Microsoft Word - 00_tresc.docx © 2013 Nicolaus Copernicus University. All rights reserved. http://www.dem.umk.pl/dem D Y N A M I C E C O N O M E T R I C M O D E L S DOI: http://dx.doi.org/10.12775/DEM.2013.005 Vol. 13 (2013) 87−106 Submitted October 21, 2013 ISSN Accepted December 30, 2013 1234-3862 Agata Kliber, Barbara Będowska-Sójka* Economic Situation of the Country or Risk in the World Financial Market? The Dynamics of Polish Sovereign Credit Default Swap Spreads∗∗ A b s t r a c t. In the article we examine what determines the Polish sovereign Credit Default Swap dynamics. We consider not only measures of changes of the economic situation of the country, but also the impact of the international data. We find that the dynamics of the Polish sCDSs is very vulnerable to the dynamics of exchange rates, stock indices and bond spreads. These variables allow us to explain its behavior without including variables reflecting eco- nomic situation of the country. It is shown that the impact of information inflow is also im- portant. K e y w o r d s: sovereign Credit Default Swap, Bond spread, Stock Exchange indices, ex- change rates, sunspots, volatility transmission, volatility models, principal component analy- sis, event analysis. J E L Classification: C22, G14, G32. Introduction Credit derivatives were perceived as a successful financial innovation in the 90s. The most common type of credit derivatives are credit default swaps * Correspondence to: Agata Kliber, Poznań University of Economics, Department of Ap- plied Mathematics, Al. Niepodległości 10, 61-875 Poznań, Poland, e-mail: agata.kli- ber@ue.poznan.pl; Barbara Będowska-Sójka, Poznań University of Economics, Department of Econometrics, Al. Niepodległości 10, 61-875 Poznań, Poland, barbara.bedowska- sojka@ue.poznan.pl. ∗∗ This work was partially financed by the Polish Ministry of Science and Higher Educa- tion through the project number N N112 372340. Agata Kliber, Barbara Będowska-Sójka DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 88 (CDS). In a credit default swap one party of the contract buys protection and pays the seller a fixed premium each period, until either default occurs or the swap contract matures. If a default occurs, the seller is obligated to buy back from the buyer the defaulted bond at its nominal value. The sovereign credit default swaps (sCDS) are financial instruments perceived as a protection against insolvency on debt issued by the sovereign borrower (a country). The protection buyer pays a regular premium, the so- called CDS spread. During the financial crisis in 2008–2009 investors became concerned about the overall economic situation and as a result sCDS spreads rose sharply. The reason is that the price of the sCDS contracts is believed to represent the risk associated with the country. This is embedded in the nature of the contract, which can be interpreted as a bet on the country default or the “insurance” against the situation that the country would not pay its obli- gations. If the risk associated with the country grows, the price of the “insur- ance” must grow as well. CDS contract to some extent may be perceived as an insurance, although it differs in the sense that the protection buyer may receive the payment without suffering any loses. As from the start of global financial crisis sCDS spreads have risen substantially and then dropped al- most to the initial level, of particular interest is if these changes of spreads are driven by real economic situation. Usually the economic indicators are perceived as those that represent the economic situation of the country (see e.g. Kosmidou, 2008). However, most of the indicators are of monthly or quarterly frequency, while the sCDS in- struments are traded daily. Therefore, researchers point out that the sCDS premia is very vulnerable to sunspots and expectations and it may not reflect the risk properly (see eg. Longstaff et al., 2005; Longstaff et al., 2011; Plank, 2010). By sunspots we refer to extrinsic variables in the way that contagion is neither caused by the fundamentals deterioration nor by trade relation- ships. Moreover, the models for sCDS with macro-factors as the explanatory variables are usually capable of explaining about 50% of the sCDS dynamics (see e.g. Plank, 2010). In the case of the Polish market such a model is pre- sented in Kliber (2013b), where the monthly dynamics of sCDS premium is explained by the macro-data of monthly frequency. In the literature sCDS spreads are highly related to bond spreads and stock