et al. 2016;Monasterolo and de Angelis 2020;Ramadorai and Zeni 2019). This paper is among the first to apply an event study on green bonds. This work is complementary to Seltzer et al. (2021), which looked at the J. Risk Financial Manag. 2021,14, 597 3 of 19 effect of climate regulatory risk on conventional corporate bonds, while ours investigates green corporate bonds and extends the analysis to municipal bonds and the secondary bond market. 2. Literature Review We consider two strands of literature that are related to our research. The first covers green bonds, and the other is related to studies on climate regulation. 2.1. Green Bonds Earlier studies looked at the definition of green bonds, general market trends (Kochetygova and Jauhari 2014), and barriers for its further development (Clapp 2014). Later research focused on GB performance, how GBs are different from conventional bonds, and how they are related to other assets. The differences between green and conventional bonds have received much attention. The research interest is a green premium, or greenium, a negative yield difference between green and conventional bonds, which causes GBs to have a higher price. Zerbib (2019) finds that GBs have a negative premium compared with conventional synthetic bonds of the same issuer in USD (Euro). This implies that they trade on a discount compared to comparable bonds. This discount, however, is different for bonds with a credit rating lower than AAA. Zerbib (2019) shows that this premium of -2 bp is neither a risk premium nor a market premium, and thus it could be related specifically to green bonds. A negative premium was also found by Immel et al. (2021). Partridge and Medda (2020) show that greenium exists for municipal bonds, while Fatica et al. (2021) conclude that financial issuers have a higher GB yield. Larcker and Watts (2020) suggest that green and non-green municipal bonds are seen as substitutes when risk and payoff are held constant. Overall, according to MacAskill et al. (2020), a green premium is found within 56% of primary and 70% of secondary market research papers. Wulandari et al. (2018) find that GBs are more liquid, and Nanayakkara and Colombage (2019) find that the yield spread is tighter for bonds issued in local currency. Karpf and Mandel (2018) argue that the liquidity premium for green bonds is time-varying and that the premium was negative only until 2015 and positive later. Bachelet et al. (2019) find that the GB premium is positive and about 2.09–5.9 bp but claim that correction for liquidity and issue type solves the premium puzzle. Tsoukala and Tsiotas (2021) find that GBs are riskier than conventional bonds in terms of value-at-risk and conditional value-at-risk. GBs are correlated with corporate bonds (Horsch and Richter 2017); moreover, this co-movement has a time-varying character: Broadstock and Cheng (2019) find that it was negative before 2014 and became positive after. Green bonds correlate negatively with VIX and the US dollar index (Horsch and Richter 2017;Reboredo and Ugolini 2020), making them a good tool for diversification (Ehlers and Packer 2017), i.e., by reducing the total risk of a portfolio. GB is also connected and dependent on corporate and treasury bonds (Reboredo et al. 2020), commodities (Naeem et al. 2021; and especially oil by Kanamura 2020), clean energy (Nguyen et al. 2020), and carbon futures (Hung 2021;Jin et al. 2020). Recent studies have looked at the impact of COVID-19 on this connectedness and found that it has become more prominent (Arif et al. 2021;Bouri et al. 2021;Naeem et al. 2021). COVID-19 has also affected bond market efficiency, but the green bond market is more efficient than the conventional one (Naeem et al. 2021). 2.2. Climate Regulation The impact of the climate-related policies was mostly studied for the stock market. The overall conclusion was that these policies affect market prices. Not only does the introduction of new policy cause reaction on the market, it also affects its timing. Adopting earlier climate policies helps to avoid shocks in asset pricing (Battiston et al. 2017), while introducing policies during low market sentiment or attention can lead to price decrease and volatility increase on the emission market (Deeney et al. 2016). J. Risk Financial Manag. 