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What Are Their Relationships among the Indices of Emerging ...

  1. 1. What Are Their Relationships among the Indices of Emerging Markets? Mu-Fen Chao Tam-Kang University, Taiwan Yu-yo Chen Tam-Kang University, Taiwan Abstract In this study, we employed VECM to analyze the relationship of indices among the three emerging markets, USA and the world. The variable of the three emerging markets adopts MSCI Emerging Market Series Index, the variable of world index MSCI World Index, and the variable of USA stock price S&P 500 Index. The conclusion of this study are: 1. The three emerging markets tends to be convergent in the long term; 2.USA stock price still influences the three emerging markets greatly; 3.The impact of world factor on the three emerging markets is not significant; 4. Emerging Asia market is on the rise. Keywords: emerging market, stock index, VECM 1. Introduction Since the 1980s, there have been substantial changes in political and economic environments in many regions, such as China, India, Eastern Europe, and Latin America. As a result, massive capital flows in and out of emerging stock markets last decade, and emerging markets now represent a feasible investment alternative for international investors (Bilson et al., 2001). Returns and risks in emerging markets have been found to be higher relative to developed markets (Errunza, 1983; Claessens et al., 1993; Harvey, 1995). Emerging market equities have had: (1). higher average returns; (2). lower correlation’s with developed markets; (3). greater serial correlation; and (4). greater volatility (Errunza, 1997; Harvey, 1995; Eaker et al., 2000). The main emerging markets are grouped in three areas: emerging Asia, emerging East Europe, and emerging Latin America. Emerging Asia not only is the world's most populous area but also owns huge markets. The most notable advantage of emerging East Europe is the rich natural resources. Meanwhile, emerging Latin America has 1
  2. 2. remarkable quantity of commercialization of agricultural product. All of them are attractive areas for the investors. However, they are so different from each other in many aspects. The relationships among them are ambiguous and unclear. Are they integrated or segmented? It is hard to answer. There have been numerous studies that have focused on the issue of market integration and segment. The integration and interdependence of stock markets underlies a major cornerstone of modern portfolio theory that addresses the issue of diversifying assets (Masih and Masih, 2001). For example, Wheatly (1988) who argues that even without market integration, assets that are diversified internationally could be “mean-variance efficient”. The advantages of asset diversification have already been widely discussed in the literature in which much effort was devoted to quantify risk- reduction and its associated benefits available to the internationally diversified portfolio (Solnik, 1991). Determining the extent to which a national equity market is segmented from international financial markets is thus an empirical question of great interest to both investors and researchers. Our major aim in this study is to make an attempt to extend the existing literature by focusing on the patterns of linkages among the three emerging regions, the USA, and the world portfolio. This paper is organized in the following manner: Section 2 briefly describes the theoretical basis. A discussion of the data is then presented in Section 3. Section 4 contains the methodology to be adopted, and the estimation results. Finally, the conclusions and limitations of the study are presented in Section 5. 