- Email: [email protected]
The long-run relationship between the spot and futures markets under multiple regime-shifts: Evidence from Turkish derivatives exchange
Expert Systems with Applications 40 (2013) 4206–4212
Contents lists available at SciVerse ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
The long-run relationship between the spot and futures markets under multiple regime-shifts: Evidence from Turkish derivatives exchange ˘ LI ⇑, Pınar Evrim Mandaci 1 Efe Çag˘lar ÇAG _ IR, _ Turkey Dokuz Eylül University, Faculty of Business, Department of Finance, Kaynaklar Campus, Buca-IZM
a r t i c l e Keywords: Spot price Futures price Cointegration Structural breaks Market efficiency
i n f o
a b s t r a c t The paper examines the long-run relationships between the spot and future prices of Istanbul Stock Exchange 30 index (ISE-30) and foreign currencies including the Turkish Lira-US Dollar (TL/USD) and Turkish Lira-Euro (TL/EUR). We analyze the weekly data covering the period from February 9, 2005 to October 17, 2012. Considering structural breaks is important for our analysis since our period consists of recent financial crisis. Therefore, we employ the unit root tests developed by Carrion-i-Silvestre et al. (2009) and the Maki’s (2012) cointegration test allowing for an unknown number of breaks. We find that spot and the futures prices are cointegrated in the long-run after we consider structural breaks in our data. Our results indicate that the markets are efficient. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Although it has begun its operations only a few years ago, the Turkish Derivatives Exchange (TDEX) has become one of the fastest growing emerging futures market in the world.2 There are a variety of futures contracts in TDEX; i.e., equity index futures on ISE 30 and ISE 100 indices, currency futures on US Dollars and Euro, commodity futures on gold, cotton, wheat and live cattle and energy futures on base-load electricity. However, among them index contracts have the highest trading ahead of the currency futures in the second place. While index contracts from 88.38% and 97.20% of the total number of contracts traded and the total trading value for 2010, currency contracts follow them with 11.38% and 2.58% respectively. Investors make use of stock index futures to speculate on the performance of the entire market; if they expect an improvement in the economy, they will buy the index; otherwise they will short the index. They can also use currency futures to speculate on the value of currencies thereby taking long position in futures contract on that currency or vice versa. Index futures contracts are used in speculative way in the TDEX as frequently as in the most of index futures in the world, yet investors may also use them to hedge their spot equity portfolio against the price declines by going short at the futures market. Here, it is important for the investors to ⇑ Corresponding author. Address: Dokuz Eylul Universitesi, Isletme Fakultesi, Kaynaklar Yerleskesi, Buca, IZMIR – Turkiye. Tel.: +90 232 4535060; fax: +90 232 4535062. ˘ LI), [email protected] E-mail addresses: [email protected] (E.Çag˘lar ÇAG (P. Evrim Mandaci). 1 Tel.: +90 232 4535060; fax: +90 232 4535062. 2 TURDEX has been operating since February 2005. Its trading value was only 3,029,588,946 TL in 2005 and was reached to 431,681,986,516 TL in 2010. 0957-4174/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.eswa.2013.01.026
determine their optimum hedge ratio by considering the correlation between the prices of futures and spot positions.3 Similarly, traders, particularly importers and exporters, can use currency futures to hedge their foreign exchange positions by taking a long or a short position on currency futures. In addition, arbitrage is another aim of involving into the futures contracts. Arbitrageurs make transactions in both spot and futures market for the same asset and make profit when the price of the futures contract gets out of line with its spot price. These can be summed up as the main reasons motivating the researchers to investigate the relationship between the spot and future prices. According to the efficient market hypothesis, generally in the financial markets all relevant information is always efficiently processed and reflected simultaneously into both the spot and futures prices, hence arbitrage opportunities would always be limited. Brooks, Garrett, and Hinich (1999) argue that in a perfect market with non-stochastic interest rates and dividend yields, they are perfectly contemporaneously correlated and no lead–lag relationship would exist. The relationship between the spot and futures prices can also be explained by the price discovery hypothesis. Accordingly, if the markets are efficient and frictionless, then price discovery would be instantaneous and contemporaneous. Otherwise, price discovery would occur in one market and the other market would follow it. The normal and theoretically correct relationship between the spot price and its futures can be explained by the ‘‘cost of carry model’’ or the ‘‘spot–futures parity theorem’’. The
3 For instance, if there is a high correlation between the prices of futures and spot positions, the hedge ratio will be closed to unity. The equation of the hedge ratio is; ht ¼ qt sst =sft where q is the correlation coefficient between the portfolio and futures return and r is the standard deviation over the hedging horizon.
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
parity for the index futures can be stated as:
F 0 ¼ S0 ð1 þ r f dÞT
ð1Þ
where F0 is the future price at time 0, S0 is the spot price at time 0, rf is the risk-free rate, and d is the dividend yield on the stock portfolio. It is called the ‘‘cost of carry relationship’’ because it defines a setting in which futures price must exceed the spot price by the net cost of carrying the asset until maturity date T (Bodie, Kane, & Marcus, 2009: 775). However, in practice one should take into account some market imperfections such as asymmetric information, transaction costs, short-selling, margins, and liquidity, which might cause deviations from that parity. Those deviations might induce lead–lag relationships between the spot and futures markets and enhance the arbitrage chances for investors trading in both of these markets. There are a considerable number of studies depicting that futures market leads the spot market due to deviations such as high liquidity, low transaction costs, easy availability of short positions and low margins of the futures market (e.g. see, Chan, 1992; Kawaller, Koch, & Koch, 1987; Stoll & Whaley, 1990 and Abhyankar, 1998; Pizzi, Economopoulos, & O’Neill 1998). On the other hand, Brooks, Rew, and Ritson (2001) argue that the lead–lag relationship between spot and futures markets do not last for more than half an hour and argue that the parity holds in the long-run. In the same line, Maslyuk and Smyth (2009) argue that the theoretical relationship between spot and futures prices is a long-run, rather than short-run because in the short-run, there might be deviations between spot and future prices however in the long-run they are driven by the same macroeconomic indicators. Following to these studies, in this paper our aim is to examine the long-run relationship between the spot and futures prices of both the ISE 30 and foreign currencies in order to find out whether these markets are efficient. This paper provides three contributions to the existing literature: First, many empirical studies examining the long-run relationship between the spot and futures prices have adopted the vector auto regression model (VAR) or cointegration methods proposed by Engle and Granger (1987) (EG) and Johansen (1988) (e.g. see, Ghosh, 1993; Wahab & Lashgari, 1993; Brenner & Kroner, 1995; Pizzi et al., 1998 and Brooks et al., 2001) but, none of these studies have allowed for a structural break in the cointegrating vector. Therefore, different from the previous studies we employ the unit root tests developed by Carrion-i-Silvestre, Kim, and Perron (2009) and the Maki’s (2012) cointegration test allowing for an unknown number of breaks. Considering structural breaks is important for our analysis since our period consists of the effects of the recent financial crisis. Second, many of the previous studies examine the developed futures markets but this paper analyze TDEX which is an emerging market in its early stages but has become one of the top 30 futures exchanges in the world after just eight years. Third, our data consist of the index (TDEX-30) and currency futures (TDEX-USD and TDEX-EUR) which are mostly traded contracts representing almost the whole market for the period from February 9, 2005 to October 17, 2012 covering the whole life of TDEX. Existence of the long-run relationship indicates that the markets are efficient in the long run and eliminate the diversification benefits in portfolios that consist of the stock index and its futures as well as the currencies and their futures for a long period. Our results are important for the investors and portfolio managers holding both spot and their futures to provide diversification or hedging, for security analysts to determine fair values of spot and futures and policy makers to arrange some rules and regulations in order to provide efficiency and liquidity in these markets.
4207
The remainder of this study is organized as follows. Section 2 gives a brief summary of literature. Section 3 describes the methodologies employed. Section 4 shows the data and the empirical results, and in Section 5 we draw our conclusions.