prices. Giannikos et al. (2013) find that CDS market dominates other markets in terms of price discovery and that the role of stock market dimin- ishes during the financial crisis. As in case of all other financial instruments, the sCDS premia may be also vulnerable to the macroeconomic events from the American economy (Longstaff et al., 2011). However macroeconomic Economic Situation of the Country or Risk in the World Financial Market?... DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 89 announcements constitute only a part of all incoming information and are released on the monthly basis. Lamoureux and Lastrapes (1990) use trading volume as a proxy for information arrival time. As trading volume is observ- able variable it may well provide an approximation of inflow of widely de- fined information. This paper contributes to the existing literature in a few aspects. First of all, we focus on the Polish financial market, which is usually neglected in literature. Secondly, we investigate jointly the influence of expectations and fundamentals in sovereign Credit Default Swap pricing. To examine this issue we consider proxies for domestic as well as outside-the-country “fun- damentals” and we study also the impact of selected American macroeco- nomic announcements together with information inflow measure. We focus our study on constructing a model where the explanatory variables could be of daily frequency and simultaneously account for the economic condition of the country. We examine whether the Polish sCDS premia could be treated as an indicator of the true risk of Polish economy. The remainder of the paper is structured as follows: in Section 1 we show how fundamentals influence the sCDS spreads, in Section 2 we focus on role of expectations in sCDS pricing, while in Section 3 we concentrate on the impact of macroeconomic announcements. We consider Polish sCDS of 5 years maturity over the period March 1, 2008 to May 31, 2013. 1. Interactions of the sCDS Spread with Variables Representing the Economic Situation of the Country (VAR-DCC Model) Based upon the findings in the literature we decided to include in our dataset the following variables: bond spreads, exchange rate, stock-exchange index and trading volume of the index as a proxy for incoming information. We are aware of the fact that the variables should not be considered as fun- damentals sensu stricto, since they themselves are prone to sunspot and ex- pectations. However, taking into account data of monthly frequency inevi- tably would result in loss of information about sCDS dynamics, since the latter are traded daily. Such an approach was proposed in Kliber (2013b) – the author tested vulnerability of monthly sCDS changes and volatility to the changes of such quantities as: unemployment, real wages, government earn- ings and expenditures, import, export, inflation, terms of trade, internal and external debt. The models were able to explain about 50% of the sCDS vari- ability. This result is similar to ones documented for another economies (see eg. Longstaff et al., 2011). Thus, we decided to use data of daily frequency DYNAMIC 90 that refl imperfe The the CEI yield of of the lo German the yield (see Fig Figure 1 Sinc sCDS s Eventua Polish s preted a Let are pron variable evolutio German Sinc of them tained. F mean, a – DCC( details). ECONOMETRIC lect the chan ections. e data used i IC database. f the given co owest risk in n bonds are d of 10-year gure 1). . Polish sCD turity) ce it is said spread the m ally, we take stock exchan as a proxy of us stress on ne to volatil es the most on of the risk n bonds. ce all of the m. The only e First, we run and in the se (1,1,1,1) of E . Table 1 pre Agata Klibe C MODELS 13 (2 ges of econo in the study Bond sprea ountry’s bon n the region ( considered. rs German bo S spread (5 y d, that the e most, as an e into accoun nge, as well f the informa ce again, tha lity transmis immune see k of Polish t variables are exception is n the VAR m cond step, w Engle (2002) esents the re er, Barbara Będ 2013) 87–106 omic situatio comes from ad is compu nds and the y (see e.g. Cou Thus, we ca onds from th years maturity vents from exchange ra nt WIG inde as its tradin tion flow to at we are aw ssion from o ems to be th treasury bond e non-station volume, wh model in orde we estimated ) with Studen sults of the V dowska-Sójka 6 n of Poland, m Datastream uted as a dif ield of the bo udert, Gex, 2 alculate the s he yield of Po y) and bond American m ate we took ex as a repres ng volume. T the market (F ware of the fa other market he bond-spre d in compar nary, we mod here the natu er to check fo the multiva nt distributio VAR estima being aware m, www.stoo fference betw onds of the e 010). In our spread by sub olish 10-yea spread (10 y market influe the USD/PL sentative one The volume Figure 2). act that the v ts. From the ead, represen rison with th deled the log ural logarithm or any intera ariate varianc on (see Appe ation. The nu e of their oq.pl and ween the economy case the btracting ars bonds years ma- ence the LN one. e for the is inter- variables e chosen nting the e risk of g-returns m is ob- ctions in ce model endix for umber of E lags (in and the used fun tion. Figure 2 Figure 3 The that all more cl What is not depe of the o investig Economic Situa our case thi estimation i nction VAR . WIG prices . Diagram of d e results of V the variable ear, we prese s very specia end on their other variable gated indicato ation of the Cou s is one lag) s run in R, p R, and the m and trading v dependencies VAR estimat s interact on ent the result al is that from own previou es from the s ors, they are untry or Risk in DYNAMIC ECO is chosen vi package vars model was est volume among the ec tion are pres ne with anoth ts also in the m all of the us changes, b system. This e most vulne the World Fina ONOMETRIC MO ia Schwarz in (Pfaff, 2008 timated utili conomic indic sented in the her. In order e separate dia variables on but are expla s can suggest erable to cha ancial Market?. DELS 13 (2013 nformation c 8a; Pfaff, 200 izing OLS p cators e Table 1. W r to make the agram (see F nly sCDS cha ained by the t that from a anges in expe ... 3) 87–106 91 criterion, 08b). We per equa- We notice e picture igure 3). anges do changes all of the ectations Agata Kliber, Barbara Będowska-Sójka DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 92 about future development of economic situation of the country (if we assume that such information are incorporated in bond prices, exchange rates and stock indices). In the next step, we estimate the multivariate conditional variance model with dynamic correlation (Engle, 2002), DCC(1,1,1,1) model with Student distribution, for the residuals obtained from the VAR model. Estimation is done in two steps. First, we estimate univariate volatilities (GARCH mod- els), and in the next step – the correlation equation. The estimation was run via OxMetrics6 software with package G@RCH (Laurent and Peters, 2002). The results of estimation are presented in Table 2. As we can see, all the variables (apart from trading volume) are significant in all equations. Also the average values of correlations are significant in the case of each pairs excluding the ones with volume. Absolute values of the correlations are ap- proximately 0.4. In Figure 4 we present the obtained estimates of conditional correlations for each pairs apart from the ones including volume, while in Figure 5 – the estimates of conditional variances. 2. Changes of Economic Situation in the World and Polish sCDS Pricing In this Section we examine the vulnerability of Polish sCDS prices to the changes of similar indicators from the neighbor countries. Again, we take into account: bond spreads, exchange rates and stock exchange indices. In order to account for as much of the variability of the data as possible and to reduce the number of explanatory variables we decide to use Principal Component Analysis and check the reaction of Polish sCDS prices to the changes of the first principal components of each group of variables. We calculate the bond spreads assuming again that the risk free rate of the region is represented by the German bonds yield. Based upon the previ- ous studies (Kliber, 2013a) we are aware of the fact that in the case of some countries such spreads in some periods appear to be negative. Hence, we excluded some of the countries from the analysis. Eventually, we took into account the following bond spreads: French and British (so called low-yield Western European countries), Spanish (Southern Europe), Swedish and Finnish (Northern Europe) and Hungarian one (Central Europe). The dynam- ics of the spreads is presented in Figure 6. At the time of the study Hungary was the country of the highest bond spread, i.e. its risk was the highest among all analyzed countries, compared to the German bonds. We observe also a gradual growth of risk of Spain, which equaled the Hungarian one at the end of the studied period. Yields of bonds in France and UK are very low E Figure 4 Figure 5 Economic Situa . Conditional WIG returns . Volatilities and returns o ation of the Cou correlations s and returns f of CDS spre of USD/PLN untry or Risk in DYNAMIC ECO of CDS spre from USD/PL ead changes, b exchange rate the World Fina ONOMETRIC MO ead changes, LN exchange r bond spread e (DCC model ancial Market?. DELS 13 (2013 bond spread rate (DCC mo changes, WIG l) ... 