2. Literalities Review A persistent issue of international finance is the extent to which international financial markets are integrated. One important implication of integrated markets is that assets associated with similar levels of risk in different countries should also lead to a similar level of return. This issue has been empirically addressed in several studies (Errunza and Losq, 1985; Hietala, 1989; Brealey et al., 1999) as well as placed under critical scrutiny due to inconsistent results. That is, the same asset pricing relationships apply in all countries regardless of their geographical location in fully integrated capital markets. In financial economics, the assumption of the markets are integrated is often employed (Peresetsky & Ivanter, 2000). For example, the Black-Scholes model assumed that stock, bond and options markets are perfectly integrated so that no cross- market arbitrage opportunities exist. On the other hand, when markets are segmented, the risk return relationship varies across markets and a project which might be considered to provide unequal return in different market. Financial market segmentation could arise, for example, from market 2
  3. 3. imperfections, differences in taxes or other restrictions on the ownership of securities (e.g., Eun, 1985; Eun & Janakiramanan, 1986). Research over the past suggests that different national markets exhibit different level of integration to international financial markets and that the degree of integration vary over time (e.g., Hodrick, 1981; Bekaert & Harvey, 1995; Stulz & Wasserfallen, 1995; Carrieri et al., 2002). In last decades, empirical studies investigating financial integration have tended to focus on developed markets (e.g., Jorion & Schwartz, 1986; Korajczyk & Viallet, 1989; Campbell & Hamao, 1992;Bekaert & Harvey, 1995; Carrieri et al., 2002;). Recently, more papers have focused on emerging markets, and several studies have implied significant benefits from adding emerging markets to global portfolios (e.g., Bekaert & Urias, 1996; Errunza & Losq, 1985, 1989; De Santis & Imrohoroglu, 1997; Bekaert et al., 1998; Bekaert, 1999; Rockinger & Urga, 2001; Bilson et al., 2001; Gerard et al. , 2003; Verma & Ozuna, 2005; Tai, 2007). However, the focuses of these studies are always on countries not areas, none study has ever worked on regions including several domestic countries. Now, the exchange traded funds (hereafter ETFs) make that kind of diversification available. They offer, in one trade, the benefits of diversification and index tracking at a low cost. ETFs assets under management grew at a 132 percent average annual rate from 1995 to 2000 (Investment Company Institute, 2005). Apparently, ETFs make it easier to invest directly in a region. We investigate whether three key emerging regions are fully integrated into or partially segmented from each, and the world financial markets. 3. Data Our sample covers the period from January 2007 to December 2008. We use daily percentage returns on stock indices for three emerging markets, Emerging Asia, Emerging East Europe, Emerging Latin America, one developed market, USA, and world portfolio returns. There are two reasons for choosing the returns on stock indices: first, we could observe the relationships of areas instead of countries; second, the effect of exchange rate could be deleted. The emerging markets returns as well as the world portfolio returns series are from Morgan Stanley Capital International (hereafter MSCI). MSCI Emerging Asia Index, MSCI Emerging Eastern Europe Index, and MSCI Latin America Index are the indices of the three emerging areas respectively. Each index is a weighted average portfolio of some notable countries of that area. Table 1 reports the countries and the relevant weights. 3