2. Literature review A large number of studies analyzing the relationship between the spot and its futures market mostly focus on the short-run relationships by applying the modified and non-modified Granger Causality (GC) tests with the intraday data. Since our focus is the long-run interactions between these markets here we will just give a review on studies using cointegration techniques most of which employ Error Correction Models (ECM) and GC tests after they find the evidence of cointegration. Among them, Ghosh (1993) applies EG cointegration test to analyze the long-term equilibrium relationship between S&P 500 index prices and futures prices covering the time period from June 12, 1986, through December 31, 1989. He finds that there exists a cointegration relationship between futures and spot markets, in addition he estimates short-run relationship between them and argues that future prices GrangerCause cash prices in the case of the S&P 500 index. Similar to this study, Wahab and Lashgari (1993) examine the long-run relationship between the futures and spot markets of S&P 500 and FTSE 100 over the period from 1988 to 1992 by using daily closing prices and applying the same methodology and find that they are cointegrated. However in contrast to Ghosh (1993), they indicate that spot returns contribute more than future returns. Tse (1995) examines the relationship between the spot and futures price of the Nikkei stock exchange by using daily data from December 1988 through January 1993 and find that the series are cointegrated. Pizzi et al. (1998) examine the price discovery in S&P 500 cash index and its futures using intraday data for the period from Jan 1987 to March 1987 applying the EG methodology and find that they are cointegrated indicating market efficiency. In addition, their results show that the spot prices lead the futures prices. Brooks et al. (2001) employ the EG method to test cointegration between the FTSE 100 index and its futures by using 10 min data for the period from June 1996 to 1997 and find a strong relationship between them. They also find that changes in spot index depend on the lagged changes in the spot index and futures price, while the lead–lag relationship between spot and futures markets do not last for more than half an hour. Chai and Gou (2009) examines five International stock index spot and futures data including S&P 500 index futures, Dow Jones index futures and NASDAQ 100 index futures in the USA, Nikkei 225 index futures in Japan, Hang Seng index futures in Hong Kong of China, to verify whether there exists long-term steady relationship between the index spot and futures prices. They apply the EG cointegration method and based on the cointegration theory and ECM, conclusions are drawn that index spot and futures are cointegrated in most cases and it is possible to do the corresponding short term dynamic adjustment for reaching new equilibrium in next period. Nieto, Fernandez, and Muñoz (1998) apply the Johansen cointegration test to examine the relationship between Spanish stock index and its futures by using daily data from March 1, 1994 through Sep 30, 1996. They find a long-run relation between them indicating that the cost of carry model holds in the long run. Pattarin and Ferretti (2004) study the relationship between the Italian MIB30 index and futures log-prices with a bivariate ECM and apply the Johansen cointegration test by using daily observations beginning from November 28, 1994 to September 19, 2002 and find that the relationship is hold in the long-run. Very little work has investigated the impact of stock index futures trading in the emerging markets. Among them, Cheng and
4208
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
Liu (2003) tests Hang Seng index spot and futures series data from April 26th, 2001 to December 28th, 2001 by cointegration approach, and draw the conclusion that the spot–futures relationship is long-term stable. Gee and Karim (2005) analyze the lead–lag relationship between spot and futures markets of the Malaysian Kuala Lumpur Composite Index (KLCI) by employing the cointegration and error-correction approach. Results of the study suggest that cash market and futures market are cointegrated. The results of the ECM suggest that futures price lead spot price depicting that the investors are able to use futures price as a good indicator in predicting spot price. Rajaguru and Pattnayak (2007) use daily observations of spot index and the future prices of the Hang Seng indices, covering the period from January 1988 through October 2001. They measure performance of Fractionally Integrated ECM (FIECM) against the possible alternative models and find that the best forecasting performance is obtained from error correction and fractional cointegrated models for the short and long forecasting horizon respectively. They find the evidence of lead and lad relationships between spot and futures prices in the short-run while the futures prices are led by spot prices in the long-run. Li (2009) examines the dynamic spot–futures relationship from three mature including the U.S. S&P 500, the U.K. FTSE100 and the German DAX 30, and two emerging markets including the Brazil Bovespa and the Hungary BSI, using Markov-switching vector ECM. His empirical finding is that the futures price is shown to lead the spot price in the price discovery process. Özen, Bozdog˘an, and Zügül (2009) examine the long-run relationship between the ISE 30 index and its futures by applying the Johansen (1988) and Johansen and Juselius (1992) cointegration tests for the period beginning from February 4, 2005 and ending at February 27, 2009. They use daily closing prices and conclude that there exists a bidirectional relationship between them. Özün and Erbaykal (2009) analyze the relationship between spot and futures markets in Turkish foreign-exchange markets by employing Bounds cointegration test to daily data covering the period of January 2, 2006 to March 25, 2008. Their results indicate that the spot and futures foreign exchange markets of Turkey have informational efficiency. However, in their study, Lien, Tse, and Zhang (2003) argue that due to the dominance of the ‘normal’ period in sample data, the lead–lag relationship identified in the spot–futures system based on conventional methods such as the test for GC pertains to the normal period and may not be applicable in an ‘extreme’ period. Therefore, they employ a nonparametric genetic programming (GP) approach to identify the structural changes in the Nikkei spot index and futures price. They find that the major market changes originated from the spot market and spread over to the futures market. Similar to Lien et al. (2003), we consider structural breaks in our data series but different from it, we examine long-run relationship between the spot and futures prices by employing Maki (2012) cointegration test that accounts for the effect of multiple unknown structural breaks.
3. Methodology 3.1. Testing for breaks in the trend function of a time series Perron and Yabu (2009) develop a procedure in order to test whether there is any structural change in a univariate time series. The procedure computes the test, so called Exp-WRQF, for breaks in the trend function of a time series valid whether the noise component is stationary or integrated. Put another way, Exp-WRQF test can be applied when it is a priori unknown whether the series is trendstationary or contains an AR unit root. This test based on robust
quasi-flexible generalized least squares allows for an unknown break in the intercept, deterministic time trend or in both (Perron & Yabu, 2009:370). 3.2. Unit root test In the case of the existence of a structural break in the deterministic trend, the conventional unit root tests, such as Augmented Dickey–Fuller (ADF), lose their power and lead researchers to unreliable conclusions. In this way, Perron (1989) suggests unit root tests that allow the possibility of a break under null hypothesis of unit root against alternative of stationarity. However, the Perron’s (1989) test (PT) procedures suffer from the assumption of that the timing of the break date is known a priori since incorrect break date causes size distortions and power loss (Hecq and Urbain (1993)). Accordingly, Zivot and Andrews (2002) (ZA) develop alternative unit root test allowing an unknown structural breaks in the data. However, ZA type test statistics lose power when the noise component has a unit root and a break occurs in the trend function since they do not allow a break under the null hypothesis. To overcome those types of shortcomings, Kim and Perron (2009) (KP) propose a new methodology which allows a break in the trend function at an unknown time under both the null and alternative hypotheses. By doing so, KP relaxes the most controversial assumption (known break date) of PT. In addition, the limit distribution of the KP test becomes the same as in the case of Perron (1989). Carrion-i-Silvestre et al. (2009), Kim and Perron (2009) (CKP) extend the methodology of KP by allowing for an arbitrary number of changes up to five structural breaks in both the level and slope of the trend function. The break dates in CKP test are estimated depending on the data using an algorithm based on Bai and Perron (2002). CKP test considers M-class unit root tests, introduced in Stock (1999) and analyzed in Ng and Perron (2003), adopting the quasi-GLS detrending method advocated by Elliot et al. (1996). CKP reports that, their tests have good power and size properties based on the Monte Carlo simulations. In this way, CKP tests with good power and size properties solve many aforementioned problems of previous methods widely employed in the literature.4 3.3. Cointegration Maki (2012) develops cointegration test (MBk) with unknown number of structural breaks. The methodology introduced in Maki’s (2012) paper has two main advantages over the methods widely used in the literature. First, the MBk based on tests for structural breaks proposed by Bai and Perron (1998) and a unit root test with structural breaks developed by Kapetanios (2005), assumes that unspecified number of breaks of the cointegrating vector is smaller than or equal to the maximum number of breaks set a priori. Second, the methodology of MBk is substantially less computationally intensive than the previous methods (Maki, 2012: 2011). In addition to aforementioned issues, the results of the Monte Carlo simulations suggest that MBk test performs better than the tests of Gregory and Hansen (1996) and Hatemi-J (2008) when the cointegration relationship has more than three breaks or persistent Markov switching shifts (Maki, 2012). Maki (2012) proposes four regression models in order to test cointegration allowing for multiple structural breaks:
yt ¼ l þ
k X
li Di;t þ b0 xt þ ut
ð2Þ
i¼1
4 See Carrion-i-Silvestre et al. (2009) for detailed technical explanations for the procedures of tests.
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
yt ¼ l þ
k X
li Di;t þ b0 xt þ
i¼1
yt ¼ l þ
k X
k X b0i xt Di;t þ ut
ð3Þ
Table 1 The Perron and Yabu (2009) test for a break.
