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  1. 1. Proceedings of the 2nd IMT-GT Regional Conference on Mathematics, Statistics and Applications Universiti Sains Malaysia, Penang, June 13-15, 2006 CAUSAL RELATIONSHIP BETWEEN STOCK PRICE AND MACROECONOMIC VARIABLES IN MALAYSIA Cheah Lee Hen 1 , Zainudin Arsad 2 , Husna Hasan 3 1 School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia. cheah_00@yahoo.com.my 2 School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia. zainudin@cs.usm.my 3 School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia. husna@cs.usm.my Abstract: Financial markets are interrelated and increasingly global. When making decisions, traders incorporate information pertaining to price movements and volatility in the asset they are trading. Thus, understanding how markets influence one another is important for pricing, hedging and regulatory policy. This study makes use of Kalman filter and variety of ARCH- type models to investigate the feedback causal relationship between stock prices with each of currency exchange and derivative product. Since the development by Kalman and Bucy in 1960s, Kalman filter technique has been the subject of extensive research and application. It is a set of equations which allows an estimator to be updated once a new observation becomes available. Three series used are monthly Kuala Lumpur Composite Index (KLCI), Pound Sterling (STL) and Kuala Lumpur Composite Index Futures (FKLI). All data covered from January 1997 to February 2005. In general, the results show that dynamic linkages between stock market and derivative are relatively weak. For the asymmetry GARCH models, there is a bi-directional causality runs between KLCI and FKLI. On the other hand, the symmetry GARCH models fail to reveal any recognizable pattern between the two variables. For the dynamic between KLCI and STL, the results suggest that many of the relationships or effects between the two series are significant. However, only KF-GARCH-M model has a bi- directional feedback effect between KLCI and STL. In addition, the result proves the existence of leverage effect in the stock market. However, the there is no evidence of risk-return trade- off in the Malaysian stock market. Keywords: Kalman filter, GARCH, stock market, currency exchange 1. Introduction and Literature Review Establishing the lead-lag relationship between stock prices and macroeconomic variables is important. By knowing these relationship, investors can earn profits by exploiting past information of the variables. In addition, they may be used as indicator to formulate current economic stabilization policies. Therefore, the issues of whether stock prices and macroeconomic variables are related or not have received considerable attention. Many works have been done for past few decades to examine the relationship between stock prices and financial futures as well as the currency exchange. However, there is no empirical or theoretical consensus on the issue of whether these variables are related and the direction of causation if they are related. This paper provides further empirical evidence on the above issue. The relationship between Kuala Lumpur Composite Index (KLCI), Pound Sterling (STL) and Composite Index Futures (FKLI) are investigated using the Kalman filter technique (KF) and Generalised Autoregressive Conditional Heteroskedasticity (GARCH). Arsad et. al. (2004) (see Reference [2]) found that foreign currency and interest rate significantly affect the stock prices. In addition, there is a negative relationship between the stock prices and money supply. Mansor (1999) (see Reference [11]) investigated the dynamic between seven macroeconomics and the Malaysian stock prices using cointegration and Granger-causality tests. The results show that changes in the official reserves and exchange rates affect the KLCI. Mukesh et. al. (1996) (see Reference [12]) examined co-movement in the Japanese Yen, Australian Dollar, Singapore Dollar, Malaysian Ringgit and New Zealand Dollar exchange rates. 1