  4. 4. Table 1 Countries and Weights of the Stock Indices MSCI Emerging Asia Index MSCI Latin America Index MSCI Emerging Eastern Europe Index CHINA (28.34%) ARGENTINA (2.27%) CZECH REPUBLIC (7.82%) INDIA (13.17%) BRAZIL (63.92%) HUNGARY (6.89%) INDONESIA (3.22%) CHILE (5.75%) POLAND (15.49%) KOREA (25.91%) COLOMBIA (2.36%) RUSSIA (69.80%) MALAYSIA (5.05%) MEXICO (23.02%) PAKISTAN (0.27%) PERU (2.68%) PHILIPPINES (0.95%) TAIWAN (20.33%) THAILAND (2.77%) Source: the website of MSCI, 09/30/2008 Note that our proxy for world equity market portfolio is the MSCI world index (hereafter WI), which is a value-weighted portfolio of 20 developed markets, and hence does not include the three emerging markets in our sample. And the USA market index data is S&P 500 index. For the five indices, we calculate the percentage return respectively, and name the percentage returns of MSCI Emerging Asia Index as EMA, the ones of MSCI Emerging Eastern Europe Index as EMEE, the ones of MSCI Latin America Index as EMLA. WI is for the percentage returns of MSCI world index, and S&P 500 is represented as the rates of return of USA market. During the study period, the percentage returns are illustrated following figures. Fig.1 Time data of EMA Fig.2 Time data of EMEE 4
  5. 5. Fig.3 Time data of EMLA Fig.4 Time data of WI Fig.5 Time data of S&P 500 4. METHODOLOGY AND EMPIRICAL RESULTS A large proportion of the empirical literature concerning stock market dynamics which employs times series techniques can be broadly classified into two groups. One group follows the work initiated by Kasa (1992) which uses multivariate cointegration techniques to examine the number of common stochastic trends in a system of national stock market prices. Relevant studies include Chung and Liu (1994) and Corhay et al. (1995) on Pacific-Rim country stock markets, Blackman et al. (1994) on 17 OECD markets, Jeon and von Furstenberg (1990) and Kwan et al. (1995) on major world equity markets. The second group has attempted to investigate lead–lag relationships among prices of national stock markets (Eun & Shim, 1989; Cheung & Mak, 1992; Malliaris & Urrutia, 1992; Arshanapalli & Doukas, 1993; Smithi et al., 1993; Brocato, 1994). We estimate a vector error-correction model (VECM) to test the relationship among the percentage returns of stock indices of Emerging Asia (EMA), Emerging East Europe (EMEE), Emerging Latin America (EMLA), USA (S&P500), and World index(WI). Since the use of VECM is contingent upon stationary conditions of the data set, a brief discussion of unit root test and cointegration test is in order. 4.1 Unit root tests A series is considered stationary if its mean, variance and covariances are time- independent. Augmented Dickey-Fuller (ADF, 1981) tests are used to test for the presence of unit root in the series. The ADF method was applied to assess the existence 5