3) 87–106 93 changes, del) G returns DYNAMIC 94 compare spread i The that the variance tributed Souther countrie Figure 6 From pean Un dollar U nent An explana of the SEK/PL Fina and S& and the ance (se We transmis stock ex sions. ECONOMETRIC ed to Germa is occasional e results of P e first princip e of the syst d to Spain, rn Europe ha es. . Bond spread m the exchan nion: EUR/P USD/PLN (se nalysis in Tab atory power, system. Th LN – that is t ally, we ana &P500 (see F first compo ee Table 5). conclude th ssion from a xchange ind Agata Klibe C MODELS 13 (2 an bonds, wh lly even nega CA on bond pal compone tem. The hi France and ad indeed a ds of the selec nge rates we PLN, GBP/P ee Figure 7). ble 4. In this since it was he highest the EU curre alyse four sto Figure 8). Th onent was ab hat the bond all of the an dices are stro er, Barbara Będ 2013) 87–106 hile in the N ative. d spreads are ent explained ghest loadin Finland, wh an impact on cted European choose the m PLN, SEK/P . We present s case the fir s able to exp loadings ha ncies. ock exchang heir dynamic ble to explain d spreads are nalyzed indic ongly affecte dowska-Sójka 6 Northern Eur presented in d only about ngs in the fir hich sugges n the volatil countries most represe PLN as well t the results rst componen plain 55% of ave EUR/PL ge indices: C cs at that tim n already 75 e the most i cators of da ed by comm ropean coun n Table 3. W t 40% of the rst compone ts that the lity of the E entative for th as the pric of Principal nt has much f the overall LN, GBP/PL CAC40, DAX me was quite 5% of comm immune to v ily frequenc mon shocks tr ntries the We notice e overall ent is at- crisis in European he Euro- e of US Compo- stronger variance LN and X, BUX e similar, mon vari- volatility cy, while ransmis- E Figure 7 Afte we run In the f plained we add we add subsecti embedd the mod assumin the sam case of ables in first pri equation tility eq lagged between compare formatio els with that the Economic Situa . Exchange SEK/PLN an er computing the series of first model w by the histor the PC1s as the explana ion (Model ded. The resu dels are esti ng that the ω mple. In all c the conditio n the form of incipal comp n at their cur quation are th changes of n the sCDS c e the models on criteria. W h lower numb explanatory ation of the Cou rates of cu nd USD/PLN g the first pri f ARMA-GA we assume t rical values o s the explana atory variab 2). In the th ults of the es imated via th (see equatio cases the val onal mean eq f lagged retur ponent of bo rrent values) he squared l bond spread changes and b s on the bas We follow th ber of explan variables ar untry or Risk in DYNAMIC ECO urrencies: E N incipal comp ARCH mode that changes of the spread atory variabl les used in hird model ( timation are he so called on 1) is equal lues of this p quation, we rns (the exce ond spreads , while the e lagged return d, however i bonds’ sprea sis of the log he Schwarz cr natory variab re not redund the World Fina ONOMETRIC MO UR/PLN, G ponents of ea els (see mod of Polish s d only (Mode es (Model 1 VAR mode (Model 3) th presented in d variance-ta l to the unco parameter ar introduced t eption is the , which are explanatory v ns. In the fir it appeared ad changes ar g-likelihood riterion, sinc bles and hen dant. ancial Market?. DELS 13 (2013 GBP/PLN, H ach group of del (1) in Ap CDS are can el 0). In the n ). In the thir el from the p he previous n table 6. In argeting met nditional var re very smal the explanato bond spread introduced variables in t rst step we u that the inte re instantane function and ce it prefers t nce we could ... 