  2. 2. The Vector Autoregressive (VAR) model is used to investigate the channels of influence among these currencies. In addition, analyses are carried out to investigate the changes of these channels over two important currency-coordinating agreements, namely the Louvre Accord and Plaza Accord. There are many other studies that have investigated the lead-lag relationship between futures market and cash market. Those papers including Lim (1992) (see Reference [10]) who found that there is no lead lag relationship between the Nikkei Stock Average (NSA) stock and futures markets. Wong and Meera (2001) (see Reference [15]) studied the market efficiency between KLCI and FKLI by using Granger causality and error correction approaches. The data are divided into two sub-samples: before financial crisis, January 1996 to March 1997 and during the financial crisis, April 1997 to September 1998. The results show that KLCI price lead the stock index futures market before the economic crisis but not vice versa. In addition, there is no long run equilibrium relationship between both markets. Chan and Karim (2004) (see Reference [5]) analyse the lead lag relationship between spot and futures market of the KLCI. They used cointegration and error-correction model in their analysis. Daily closing price from January 1996 to December 2002 is used. It is suggested that KLCI price and the corresponding futures markets are cointegrated. Also, it is proven that futures prices can be a good indicator on predicting spot prices due to the stronger impacts of futures prices on cash markets compared to that from cash market to futures market. The paper is organized as follows: Section two discusses empirical methodology and data, while Section three presents empirical results. In Section four concluding remarks is provided. 2. Data and Methodology One of the methodologies used in this study is Kalman filter (KF). The existence of Kalman filter is due to the work by Kalman and Bucy in 1960. It is an algorithm for sequentially updating a linear projection for the system. This algorithm consists of recursions estimating the parameter vector before a new observation becomes available, forecasting this observation and updating the state vector once the new observation is available. Details of this method can be found in Harvey (1981) (see Reference [1]). State-space representation of the model can be written: xt = αθt + εtx (2.1) θt = βθt −1 + Sεtθ (2.2) εtx ~ i.i.d .N (0, C ), εtθ ~ i.i.d .N (0, Q), E (εty εtθ ) = 0. where Equation (2.1) and Equation (2.2) are the measurement equation and transition equation respectively. xt and θt are n × 1 vector of observed variables and m × 1 vector of unobserved state variables at time t respectively. The system matrices α, β and S are matrices of parameters of dimension (n × m), (m × m) and (m × r ) respectively. The matrices C and Q are assumed to be constant. Once the model is written in state-space form, parameters estimates can be obtained by maximum likelihood function, where the Kalman filter is used to update the unobserved components. The Kalman filter algorithm is given as follows: θt|t −1 = μ + βθt −1|t −1 % (2.3) Pt|t −1 = βPt −1|t −1 β ' + Q (2.4) ηt|t −1 = xt − xt |t −1 = xt − αθt|t −1 ˆ (2.5) 2
  3. 3. ft|t −1 = αPt −1|t −1α ' + C (2.6) θt|t = θt −1|t −1 + K t ηt|t −1 (2.7) Pt|t = Pt −1|t −1 − Kt αPt|t −1 (2.8) where Kt = Pt −1|t −1α ' ft'|t −1 is the Kalman gain, which determine the weight assigned to new information about θt contained in the prediction error. θt|t −1 is the one-step-ahead estimate of the state vector and Pt|t −1 is the corresponding mean squared error (MSE). Equation(2.5) is the prediction error. Its corresponding MSE is given by Equation(2.6), Equation(2.7) and Equation (2.8) are the updating equations after incorporating the new information supplied by xt . The algorithm of Kalman filter can be used to construct the likelihood function which will be used for numerical computation of the parameters. The likelihood function can be