i¼1
li Di;t þ ct þ b0 xt þ
i¼1
k X b0i xt Di;t þ ut
ð4Þ
i¼1
4209
Panel A Exp-WRQF TB
TDEX-30
TDEX-USD
TDEX-EUR
5.5426a 12-Mar-08
26.4516 a 3-Oct-08
9.5343 a 13-Jul-11
ISE-30 5.6626 a 12-Mar-08
TL/USD 10.5045 a 3-Oct-08
TL/EUR 7.1225 a 20-Jul-11
Panel B
yt ¼ l þ
k X
li Di;t þ ct þ
i¼1
k X
k X ci tDi;t þ b0 xt þ b0i xt Di;t þ ut
i¼1
ð5Þ
i¼1
where t ¼ 1; 2; . . . ; T. yt (dependent) and xt ¼ ðx1t ; . . . ; xmt Þ0 (regressors) indicate observable integrated of order one (I(1)) variables, and ut is the equilibrium error. Di,t takes value of 1 if t > TBi ði ¼ 1; . . . ; kÞ and of 0 otherwise, where k is the maximum number of breaks and TBi indicates the time period of break. The first model, level shift model, captures changes in the level (l) only. Second model accounts for structural breaks both in the level (l) and regressors (x), called regime shift model. Third model is regime shift model with trend (c); and the fourth model constitutes structural breaks of levels, trends, and regressors. MBk with the null hypothesis of no cointegration against the alternative hypothesis of cointegration with i breaks (i 6 k) are implemented in the following steps (Maki, 2012:2012)5: First, we estimate one of the four regression models and then save the residuals. Second, we compute the t-statistics in order to test for unit root in the residuals, obtained from the estimated model, for all possible periods of the break. Let the set of all possible partitions and the tstatistics be represented by T ai , and siq , respectively. Third, the ith ^ ) is chosen by minimizing the sum of squared residbreakpoint (bp i uals (SSR) for the estimated model. Here, the breakpoint i can be ^ ¼ arg min SSRi . Finally, we adopt sk as the test staindicated as bp i min Ta tistic (MBk), that is, i the minimum t-statistic over the set skq ¼ s1 [ s2 [ ::: [ sk . 4. Data and empirical results 4.1. Data All data are weekly from February 9, 2005 to October 17, 2012 for a total of 401 observations and obtained from three sources. We collect data for ISE-30 price index from the web page of the Istanbul Stock Exchange (ISE); settlement prices of TDEX-30 index, TDEX-USD and TDEX-EUR from the web page of the TDEX, and the spot prices of Turkish Lira-US Dollar (TL/USD) and Turkish Lira-Euro (TL/EUR) exchange rates from the Electronic Data Delivery System (EDDS) of the Central Bank of the Republic of Turkey (CBRT). 5. Empirical results In this study, the long-run relationship between the spot and futures prices of both the ISE-30 and foreign currencies are analyzed in order to check whether these markets are efficient. Table 1 reports the Perron and Yabu (2009) Exp-WRQF test statistics and the dates of the structural changes. Panel A and B presents the results for the future and spot price indices, respectively. We estimate Exp-WRQF test statistic based on the Model III of Perron and Yabu (2009) which allows structural change in both intercept and slope (Perron & Yabu, 2009:370). The estimation results, reported in Table 1, suggest strong rejection of the null hypothesis that the trend function is stable in favor of a trend function with a shift for all indices indicating that there is at least one structural 5 See also Maki (2012) for detailed explanations of the estimation steps for the test statistic, MBk.
Exp-WRQF TB
A Note: statistical significance at 1% level. The asymptotic critical values for the Exp-WRQF are 2.48, 3.12, and 4.47 (for a break in the constant and time trend slope) at 10%, 5%, and 1% significance level, respectively (Perron & Yabu, 2009).
break in each spot/future price series when we allow structural change in both intercept and slope. After we find that there is at least one break in each price series, we estimate M-class unit root tests of CKP based on the Model II allowing structural break in both the level and the slope of the time trend (see Carrion-i-Silvestre et al., 2009:1757) with five (5) unknown break points. Table 2 presents the estimated GLS MZGLS ðkÞ, and MZGLS ðkÞ statistics and the break dates. a ðkÞ; MZB t Our findings indicate that the null hypothesis of unit root cannot be rejected for all time-series. In other words, M-Class unit root tests provide clear evidence of I(1) with five structural changes for all price indices. In 2006 diplomacy between the EU and Turkey gained momentum. The onset of accession negotiations with EU arose the hopes to that Turkey would eventually become a member of the Union. The breaks in ISE 30, VOB-30 and the currencies at the end of February and the beginning of March seemed to be the result of these positive expectations. In addition in February, for the first time after 17 years Turkey saw a surplus in its budget and concomitantly ISE index reached its climax. The reason for the break in USD in June 2006 can be seen as the result of the withdrawal of foreign investors from the Turkish Stock Market and Turkish Lira thereby leading to devaluation of the latter. Notwithstanding the Turkish Central Bank intervened and the government put into force precautions the USD continued to boost. On October 11, 2007, ISE index saw its highest level ever by leading to another significant break. It was followed by a new series of breaks stemmed from the mortgage crises that began in US in August 2007 and diffused throughout global financial market. In the initial faces of the crisis the USD lost in value rapidly. The real impact of the crisis was felt in emerging economies after November 2008, a development which seemed to have culminated in a new break on the ISE 30. It is highly probable that the tidings relating bankruptcy of the major financial giants like Lehman Brothers played an important role in those breaks. The break on ISE 30 in March 2009 seems to be the result of the measures relating global financial crisis. On March 16 the Turkish government declared that it would decrease the tax rates on houses, automotive and some other consumer goods in order to animate the market. The breaks of 2010 seem to have resulted from without. In this period the financial crisis affected rather European countries and Euro. No doubt the break on the VOB Euro in March was the result of the compromise between European countries to aid Greece. The decision of the European Council of Ministers to help the Italian government which had long been in financial dire straits seems to be the reason behind a new break on Euro in the early December. Moody’s upgrade of Turkey’s credit rating in January 2010 yet let to a new and this time a positive break on USD.
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
4210
Table 2 The Carrion-i-Silvestre et al. (2009) unit root tests. TDEX-30
TDEX-USD
TDEX-EUR
ISE-30
TL/USD
TL/EUR
MZa ðkÞ
25.714
27.5609
23.6057
30.098
20.1168
24.0679
MZBGLS ðkÞ
0.1364
0.1347
0.1453
0.1277
0.1572
0.1438
MZGLS ðkÞ t TB1 TB2 TB3 TB4 TB5
3.5083
3.7115
3.4306
3.8433
3.1629
3.4607
1-Mar-06 10-Jan-07 17-Oct-07 18-Mar-09 10-Nov-10
22-Feb-06 29-Nov-06 5-Sep-07 24-Sep-08 8-Jul-09
26-Apr-06 26-Dec-07 3-Oct-08 17-Mar-10 19-Oct-11
1-Mar-06 12-Dec-07 19-Nov-08 14-Apr-10 4-May-11
28-Jun-06 16-Jan-08 30-Oct-08 20-Jan-10 4-May-11
22-Feb-06 29-Nov-06 10-Oct-07 10-Sep-08 8-Dec-10
GLS
Table 3 Maki (2012) Cointegration test with unknown breaks. TB1
TB2
TB3
TB4
TB5
Panel A regime shifts Stock 7.7096a USD 12.3542a EUR 7.9059a
MBk
28-Sep-2005 14-Nov-2007 12-Jul-2006
11-Oct-2006 27-Aug-2008 15-Aug-2007
21-Nov-2007 25-Mar-2009 3-Oct-2008
30-Oct-2008 21-Oct-2009 21-Oct-2009
29-Apr-2009 30-Mar-2011
Panel B trend and regime shifts Stock 8.1107a USD 7.6680b EUR 8.8812a
21-Nov-2007 12-Sep-2007 15-Aug-2007
16-Jul-2008 30-Apr-2008 23-Jul-2008
3-Dec-2008 22-Oct-2008 14-Jan-2009
29-Apr-2009 18-Mar-2009 16-Dec-2009
21-Oct-2009 7-Oct-2009 12-Jan-2011
Note: Critical values are taken from Maki (2012), Table 1, p. 2003. a The presence of cointegration at significance level of 1%. b The presence of cointegration at significance level of 5%.
The breaks on both ISE 30 and USD in May 2011 seem to have stemmed from the general elections in Turkey. On the other side, the break on VOB Euro in October 2011 seems to be the result of EU’s acknowledge of Greece’s disability to meet the targets of the debt-reduction program. Lastly, this was followed by sharp falls in European markets and devaluation of Euro against USD. The same period saw reductions in the ratings of both Italy and Spain and rumors that France was the next took their place even in the most serious journals. Table 3 presents the Maki (2012) cointegration test results. Panel A and B of the Table 3 reports the MBk statistics and the timing of structural breaks in the cointegration vectors obtained from the third (Eq. (4)) and the fourth (Eq. (5)) regression models, respectively. The MBk statistics strongly reject null hypotheses of no cointegration between the spot prices and their futures prices including stock index and its futures (ISE-30TDEX-30), USD and its futures (TDEX-USD-TL/USD), and EUR and its futures (TL/EuroTDEX-EUR). These results reveal the fact that the spot prices of those three financial assets have long-run relationships with their futures having multiple breaks smaller than or equal to the maximum five (5) breaks.
in this study we fill this gap by applying a cointegration methodology in the presence of structural breaks to test for a long-run relationship between spot and futures prices. Our results indicate the existence of structural breaks in our data and the estimated break dates are mostly clustered around the important economic and political events during the global financial turmoil which was triggered by the mortgage delinquencies6 after the mid of 2007. In addition, we find that the spot and future prices of the underlying assets including the ISE30 index, USD and EUR are cointegrated. Our results indicate that these markets have a long-run relationship under multiple structural breaks and the markets are efficient in the long-run. Further study might be on the estimation of the relationship between the prices of the futures and their underlying assets which are not examined in this paper. However, the results of these studies can be more valid only after these contracts will reach enough transaction volumes. In addition, the cointegration analysis considering the structural breaks might be used to examine the relationship between spot and futures markets of the other emerging economics. Acknowledgements
6. Conclusions and future work This paper examines the long-run relationship between the spot prices of index and currencies and their futures contracts by using weekly data from February 9, 2005 to October 17, 2012. The paper contributes to the growing literature of linkages between spot and futures prices by examining the long-run relationship between the spot and futures prices while most of the previous studies focus on the short-term interactions between them. In addition, while a considerable number of studies focus on the developed futures markets, this paper examine TDEX which is the highly growing futures markets in terms of its trading value. And more importantly while the previous studies do not considers the structural breaks,
The authors are indebted to Daiki Maki for providing GAUSS program codes used in the estimation of the cointegration tests. We are also grateful to Professors Carrion-i-Silvestre, Kim, and Perron for making their GAUSS program code publicly available. Appendix A. Spot and Future Prices See Figs. 1–3. 6 The discussion about the structural break dates is suggestive. Any economic event can always be found relatively close to the estimated timing of structural break that could have caused the break.