3) 87–106 95 HUF/PLN, f factors, ppendix). n be ex- next one, rd model previous two are all cases thod, i.e. riance of ll. In the ory vari- d and the into the the vola- used also eractions eous. We d the in- the mod- d be sure DYNAMIC 96 Figure 8 The terion) i by princ Change spreads spread. exchang change nificant expect t the USD PC1-exc We pal com Thus, in need an drives t Europea 3. Imp The differen market ECONOMETRIC . Stock Excha axis) e best model is the most g cipal compon s of the spre of the neigh Additional s ge rates and rate. In the t variable is the special r D/PLN rate i change-rate would like t mponents outp n order to exp ny variables r the dynamic an countries, act of the A e literature o nt financial in (see e.g. Ed Agata Klibe C MODELS 13 (2 ange indices: (taking into general one – nents) and in ead can be th hbour countr significant ex d stock exch case of the the lagged s role of US ec s present in t component, to stress the performed th plain the dyn representing cs of this ris , as well as th Announcem on the effect nstruments is erington, Le er, Barbara Będ 2013) 87–106 CAC, DAX, account the – it includes ndicators of t hus explaine ries, as well xplanatory v hange indices conditional squared valu conomy on t the explanato and as the U fact that the he model inc namics of the the econom sk indicator he risk of Am ments from of macro n s huge and in ee, 1993), for dowska-Sójka 6 S&P (main ax e log-likeliho both the env the country‘ ed by the cur as the chang variables are s, as well as variance equ ue of WIG r the risk perc ory variables USD/PLN exc model inclu cluding the “ e Polish sCD mic situation o is the risk merican econ m the Ame news on retu ncludes surv reign exchan xis), and BUX ood and Schw vironment (ex s economic s rrent change ge of domes the lagged v s the USD/P uation, the o returns. We ception of Po s in two form change rate. uding only th “domestic” v DS we actuall of the countr perception nomy. rican Mark urns and vola eys concerni nge market ( X (second warz cri- xpressed stability. of bond stic bond values of PLN ex- only sig- can thus oland, as ms: in the he princi- variables. ly do not ry. What of other ket atility of ing bond (e.g. An- Economic Situation of the Country or Risk in the World Financial Market?... DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 97 dersen, Bollerslev, 1998) and equity market (e.g. Będowska-Sójka, 2011). Longstaff et al. (2005) confirm the impact of macroeconomic measures of bonds liquidity on CDS spreads. We examine to what extent are sCDS sensi- tive to macro news announcements and information flow to the market. Therefore, we use seven macro releases commonly used in the literature of macro news announcements effect (e.g. Almeida et al., 1998; Będowska- Sójka, 2011). These are: industrial production, retail sales, consumer confi- dence, durable goods order, unemployment rate, producer price index, new home sales and purchasing manager index. These announcements are aggre- gated into indicator variable (DV) taking value of 1 if at least one release occur within the day and zero otherwise. The data considering macro an- nouncements are from www.bankier.pl. As a measure of intensity of unobservable information arrival we use trading volume of WIG index (Lamoureux, Lastrapes, 1990). We assume that information arrival may influence the sCDS spreads. However, we are aware of the fact that in some cases trading volume cannot be an accurate proxy for information arrival. It refers to the liquidity motivated trading ac- tivities, heterogeneity among traders’ expectations and beliefs etc. (see Kalev et al., 2004). By incorporating lagged trading volume into the condi- tional volatility equation of the FIGARCH(1,d,1) model we examine if the rate of news arrivals significantly influence the conditional volatility. We model sCDS return series, rt, with AR(1)-FIGARCH (1,d,1) process (see Appendix 2). We introduce into the conditional variance equations indi- cator variable standing for aggregated macro announcements. Dummy varia- ble, DVt, has a value of 1 at the day of macro announcements and zero oth- erwise. This variable is responsible for the impact of the macro releases on the conditional volatility. If there is any influence of these macro releases, the estimated parameter should be significant. In another model we introduce the lagged volume, VOLt-1, into the conditional variance equation in order to account for undefined information. The significance of the parameter stand- ing by the volume variable would suggest that information inflow affect sCDS volatility. The FIGARCH model is chosen from the GARCH class models – the choice is based on information criteria and the value of loga- rithm of likelihood function. The results of model estimation are shown in Table 7. The impact of macro news is not significant. However, the lagged stock index volume vari- able appeared to be significant. It suggests that overall activity driven at least by incoming information or the rate of news arrivals are influencing sCDS premia’s volatility significantly. Agata Kliber, Barbara