written as: 1 N 1 N ' −1 log Lα − ∑ log | ft | − ∑ ηt ft ηt (2.9) 2 t =1 2 t =1 where f t = αPt|t −1α ' + C and ηt|t −1 = xt − xt|t −1 = xt − αθt|t −1 is the prediction error. Equation (2.9) is ˆ also known as the prediction error decomposition form of the likelihood. In this paper, state-space models with conditional heteroskedasticity will also be considered. Engle (1982) (see Reference [6]) introduced the Autorgressive Conditional Heteroscedasticity (ARCH) model to cope with changing variance. Bollerslev (1986) (see Reference [3]) proposed a Generalized ARCH (GARCH) model which has a more flexible lag structure, modeling the error variance as an Autoregressive Moving Average (ARMA) process. Over the years extension to the GARCH model have been developed by Engle et. al. (1987) (see Reference [7]), Glosten et. al (1993) (see Reference [8]) and Nelson (1991) (see Reference [13]) (GARCH-M, TARCH and EGARCH respectively). The use of ARCH-type models for modelling and predicting volatility is now very common in finance. A typical finding is that these models provide superior forecasts of volatility than those which simply assume homoscedasticity of the error squared. The state-space model with ARCH disturbances as proposed by Harvey, Ruiz and Sentana (1992) (see Reference [9]) is given as: xt = αθt + εt* (2.10) θt = βθt −1 + Sεtθ (2.11) εt* ~ N (0, ht ) (2.12) and ht is assumed to follow various ARCH-type equations as given below: ARCH(1): ht = β0 + β1εt2−1 (2.13) GARCH(1,1): ht = β0 + β1εt2−1 + β2 ht −1 (2.14) GARCH(1,1)-M: xt = αθt + γht + εt* ht = β0 + β1εt2−1 + β2 ht −1 (2.15) Threshold-ARCH: ht = δ0 + δ1εt2−1 + δ2 εt2−1D + δ3 ht −1 (2.16) 3
  4. 4. εt −1 εt −1 Exponential-GARCH: ln ht = λ0 + λ1 + λ2 + λ3 ln ht −1 (2.17) ht −1 ht −1 The conditional volatility equations shown by Equation (2.16) and Equation (2.17) differentiate between positive and negative shocks in term of the magnitudes of their impacts on the future volatility of asset returns. Equation (2.16) models the asymmetry (measured by δ2 ) in the stock price volatility reaction to information shocks by utilizing dummy variables, while Equation (2.17) models the leverage effect (measured by λ2 ) to be exponential. It is a common finding in the finance literature that bad news ( εt −1 < 0 ) has a larger impact on the future volatility of asset returns than good news ( εt −1 > 0 ). The monthly data of Kuala Lumpur Composite Index (KLCI) and Kuala Lumpur Composite Index Futures (FKLI) are used as proxy to the movement of stock prices for overall market and to represent the overall market futures respectively. The KLCI was introduced in 1986 and it consists of some Malaysia’s largest publicly corporations. Note that the KLCI series is the underlying instrument of the FKLI, the financial future contracts traded in Malaysia Derivatives Exchange (MDEX). The exchange rate is represented by one of the world's most widely traded currencies, STL. The UK has the fifth largest economy in the world and the second largest in Europe. Its capital, London is one of the largest financial center in the world. Therefore, it is believed that the UK’s economy is associated with many other capitalist economies in the world. The three series are collected from January 1997 to February 2005 and they are transformed into returns to obtain the stationary series, using the formula as below: Rt = log( Pt / Pt −1 ) *100 (2.18) where Rt is the returns, Pt is the price at last trading day on month t. 3. Results and Discussion Column two and three in Table 1 shows the estimated parameter of the Kalman filter models relating KLCI & STL and KLCI & FKLI respectively. The numbers in the parathesis are standard errors which are calculated numerically. The results show that there is only one significant relationship from the KLCI & STL model, whereby the estimate of α3 is significant at 1% level (-0.1130). This result suggests that STL at current month is significantly affected by last month’s KLCI price at 1% level. The negative sign of α3 indicates that