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
4211
4.8
11.6
4.4
11.2
4.0
10.8
3.6
10.4
3.2
2012
2011
2010
2009
2008
2007
2005
2006
10.0
Fig. 1. Daily log prices of ISE-30 and TDEX-30. Blue (left-axis) and red (right-axis) lines represent ISE-30 index and TDEX-30, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
.7 .6
.7
.5
.6
.4
.5
.3
.4
.2
.3
.1
.2
2012
2011
2010
2009
2008
2007
2006
2005
.1
Fig. 2. Daily log prices of Spot (TL/USD) and TDEX-USD. Blue (left-axis) and red (right-axis) lines represent spot (TL/USD) and TDEX-USD, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
1.0 1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
2012
2011
2010
2009
2008
2007
2006
2005
0.4
Fig. 3. Spot (TL/EUR) and TDEX-EUR. Blue (left-axis) and red (right-axis) lines represent spot (TL/EUR) and TDEX-EUR, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4212
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
References Abhyankar, A. (1998). Linear and nonlinear Granger causality: Evidence from the U.K. stock index futures market. Journal of Futures Markets, 18(5), 519–540. Bai, J., & Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 47–78. Bai, J., & Perron, P. (2002). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18(1), 1–22. Bodie, Z., Kane, A., & Marcus, A. J. (2009). Investments (8th ed.). New York: McGrawHill/Irwin. Brenner, R. J., & Kroner, K. F. (1995). Arbitrage, cointegration, and testing the unbiasedness hypothesis in financial markets. The Journal of Financial and Quantitative Analysis, 30(1), 23–42. http://dx.doi.org/10.2307/2331251. Brooks, C., Garrett, I., & Hinich, M. J. (1999). An alternative approach to investigating lead–lag relationships between stock and stock index futures markets. Applied Financial Economics, 9(6), 605–613. http://dx.doi.org/10.1080/09603109 9332050. Brooks, C., Rew, A. G., & Ritson, S. (2001). A trading strategy based on the lead–lag relationship between the spot index and futures contract for the FTSE 100. International Journal of Forecasting, 17(1), 31–44. http://dx.doi.org/10.1016/ S0169-2070(00)00062-5. Carrion-i-Silvestre, J. L., Kim, D., & Perron, P. (2009). GLS-based unit root tests with multiple structural breaks under both the null and the alternative hypotheses. Econometric Theory, 25(06), 1754–1792. Chai, S., & Guo, C. (2009). The co-integrating relationship between stock index and futures prices. In Proceedings of the 2009 international conference on new trends in information and service science, NISS ‘09 (pp. 1389–1392). Washington, DC, USA: IEEE Computer Society. http://dx.doi.org/10.1109/NISS.2009.200. Chan, K. (1992). A further analysis of the lead–lag relationship between the cash market and stock index futures market. The Review of Financial Studies, 5(1), 123–152. Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813. http://dx.doi.org/10.2307/2171846. Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276. http:// dx.doi.org/10.2307/1913236. Gee, C. S., & Karim, M. Z. A. (2005). The lead–lag relationship between stock index futures and spot market in malaysia: A cointegration and error correction model approach. Chulalongkorn Journal of Economics, 17(1), 53–72. Ghosh, A. (1993). Cointegration and error correction models: Intertemporal causality between index and futures prices. Journal of Futures Markets, 13(2), 193–198. http://dx.doi.org/10.1002/fut.3990130206. Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99–126. http:// dx.doi.org/10.1016/0304-4076(69)41685-7. Hatemi-J, A. (2008). Tests for cointegration with two unknown regime shifts with an application to financial market integration. Empirical Economics, 35(3), 497–505. Hecq, A., & Urbain, J. P. (1993). Misspecification tests, unit roots and level shifts. Economics Letters, 43(2), 129–135. Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12(2–3), 231–254. Johansen, S., & Juselius, K. (1992). Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK. Journal of Econometrics, 53(1–3), 211–244. Kapetanios, G. (2005). Unit-root testing against the alternative hypothesis of up to m structural breaks. Journal of Time Series Analysis, 26(1), 123–133. Kawaller, I. G., Koch, P. D., & Koch, T. W. (1987). The temporal price relationship between S&P 500 futures and the S&P 500 index. The Journal of Finance, 42(5), 1309–1329. http://dx.doi.org/10.2307/2328529.
Kim, D., & Perron, P. (2009). Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses. Journal of Econometrics, 148(1), 1–13. Li, M.-Y. L. (2009). The dynamics of the relationship between spot and futures markets under high and low variance regimes. Applied Stochastic Models in Business and Industry, 25(6), 696–718. http://dx.doi.org/10.1002/asmb.753. Lien, D., Tse, Y. K., & Zhang, X. (2003). Structural change and lead–lag relationship between the Nikkei spot index and futures price. A genetic programming approach. Quantitative Finance, 3(2), 136–144. http://dx.doi.org/10.1088/14697688/3/2/307. Maki, D. (2012). Tests for cointegration allowing for an unknown number of breaks. Economic Modelling, 29(5), 2011–2015. http://dx.doi.org/10.1016/j.econmod. 2012.04.022. Maslyuk, S., & Smyth, R. (2009). Cointegration between oil spot and future prices of the same and different grades in the presence of structural change. Energy Policy, 37(5), 1687–1693. Ng, S., & Perron, P. (2003). Lag length selection and the construction of unit root tests with good size and power. Econometrica, 69(6), 1519–1554. Nieto, M., Fernandez, A., & Muñoz, M. (1998). Market efficiency in the Spanish derivatives markets: An empirical analysis. International Advances in Economic Research, 4(4), 349–355. http://dx.doi.org/10.1007/BF02295688. Özen, E., Bozdog˘an, T., & Zügül, M. (2009). The relationship of causality between the price of futures transactions underlying stock exchange and price of cash market: The case of Turkey. Middle Eastern Finance and Economics, 4, 28–37. Özün, A., & Erbaykal, E. (2009). Detecting risk transmission from futures to spot markets without data stationarity: Evidence from Turkey’s markets. Journal of Risk Finance, The, 10(4), 365–376. http://dx.doi.org/10.1108/1526594091 0980669. Pattarin, F., ⁄, & Ferretti, R. (2004). The Mib30 index and futures relationship: Econometric analysis and implications for hedging. Applied Financial Economics, 14(18), 1281–1289. http://dx.doi.org/10.1080/09603100412331313578. Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica Journal of the Econometric Society, 1361–1401. Perron, P., & Yabu, T. (2009). Testing for shifts in trend with an integrated or stationary noise component. Journal of Business & Economic Statistics, 27(3), 369–396. Pizzi, M. A., Economopoulos, A. J., & O’Neill, H. M. (1998). An examination of the relationship between stock index cash and futures markets: A cointegration approach. Journal of Futures Markets, 18(3), 297–305. http://dx.doi.org/10.1002/ (SICI)1096-9934(199805)18:3<297::AID-FUT4>3.0.CO;2-3. Rajaguru, G., & Pattnayak, S. S. (2007). Investigation of a lead–lag relationship between spot and futures indices of the hang seng stock average. International Journal of Business Studies: A Publication of the Faculty of Business Administration, Edith Cowan University, 15(1), 69. Stock, J. H. (1999). A class of tests for integration and cointegration. In R. F. Engle & H. White (Eds.), Cointegration, causality, and forecasting: A festschrift for Clive W.J. Granger (pp. 135–167). Oxford University Press. Stoll, H. R., & Whaley, R. E. (1990). The dynamics of stock index and stock index futures returns. The Journal of Financial and Quantitative Analysis, 25(4), 441–468. http://dx.doi.org/10.2307/2331010. Tse, Y. K. (1995). Lead–lag relationship between spot index and futures price of the nikkei stock average. Journal of Forecasting, 14(7), 553–563. http://dx.doi.org/ 10.1002/for.3980140702. Wahab, M., & Lashgari, M. (1993). Price dynamics and error correction in stock index and stock index futures markets: A cointegration approach. Journal of Futures Markets, 13(7), 711–742. Zivot, E., & Andrews, D. W. K. (2002). Further evidence on the great crash, the oilprice shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 20(1), 25–44.