  6. 6. of unit roots and identify the order of integration for each variable. The results, as summarized in Table 2, suggest that all series are I(0). Table 2 Tests for Unit Root VARIABLE ADF(t-statistic) VARIABLE ADF(t-statistic) EMA -6.42356 *** EMLA -4.33137 *** EMEE -5.71298 *** S&P 500 -5.64968 *** WI -12.99637 *** Note: *** denotes statistical significance at the 1% level The ADF statistics for the level of four series are significant at the 1% significance level, implying that the null hypothesis of a unit root can be rejected. Therefore, this study proceeded with a long-run equilibrium analysis using the cointegration technique. 4.2 Johansen Cointegration Test Cointegration test is a test for the existence of a long run equilibrium relationship between variables. In a bivariate case, each of the two series, xt and yt can individually be non-stationary, say I(1), but a linear combination of the two, say, zt = xt-σyt, can either be non-stationary, I(1), or stationary, I(0). A test of cointegration involves subjecting the residuals from the cointegrating equation to DF and ADF tests. However, the critical values used in the cointegration tests are different from those used in the unit root tests. The variables are said to be cointegrated if these residuals are found to be integrated of order zero, or I(0). In general, two variables are said to be cointegrated if both are integrated of order k, but a linear combination of the two is integrated of order less than k. Thus, a necessary condition for cointegration is that all variables should have the same order of integration. The two most frequently used methods to test cointegration are the two-step Engle and Granger test (Engle and Granger, 1987) and the Johansen test (Johansen, 1988). We employed the Johansen (1988) methodology to test for existence of cointegration. 6
  7. 7. Table 3 presents the results of cointegration test. As shown in Table 3, the trace statistics and maximum eigen-value statistics suggest that EMA, EMEE, EMLA, S&P 500, and WI variables cointegrated. There are some long-term relationships among the five variables. This implies that the EMA, EMEE, EMLA, S&P 500, and WI would not move too far away from each other. And the tests are compared against the asymptotic critical values of the two test statistics by MacKinnon-Haug-Michelis (1999). Table 3 Tests for Cointegration Hypothesized Trace 0.05 Prob. 1 Max-Eigen 0.05 Prob. 1 No. of CE(s) Statistic Critical Statistic Critical Value Value 111.745 60.061 0.0000 0.0106 None 35.556 30.440 76.189 40.175 0.0000 0.0040 At most 1 31.696 24.159 44.493 24.276 0.0000 0.0316 At most 2 19.105 17.797 25.387 12.321 0.0002 0.0088 At most 3 15.377 11.225 10.010 4.130 0.0018 10.010 4.130 0.0018 At most 4 1: MacKinnon-Haung-Michelis(1999) p-value 4.3 Vector Error-Correction Model (VECM) After determining the number of cointegration vectors through the trace test and maximal eigen-value test, this study continue to estimate the following vector error- correction model (VECM) of the EMA, EMEE, EMLA, WI, and S&P 500. The result is shown in Table 4. The regression equations are reported in the appendix. There are three lagged error-correction terms, CointEq1, CointEq2, and CointEq3, significant in this study. They indicate the speed of adjustment from a short-run disequilibrium. In all three cases, the coefficients of the lagged error-correction terms are quite high, suggesting that convergence to the long-run equilibrium path following a shock is fast. 7
  8. 8. For EMA, the coefficients of the explanatory variables EMEE, EMLA, and S&P500 are significant at the 10 percentage level, and the signs of the coefficients reveal the causal effect on EMA is positive or negative. The explanatory variables EMA, WI, and S&P500 are significant at the 10 percentage level on EMEE. For EMLA, the significant explanatory variables are EMA, EMEE, and S&P500. The explanatory variables EMA, EMLA, and S&P500 are significant on WI. And for S&P500, the significant explanatory variables are EMA, EMEE, and WI. Undoubtedly, S&P500 is the most important explanatory variable for the three main emerging markets, and WI. EMA could play another important role to produce an effect on the other two emerging markets, S&P500, and WI. Relatively, S&P 500, and EMA seem to be influenced less by EMLA, and EMEE. 8