Będowska-Sójka DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 98 Parameters are stable across different specifications. When included in the equation, the lagged volume causes substantial reduction in the value of the constants’ parameter in the conditional variance equation. However, both α and β do not change substantially. Thus sCDS returns are not sensitive to the examined public macro announcements, but they are to some extent in- fluenced by unspecified information. Conclusions In the paper we analyzed dynamics of Polish sovereign Credit Default Swaps and checked its reaction to the changes of variables reflecting eco- nomic situation of the country, as well as the ones connected with economic situation in the world financial markets. In order not to replicate our previous findings, as well as not to lose too much information, we did not consider the actual fundamentals (of monthly or quarterly frequency), but concentrated on the variables from financial markets, such as bonds, exchange rates and stock indices. We compared the models that included the “domestic” varia- bles with the ones including the analogous variables from neighborhood countries. We found that although the variables reflecting the economic situation of the country play a significant role in explaining the dynamics of the sCDS premia, the model that take into account only the environment variables is capable to explain the dynamics of the premia even better. Both the ex- change rates and bond spreads have a strong explanatory power in explain- ing the sCDS premia. We find also that the impact of important macro news from the American economy on the dynamics of the sCDS premia is insig- nificant. However, we show that the impact of information inflow proxied by trading volume is strong. Taking into account the findings presented in the paper, we doubt whether the premium of the Polish Sovereign Credit Default Swaps should be treated as the risk indicator of the Polish economy. Moreover, the results of the research suggest that the links among some segments of world finan- cial markets can be stronger than the links among these segments within one country. References Almeida, A., Goodhart, C., Payne, R. (1998), The Effects of Macroeconomic News on High Frequency Exchange Rate Behavior, Journal of Financial and Quantitative Analysis, 33, 383–408, DOI: http://dx.doi.org/10.2307/2331101. 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(2011), How Sovereign is Sover- eign Credit Risk? American Economic Journal: Macroeconomics, American Economic Association, 3(2), 75–103, DOI: http://dx.doi.org/10.1257/mac.3.2.75. Pfaff, B. (2008a), VAR, SVAR and SVEC Models: Implementation Within R Package vars, Journal of Statistical Software, 27(4), http://www.jstatsoft.org/v27/i04/, (01.08.2010). Pfaff, B. (2008b), Analysis of Integrated and Cointegrated Time Series with R. Second Edi- tion, Springer, New York. Agata Kliber, Barbara Będowska-Sójka DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 100 Plank, T. (2010), Do Macro-Economic Fundamentals Price Emerging Market Sovereign CDS Spreads?, Working Paper: http://finance.wharton.upenn.edu/weiss/wpapers/2010/10- 5.pdf, (10.06.2013). Sytuacja gospodarcza kraju, czy oczekiwania? Co decyduje o dynamice polskich kontraktów CDS? Z a r y s t r e ś c i. W artykule dokonano analizy dynamiki kontraktów CDS (Credit Default Swap – instrumentów zamiany ryzyka kredytowego) wystawianych na polskie euroobligacje. Badanie dotyczy okresu 2008-2013. Celem badania jest określenie, czy na dynamikę kontrak- tów wpływ mają wydarzenia międzynarodowe, czy też krajowe, a w rezultacie, czy spread kontraktów, interpretowany jako wskaźnik ryzyka danego kraju, faktycznie to ryzyko od- zwierciedla. Na podstawie uzyskanych wyników można stwierdzić, że do opisu dynamiki i zmienności kontraktów CDS wystarczy model ze zmiennymi reprezentującymi ryzyko krajów sąsiadujących, nie uwzględniający wielkości związanych z jego gospodarką. S ł o w a k l u c z o w e: CDS, obligacje, indeksy giełdowe, kurs walutowy, zmienność, przenoszenie zmienności, analiza zdarzeń. Economic Situation of the Country or Risk in the World Financial Market?... DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 101 Appendix 1 – Tables Table 1. Estimates of the unrestricted VAR model for Polish sCDS, bond spread, exchange rate, WIG and its volume Dependent variable Explanatory variable Coeff. Standard error CDS CDS(–1) 0.0011 0.0359 WIG(–1) –0.3740 0.1062 VOL(–1) –0.0029 0.0022 bond(–1) 0.2365 0.0571 plnusd(–1) –0.0004 