Contents lists available at SciVerse ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
The long-run relationship between the spot and futures markets under multiple regime-shifts: Evidence from Turkish derivatives exchange ˘ LI ⇑, Pınar Evrim Mandaci 1 Efe Çag˘lar ÇAG _ IR, _ Turkey Dokuz Eylül University, Faculty of Business, Department of Finance, Kaynaklar Campus, Buca-IZM
a r t i c l e Keywords: Spot price Futures price Cointegration Structural breaks Market efficiency
i n f o
a b s t r a c t The paper examines the long-run relationships between the spot and future prices of Istanbul Stock Exchange 30 index (ISE-30) and foreign currencies including the Turkish Lira-US Dollar (TL/USD) and Turkish Lira-Euro (TL/EUR). We analyze the weekly data covering the period from February 9, 2005 to October 17, 2012. Considering structural breaks is important for our analysis since our period consists of recent financial crisis. Therefore, we employ the unit root tests developed by Carrion-i-Silvestre et al. (2009) and the Maki’s (2012) cointegration test allowing for an unknown number of breaks. We find that spot and the futures prices are cointegrated in the long-run after we consider structural breaks in our data. Our results indicate that the markets are efficient. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Although it has begun its operations only a few years ago, the Turkish Derivatives Exchange (TDEX) has become one of the fastest growing emerging futures market in the world.2 There are a variety of futures contracts in TDEX; i.e., equity index futures on ISE 30 and ISE 100 indices, currency futures on US Dollars and Euro, commodity futures on gold, cotton, wheat and live cattle and energy futures on base-load electricity. However, among them index contracts have the highest trading ahead of the currency futures in the second place. While index contracts from 88.38% and 97.20% of the total number of contracts traded and the total trading value for 2010, currency contracts follow them with 11.38% and 2.58% respectively. Investors make use of stock index futures to speculate on the performance of the entire market; if they expect an improvement in the economy, they will buy the index; otherwise they will short the index. They can also use currency futures to speculate on the value of currencies thereby taking long position in futures contract on that currency or vice versa. Index futures contracts are used in speculative way in the TDEX as frequently as in the most of index futures in the world, yet investors may also use them to hedge their spot equity portfolio against the price declines by going short at the futures market. Here, it is important for the investors to ⇑ Corresponding author. Address: Dokuz Eylul Universitesi, Isletme Fakultesi, Kaynaklar Yerleskesi, Buca, IZMIR – Turkiye. Tel.: +90 232 4535060; fax: +90 232 4535062. ˘ LI), [email protected] E-mail addresses: [email protected] (E.Çag˘lar ÇAG (P. Evrim Mandaci). 1 Tel.: +90 232 4535060; fax: +90 232 4535062. 2 TURDEX has been operating since February 2005. Its trading value was only 3,029,588,946 TL in 2005 and was reached to 431,681,986,516 TL in 2010. 0957-4174/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.eswa.2013.01.026
determine their optimum hedge ratio by considering the correlation between the prices of futures and spot positions.3 Similarly, traders, particularly importers and exporters, can use currency futures to hedge their foreign exchange positions by taking a long or a short position on currency futures. In addition, arbitrage is another aim of involving into the futures contracts. Arbitrageurs make transactions in both spot and futures market for the same asset and make profit when the price of the futures contract gets out of line with its spot price. These can be summed up as the main reasons motivating the researchers to investigate the relationship between the spot and future prices. According to the efficient market hypothesis, generally in the financial markets all relevant information is always efficiently processed and reflected simultaneously into both the spot and futures prices, hence arbitrage opportunities would always be limited. Brooks, Garrett, and Hinich (1999) argue that in a perfect market with non-stochastic interest rates and dividend yields, they are perfectly contemporaneously correlated and no lead–lag relationship would exist. The relationship between the spot and futures prices can also be explained by the price discovery hypothesis. Accordingly, if the markets are efficient and frictionless, then price discovery would be instantaneous and contemporaneous. Otherwise, price discovery would occur in one market and the other market would follow it. The normal and theoretically correct relationship between the spot price and its futures can be explained by the ‘‘cost of carry model’’ or the ‘‘spot–futures parity theorem’’. The
3 For instance, if there is a high correlation between the prices of futures and spot positions, the hedge ratio will be closed to unity. The equation of the hedge ratio is; ht ¼ qt sst =sft where q is the correlation coefficient between the portfolio and futures return and r is the standard deviation over the hedging horizon.
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
parity for the index futures can be stated as:
F 0 ¼ S0 ð1 þ r f dÞT
ð1Þ
where F0 is the future price at time 0, S0 is the spot price at time 0, rf is the risk-free rate, and d is the dividend yield on the stock portfolio. It is called the ‘‘cost of carry relationship’’ because it defines a setting in which futures price must exceed the spot price by the net cost of carrying the asset until maturity date T (Bodie, Kane, & Marcus, 2009: 775). However, in practice one should take into account some market imperfections such as asymmetric information, transaction costs, short-selling, margins, and liquidity, which might cause deviations from that parity. Those deviations might induce lead–lag relationships between the spot and futures markets and enhance the arbitrage chances for investors trading in both of these markets. There are a considerable number of studies depicting that futures market leads the spot market due to deviations such as high liquidity, low transaction costs, easy availability of short positions and low margins of the futures market (e.g. see, Chan, 1992; Kawaller, Koch, & Koch, 1987; Stoll & Whaley, 1990 and Abhyankar, 1998; Pizzi, Economopoulos, & O’Neill 1998). On the other hand, Brooks, Rew, and Ritson (2001) argue that the lead–lag relationship between spot and futures markets do not last for more than half an hour and argue that the parity holds in the long-run. In the same line, Maslyuk and Smyth (2009) argue that the theoretical relationship between spot and futures prices is a long-run, rather than short-run because in the short-run, there might be deviations between spot and future prices however in the long-run they are driven by the same macroeconomic indicators. Following to these studies, in this paper our aim is to examine the long-run relationship between the spot and futures prices of both the ISE 30 and foreign currencies in order to find out whether these markets are efficient. This paper provides three contributions to the existing literature: First, many empirical studies examining the long-run relationship between the spot and futures prices have adopted the vector auto regression model (VAR) or cointegration methods proposed by Engle and Granger (1987) (EG) and Johansen (1988) (e.g. see, Ghosh, 1993; Wahab & Lashgari, 1993; Brenner & Kroner, 1995; Pizzi et al., 1998 and Brooks et al., 2001) but, none of these studies have allowed for a structural break in the cointegrating vector. Therefore, different from the previous studies we employ the unit root tests developed by Carrion-i-Silvestre, Kim, and Perron (2009) and the Maki’s (2012) cointegration test allowing for an unknown number of breaks. Considering structural breaks is important for our analysis since our period consists of the effects of the recent financial crisis. Second, many of the previous studies examine the developed futures markets but this paper analyze TDEX which is an emerging market in its early stages but has become one of the top 30 futures exchanges in the world after just eight years. Third, our data consist of the index (TDEX-30) and currency futures (TDEX-USD and TDEX-EUR) which are mostly traded contracts representing almost the whole market for the period from February 9, 2005 to October 17, 2012 covering the whole life of TDEX. Existence of the long-run relationship indicates that the markets are efficient in the long run and eliminate the diversification benefits in portfolios that consist of the stock index and its futures as well as the currencies and their futures for a long period. Our results are important for the investors and portfolio managers holding both spot and their futures to provide diversification or hedging, for security analysts to determine fair values of spot and futures and policy makers to arrange some rules and regulations in order to provide efficiency and liquidity in these markets.
4207
The remainder of this study is organized as follows. Section 2 gives a brief summary of literature. Section 3 describes the methodologies employed. Section 4 shows the data and the empirical results, and in Section 5 we draw our conclusions.