  9. 9. Table 4 Result of VECM Error Correction/ explanatory D(EMA) D(EMEE) D(EMLA) D(WI) D(SP500) variables: CointEq1 -1.417158*** -0.587367 0.645201 0.108474 0.136874 CointEq2 0.058924 -1.362301*** -0.176502 -0.078728 -0.129101 CointEq3 0.446855 0.992519* -0.817328 0.085343 -0.106931 D(EMA(-8)) -0.058976 -0.495815 -0.877564* -0.328847 -0.435143 D(EMA(-9)) 0.009457 -0.574141 -0.869452* -0.318064 -0.404457 D(EMA(-10)) 0.013005 -0.618971 -0.765213* -0.296618 -0.350911 D(EMA(-11)) -0.105103 -0.691787* -0.747382* -0.312642 -0.333722 D(EMA(-14)) -0.040128 -0.560701* -0.560287* -0.268402 -0.281065 D(EMA(-15)) 0.005296 -0.567842** -0.550196* -0.330476** -0.353577* D(EMA(-20)) -0.054531 -0.146648 -0.186650** -0.082515* -0.081202 D(EMEE(-11)) -0.037846 -0.502961* -0.304679 -0.260751 -0.271080 D(EMEE(-15)) 0.269395* -0.033971 -0.033273 -0.136018 -0.207909 D(EMEE(-16)) 0.257743* -0.029092 0.086205 -0.083620 -0.179271 D(EMEE(-17)) 0.340063*** -0.084696 0.082665 -0.014248 -0.111277 D(EMEE(-18)) 0.289392*** -0.050495 0.083803 0.028386 -0.037977 D(EMEE(-19)) 0.090430 -0.147867 -0.238544** -0.089071 -0.140039* D(EMLA(-12)) -0.479684* -0.156018 -0.565763 -0.031049 0.037455 D(EMLA(-16)) -0.302321* -0.106295 -0.278675 0.024121 0.145415 D(EMLA(-18)) -0.283855** -0.250531 -0.302647 -0.082697 -0.034232 D(EMLA(-19)) -0.214227** -0.185953 -0.375688*** -0.143945* -0.157401 D(WI(-2)) -0.243192 -2.241836 -0.343029 -1.682550 -3.035289* D(WI(-3)) -0.468311 -2.965631 -0.530569 -1.894427 -3.007678* D(WI(-6)) -0.313233 -2.020676 0.068328 -1.916069 -2.789908* D(WI(-10)) -0.292561 -0.901218 0.128875 -1.406964 -2.144756* D(WI(-12)) -0.677952 -0.554550 -0.451059 -1.412666 -2.185012* D(WI(-13)) -0.518422 -0.475024 -0.693591 -1.321226 -2.140248** D(WI(-15)) -1.124984 -0.546956 -0.681197 -0.947016 -1.547127* D(WI(-16)) -0.914714 -0.849835 -1.120646 -0.957148* -1.408422*** D(WI(-17)) -0.755860 -0.411617 -1.054939 -0.931275** -1.335792** D(WI(-18)) -0.529917 0.253305 -0.732610 -0.623344 -1.008159** D(WI(-19)) 1.232811* 1.901292*** 1.184695*** 1.538769*** 0.008966 D(WI(-20)) 0.444318 1.236979** 0.787704** 1.150418*** -0.015676 D(SP500(-10)) 0.499118 1.712793 0.799420 1.359263* 2.044115** D(SP500(-11)) 0.499480 1.553840 1.018303 1.257958 1.884708* D(SP500(-12)) 1.045824 1.974171 1.994505 1.703525** 2.432810*** D(SP500(-13)) 0.933145 1.947289 2.197640* 1.678048** 2.410553*** D(SP500(-14)) 0.821489 1.868274* 1.831470* 1.283666** 1.866710** D(SP500(-15)) 1.093550 1.689051* 1.610657* 1.134302** 1.625303** D(SP500(-16)) 1.128710* 1.797660** 2.046526** 1.290281*** 1.700418*** D(SP500(-17)) 0.864196* 1.232811* 1.901292*** 1.184695*** 1.538769*** D(SP500(-18)) 0.590863 0.444318 1.236979** 0.787704** 1.150418*** Notes:1. * denotes statistical significance at the 10%t level; ** denotes statistical significance at the 5% level; *** denotes statistical significance at the 1% level 9
