SPILLOVER EFFECT BETWEEN TAIWAN STOCK MARKET AND TAIWAN FUTURES MARKET. Author: Tsung-Min, Yeh. Advisor: Ph.D. Wei-Yu, Kuo 學.

Transcription

1 SPILLOVER EFFECT BETWEEN TAIWAN STOCK MARKET AND TAIWAN FUTURES MARKET Author: Tsun-Min, Yeh Advisor: Ph.D. Wei-Yu, Kuo June 21 A Thesis for the deree of Master in International Business

2 Abstract: This paper examines daily return and volatility spillovers in Taiwan spot and futures stock index markets by usin a eneralized vector autoreressive (eneralized VAR) model where forecast-error variance decompositions are invariant to variable orderin. We measure both total and directional volatility spillovers. This study has used six spot and futures indices, Taiwan Stock Exchane Capitalization Weihted Stock (TX), Taiwan Stock Exchane Electronic Sector (TE), Taiwan Stock Exchane Finance Sector (TF), Future index of TAIEX (FITX), Future index of TE (FITE) and Future index of TF (FITF), daily data spannin over 1th January 21 to 31st March 21. From empirical result, the eneralized vector autoreressive model shows that the return and volatility spillovers from FITE and FITF to other indices are relatively lare. It is clear that futures market is more dominantly to have an effect on spot market but return spillovers from spot to futures could not be inored. i

3 Contents Chapter 1. Introduction... 1 Chapter 2. Generalized Spillover Definition and Measurement... 3 Chapter 3. Estimates of Equity and Spillovers Across Taiwan Spot and Futures Markets Full-sample analysis rollin-sample analysis rollin-sample directional spillover... 9 Chapter 4. Conclusion References ii

4 Tables Table Table Table 3a Table 3b Table 3c Table 3d Table 4a Table 4b Table 4c Table 4d Fiures Fiure Fiure Fiure Fiure Fiure Fiure iii

5 1. Introduction: Stock index futures markets have two important functions. First, they provide forecasts of stock index, and second, they help to transfer stock index returns risk. Rationally, the returns on stock index and stock index futures contracts should be contemporaneously correlated in efficient markets. Althouh futures returns tend to lead stocks returns, the effect is not completely unidirectional, with laed stock index returns havin a mild positive predictive impact on futures returns (e.., Stoll and Whaley, 199). There are papers which considered information transmission between stock index and index futures markets. Bhar (21) examined Australian equity index futures and spot prices with EGARCH model. The result of this study shows that information transmission from futures to spot and reverse case both exist. Meneu and Torro (23) computed the Asymmetric Impulse Response Function for the Spanish stock index and its futures contract. The Impulse Response Function (VIRF) for asymmetric multivariate GARCH structures is extendin from Lin (1997) findins for symmetric GARCH models. The empirical results indicate that the spot-futures variance system is more sensitive to neative than positive shocks, and that spot volatility shocks have much more impact on futures volatility than vice versa. Fu and Qin (26) examined the price discovery process and volatility spillovers in Chinese spot-futures markets throuh Johansen cointeration and bivariate EGARCH model. The empirical results indicated that the models provided evidence supportin the volatility spillovers from futures to spot were more sinificant than the other way round. 1