2. Literature review A large number of studies analyzing the relationship between the spot and its futures market mostly focus on the short-run relationships by applying the modified and non-modified Granger Causality (GC) tests with the intraday data. Since our focus is the long-run interactions between these markets here we will just give a review on studies using cointegration techniques most of which employ Error Correction Models (ECM) and GC tests after they find the evidence of cointegration. Among them, Ghosh (1993) applies EG cointegration test to analyze the long-term equilibrium relationship between S&P 500 index prices and futures prices covering the time period from June 12, 1986, through December 31, 1989. He finds that there exists a cointegration relationship between futures and spot markets, in addition he estimates short-run relationship between them and argues that future prices GrangerCause cash prices in the case of the S&P 500 index. Similar to this study, Wahab and Lashgari (1993) examine the long-run relationship between the futures and spot markets of S&P 500 and FTSE 100 over the period from 1988 to 1992 by using daily closing prices and applying the same methodology and find that they are cointegrated. However in contrast to Ghosh (1993), they indicate that spot returns contribute more than future returns. Tse (1995) examines the relationship between the spot and futures price of the Nikkei stock exchange by using daily data from December 1988 through January 1993 and find that the series are cointegrated. Pizzi et al. (1998) examine the price discovery in S&P 500 cash index and its futures using intraday data for the period from Jan 1987 to March 1987 applying the EG methodology and find that they are cointegrated indicating market efficiency. In addition, their results show that the spot prices lead the futures prices. Brooks et al. (2001) employ the EG method to test cointegration between the FTSE 100 index and its futures by using 10 min data for the period from June 1996 to 1997 and find a strong relationship between them. They also find that changes in spot index depend on the lagged changes in the spot index and futures price, while the lead–lag relationship between spot and futures markets do not last for more than half an hour. Chai and Gou (2009) examines five International stock index spot and futures data including S&P 500 index futures, Dow Jones index futures and NASDAQ 100 index futures in the USA, Nikkei 225 index futures in Japan, Hang Seng index futures in Hong Kong of China, to verify whether there exists long-term steady relationship between the index spot and futures prices. They apply the EG cointegration method and based on the cointegration theory and ECM, conclusions are drawn that index spot and futures are cointegrated in most cases and it is possible to do the corresponding short term dynamic adjustment for reaching new equilibrium in next period. Nieto, Fernandez, and Muñoz (1998) apply the Johansen cointegration test to examine the relationship between Spanish stock index and its futures by using daily data from March 1, 1994 through Sep 30, 1996. They find a long-run relation between them indicating that the cost of carry model holds in the long run. Pattarin and Ferretti (2004) study the relationship between the Italian MIB30 index and futures log-prices with a bivariate ECM and apply the Johansen cointegration test by using daily observations beginning from November 28, 1994 to September 19, 2002 and find that the relationship is hold in the long-run. Very little work has investigated the impact of stock index futures trading in the emerging markets. Among them, Cheng and
4208
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
Liu (2003) tests Hang Seng index spot and futures series data from April 26th, 2001 to December 28th, 2001 by cointegration approach, and draw the conclusion that the spot–futures relationship is long-term stable. Gee and Karim (2005) analyze the lead–lag relationship between spot and futures markets of the Malaysian Kuala Lumpur Composite Index (KLCI) by employing the cointegration and error-correction approach. Results of the study suggest that cash market and futures market are cointegrated. The results of the ECM suggest that futures price lead spot price depicting that the investors are able to use futures price as a good indicator in predicting spot price. Rajaguru and Pattnayak (2007) use daily observations of spot index and the future prices of the Hang Seng indices, covering the period from January 1988 through October 2001. They measure performance of Fractionally Integrated ECM (FIECM) against the possible alternative models and find that the best forecasting performance is obtained from error correction and fractional cointegrated models for the short and long forecasting horizon respectively. They find the evidence of lead and lad relationships between spot and futures prices in the short-run while the futures prices are led by spot prices in the long-run. Li (2009) examines the dynamic spot–futures relationship from three mature including the U.S. S&P 500, the U.K. FTSE100 and the German DAX 30, and two emerging markets including the Brazil Bovespa and the Hungary BSI, using Markov-switching vector ECM. His empirical finding is that the futures price is shown to lead the spot price in the price discovery process. Özen, Bozdog˘an, and Zügül (2009) examine the long-run relationship between the ISE 30 index and its futures by applying the Johansen (1988) and Johansen and Juselius (1992) cointegration tests for the period beginning from February 4, 2005 and ending at February 27, 2009. They use daily closing prices and conclude that there exists a bidirectional relationship between them. Özün and Erbaykal (2009) analyze the relationship between spot and futures markets in Turkish foreign-exchange markets by employing Bounds cointegration test to daily data covering the period of January 2, 2006 to March 25, 2008. Their results indicate that the spot and futures foreign exchange markets of Turkey have informational efficiency. However, in their study, Lien, Tse, and Zhang (2003) argue that due to the dominance of the ‘normal’ period in sample data, the lead–lag relationship identified in the spot–futures system based on conventional methods such as the test for GC pertains to the normal period and may not be applicable in an ‘extreme’ period. Therefore, they employ a nonparametric genetic programming (GP) approach to identify the structural changes in the Nikkei spot index and futures price. They find that the major market changes originated from the spot market and spread over to the futures market. Similar to Lien et al. (2003), we consider structural breaks in our data series but different from it, we examine long-run relationship between the spot and futures prices by employing Maki (2012) cointegration test that accounts for the effect of multiple unknown structural breaks.
3. Methodology 3.1. Testing for breaks in the trend function of a time series Perron and Yabu (2009) develop a procedure in order to test whether there is any structural change in a univariate time series. The procedure computes the test, so called Exp-WRQF, for breaks in the trend function of a time series valid whether the noise component is stationary or integrated. Put another way, Exp-WRQF test can be applied when it is a priori unknown whether the series is trendstationary or contains an AR unit root. This test based on robust
quasi-flexible generalized least squares allows for an unknown break in the intercept, deterministic time trend or in both (Perron & Yabu, 2009:370). 3.2. Unit root test In the case of the existence of a structural break in the deterministic trend, the conventional unit root tests, such as Augmented Dickey–Fuller (ADF), lose their power and lead researchers to unreliable conclusions. In this way, Perron (1989) suggests unit root tests that allow the possibility of a break under null hypothesis of unit root against alternative of stationarity. However, the Perron’s (1989) test (PT) procedures suffer from the assumption of that the timing of the break date is known a priori since incorrect break date causes size distortions and power loss (Hecq and Urbain (1993)). Accordingly, Zivot and Andrews (2002) (ZA) develop alternative unit root test allowing an unknown structural breaks in the data. However, ZA type test statistics lose power when the noise component has a unit root and a break occurs in the trend function since they do not allow a break under the null hypothesis. To overcome those types of shortcomings, Kim and Perron (2009) (KP) propose a new methodology which allows a break in the trend function at an unknown time under both the null and alternative hypotheses. By doing so, KP relaxes the most controversial assumption (known break date) of PT. In addition, the limit distribution of the KP test becomes the same as in the case of Perron (1989). Carrion-i-Silvestre et al. (2009), Kim and Perron (2009) (CKP) extend the methodology of KP by allowing for an arbitrary number of changes up to five structural breaks in both the level and slope of the trend function. The break dates in CKP test are estimated depending on the data using an algorithm based on Bai and Perron (2002). CKP test considers M-class unit root tests, introduced in Stock (1999) and analyzed in Ng and Perron (2003), adopting the quasi-GLS detrending method advocated by Elliot et al. (1996). CKP reports that, their tests have good power and size properties based on the Monte Carlo simulations. In this way, CKP tests with good power and size properties solve many aforementioned problems of previous methods widely employed in the literature.4 3.3. Cointegration Maki (2012) develops cointegration test (MBk) with unknown number of structural breaks. The methodology introduced in Maki’s (2012) paper has two main advantages over the methods widely used in the literature. First, the MBk based on tests for structural breaks proposed by Bai and Perron (1998) and a unit root test with structural breaks developed by Kapetanios (2005), assumes that unspecified number of breaks of the cointegrating vector is smaller than or equal to the maximum number of breaks set a priori. Second, the methodology of MBk is substantially less computationally intensive than the previous methods (Maki, 2012: 2011). In addition to aforementioned issues, the results of the Monte Carlo simulations suggest that MBk test performs better than the tests of Gregory and Hansen (1996) and Hatemi-J (2008) when the cointegration relationship has more than three breaks or persistent Markov switching shifts (Maki, 2012). Maki (2012) proposes four regression models in order to test cointegration allowing for multiple structural breaks:
yt ¼ l þ
k X
li Di;t þ b0 xt þ ut
ð2Þ
i¼1
4 See Carrion-i-Silvestre et al. (2009) for detailed technical explanations for the procedures of tests.
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
yt ¼ l þ
k X
li Di;t þ b0 xt þ
i¼1
yt ¼ l þ
k X
k X b0i xt Di;t þ ut
ð3Þ
Table 1 The Perron and Yabu (2009) test for a break.