  10. 10. 2. CointEq1= EMA(-1) - 1.539473*SP500(-1); CointEq2 = EMEE(-1) - 1.708376*SP500(-1); CointEq3 = EMLA(-1) - 1.523868*SP500(-1) 5. CONCLUSIONS Using a five-variable VEC model, we have investigated the nature of the relationships of the returns of the stock index among the three emerging regions (Asia, East Europe, and Latin America), USA and the world from January 2007 to December 2008. The empirical results show that the indices of the three emerging markets, USA, and the world tend to be in equilibrium in the long term but not so in the short term. Then with VECM, the findings are that USA stock returns have the greatest positive effect on all indices while the effect of world index returns on emerging markets is not significant; on the contrary, the index returns of Emerging Asia have negative effect on almost all index returns and th lag-time 2-3 weeks. The conclusion of this research: 1. The three emerging markets tends to be convergent in the long term; 2.USA stock price still influences the three emerging markets greatly; 3.The impact of world factor on the three emerging markets is not significant; 4. Emerging Asia market is on the rise. 10
  11. 11. References 1. Abugri, B. A. (2008), “Empirical Relationship between Macroeconomic Volatility and Stock Returns: Evidence from Latin American Markets,” International Review of Financial Analysis, Vol.17, No.2, pp.396-410. 2. Bodie, Z., Kane, A. and Marcus, A. J.(2008), Investments(7th ed.). New York: McGraw-Hill. 3. Bekaert, G. (1995), “Market Integration and Investment Barriers in Emerging Equity Markets,” World Bank Economy Review, Vol.9, No.1, pp.75-107. 4. Bekaert, G. and C. R. Harvey (1995), “Time-Varying World Market Integration,” Journal of Finance, Vol.50, No.2, pp.403-444. 5. Bekaert, G. and C. R. Harvey (1997), “Emerging Equity Market Volatility,” Journal of Financial Economics, Vol.43, pp.29-77. 6. Bekaert, G. and C. R. Harvey (2000), “Foreign Speculators and Emerging Equity Markets,” Journal of Finance, Vol.55, No.2, pp.565-613. 7. Bilson, C. M., T. J. Brailsford and V. J. Hopper (2001), “Selecting Macroeconomic Variables as Explanatory Factors of Emerging Stock Market Returns,” Pacific- Basin Finance Journal, Vol9, No.4, pp.401-426. 8. Conover, C. Mitchell, Gerald R. Jensen, and Robert R. Johnson (2002), “Emerging Markets: When are they worth it?”Financial Analysts Journal, March/April 2002, Vol.58, No.2, pp.86-95. 9. Beim, D. O. and Calomiris, C. W.(2001), Emerging Financial Markets. New York: McGraw-Hill. 10. Eun, C. and S. Shim (1989), “International Transmission of Stock Market Movements,” Journal of Financial and Quantitative Analysis, Vol.24, No.2, pp.241-256. 11. Eaker, Mark, Dwight Grant, and Nelson Woodard (2000), “Realized Rates of Return in Emerging Equity Markets,” Journal of Portfolio Management, Spring2000, pp.41-49. 12. Gerard, B., K. Thanyalakpark and J. A. Batten (2003), “Are the East Asian Markets Integrated? Evidence from the ICAPM,” Journal of Economics and Business, Vol.55, pp.585-607. 13. Grubel, H. G. (1968), “Internationally diversified Portfolio: Welfare Gains and Capital Flows,” American Economics Review, Dec.1968, Vol.58, pp.1299-1314. 14. Harvey, Campbell R. (1995), “The Risk Exposure of emerging Equity Markets,” World Bank Economic Review, Vol.9, No.1, pp.19-50. 15. Harvey, Campbell R. (1995b),“Predictable Risk and Returns in Emerging Markets.”Review of Financial Studies, Vol.8, No.3, pp.773-816. 11