2021,14, 597 4 of 19 Some studies look closer at specific events related to climate change. Birindelli and Chiappini (2021) find that only EU high-score firms reacted positively to the Paris agreement, but all companies had an extensive negative wealth effect after it. After this event, the correlation between low-carbon and carbon-intensive indices became lower, and investors started to consider an opportunity to invest in low-carbon assets (Monasterolo and de Angelis 2020). The 2016 US Presidential election’s impact on the stock market was evaluated for fossil and oil companies (Diaz-Rainey et al. 2021), for different types of energy companies (Mukanjari and Sterner 2018), and for other sectors that are climate-sensitive (Antoniuk and Leirvik 2021). All of them found a non-positive reaction to the election results. The only companies with gain in returns are those with large deferred tax liabilities (Wagner et al. 2018). These events were only touched in few studies on the bond market. Seltzer et al. (2021) studied corporate bonds and found that differences in credit ranking and the yield spread between companies with poor and rich environmental profiles were more prominent after the Paris agreement, with some reversal after the US pullout from the agreement. The Paris agreement also played an important role in the green bond market in general by significantly affecting its growth (Tolliver et al. 2020a) and increasing green bond allocation to renewable energy (Tolliver et al. 2020b). 3. Materials and Method In this paper, we apply daily prices for July 2014–November 2021 for a sample of green bond indices available from S&P. They include: GB: S&P Green Bond Index, which tracks the global green bond market and includes only bonds whose proceeds are used to finance environmentally friendly projects. GB S: S&P Green Bond Select Index, which is a market-value-weighted subset of the GB bonds issued globally, subject to stringent financial and extra-financial eligibility criteria. Muni GB : S&P Municipal Green Bond Index, which tracks the US green municipal bond market. Additionally, we consider the S&P International Corporate Bond Index (Corp B) and the S&P Municipal Bond Index (Muni B) for comparative purposes. The S&P 500 (SP500) is used as a reference for the stock market, and the S&P US Treasury Bond Index ( T-BondI ) is a factor that affects the bond market in general. Previous research finds a connection between green bonds and other assets; therefore, we also include data on: Dollar: US dollar index is obtained from the St. Louis Federal Reserve.1 Commodity: S&P GSCI Index, which is a benchmark for investment in the commodity markets and a measure of commodity performance over time. Brent: daily Brent Crude Oil price. Clean energy: S&P Global Clean Energy Index, tracks the performance of companies in global clean energy-related businesses from both developed and emerging markets. CO2: CO2 European Emission Allowance, which prices climate credits used in the EU Emission Trading Scheme. VIX: CBOE Market Volatility Index, measures 30-day expected volatility of the stock market. Our sample starts in July 2014, although a more extended time series for the S&P green bond indices is available. Since most of the green bond indices from S&P were launched in 2014, we argue that only after that would index prices reflect the event’s impact. Table 1 shows the summary statistics of the assets we investigate in this study. The GB has the lowest mean return at 0.42 bp (0.0042%), and Muni B had the lowest risk, as measured by the standard deviation of the returns. J. Risk Financial Manag. 2021,14, 597 5 of 19 Table 1. Summary statistics. The numbers in this table are given in percentages using daily data over the period we investigate. The Green Bond Index (GB) has the lowest mean daily return at 0.42 bp (0.0042%), and the Municipal Bond Index (Muni B) has the lowest daily volatility at 0.191% among bond indices. Mean Std. Dev Min Median Max Skewness Kurtosis N.Valid GB 0.0042 0.312 −2.386 0.003 2.033 −0.526 5.794 1825 GB S 0.0047 0.355 −2.913 0.008 2.292 −0.523 6.004 1825 Corp B 0.0043 0.495 −4.547 0.010 2.990 −0.858 9.661 1825 Muni GB 0.0153 0.267 −3.330 0.019 4.221 −0.899 86.031 1825 Muni B 0.0143 0.191 −2.592 0.019 3.394 −0.379 124.893 1825 T-BondI 0.0095 0.216 −1.674 0.012 1.805 0.239 8.160 1825 SP500 0.0466 1.124 −12.765 0.066 8.968 −1.039 21.247 1825 