i¼1
li Di;t þ ct þ b0 xt þ
i¼1
k X b0i xt Di;t þ ut
ð4Þ
i¼1
4209
Panel A Exp-WRQF TB
TDEX-30
TDEX-USD
TDEX-EUR
5.5426a 12-Mar-08
26.4516 a 3-Oct-08
9.5343 a 13-Jul-11
ISE-30 5.6626 a 12-Mar-08
TL/USD 10.5045 a 3-Oct-08
TL/EUR 7.1225 a 20-Jul-11
Panel B
yt ¼ l þ
k X
li Di;t þ ct þ
i¼1
k X
k X ci tDi;t þ b0 xt þ b0i xt Di;t þ ut
i¼1
ð5Þ
i¼1
where t ¼ 1; 2; . . . ; T. yt (dependent) and xt ¼ ðx1t ; . . . ; xmt Þ0 (regressors) indicate observable integrated of order one (I(1)) variables, and ut is the equilibrium error. Di,t takes value of 1 if t > TBi ði ¼ 1; . . . ; kÞ and of 0 otherwise, where k is the maximum number of breaks and TBi indicates the time period of break. The first model, level shift model, captures changes in the level (l) only. Second model accounts for structural breaks both in the level (l) and regressors (x), called regime shift model. Third model is regime shift model with trend (c); and the fourth model constitutes structural breaks of levels, trends, and regressors. MBk with the null hypothesis of no cointegration against the alternative hypothesis of cointegration with i breaks (i 6 k) are implemented in the following steps (Maki, 2012:2012)5: First, we estimate one of the four regression models and then save the residuals. Second, we compute the t-statistics in order to test for unit root in the residuals, obtained from the estimated model, for all possible periods of the break. Let the set of all possible partitions and the tstatistics be represented by T ai , and siq , respectively. Third, the ith ^ ) is chosen by minimizing the sum of squared residbreakpoint (bp i uals (SSR) for the estimated model. Here, the breakpoint i can be ^ ¼ arg min SSRi . Finally, we adopt sk as the test staindicated as bp i min Ta tistic (MBk), that is, i the minimum t-statistic over the set skq ¼ s1 [ s2 [ ::: [ sk . 4. Data and empirical results 4.1. Data All data are weekly from February 9, 2005 to October 17, 2012 for a total of 401 observations and obtained from three sources. We collect data for ISE-30 price index from the web page of the Istanbul Stock Exchange (ISE); settlement prices of TDEX-30 index, TDEX-USD and TDEX-EUR from the web page of the TDEX, and the spot prices of Turkish Lira-US Dollar (TL/USD) and Turkish Lira-Euro (TL/EUR) exchange rates from the Electronic Data Delivery System (EDDS) of the Central Bank of the Republic of Turkey (CBRT). 5. Empirical results In this study, the long-run relationship between the spot and futures prices of both the ISE-30 and foreign currencies are analyzed in order to check whether these markets are efficient. Table 1 reports the Perron and Yabu (2009) Exp-WRQF test statistics and the dates of the structural changes. Panel A and B presents the results for the future and spot price indices, respectively. We estimate Exp-WRQF test statistic based on the Model III of Perron and Yabu (2009) which allows structural change in both intercept and slope (Perron & Yabu, 2009:370). The estimation results, reported in Table 1, suggest strong rejection of the null hypothesis that the trend function is stable in favor of a trend function with a shift for all indices indicating that there is at least one structural 5 See also Maki (2012) for detailed explanations of the estimation steps for the test statistic, MBk.
Exp-WRQF TB
A Note: statistical significance at 1% level. The asymptotic critical values for the Exp-WRQF are 2.48, 3.12, and 4.47 (for a break in the constant and time trend slope) at 10%, 5%, and 1% significance level, respectively (Perron & Yabu, 2009).
break in each spot/future price series when we allow structural change in both intercept and slope. After we find that there is at least one break in each price series, we estimate M-class unit root tests of CKP based on the Model II allowing structural break in both the level and the slope of the time trend (see Carrion-i-Silvestre et al., 2009:1757) with five (5) unknown break points. Table 2 presents the estimated GLS MZGLS ðkÞ, and MZGLS ðkÞ statistics and the break dates. a ðkÞ; MZB t Our findings indicate that the null hypothesis of unit root cannot be rejected for all time-series. In other words, M-Class unit root tests provide clear evidence of I(1) with five structural changes for all price indices. In 2006 diplomacy between the EU and Turkey gained momentum. The onset of accession negotiations with EU arose the hopes to that Turkey would eventually become a member of the Union. The breaks in ISE 30, VOB-30 and the currencies at the end of February and the beginning of March seemed to be the result of these positive expectations. In addition in February, for the first time after 17 years Turkey saw a surplus in its budget and concomitantly ISE index reached its climax. The reason for the break in USD in June 2006 can be seen as the result of the withdrawal of foreign investors from the Turkish Stock Market and Turkish Lira thereby leading to devaluation of the latter. Notwithstanding the Turkish Central Bank intervened and the government put into force precautions the USD continued to boost. On October 11, 2007, ISE index saw its highest level ever by leading to another significant break. It was followed by a new series of breaks stemmed from the mortgage crises that began in US in August 2007 and diffused throughout global financial market. In the initial faces of the crisis the USD lost in value rapidly. The real impact of the crisis was felt in emerging economies after November 2008, a development which seemed to have culminated in a new break on the ISE 30. It is highly probable that the tidings relating bankruptcy of the major financial giants like Lehman Brothers played an important role in those breaks. The break on ISE 30 in March 2009 seems to be the result of the measures relating global financial crisis. On March 16 the Turkish government declared that it would decrease the tax rates on houses, automotive and some other consumer goods in order to animate the market. The breaks of 2010 seem to have resulted from without. In this period the financial crisis affected rather European countries and Euro. No doubt the break on the VOB Euro in March was the result of the compromise between European countries to aid Greece. The decision of the European Council of Ministers to help the Italian government which had long been in financial dire straits seems to be the reason behind a new break on Euro in the early December. Moody’s upgrade of Turkey’s credit rating in January 2010 yet let to a new and this time a positive break on USD.
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
4210
Table 2 The Carrion-i-Silvestre et al. (2009) unit root tests. TDEX-30
TDEX-USD
TDEX-EUR
ISE-30
TL/USD
TL/EUR
MZa ðkÞ
25.714
27.5609
23.6057
30.098
20.1168
24.0679
MZBGLS ðkÞ
0.1364
0.1347
0.1453
0.1277
0.1572
0.1438
MZGLS ðkÞ t TB1 TB2 TB3 TB4 TB5
3.5083
3.7115
3.4306
3.8433
3.1629
3.4607
1-Mar-06 10-Jan-07 17-Oct-07 18-Mar-09 10-Nov-10
22-Feb-06 29-Nov-06 5-Sep-07 24-Sep-08 8-Jul-09
26-Apr-06 26-Dec-07 3-Oct-08 17-Mar-10 19-Oct-11
1-Mar-06 12-Dec-07 19-Nov-08 14-Apr-10 4-May-11
28-Jun-06 16-Jan-08 30-Oct-08 20-Jan-10 4-May-11
22-Feb-06 29-Nov-06 10-Oct-07 10-Sep-08 8-Dec-10
GLS
Table 3 Maki (2012) Cointegration test with unknown breaks. TB1
TB2
TB3
TB4
TB5
Panel A regime shifts Stock 7.7096a USD 12.3542a EUR 7.9059a
MBk
28-Sep-2005 14-Nov-2007 12-Jul-2006
11-Oct-2006 27-Aug-2008 15-Aug-2007
21-Nov-2007 25-Mar-2009 3-Oct-2008
30-Oct-2008 21-Oct-2009 21-Oct-2009
29-Apr-2009 30-Mar-2011
Panel B trend and regime shifts Stock 8.1107a USD 7.6680b EUR 8.8812a
21-Nov-2007 12-Sep-2007 15-Aug-2007
16-Jul-2008 30-Apr-2008 23-Jul-2008
3-Dec-2008 22-Oct-2008 14-Jan-2009
29-Apr-2009 18-Mar-2009 16-Dec-2009
21-Oct-2009 7-Oct-2009 12-Jan-2011
Note: Critical values are taken from Maki (2012), Table 1, p. 2003. a The presence of cointegration at significance level of 1%. b The presence of cointegration at significance level of 5%.
The breaks on both ISE 30 and USD in May 2011 seem to have stemmed from the general elections in Turkey. On the other side, the break on VOB Euro in October 2011 seems to be the result of EU’s acknowledge of Greece’s disability to meet the targets of the debt-reduction program. Lastly, this was followed by sharp falls in European markets and devaluation of Euro against USD. The same period saw reductions in the ratings of both Italy and Spain and rumors that France was the next took their place even in the most serious journals. Table 3 presents the Maki (2012) cointegration test results. Panel A and B of the Table 3 reports the MBk statistics and the timing of structural breaks in the cointegration vectors obtained from the third (Eq. (4)) and the fourth (Eq. (5)) regression models, respectively. The MBk statistics strongly reject null hypotheses of no cointegration between the spot prices and their futures prices including stock index and its futures (ISE-30TDEX-30), USD and its futures (TDEX-USD-TL/USD), and EUR and its futures (TL/EuroTDEX-EUR). These results reveal the fact that the spot prices of those three financial assets have long-run relationships with their futures having multiple breaks smaller than or equal to the maximum five (5) breaks.
in this study we fill this gap by applying a cointegration methodology in the presence of structural breaks to test for a long-run relationship between spot and futures prices. Our results indicate the existence of structural breaks in our data and the estimated break dates are mostly clustered around the important economic and political events during the global financial turmoil which was triggered by the mortgage delinquencies6 after the mid of 2007. In addition, we find that the spot and future prices of the underlying assets including the ISE30 index, USD and EUR are cointegrated. Our results indicate that these markets have a long-run relationship under multiple structural breaks and the markets are efficient in the long-run. Further study might be on the estimation of the relationship between the prices of the futures and their underlying assets which are not examined in this paper. However, the results of these studies can be more valid only after these contracts will reach enough transaction volumes. In addition, the cointegration analysis considering the structural breaks might be used to examine the relationship between spot and futures markets of the other emerging economics. Acknowledgements
6. Conclusions and future work This paper examines the long-run relationship between the spot prices of index and currencies and their futures contracts by using weekly data from February 9, 2005 to October 17, 2012. The paper contributes to the growing literature of linkages between spot and futures prices by examining the long-run relationship between the spot and futures prices while most of the previous studies focus on the short-term interactions between them. In addition, while a considerable number of studies focus on the developed futures markets, this paper examine TDEX which is the highly growing futures markets in terms of its trading value. And more importantly while the previous studies do not considers the structural breaks,
The authors are indebted to Daiki Maki for providing GAUSS program codes used in the estimation of the cointegration tests. We are also grateful to Professors Carrion-i-Silvestre, Kim, and Perron for making their GAUSS program code publicly available. Appendix A. Spot and Future Prices See Figs. 1–3. 6 The discussion about the structural break dates is suggestive. Any economic event can always be found relatively close to the estimated timing of structural break that could have caused the break.