  12. 12. 16. Huang, B. N., C. W. Yang, and W. S. Hu (2000), “Causality and Cointegration of Stock Market among the United States, Japan, and the South China Growth Triangle,” International Review of Financial Analysis, Vol.9, No.3, pp.281-297. 17. Jeon, B. N. and T. C. Chiang (1991), “A System of Stock Prices in World Stock Exchanges: Common Stochastic Trends for 1975-1990,”Journal of Economics and Business, Vol.43, No.4, pp.329-338. 18. Knif, J. and S. Pynnonen (1999), “Local and Global Price Memory of International Stock Markets,” Journal of International Finance Markets, Institutions and Money, Vol.9, No.2, pp.129-147. 19. Liu, Y. A., M. S. Pan and J. C. P. Shieh (1998), “International Transmission of Stock Price Movements: Evidence from the U.S. and Five Asian-Pacific Markets,” Journal of Economics and Finance, Vol.22, No.1, pp.56-69. 20. Morck, R., B. Yeung, and W. Yu (2000), “The Information Content of Stock Markets: Why Do Emerging Markets Have Synchronous Stock Price Movements?”Journal of Financial Economics, Vol.58, pp.215-260. 21. Masih, R. and A. M. M. Masih (2001), “Long and Short Term Dynamic Causal Transmission amongst International Stock Markets,” Journal of International Money and Finance, Vol.20, No.4, pp.563-587. 22. Roll, R. (1992), “Industrial Structure and the Comparative Behavior of International Stock Market Indices,”Journal of Finance, Vol.47, No.1, pp.3-42. 23. Tai, CS (2007), “Market Integration and Currency Risk in Asian Emerging Markets,” Research in International Business and Finance, Vol.21, No.1, pp.98-117. 24. Uribe, M. and Z. Y. Vivian (2006), “Country Spreads and Emerging Countries: Who Drives Whom?”Journal of International Economics, Vol.69, pp.6-36. 25. Verma, R. and T. Ozuna (2005), “Are emerging equity markets responsive to cross- country macroeconomic movements? Evidence from Latin America,” Journal of International Financial Markets, Institutions and Money, Vol.15, No.1, pp.73-87. 12
  13. 13. Appendix: the VECM of this study 1. The regression for EMA: D(EMA) = (-1.417158)*( EMA(-1) - 1.539473*SP500(-1) ) + ( 0.269395)*D(EMEE(-15)) + ( 0.257743)*D(EMEE(-16)) + (0.340063)*D(EMEE(-17)) + (0.289392)*D(EMEE(-18)) + (-0.479684)*D(EMLA(-12)) + (-0.302321)*D(EMLA(-16)) + (-0.283855)*D(EMLA(-18)) + (-0.214227)*D(EMLA(-19)) + (1.128710)*D(SP500(-16)) + (0.864196)*D(SP500(-17)) 2. The regression for EMEE: D(EMEE) = (-1.362301)*( EMEE(-1) - 1.708376*SP500(-1) ) + (0.992519)*( EMLA(-1) - 1.523868*SP500(-1) ) + (-0.691787)*D(EMA(-11)) + (-0.560701)*D(EMA(-14)) + (-0.567842)*D(EMA(-15)) + (-0.502961)*D(EMEE(-11)) + ( 1.901292)*D(WI(-19)) + ( 1.236979)*D(WI(-20)) + (1.868274)*D(SP500(-14)) + (1.689051)*D(SP500(-15)) + ( 1.797660)*D(SP500(-16)) + (1.232811)*D(SP500(-17)) 3. The regression for EMLA: D(EMLA) = (-0.877564)*D(EMA(-8)) + (-0.869452)*D(EMA(-9)) + (-0.765213)*D(EMA(-10)) + (-0.747382)*D(EMA(-11)) + (-0.560287)*D(EMA(-14)) + (-0.550196)*D(EMA(-15)) + (-0.186650)*D(EMA(-20)) + (-0.238544)*D(EMEE(-19)) + (-0.375688)*D(EMLA(-19)) + (2.197640)*D(SP500(-13)) + (1.831470)*D(SP500(-14)) + (1.610657)*D(SP500(-15)) + (2.046526)*D(SP500(-16)) + (1.901292)*D(SP500(-17)) + (1.236979)*D(SP500(-18)) 4. The regression for WI: D(WI) = (-0.330476)*D(EMA(-15)) + (-0.082515)*D(EMA(-20)) + (-0.143945)*D(EMLA(-19)) + (-0.957148)*D(WI(-16)) + (-0.931275)*D(WI(-17)) + (1.359263)*D(SP500(-10)) + (1.703525)*D(SP500(-12)) + (1.678048)*D(SP500(-13)) + (1.283666)*D(SP500(-14)) + (1.134302)*D(SP500(-15)) + (1.290281)*D(SP500(-16)) + (1.184695)*D(SP500(-17)) + (0.787704)*D(SP500(-18)) 5. The regression for S&P500: D(SP500) = (-0.353577)*D(EMA(-15)) + (-0.140039)*D(EMEE(-19)) + (-3.035289)*D(WI(-2)) + (-3.007678)*D(WI(-3)) + (-2.789908)*D(WI(-6)) + (-2.144756)*D(WI(-10)) + (-2.185012)*D(WI(-12)) + (-2.140248)*D(WI(-13)) + (-1.547127)*D(WI(-15)) + (-1.408422)*D(WI(-16)) + (-1.335792)*D(WI(-17)) + (-1.008159)*D(WI(-18)) + ( 2.044115)*D(SP500(-10)) + (1.884708)*D(SP500(-11)) + (2.432810)*D(SP500(-12)) + (2.410553)*D(SP500(-13)) + (1.866710)*D(SP500(-14)) + (1.625303)*D(SP500(-15)) + (1.700418)*D(SP500(-16)) + (1.538769)*D(SP500(-17)) + (1.150418)*D(SP500(-18)) 13