6 Given the above backround, I am interested in the relationship between Taiwan spot and futures markets. In the followin section, I will us a eneralized vector autoreressive (eneralized VAR) model, developed by Diebold and Yilmaz (29), to examine daily return and volatility spillovers. Sims (198) introduced VAR variance decompositions, which record how much of the H-step-ahead forecast error variance of some variable, i, is due to innovations in another variable, j. 1 Diebold and Yilmaz (29) introduce a method used to measure spillovers in returns and return volatilities based on forecast error variance decompositions from vector autoreressive model. But the framework has an orderin problem since it relies on Cholesky-factor identification of VARs. Diebold and Yilmaz solve this problem by constructin a eneralized vector autoreressive framework in which forecast-error variance decompositions are invariant to variable orderin. The empirical results of this study indicate that directional return/volatility spillovers to others are mainly from FITE and FITF. Considerin net directional returns and volatility spillovers, future markets have positive and spot markets have neative net spillovers. However, in rollin sample analysis, we can still observe net return spillovers from TE index to others and net return spillovers from TF index to others. The above empirical findins reveal that, in Taiwan, the future markets play a dominant role in the return and volatility spillover to spot markets but we could not inore return spillovers from spot to futures. This paper proceeds as follows. Section 2 discusses the methodoloical 1 Assume that y t is a covariance stationary time series. Let y ˆ denote the h-step ahead T h, T forecast of y formed at time T (=E(y T+h y T,y T-1, )). The h-step ahead forecast error is: y y e ˆ T h, T T h T h, T 2

7 approach, usin eneralized variance decompositions and directional spillovers. Section 3 contains data and presents the results. There are a summary and a conclusion in section Generalized Spillover Definition and Measurement Diebold and Yilmaz s framework is proressed by measurin directional spillovers in a eneralized VAR model that eliminates the possible orderin problem. Consider a covariance stationary N-variable VAR(p), p (1) x x t i i 1 t i 1,where ~ (, ). The movin averae is,,where the N x t i A i t i (2) N coefficient matrices A i obey the recursion A A A A... i 1 i 1 2 i 2 p i p (3) with A an N N identity matrix and A (4) i for i. By exploitin the eneralized VAR framework of Koop, Pesaran and Potter (1996) and Pesaran and Shin (1998), hereafter KPPS, variance 3

8 decompositions are invariant to orderin. Variance decompositions allow us to split the forecast error variances of each variable into parts attributable to the various shocks. The own variance shares is defined as the fraction of the H-step-ahead error variances in forecastin x i due to shocks to x i, for i 1, 2,..., N. The cross variance shares, called spillovers, is defined as the fractions of the H-step-ahead error variances in forecastin x i due to shocks to x j, for i, j 1, 2,..., N, such that j i. Defined ( H ) represents the KPPS H-step-ahead forecast error variance ij decompositions, for H = 1,2,, Normalized as ( H ) ij ( H ) ij H ii ( e ` ) i Ah e j h H 1 j 1 h e ij ( H ), so that N ( H ) ij ( ` ` ) i Ah A h e i (5) N ij ( H) 1 and j 1 N ij ( H ) N. (6) i, j 1 Then we can construct a total returns/volatility spillover index by usin the volatility contributions from the KPPS variance decomposition. 4

9 Total Spillover = S N N ij H i, j 1 i, j 1 i j i j N ij ( H ) i, j 1 ( ) ( H ) ( H ) 1 1 N ij (7) We measure directional returns/volatility spillovers received by market i from all other markets j as: Directional Spillover (Received) = i S N j 1 i j N j 1 ( H ) ij ( H ) 1 ( H ) We measure directional returns/volatility spillovers transmitted by market i to all other markets j as: Directional Spillover (Transmitted) = S i ij N j 1 i j N j 1 ( H ) ( H ) 1 ( H ) We can simply measure the net returns/volatility spillovers transmitted from market i to all other markets j as: ji ji (8) (9) Net Spillover = S ( H ) S ( H ) S ( H ) (1) i i i 3. Estimates of Equity and Spillovers Across Taiwan Spot and Futures Markets I use the framework to measure returns and volatility spillovers amon six key Taiwan stock index classes: Taiwan Stock Exchane Capitalization Weihted Stock (TX), Taiwan Stock Exchane Electronic Sector (TE), Taiwan Stock Exchane Finance Sector (TF), Future index of TAIEX (FITX), Future index of TE (FITE) and Future index of TF (FITF). 5