domestic stock prices have negative effects on exchange rates, implying that a past increase of stock prices appreciates domestic currency (i.e. decreasing exchange rate). For KLCI & FKLI model, the results suggest that many of the feedback effects between the two series are not significant. The results suggest the existence of other variables that may affect the KLCI. From Table 1, it is known that most of the parameters in matrix S are statistically significant from zero. The higher value of S12 for the KLCI & FKLI model indicates the higher correlation between noise of KLCI and FKLI for the model as compared to that from the KLCI & STL model. Note that magnitudes of S11 are larger than the magnitudes of S22 for KLCI & STL model, indicating that the KLCI market is noisier than the STL market. However, the opposite occurrence is found form the KLCI & FKLI model. Table 2 shows the dynamic between KLCI and STL series. The results show that KF- EGARCH has the highest log likelihood value (-396.6206) among the tabulated models. This result coincides as the smallest values of both AIC and BIC (813.2412 and 837.9003). From Table 2, most of the parameters are significantly different from zero. Therefore, the results suggest that many of the feedback effects between the two series are significant. Note that the 4
  5. 5. autoregressive coefficient α1 and α4 are both significant at the 1% level for all models. This shows that both the KLCI and STL are dependent on observations in the previous month. In addition, the results show that α2 from KF-GARCH, KF-GARCH-M, KF-EGARCH and KF- TARCH are significant, indicating that KLCI series is influenced by STL series (4.9388, 4.9758, 3.4791 and 2.5643 respectively). The positive coefficient implies that past increases of exchange rate have long-run positive effects on asset prices, increasing stock prices in KLCI. The positive effects of exchange rate in stock prices imply that depreciation of domestic currency boosts asset prices because domestic assets become more attractive to foreign investors and thus increase the profits of exporting firms. From Table 2, it can be seen that α3 is also significantly different from zero for KF- ARCH and KF-GARCH-M models. The result indicates that current value of STL is affected by the last value of KLCI price (0.0686 and -0.1222). This result is similar to that found in pure KF model. The negative sign of α3 suggests that domestic stock prices have negative effects on exchange rates, implying that a past increase of stock prices appreciates domestic currency. From Table 2, note that only KF-GARCH-M model has a bi-directional feedback effect between KLCI and STL. However, the coefficient on the expected risk, γ is not statistically significant (0.0107). Results from analyses also show that both parameter of leverage effect significant at 1% level in KF-EGARCH and KF-TARCH models. From Table 2, it is also noted that almost all parameters in covariance matrices of S are significant at 1% level. Table 1: Dynamic between KLCI and exchange rates Parameter KLCI & STL KLCI & FKLI Log L -427.83 -233.99 AIC 869.66 418.98 BIC 886.92 499.24 α1 0.2056 0.1019 (0.1497) (1.7978) α2 0.1634 0.0820 (0.2426) (1.7951) α3 -0.1130 0.6161 (0.0578)*** (1.7982) α4 -0.1579 -0.4348 (0.1356) (1.7956) S11 9.5750 0.5394 (0.1361)*** (0.0412)*** S12 -1.9050 9.7854 (0.8627)*** (0.7431)*** S22 5.2510 9.8022 (0.1082)*** (0.7421)*** Note: *** denotes significant at 1% level. Table 3 shows the dynamic between KLCI and FKLI series. The results show that KF- GARCH-M has the highest log likelihood value (-207.5728). The KF-GARCH-M model also ranks the second small of both AIC and BIC among the tabulated models. It can be seen from Table 3 that the asymmetry GARCH-type model has significant parameters at the Ω structure. For KF-EGARCH model, it is shown that α3 significantly different from zero at 1% level. The result indicates that the previous value of KLCI has significant effect on the FKLI. In other words, there is a uni-directional relationship running from stock market to futures market. This shows that trading of FKLI very much rely on the movement of its underlying asset, KLCI. This 5