0.1110 const –0.0006 0.0012 WIG CDS(–1) 0.0078 0.0121 WIG(–1) 0.0790 0.0358 VOL(–1) –0.0014 0.0007 bond(–1) –0.0408 0.0193 plnusd(–1) –0.0131 0.0375 const 0.0004 0.0004 Volume (WIG) CDS(–1) 0.3037 0.4480 WIG(–1) 0.8220 1.3266 VOL(–1) –0.3923 0.0272 bond(–1) 0.1560 0.7137 plnusd(–1) –2.8653 1.3867 const 0.0004 0.0146 bond spread CDS(–1) –0.0060 0.0220 WIG(–1) 0.1329 0.0651 VOL(–1) –0.0010 0.0013 bond(–1) 0.0910 0.0350 plnusd(–1) 0.0277 0.0681 const –0.0003 0.0007 PLN/USD CDS(–1) –0.0240 0.0108 WIG(–1) 0.1525 0.0319 VOL(–1) 0.0007 0.0007 bond(–1) –0.0669 0.0172 plnusd(–1) –0.2078 0.0333 const –0.0003 0.0004 Note: the bolded parameters are statistically significant at α=0.05. CDS(–1) denotes the lagged change of CDS, WIG(–1) – lagged change of WIG, VOL(–1) – lagged volume, bond(–1) – lagged change of bond, plnusd(–1) – laggech change of exchange rate, while const – a constant. Agata Kliber, Barbara Będowska-Sójka DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 102 Table 2. Estimates of the DCC–Engle model – univariate GARCH models and con- ditional correlations Variable Coefficient Std.Error CDS ω x 10^4 0.3946 0.1872 α 0.1082 0.0301 β 0.8680 0.0304 WIG ω x 10^4 0.0103 0.0052 α 0.0674 0.0128 β 0.9259 0.0130 Volume ω 0.0098 0.0114 α 0.0536 0.0362 β 0.9062 0.0808 Bond spread ω x 10^4 0.1408 0.0582 α 0.0885 0.0217 β 0.8878 0.0254 Exchange rate ω x 10^4 0.0217 0.0103 α 0.0705 0.0208 β 0.9123 0.0230 Correlations ρ_(CDS, WIG) –0.4638 0.0350 ρ_(CDS, volume) –0.0081 0.0449 ρ_(CDS, bond) 0.4456 0.0359 ρ_(CDS, exR) –0.4216 0.0364 ρ_(WIG, volume) 0.0145 0.0440 ρ_(WIG, bond) –0.4154 0.0363 ρ_(WIG, exR) 0.3613 0.0388 ρ_(volume, bond) 0.0036 0.0415 ρ_(volume, exR) 0.0031 0.0437 ρ_(bond, exR) –0.3329 0.0377 a 0.0160 0.0040 b 0.9554 0.0154 df 11.1557 1.1568 Note: the bolded parameters are statistically significant at α=0.05. All the parameters named according to Formulas (3) and (4) in Appendix 2. Economic Situation of the Country or Risk in the World Financial Market?... DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 103 Table 3. Principal Component Analysis – bond spread. Components loadings and explanatory power of the variance of the system PC1 PC2 PC3 PC4 PC5 PC6 HU.spread 0.3204 –0.4507 –0.7563 0.0408 –0.3473 –0.0056 ESP.spread 0.5082 –0.1212 –0.0171 0.1036 0.6836 –0.4987 FR.spread 0.5409 –0.1180 0.2363 0.1014 0.1367 0.7802 UK.spread 0.1981 0.7156 –0.2518 0.6077 –0.1260 –0.0097 SVE.spread 0.3007 0.5036 –0.2166 –0.7796 0.0033 0.0341 FI.spread 0.4657 –0.0503 0.5114 –0.0140 –0.6144 –0.3759 Standard deviation 1.5202 1.045 0.9043 0.8842 0.77257 0.63295 Proportion of Variance 0.3852 0.182 0.1363 0.1303 0.09948 0.06677 Cumulative Proportion 0.3852 0.5672 0.7035 0.8337 0.93323 1 Note: first component explained only about 40% of the system variance. HU.spread denotes spread of Hungarian bonds, ESP – the Spanish ones, FR– the French ones, UK – the British ones, SVE – the Swe- dish ones, while FI – the Finnish ones. Table 4. Principal Component Analysis – exchange rates. Component loadings and explanatory power of the variance of the system PC1 PC2 PC3 PC4 PC5 eurpln 0.5531 –0.0157 0.1965 –0.1719 –0.7910 gbppln 0.5140 –0.1654 0.3073 –0.5496 0.5585 hufpln 0.2960 0.7208 –0.5928 –0.1847 0.0856 sekpln 0.4946 0.1695 0.2425 0.7835 0.2324 usdpln 0.3124 –0.6512 –0.6758 0.1432 0.0324 Standard deviation 1.6563 0.985 0.8267 0.6385 0.44174 Proportion of Variance 0.5487 0.1941 0.1367 0.08154 0.03903 Cumulative Proportion 0.5487 0.7428 0.8794 0.96097 1 Note: first component explained almost 55% of the system variance. The eurpln denotes the exchange rate of euro, gbppln – of British pound, hufpln – of Forint, sekpln – of Sweden, while usdpln – the American one. Table 5. Principal Component Analysis – stock exchange indices. Component load- ings and explanatory power of the variance of the system PC1 PC2 PC3 PC4 BUX –0.4351 0.8218 –0.3677 0.0113 CAC –0.5448 –0.0776 0.4497 –0.7035 DAX –0.5455 –0.1052 0.4323 0.7103 S&P –0.4651 –0.5546 –0.6897 –0.0196 Standard deviation 1.737 0.7495 0.6061 0.2347 Proportion of Variance 0.754 0.1404 0.0918 0.0138 Cumulative Proportion 0.754 0.8944 0.9862 1 Note: first component explained over than 75% of the system variance. BUX denotes the Hungarian stock exchange index, CAC – the French one, DAX – the German one, while S&P – the American Standard and Poor’s. Agata Kliber, Barbara Będowska-Sójka DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 104 Table 6. Estimates of ARMA–GARCH Models of the dynamics of Polish sCDS spread (model 0–4) . model 0 model 1 model 2 