10 The underlyin data are daily closin price of stock and future market indexes, January 21~March 21, taken from TEJ Database. I calculate daily returns as the chane in lo price, day to day. I provide a variety of descriptive statistics for returns in Table 1 and plot the six indices returns in Fiure 1. We can see that the Finance Sector and it s future has relative lower mean returns than the other indices. All the six indices have dramatically returns fluctuation around 22~24 and 27~29. Followin Alizadeh, Brandt and Diebold (22), we estimate daily variance usin daily hih and low prices. For market i on day t, σ =.361 ln P ln P, where P is the hihest price in market i on day t, and P is the daily lowest price. Because σ is an estimator of the daily variance, the correspondin estimate of the annualized daily percent standard deviation (volatility) is σ =1 365 σ. The formula here usin 365 days instead of 24 days (actually tradin days in a year) is the same with Diebold and Yilmaz s approach and will not affect our outcome. I provide descriptive statistics for volatilities in Table 2 and ive the plot in Fiure 2. We find that FITF has the hihest mean and standard deviation. It means that FITF has reater daily volatility in the past 1 years, especially from 27 to 29. [Insert Table 1, Table 2, Fiure 1and Fiure 2 Here] 3.1 Full-sample analysis Here I provide a full-sample analysis of Taiwan six key index classes return and volatility spillovers. I bein by characterizin return and volatility spillovers over 6

11 the entire sample, January 21~March 21. Later I will track time variation in spillovers via rollin sample estimation. Before I test for eneralized VAR model, it is necessary to do the unit root tests of each variable. The result from Aumented Dickey-Fuller Unit Root Test shows that all the variables are stationary at their levels. In the followin empirical work, I use first-order eneralized VAR with 1-step-ahead forecasts. 2 I report Spillover es for returns and volatility in Tables 3 and 4, respectively. [Insert Table 3 and Table 4 Here] The xy entry in the spillover table is the estimated contribution to the forecast error variance of index x comin from shocks to index y. The off-diaonal column sums represent directional to others and the off-diaonal row sums represent directional from others. The total spillover rate, which appears in the lower riht corner of the table, is approximately the off-diaonal column (or row) sums relative to the column (or row) sums includin diaonals. The spillover table shows a to and from two-way decomposition of the total spillover effect. In Table 3, we can see that ross directional returns spillovers to others from the future markets are relatively lare (especially FITE), at 82.6 percent, percent and 88.1 percent, respectively. From the directional from others column, ross directional return spillovers from others to TX is relatively lare, at percent. In Table 4, we can also see that ross directional volatility spillovers to others from the future markets are relatively lare (especially FITF), at 84.6 percent, The method is the same with Diebold and Yilmaz s approach and it will not affect our key conclusions. 7

12 percent and percent, respectively. The spillovers here exceed 1 percent is mainly because we standardize the formulae for row sums (directional from others) and the sum of directional to others column must equal the sum of directional from others column. From the directional from others column, ross directional volatility spillovers from others to TX is relatively lare, at 87.3 percent. Considerin net directional returns and volatility spillovers, future markets have positive and spot markets have neative net spillovers. As for net directional return spillovers, the larest SPT and SPF are to others from FITE and from others to TX. As for net directional volatility spillovers, the larest SPT and SPF are to others from FITF and from others to TX. The total spillovers are important in both returns and volatilities since almost 75% of forecast error variance comes from spillovers, both for returns (78%) and volatilities (75%). Here I use the nonparametric bootstrappin method (Efron, 1979) to conduct the sinificant test. By simulatin 1 replications, I calculate the 95% confidence interval and check the p-value of the directional spillover 1-ahead forecast. In table 3, SPF and SPT are all statistically sinificant. Considerin NET spillovers, except FITX is insinificant, all others are statistically sinificant. In Table 4, SPF, SPT and SPN are all statistically sinificant. 3.2 rollin-sample analysis The full-sample Spillover Tables and Spillover es provide a useful summary of averae behavior, but they are likely to miss the potentially cyclical movements in spillovers. To address this issue, I estimate the models usin 1 days 8