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
4211
4.8
11.6
4.4
11.2
4.0
10.8
3.6
10.4
3.2
2012
2011
2010
2009
2008
2007
2005
2006
10.0
Fig. 1. Daily log prices of ISE-30 and TDEX-30. Blue (left-axis) and red (right-axis) lines represent ISE-30 index and TDEX-30, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
.7 .6
.7
.5
.6
.4
.5
.3
.4
.2
.3
.1
.2
2012
2011
2010
2009
2008
2007
2006
2005
.1
Fig. 2. Daily log prices of Spot (TL/USD) and TDEX-USD. Blue (left-axis) and red (right-axis) lines represent spot (TL/USD) and TDEX-USD, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
1.0 1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
2012
2011
2010
2009
2008
2007
2006
2005
0.4
Fig. 3. Spot (TL/EUR) and TDEX-EUR. Blue (left-axis) and red (right-axis) lines represent spot (TL/EUR) and TDEX-EUR, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4212
˘ LI, P. Evrim Mandaci / Expert Systems with Applications 40 (2013) 4206–4212 E.Çag˘lar ÇAG
References Abhyankar, A. (1998). Linear and nonlinear Granger causality: Evidence from the U.K. stock index futures market. Journal of Futures Markets, 18(5), 519–540. Bai, J., & Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 47–78. Bai, J., & Perron, P. (2002). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18(1), 1–22. Bodie, Z., Kane, A., & Marcus, A. J. (2009). Investments (8th ed.). New York: McGrawHill/Irwin. Brenner, R. J., & Kroner, K. F. (1995). Arbitrage, cointegration, and testing the unbiasedness hypothesis in financial markets. The Journal of Financial and Quantitative Analysis, 30(1), 23–42. http://dx.doi.org/10.2307/2331251. Brooks, C., Garrett, I., & Hinich, M. J. (1999). An alternative approach to investigating lead–lag relationships between stock and stock index futures markets. Applied Financial Economics, 9(6), 605–613. http://dx.doi.org/10.1080/09603109 9332050. Brooks, C., Rew, A. G., & Ritson, S. (2001). A trading strategy based on the lead–lag relationship between the spot index and futures contract for the FTSE 100. International Journal of Forecasting, 17(1), 31–44. http://dx.doi.org/10.1016/ S0169-2070(00)00062-5. Carrion-i-Silvestre, J. L., Kim, D., & Perron, P. (2009). GLS-based unit root tests with multiple structural breaks under both the null and the alternative hypotheses. Econometric Theory, 25(06), 1754–1792. Chai, S., & Guo, C. (2009). The co-integrating relationship between stock index and futures prices. In Proceedings of the 2009 international conference on new trends in information and service science, NISS ‘09 (pp. 1389–1392). Washington, DC, USA: IEEE Computer Society. http://dx.doi.org/10.1109/NISS.2009.200. Chan, K. (1992). A further analysis of the lead–lag relationship between the cash market and stock index futures market. The Review of Financial Studies, 5(1), 123–152. Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813. http://dx.doi.org/10.2307/2171846. Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276. http:// dx.doi.org/10.2307/1913236. Gee, C. S., & Karim, M. Z. A. (2005). The lead–lag relationship between stock index futures and spot market in malaysia: A cointegration and error correction model approach. Chulalongkorn Journal of Economics, 17(1), 53–72. Ghosh, A. (1993). Cointegration and error correction models: Intertemporal causality between index and futures prices. Journal of Futures Markets, 13(2), 193–198. http://dx.doi.org/10.1002/fut.3990130206. Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99–126. http:// dx.doi.org/10.1016/0304-4076(69)41685-7. Hatemi-J, A. (2008). Tests for cointegration with two unknown regime shifts with an application to financial market integration. Empirical Economics, 35(3), 497–505. Hecq, A., & Urbain, J. P. (1993). Misspecification tests, unit roots and level shifts. Economics Letters, 43(2), 129–135. Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12(2–3), 231–254. Johansen, S., & Juselius, K. (1992). Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK. Journal of Econometrics, 53(1–3), 211–244. Kapetanios, G. (2005). Unit-root testing against the alternative hypothesis of up to m structural breaks. Journal of Time Series Analysis, 26(1), 123–133. Kawaller, I. G., Koch, P. D., & Koch, T. W. (1987). The temporal price relationship between S&P 500 futures and the S&P 500 index. The Journal of Finance, 42(5), 1309–1329. http://dx.doi.org/10.2307/2328529.
Kim, D., & Perron, P. (2009). Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses. Journal of Econometrics, 148(1), 1–13. Li, M.-Y. L. (2009). The dynamics of the relationship between spot and futures markets under high and low variance regimes. Applied Stochastic Models in Business and Industry, 25(6), 696–718. http://dx.doi.org/10.1002/asmb.753. Lien, D., Tse, Y. K., & Zhang, X. (2003). Structural change and lead–lag relationship between the Nikkei spot index and futures price. A genetic programming approach. Quantitative Finance, 3(2), 136–144. http://dx.doi.org/10.1088/14697688/3/2/307. Maki, D. (2012). Tests for cointegration allowing for an unknown number of breaks. Economic Modelling, 29(5), 2011–2015. http://dx.doi.org/10.1016/j.econmod. 2012.04.022. Maslyuk, S., & Smyth, R. (2009). Cointegration between oil spot and future prices of the same and different grades in the presence of structural change. Energy Policy, 37(5), 1687–1693. Ng, S., & Perron, P. (2003). Lag length selection and the construction of unit root tests with good size and power. Econometrica, 69(6), 1519–1554. Nieto, M., Fernandez, A., & Muñoz, M. (1998). Market efficiency in the Spanish derivatives markets: An empirical analysis. International Advances in Economic Research, 4(4), 349–355. http://dx.doi.org/10.1007/BF02295688. Özen, E., Bozdog˘an, T., & Zügül, M. (2009). The relationship of causality between the price of futures transactions underlying stock exchange and price of cash market: The case of Turkey. Middle Eastern Finance and Economics, 4, 28–37. Özün, A., & Erbaykal, E. (2009). Detecting risk transmission from futures to spot markets without data stationarity: Evidence from Turkey’s markets. Journal of Risk Finance, The, 10(4), 365–376. http://dx.doi.org/10.1108/1526594091 0980669. Pattarin, F., ⁄, & Ferretti, R. (2004). The Mib30 index and futures relationship: Econometric analysis and implications for hedging. Applied Financial Economics, 14(18), 1281–1289. http://dx.doi.org/10.1080/09603100412331313578. Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica Journal of the Econometric Society, 1361–1401. Perron, P., & Yabu, T. (2009). Testing for shifts in trend with an integrated or stationary noise component. Journal of Business & Economic Statistics, 27(3), 369–396. Pizzi, M. A., Economopoulos, A. J., & O’Neill, H. M. (1998). An examination of the relationship between stock index cash and futures markets: A cointegration approach. Journal of Futures Markets, 18(3), 297–305. http://dx.doi.org/10.1002/ (SICI)1096-9934(199805)18:3<297::AID-FUT4>3.0.CO;2-3. Rajaguru, G., & Pattnayak, S. S. (2007). Investigation of a lead–lag relationship between spot and futures indices of the hang seng stock average. International Journal of Business Studies: A Publication of the Faculty of Business Administration, Edith Cowan University, 15(1), 69. Stock, J. H. (1999). A class of tests for integration and cointegration. In R. F. Engle & H. White (Eds.), Cointegration, causality, and forecasting: A festschrift for Clive W.J. Granger (pp. 135–167). Oxford University Press. Stoll, H. R., & Whaley, R. E. (1990). The dynamics of stock index and stock index futures returns. The Journal of Financial and Quantitative Analysis, 25(4), 441–468. http://dx.doi.org/10.2307/2331010. Tse, Y. K. (1995). Lead–lag relationship between spot index and futures price of the nikkei stock average. Journal of Forecasting, 14(7), 553–563. http://dx.doi.org/ 10.1002/for.3980140702. Wahab, M., & Lashgari, M. (1993). Price dynamics and error correction in stock index and stock index futures markets: A cointegration approach. Journal of Futures Markets, 13(7), 711–742. Zivot, E., & Andrews, D. W. K. (2002). Further evidence on the great crash, the oilprice shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 20(1), 25–44.