  6. 6. is due to the fact that traders will look upon the movement of KLCI to anticipate future movement of FKLI price. For KF-TARCH model, however, there is a bi-directional causality runs between KLCI and FKLI. The causal effect from futures prices to stock prices is found to be stronger (2.8975 as compared to 2.0218) than that from stock market to future market. Stoll and Whaley (1990) (see Reference [14]) interpret this evidence as meaning that futures market reflects new information more quickly than the stock market. According to Chan (1991) (see Reference [4]), since firm specific information is diversifiable and market-wide information is systematic, the discovery of market wide information is more important, so he hypothesized that the feedback from the futures market into the stock market is larger than the reverse. On the other hand, the symmetry ARCH – type models fail to reveal any recognizable patterns between KLCI and FKLI series. Table 2: Dynamic between KLCI and STL for Kalman filter-ARCH-type models Parameter Model KF-ARCH KF-GARCH KF-GARCH-M KF-EGARCH KF-TARCH Log L -411.0060 -400.5679 -400.5625 -396.6206 -418.1397 AIC 840.0120 821.1358 823.1250 813.2412 858.2794 BIC 862.2052 845.7949 850.2500 837.9003 885.4044 α1 0.2978 0.8491 0.8583 0.4955 0.3127 (0.1587)*** (0.2174)*** (0.3270) *** (0.1756)*** (0.1724)** α2 1.4101 4.9388 4.9758 3.4791 2.5643 (1.6117) (1.1486)*** (2.1719) *** (1.3185)*** (0.2132)*** α3 0.0686 -0.1194 -0.1222 -0.0300 -0.0033 (0.0368)*** (0.0916) (0.0948) *** (0.0572) (0.0127) α4 0.4276 -0.9411 -0.9832 -0.7277 -0.3142 (0.2147)*** (0.3196)*** (0.4533) *** (0.2706)*** (0.1420)*** S11 11.2593 6.6811 6.6321 9.5293 -10.8421 (0.9191)*** (0.9481)*** (2.9245) *** (1.6049)*** (1.2891)*** S12 -0.9673 -0.4622 -0.0771 0.2042 0.6001 (0.3449)*** (1.7635) (1.1177) (3.6211) (1.1023) S22 0.0011 1.3537 1.3368 1.3921 -1.9273 (0.7422) (0.3626)*** (0.0708) *** (0.2984)*** (0.5037)*** δ0 / λ0 5.5325 0.2251 0.2271 0.0766 0.8355 (1.3367)*** (0.0658)*** (0.0124) *** (0.1159) (0.2885)*** δ1 / λ1 0.8485 0.3402 0.3385 0.9890 1.0614 (0.1614)*** (0.0473)*** (0.0000) *** (0.4312)*** (0.2753)*** δ2 / λ2 0.6596 0.6613 0.4021 (0.0469)*** (0.0000)*** (0.0827)*** δ3 / λ3 0.6264 0.3043 (0.0455)*** (0.1103)*** γ 0.0107 (0.1010) Note: *** and ** denote significance at 1% and 10% level respectively 6
  7. 7. Table 3: Dynamic between KLCI and FKLI for Kalman filter-ARCH-type models Model Parameter KF-ARCH KF-GARCH KF-GARCH-M KF-EGARCH KF-TARCH Log L -220.7034 -208.0228 -207.5728 -222.3188 -209.6269 AIC 459.4068 436.0456 437.1456 464.6376 441.2538 BIC 481.6000 460.7047 464.2706 489.2967 468.3788 α1 -0.1080 -0.0651 -0.0656 -0.0113 -1.9520 (0.1061) (0.1499) (0.1498) (0.0201) (0.4376)*** α2 0.1707 -0.1031 -0.1079 0.0195 2.8975 (0.1708) (0.3030) (0.3244) (0.0199) (0.4813)*** α3 0.0065 0.0282 0.0266 0.2498 -1.3473 (0.1668) (0.1477) (0.1461) (0.0158)*** (0.4302)*** α4 -0.0352 0.0675 0.0725 0.0870 2.0218 (0.1273) (0.1813) (0.1853) (0.0162)*** (0.4476)*** S11 1.0729 0.00002 1.8238 0.0001 -0.000003 (0.4040)*** (0.0749) (0.6309)*** (0.0288) (0.0652)*** S12 1.5286 1.8663 1.3567 1.3756 0.1058 (0.4082)*** (0.6987)*** (0.0624)*** (0.0265)*** (0.4949) S22 0.00001 1.3990 0.000007 0.9177 0.5602 (0.0253) (0.6914)*** (0.0057) (0.0202)*** (0.4940) δ0 / λ0 79.4829 0.1475 0.0560 3.4175 7.6290 (20.3967)*** (0.2119) (0.0037)*** (0.2865)*** (3.5286) δ1 / λ1 0.2023 0.1404 0.1434 0.1303 -0.0244 (0.1797) (0.0002)*** (0.0000)*** (0.0499)*** (0.0690)*** δ2 / λ2 - 0.8591 0.8564 - 0.7138 (-) (0.0002)*** (0.0000)*** (-) (0.1024) δ3 / λ3 - - - -0.4882 0.4612 (-) (-) (-) (0.2457)*** (0.1990)*** γ - - 0.1282 - - (-) (-) (0.1319) (-) (-) Note: *** and ** denote significance at 1% and 10% level respectively. For GARCH model, it is noted that the ARCH and GARCH terms (0.1404 and 0.8591 respectively) sum to be less than unity. Therefore, the sample estimation holds the stationarity condition for both the ARCH and GARCH models. Besides, it is found from KF-GARCH-M model that the coefficient on the expected risk, γ is not statistically significant (0.1282). Thus, the result provides no evidence of risk-return trade-off in the Malaysian stock market. In addition, both the KF-EGARCH and KF-TARCH models suggest the existence of leverage effect in the Malaysian stock market. 