13 rollin samples. I present the Spillover Plot for returns and volatility in Fiure 3. [Insert Fiure 3 Here] The total return spillover plot usually fluctuates between seventy-five and eihty percent, occasionally fallin below seventy-five percent. The total volatility spillover plot usually fluctuates between seventy and eihty percent, occasionally fallin below seventy percent. The total volatility spillover plot (TVS) and the total return spillover plot (TRS) display similar trend pattern, but TVS ranes widely than TRS. At the beinnin of 27, the total return spillovers and the total volatility spillovers both dropped to around sixty-five percent (the relative lower rate in the decade). Soon after the fallin, they climbed up dramatically to about eihty percent (the relative hiher rate in the decade) and then the lobal financial crisis occurred, lastin from 27~29. Durin this period, the total return spillovers maintained around eihty percent. The total volatility spillovers also came to the hihest level (over seventy-five percent). 3.3 rollin-sample directional spillover After discussin the total dynamic spillover plot, we now also want to estimate the row and column dynamically. We call these directional spillover plots. In Fiure 4, I present the directional return and volatility spillovers from the six stock index classes. The fluctuation of TX, TE and TF is about ten percent, twenty percent and thirty percent. The fluctuation of FITX, FITE and FITF is about twenty percent, forty percent and sixty percent. The plots show that the directional return and volatility spillover lines of all six indices vary obviously over time and FITF fluctuates larer than other indices. In Fiure 5, I present the directional return and volatility spillovers 9

14 to the six stock index classes. Comparin with the directional spillovers from others, the spillovers to others vary reatly over time. We can find the Finance Sector Indices (TF and FITF) have an increasin trend. This can be easily fiured out because there was a lobal financial crisis durin 27~29 and MOU aenda between Taiwan and Mainland China overnments durin 29~21. [Insert Fiure 4 and Fiure 5 Here] Calculatin difference between the Contribution from column sum and the Contribution to row sum, we can derive the net directional spillovers movin pattern. Fiure 6 shows the net directional spillover plot. Overall, there has been very little net return and volatility transmission from the spot markets. This result is quite easy to understand owin to stock index futures havin the function on forecastin stock index and helpin to transfer stock index returns risk. But we can still observe net return spillovers from TE index to others reach about twenty percent durin 25~mid 26. Net return spillovers from TF index to others reach about fifty percent durin 29 and the first half of 24. Further, net return and volatility spillovers from FITE and FITF appear the most consistently positive and lare. Althouh FITX is a future index, it is not an important net transmitter of return and volatility. This is because FITE and FITF also influence FITX a lot. 3 Followin the financial market turmoil associatin with the subprime mortae market that started in July-Auust, 27, net return spillover plot of FITF had an upward trend, and net return spillover plot of FITE had a downward trend. We can say that durin the lobal financial crisis 27~29, net return and volatility spillovers from FITF affected mostly the other index. 3 The two major components of Taiwan stock market are Electronic sector and Finance sector. 1

15 [Insert Fiure 6 Here] 4. Conclusion In this paper I examine daily return and volatility spillovers of Taiwan spot and futures stock indices by usin a eneralized vector autoreressive model where forecast-error variance decompositions are invariant to variable orderin. I also calculate both ross and net directional return/volatility spillovers and look further in dynamic analysis. The result of empirical analysis can be summarized as follows: The clear channels of directional return/volatility spillovers to others are from FITE and FITF. Althouh tradin volume of FITX are much larer than tradin volume of FITE and FITF in Taiwan futures market, FITE and FITF are mainly traded by Institutional investors such as Securities Investment Trust, Forein investors and Securities Dealers. These Institutional investors are more professional and have more market information. That is why the return and volatility spillovers from FITE and FITF to other indices are relatively lare. Considerin net directional returns and volatility spillovers, future markets have positive and spot markets have neative net spillovers. However, in rollin sample analysis, we can still observe net return spillovers from TE index to others reach about twenty percent durin 25~mid 26. Net return spillovers from TF index to others reach about fifty percent durin 29 and the first half of 24. The above empirical findins reveal that the future markets play a dominant role in the return and volatility spillover to spot markets but we could not inore return spillovers from spot to futures. Since the occurrence of the lobal financial crisis from 27 and the MOU issue neotiated between Taiwan and Mainland China overnments durin 29~21, the Finance sector has a reater influence over Taiwan stock markets than Electronic sector in recent years. 11