Brent − 0.0144 2.647 −27.976 0.040 27.419 −0.521 21.982 1825 Clean Energy 0.0484 1.456 −11.748 0.083 11.666 −0.480 10.315 1825 CO2 0.1230 2.773 −18.969 0.132 12.497 −0.438 4.497 1825 Dollar 0.0111 0.317 −2.089 −0.004 1.925 0.165 3.949 1825 Commodity 0.0074 1.404 −11.770 0.074 7.986 −0.629 7.914 1825 VIX − 0.0034 8.348 −29.983 −0.723 76.825 1.261 6.897 1825 We apply a standard event study methodology, which has been widely applied in financial research to investigate how significant news (the event) affects stock prices and returns; see, for example, Bessembinder and Zhang (2013), Duarte-Silva and Tripolski Kimel (2014), Buigut and Kapar (2019), Heyden and Heyden (2020). We have identified three events relevant for our study: the Paris agreement (PA), the 2016 US presidential election (USPE), and the announcement of the US pullout from PA (USPO; Table 2). PA and USPE are of particular interest, as both were highly unanticipated political events with significant consequences for climate-relevant policies. PA initiated the adoption and gradual implementation of national plans about coping with climate change, in which investment instruments such as green bonds played a significant role. Two other events were seen as an inhibitors to climate adaptation and mitigation. We hypothesize that PA will benefit green bonds, whereas other events will affect it negatively. Our results largely confirm these hypotheses. Table 2. Set of the events for analysis. Date Event Description PA 12 December 2015 Paris agreement UN Climate Change Conference, which adopted the Paris Agreement that governs climate change reduction measures from 2020. USPE 8 November 2016 US election The 58th quadrennial US presidential election had an outcome that differed from the results of the poll. USPO 1 June 2017 US pull out US President announced that the US would cease all participation in the 2015 Paris Agreement on climate change mitigation. COVID 13 November 2020 COVID-19 Lockdown A national emergency was declared in the US in order to reduce the spread of SARS-CoV-2. The underlying idea is to test whether realized returns around the event dates are different from the expected ones derived from the model. For each model, the estimation is done based on 200 observations 10 days before the event, meaning that if the event day is denoted as t= 0, the estimation of the relevant parameters is based on observations t∈[− 210, − 11 ] . Suppose the event does not carry new information for the market. In that case, there will be no surprise, and thus excess (abnormal) return, which is the difference between realized and expected returns, for the event should be zero. J. Risk Financial Manag. 2021,14, 597 6 of 19 We calculate abnormal returns (AR) based on three expected returns models (Warner and Brown 1985): • Mean adjusted model: the expected return is equal to the mean return in the estimation period; • Market adjusted model: the expected return is equal to the [stock] market return; • Market model: the expected returns follow a one-factor [stock] market model. The event window is then defined to include the three trading days before and three days after the event, or t∈[− 3; 3 ] . For this window, both abnormal and cumulative abnormal returns (CAR) are calculated. CARiT0,T1= T ∑ t=T0 ARit, (1) where T0indicates the number of days before the event included in the computation, and T1 indicates how many days after the event are included. We tested CAR−3,−1 , CAR−1,1 , and CAR1,3 , which means that we tested event windows of three days, though with a varying number of days before and after the event. Because events tend to affect not only returns but also volatility, we check for this simultaneously by applying [omment = Added a better explanation of the used models]exponential generalized autoregressive conditional heteroscedasticity model, EGARCH(m, s), which also includes S&P 500 as an external regressor that affects returns model with an autoregressive moving average process ARMA(p, q):generalized autoregressive conditional heteroscedasticity model, GARCH(1,1), which also includes S&P 500 as an external regressor that affects returns: Rt=µ+cXt+∑p i=1φiRt−i+at−∑q j=1θjat−j,at=σtet ln(σ2 t) = ω+∑s i=1αi|at−i|+γiat−i σt−i+∑m j=1βjln(σ2 t−j) (2) where R is daily index return, X is an explanatory variable, e is an iid standard normal error, and a