4. Conclusion This study makes use of Kalman filter and variety of ARCH-type models to investigate the feedback causal relationship between stock prices with each of currency exchange and derivative product. There are five ARCH-type models used namely ARCH, GARCH, GARCH- M, EGARCH and TARCH models. It has been frequently demonstrated that the GARCH(1,1) process is able to present the majority of financial time series and there is a tendency to favour the GARCH(1,1) model above other higher order of GARCH models. Therefore, this paper considers only the GARCH(1,1) process. In general, the results show that dynamic linkages between KLCI 7
  8. 8. and FKLI are relatively weak. For the asymmetry TARCH models, there is a bi-directional causality runs between KLCI and FKLI. On the other hand, the symmetry ARCH, GARCH and GARCH-M models fail to reveal any recognizable pattern between the two variables. On the other hands, many of the relationships between the KLCI and STL series are significant. The results suggest that only KF-GARCH-M model has a bi-directional feedback effect between KLCI and STL. In addition, the result proves the existence of leverage effect in the stock market. However, the there is no evidence of risk-return trade-off in the Malaysian stock market. References [1] Andrew C. Harvey (1998). Forecasting, Structural Time Series Models and The Kalman Filter. Cambridge University Press. [2] Arsad Z. and Kaswani (2004) Proceedings of The Malaysian Finance Association 6th Annual Symposium, Langkawi. 462-468. [3] Bollerslev, T (1986). Generalised autoregressive conditional heteroscedasticity. Journal of Econometrics, Vol. 31, 307-327. [4] Chan et. al.(1991). Intraday volatility in the stock index and stock index futures markets. Review of Financial Studies, 4, 657-683. [5] Chan and Karim (2002). The lead lag relationship between stock index futures and spot market in Malaysia: A cointegration and error-correction model approach. Proceedings of The MFA 6th Annual Conference, Langkawi, 220-239. [6] Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, Vol. 50, 987-1008. [7] Engle, Robert F., David M. Lilien, and Russell P. Robins (1987) “Estimating Time Varying Risk Premia in the Term Structure: The ARCH-M Model,” Econometrica 55, 391–407. [8] Glosten, L.R., R. Jagannathan, and D. Runkle (1993). On the Relation between the Expected Value and the Volatility of the Normal Excess Return on Stocks, Journal of Finance, 48, 1779–1801. [9] Harvey, A. C., Ruiz E. and Sentana E. Unobserved component time series models with ARCH disturbances. Journal of Econometrics, 52, 129-157. [10] Lim, K. (1992). Arbitrage and price behaviour of Nikkei Stock Index Futures. The Journal of Futures Market, 12,151-161. [11] Mansor H. Ibrahim (1999). Macroeconomic variables and stock prices in Malaysia: An empirical Analysis. Asian Economic Journal, Vol. 13, No. 2, 219-230. [12] Mukesh et. al. (1996). The Cointegration Experience of Eastern Currencies: Evidence from the 1980s. Finance India, Vol. X, No. 1, 49-59. [13] Nelson, Daniel B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, Vol. 59, 347–370. [14] Stoll, R. H. and Whale, R. E. (1990). The dynamics of stock index and stock index futures returns. Journal of Financial and Quantitative Analysis, Vol. 25, No. 3, 441-468. [15] Wong, H. S. and Meera, A. K. (2001). Lead-lag relationship between stock index futures and the spot in an emerging market: A test of efficiency of the Malaysia market in the period before and during economic crisis, using second moments. Working paper, International Islamic University Malaysia. 8

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