16 References Tse, Y. (1999), Price discovery and volatility spillovers in the DJIA index and futures markets,journal of Future Markets 29, P: Bhar, R. (21) and volatility dynamics in the spot and futures markets in Australian: An Intervention Analysis in a bivariate EGARCH-X framework. Journal of Futures markets, 21, Meneu, V. & Torro., H.(23) Asymmetric covariance in spot-futures markets. Journal of Futures Markets, 23, Fu, L.Q. and Qin, Z.J. (26), Price discovery and volatility spillovers: Evidence from Chinese spot-futures markets. Gupta, K. and Belwinder, S. (26), Price discovery and causality in spot and future markets in India, The ICFAI Journal of Derivatives. Diebold, F.X. and Yilmaz, K. (29), "Measurin Financial Asset and Spillovers, With Application to Global Equity Markets," Economic Journal, 119, Diebold, F.X. and Yilmaz, K. (29), "Better to Give than to Receive: Predictive 12 Directional Measurement of Spillovers," International Journal of Forecastin, forthcomin. (With discussion.) Forbes, K., Riobon, R. (22), No Contaion, only Interdependence: Measurin Stock Market Comovements, Journal of Finance, 57, Karolyi, G.A. (1995), A Multivariate GARCH Model of International Transmissions of Stock s and : The case of the United States and Canada, Journal of Business and Economic Statistics, 13, Kin, Mervyn A and Wadhwani, Sushil, (199). "Transmission of between Stock Markets," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(1), paes Koop, G., Pesaran, M.H., and Potter, S.M. (1996), Impulse Response Analysis in Non-Linear Multivariate Models, Journal of Econometrics, 74, Pesaran, M.H. and Shin, Y. (1998), Generalized Impulse Response Analysis in Linear Multivariate Models, Economics Letters, 58, Cho.Bauer(22), The analysis of Stock return chane to Asian Equity Markets from US,The Korean Journal of Financial Manaement, Vol.19, No.2, pp Morana, C., Beltratti, A. (26), Comovements in International Stock Markets, Journal of International Financial Markets, Institutions and Money Miyakoshi T(23), "Spillovers of Stock to Asian Equity Markets from Japan and the US", Journal of International Financial Markets, Institutions & Money, No.13. pp

17 Table 1 Descriptive Statistics of Taiwan Six Indices Daily s TX TE TF FITX FITE Mean E S.D SK Kurt Max Min Med FITF Mean 9.44E-5 S.D..277 SK Kurt Max.7713 Min Med.619 Table 2 Descriptive Statistics of Taiwan Six es Daily Volatilities TX TE TF FITX FITE Mean S.D SK Kurt Max Min Med FITF Mean 26.4 S.D SK Kurt Max 16.5 Min Med

18 14 Fiure 1 Daily s of Taiwan Six Indices /3/21 1/3/22 1/3/23 1/3/24 1/3/25 1/3/26 1/3/27 1/3/28 1/3/29 1/3/21 TX /3/21 1/3/22 1/3/23 1/3/24 1/3/25 1/3/26 1/3/27 1/3/28 1/3/29 1/3/21 FITX /3/21 1/3/22 1/3/23 1/3/24 1/3/25 1/3/26 1/3/27 1/3/28 1/3/29 1/3/21 TE /3/21 1/3/22 1/3/23 1/3/24 1/3/25 1/3/26 1/3/27 1/3/28 1/3/29 1/3/21 FITE /3/21 1/3/22 1/3/23 1/3/24 1/3/25 1/3/26 1/3/27 1/3/28 1/3/29 1/3/21 TF /3/21 1/3/22 1/3/23 1/3/24 1/3/25 1/3/26 1/3/27 1/3/28 1/3/29 1/3/21 FITF