is an innovation. σ2 is a volatility of the returns. A set of dummy variables Di is introduced in the mean and variance models to capture the event effect. Di equals one if t corresponds to event day and zero otherwise. A detailed specification of distribution and order for ARMA and EGARCH models is given in Appendix A. The advantage of this model is two-fold: firstly, we can additionally account for eventinduced changes in volatility, and secondly, we do not need to divide our sample into testing and event window because events enter the model as dummy variables (Pynnönen 2005). We also calculate correlation and different performance measures (risk, return, valueat-risk, and Sharpe (1994) ratio) for bond indices to assess a longer-term impact of four events: the Paris Agreement, the 2016 US presidential election, the announcement of the US pullout from PA, and US lockdown in 2020. Recent research shows that the COVID-19 pandemic and lockdown impact the financial markets and thus should also be considered. 4. Empirical Results As discussed previously, this study aims to investigate the impact of unexpected political events related to environmentally sensitive issues on the returns of assets related to the green bond market. The reason we choose political events, and not physical events such as a natural disasters creating destruction to plants and infrastructure, is that political events, in contrast to physical events, do not carry a direct cost for which it is possible to compute changes in cash flows to the firm. J. Risk Financial Manag. 2021,14, 597 7 of 19 The indices history shows that some of the selected events are associated with changes in returns, and others not so much; see Figure 1for an illustration. Note that the green bond indices are highly correlated with corresponding conventional bond indices. However, for both municipal and corporate bonds, green bonds slightly outperform conventional ones: for both groups, darker lines for conventional bond indices in Figure 1are mostly visible below. The municipal bond indices do not seem to be affected by the events, whereas corporate bonds, to a higher extent, increase or decrease after the events. The lockdown is associated with a bond market decline, during which corporate green bonds outperformed the conventional ones until late 2020, when this relationship reversed. In contrast, municipal green bonds also continued to outperform conventional municipal bonds after the US lockdown. We test the impact of the events on the returns statistically and find their significant effect on both green and conventional bonds (Table 3). PA USPE USPO Covid GB GB S Corp B Muni B Muni GB 90 100 110 120 130 2015 2016 2017 2018 2019 2020 2021 2022 Cumulative return Figure 1. Historical prices of the green bond indices. J. Risk Financial Manag. 2021,14, 597 8 of 19 Table 3. Estimated reaction on the events. This table shows estimated abnormal returns in percentages obtained based on the mean adjusted, market, and market adjusted models [(1), (2), and (3) respectively]. It also presents estimated abnormal returns [(4) ret.] and abnormal volatility [(4) vol.], obtained by ARMA-EGARCH with S&P500 or T-Bond index as an external regressor to mean model and event dummy variables added to mean and variance modeling. For each event, we look at the abnormal outcomes on the event day (event) and the cumulative abnormal returns three days prior to the event ( − 3; − 1) and after the event (1;3). Additionally, we report cumulative abnormal returns for one day before and after the event (−1;1). Asterisks indicate the significance of the coefficients: * p<0.1; ** p<0.05; *** p<0.01. Paris Agreement (PA) US Presidential Election (USPE) US Pullout from the PA (USPO) COVID-19 Lockdown Model event −1; 1 −3;−1 1;3 event −1; 1 −3;−1 1;3 event −1; 1 −3; −1 1;3 event −1; 1 −3; −1 1;3 GB (1) −0.13 −0.31 0.95 * −0.86 −0.05 −1.45 *** −0.48 −2.73 *** −0.13 0.62 0.41 0.52 −0.89 *** −3.81 *** −3.88 *** −4.56 *** (2) −0.10 −0.34 0.79 −0.80 −0.05 −1.52 *** −0.51 −2.75 *** −0.10 0.66 0.40 0.51 −0.17 −4.93 *** −4.70 *** −5.55 *** (3) −0.64 0.02 3.37 ** −1.94 −0.39 −5.04 *** −1.99 * −3.78 *** −0.88 * −0.46 0.55 0.55 −9.74 *** 10.14 *** 6.37 *** 7.77 *** (4) ret. −0.13 * 0.23 * −0.18 * 0.58 * (4) vol. −1.16 * 2.74 * −1.16 * 3.34 * GB S (1) −0.14 −0.28 1.12 * −0.93 −0.03 −1.51 *** −0.55 −2.74 *** −0.16 0.62 0.39 0.53 −1.09 *** −4.45 *** −4.31 *** −5.58 *** (2) −0.10 −0.31 0.90 −0.85 −0.03 −1.58 *** −0.58 −2.76 *** −0.12 0.67 0.37 0.52 −0.16 −5.90 *** −5.38 *** −6.86 *** (3) −0.65 0.06 3.53 ** −2.01 −0.37 −5.10 *** −2.05 * −3.80 *** −0.91 * −0.45 0.53 0.57 −9.94 *** 9.51 *** 5.94 *** 6.76 *** (4) ret. −0.13 *** −0.01 * −0.20 *** −0.24 * (4) vol. −0.80 * 1.96 *** −0.90 * 3.12 *** Corp B (1) −0.30 −1.05 1.07 −1.81 ** −0.06 −1.82 ** −0.29 −3.11 *** −0.22 0.38 −0.01 0.56 −1.69 *** −6.81 *** −5.53 *** −9.58 *** (2) −0.26 −1.09 0.87 −1.74 ** −0.12 −2.46 *** −0.55 −3.29 *** −0.20 0.42 −0.02 0.56 −1.25 *** −7.50 *** −6.04 *** −10.19 *** (3) −0.81 −0.73 3.48 ** −2.90 * −0.42 −5.43 *** −1.81 −4.19 *** −0.98 −0.69 0.13 0.60 −10.55 *** 7.14 *** 4.73 *** 2.76 * (4) ret. −0.31 * −0.02 * −0.12 * −2.22 * (4) vol. −0.55 * 1.39 ** 0.17 * 3.24 *** Muni B (1) −0.12 −0.11 0.29 ** −0.06 −0.06 −0.65 *** 0.00 −2.14 *** −0.03 0.30 0.34 0.34 0.07 −2.61 *** −4.35 *** −1.80 *** (2) −0.11 −0.12 0.24 * −0.04 −0.04 −0.50 *** 0.06 −2.10 *** −0.03 0.30 0.34 0.34 0.49 *** −3.26 *** −4.83 *** −2.37 *** (3) −0.58 0.34 2.82 ** −1.02 −0.42 −4.29 *** −1.55 −3.25 ** −0.79 * −0.79 0.46 0.36 −8.78 *** 11.36 *** 5.92 *** 10.56 *** (4) ret. −0.03 ** 0.14 ** −0.13 *** 1.51 *** (4) vol. 0.01 * 4.31 *** −0.62 *** 4.93 *** J. Risk Financial Manag. 2021,14, 597 15 of 19 Table A1. The top-three selected ARMA specifications by the lowest Akaike Information Criteria (AIC). Asterisks denote specifications used in the first run of ARMA-EGARCH models. Bond index Distribution AR (p) MA (q) Mean AIC Used std 4 2 0 1.2491 * std 4 2 1 1.2496 Corp B sstd 4 2 0 1.2497 std 2 4 0 0.3832 * std 2 4 1 0.3834 GB sstd 2 4 0 0.3835 ghyp 4 3 1 0.6534 * std 2 4 0 0.6539 GB S std 2 4 1 0.6543 sstd 2 4 1 −1.9055 * sstd 1 0 1 −1.9043 Muni B sstd 1 1 1 −1.9040 jsu 4 3 1 −0.9201 * jsu 1 0 1 −0.9200 Muni GB jsu 1 1 1 −0.9194 The starred ARMA specification was used in the ARMA(p, q)-EGARCH(2, 4) model. After eliminating insignificant ARMA-orders and remaining serial autocorrelation in residuals and squared residuals, the final specifications have changed (Table A2). Moreover, the serial autocorrelation in residuals of the municipal bond indices with the S&P 500 index as a regressor remained significant at high lags order. Thus, the S&P 500 was replaced with the T-Bond index for the municipal bond indices, and dummy variables for Mondays (which impacts bond indices, see Berument and Kiymaz 2001) and January were introduced. The models are tested for serial autocorrelation in residuals and squared residuals, so that final models do not have significant serial autocorrelation present. These models also have no uncaptured asymmetry present in the residuals. Estimated coefficients of the models are given in Table A3, where their significance is derived based on the robust standard errors. Table A2. The final specifications for the ARMA models with associated Akaike Information Criteria (AIC). Bond Index Distribution AR (p) MA (q) s m AIC Corp B std 4 2 2 2 1.1779 GB std 2 4 2 3 0.3183 GB S ghyp 4 2 2 2 0.6014 Muni B snorm 4 4 2 2 −1.3531 Muni GB snorm 2 2 2 2 −2.3481 J. Risk Financial Manag. 2021,14, 597 16 of 19 Table A3. Estimation results for the ARMA-EGARCH models.Asterisks indicate the significance of the coefficients: * p<0.1; ** p<0.05; *** p<0.01. GB GB S Corp B Muni B Muni GB Mean model µ0.007 * 0.010 *** 0.016 *** φ1−0.187 *** −0.162 *** −1.622 *** −0.336 *** 0.073 ** φ2−0.991 *** −0.941 *** −0.595 *** −0.386 *** 0.354 *** φ30.034 *** 0.018 *** 0.368 *** φ40.045 *** −0.009 *** 0.158 *** θ10.237 *** 0.183 *** 1.647 *** 0.710 *** 0.275 *** θ21.047 *** 0.982 *** 0.646 *** 0.705 *** −0.206 *** θ30.066 * −0.021 ** θ40.055 −0.094 *** c−0.016 * −0.024 *** 0.008 * 0.225 *** 0.336 *** Mon 0.010 *** 0.006 * Jan 0.043 *** 0.047 *** Variance model ω−0.100 * −0.107 ** −0.073 * −0.279 *** −0.183 *** α10.008 * 0.019 * −0.009 * −0.084 * −0.063 * α20.017 * 0.019 * 0.014 * 0.077 * 0.076 * β10.182 * 0.321 *** 0.440 * 1.000 *** 1.000 *** β20.333 * 0.632 *** 0.516 * −0.056 ** −0.047 β30.446 * γ10.050 * −0.013 * 0.023 * 0.407 *** 0.402 *** γ20.185 * 0.193 *** 0.192 ** −0.130 * −0.110 * Distribution skew −0.604 * 0.968 *** 0.984 *** shape 7.287 * 0.250 * 6.552 *** λgh −3.790 *** Notes 1St. Louis Federal Reserve: stlouisfed.org. 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