model 3 Variable Coeff. Std.Error Coeff. Std.Error Coeff. Std.Error Coeff. Std.Error CondME PCbond, t 0.116 0.009 0.095 0.010 PCex, t–1 0.177 0.069 0.253 0.080 PCin, t–1 0.148 0.037 0.159 0.036 Bondt 0.503 0.056 0.198 0.045 WIGt–1 –0.387 0.072 ERt–1 0.176 0.083 CVarEq (PCex, t–1)2 0.367 0.097 Vol t–1 0.000 0.001 (WIGt–1)2 0.390 0.133 0.486 0.123 (Bondt–1)2 –0.001 0.022 α 0.110 0.002 0.100 0.022 0.090 0.022 0.088 0.020 β 0.842 0.030 0.841 0.030 0.836 0.033 0.828 0.029 DF 4.230 0.388 4.218 0.366 4.258 0.418 4.332 0.402 ω 0.001 0.002 0.002 0.002 LL 2301 2460 2403 2481 LL ratio (mod. 0) 0.000 0.000 0.000 LL ratio (mod. 3) 0.000 0.000 0.000 Note: PCbond,t stands for first principal component in PCA for bond spreads. PCex, t–1 for exchange rates with lagged values, and PCin, t–1 for stock indices with lagged values. Bondt stands for domestic bond spread changes, WIGt–1 is lagged value of WIG returns, ERt–1 describes lagged returns of USD/PLN exchange rate, and Volt–1 is lagged value of trading volume of WIG index. Based upon the LL–ratio test we conclude that each of the models: 1, 2, 3 outperform the Model 0, while Model 3 outperforms all of the models: 0, 1 and 2. The bolded parameters are statistically significant at α=0.05. Table 7. Estimates of Model 4: AR(1)–FIGARCH(1,d,1) model of the dynamics of Polish sCDS spread with macro news and trading volume variables Coeff. Std.err. Coeff. Std.err. Coeff. Std.err. AR(1) 0.1017 0.0315 0.1000 0.0315 0.0979 0.0333 ω*104 306.8671 51.9121 289.8801 36.5562 262.7081 22.7071 DVt –0.0001 0.0001 Volt–1*104 2.4900 0.0359 d 0.7570 0.0452 0.7510 0.0461 0.7584 0.0444 α 0.0656 0.1051 0.0629 0.1020 0.0589 0.1104 β 0.7144 0.0587 0.7100 0.0599 0.7349 0.0548 df 3.2024 0.2381 3.2201 0.2436 3.1553 0.2245 LL 2311.7111 2312.3212 2313.1121 LL ratio test 0.27 0.09 Note: Volt–1 is lagged value of trading volume of WIG index. DVt is an indicator variable standing for aggregated macro announcements The bolded parameters are statistically significant at α=0.05. Economic Situation of the Country or Risk in the World Financial Market?... DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 105 Appendix 2 – The models ARMA–GARCH MODEL (Bollerslev, 1986) with explanatory variables. Let us denote by ty the value of the process at time t. The following model: 1 1 1 2 2 2 1 1 1 , , , m n t t i t i j t j t k i j k t t t p q r t i t i j t j k i j k r a r b y y z y y w σ ε σ ω α β σ − − = = = − − = = = = + + + = = + + + ∑ ∑ ∑ ∑ ∑ ∑ (1) is called an ARMA–GARCH model with explanatory variables iz and jw . We assume that tε is an iid process of mean 0 and unit variance. Moreover, 0, 0, 0.i iω α β> ≥ ≥ In Section 3 we use AR(1)–FIGARCH(1,d,1) model with specification given by Chung (1999): 1 1 , ,t t t t t tr r y yϕ σ ε−= + = 2 2 2 2 ,( )(1 ) ( ) [1 ( )]( ),d t i t i tL L y L yα σ β σ− − = − − (2) where: ∑∑ == −=Β−=Α p i i i q i i i LLLL 11 1)(,1)( βα , a 10 ≤≤ d is fractionally in- tegrated parameter. THE DCC MODEL (Engle, 2002). Let us denote by ty the value of the process at time t. Let us assume also that: 1| ~ ( , ), , Ft t t t t t t y N− = 0 H H D R D (3) where: 11, , 2 , , , , 1 1 1/2 1/2 ' 1 1 1 1 ( ,..., ), , 1,..., , ( ( ) ( ( )) , 1 . t t kk t q p ii t i t ij i t j ij ii t j j j t t t t M N M N t m n m t m t m n t n m n m n diag h h h y h i k R diag diag a b a b ϖ α β− − = = − − − − − = = = = = = + + = = ⎛ ⎞ = − − + +⎜ ⎟ ⎝ ⎠ ∑ ∑ ∑ ∑ ∑ ∑ D Q Q Q Q Q u u Q (4) Agata Kliber, Barbara Będowska-Sójka DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 106 The vectors tu are k–dimensional and , ,/it i t ii tu y h= .The k–dimensional matrix Q is the unconditional covariance matrix of .tu It is also assumed that the scalars ma and nb are non–negative and 1 1 1. M N m n m n a b = = + <∑ ∑ In our study we estimated the model with Student distribution, i.e. we assumed that: 1| ~ ( , , ),Ft t ty t ν− 0 H where ν denotes degrees of freedom. The value of this parameter is estab- lished through estimation. When 2ν > , then tH exists and is interpretable as a conditional variance matrix. The model was estimated using the two–step procedure. First, the Q was estimated as the unconditional correlation matrix of .tu Then, the parame- ters a and b were estimated by Gaussian quasi maximum likelihood. Bollerslev and Wooldridge (1992) showed that even in the case when data generating process is not conditionally Gaussian, we can obtain a consistent estimator using the Gaussian quasi maximum likelihood. For more details considering estimation in G@RCH package see eg. (Laurent et al., 2012).