19 15 Fiure 2 Daily Volatilities of Taiwan Six Indices /2/21 1/2/22 1/2/23 1/2/24 1/2/25 1/2/26 1/2/27 1/2/28 1/2/29 1/2/21 TX /2/21 1/2/22 1/2/23 1/2/24 1/2/25 1/2/26 1/2/27 1/2/28 1/2/29 1/2/21 FITX /2/21 1/2/22 1/2/23 1/2/24 1/2/25 1/2/26 1/2/27 1/2/28 1/2/29 1/2/21 TE /2/21 1/2/22 1/2/23 1/2/24 1/2/25 1/2/26 1/2/27 1/2/28 1/2/29 1/2/21 FITE /2/21 1/2/22 1/2/23 1/2/24 1/2/25 1/2/26 1/2/27 1/2/28 1/2/29 1/2/21 TF /2/21 1/2/22 1/2/23 1/2/24 1/2/25 1/2/26 1/2/27 1/2/28 1/2/29 1/2/21 FITF

20 Table 3a. Spillover Table, Six Classes ============================================================= TX TE TF FITX FITE FITF SPF TX TE TF FITX FITE FITF SPT Inc Own ============================================================= Notes: SPT standin for Directional To Others, SPF standin for Directional From Others, Inc Own standin for Directional includin Own, Total Spillover :77.644% Table 3b. Directional s Spillovers SPT SPF SPN TX TE TF FITX FITE FITF Notes: SPN standin for Net Directional s Spillovers 16

21 Table 3c. Sinificant Test of The Total Spillover Effect (Non-Param) H TOTAL SPO CI_low CI_up p-value Table 3d. Sinificant Test of The Directional Spillover Effect 1-step-ahead forecast (Non-Param) SPF F_CI(l) F_CI(u) p-value SPT T_CI(l) T_CI(u) p-value TX TE TF FITX FITE FITF SPN N_CI(l) N_CI(u) p-value TX TE TF FITX FITE FITF

22 Table 4a. Spillover Table, Six Classes ============================================================= TX TE TF FITX FITE FITF SPF TX TE TF FITX FITE FITF SPT Inc Own ============================================================= Notes: SPT standin for Directional To Others, SPF standin for Directional From Others, Inc Own standin for Directional includin Own, Total Spillover :75.227% Table 4b. Directional Spillovers SPT SPF SPN TX TE TF FITX FITE FITF Notes: SPN standin for Net Directional s Spillovers 18

23 Table 4c. Sinificant Test of The Total Spillover Effect (Non-Param) H TOTAL SPO CI_low CI_up p-value Table 4d. Sinificant Test of The Directional Spillover Effect 1-step-ahead forecast (Non-Param) SPF F_CI(l) F_CI(u) p-value SPT T_CI(l) T_CI(u) p-value TX TE TF FITX FITE FITF SPN N_CI(l) N_CI(u) p-value TX TE TF FITX FITE FITF

24 Fiure 3a. Total and Spillovers TVS TRS 55 Price 1,. 9,. 8,. 7,. 6,. 5,. 4,. 3,. Fiure 3b. TX daily Price 2

25 Fiure 4a. directional return and volatility spillovers, from six stock index classes 95 TX TE TF

26 Fiure 4b. directional return and volatility spillovers, from six stock index classes FITX FITE FITF

27 Fiure 5a. directional return and volatility spillovers, to six stock index classes TX TE TF

28 Fiure 5b. directional return and volatility spillovers, to six stock index classes FITX FITE FITF

29 Fiure 6a. net directional return and volatility spillovers, six stock index classes TX TE ~mid26 first half of 24 TF 29 25

30 Fiure 6b. net directional return and volatility spillovers, six stock index classes FITX FITE FITF