Leverage Effects In The Mauritian's Stock Market

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Leverage Effects In The Mauritian's Stock Market

  1. 1. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 TITLE PAGE: TITLE: LEVERAGE EFFECTS IN THE MAURITIAN’S STOCK MARKET AUTHOR’S NAME: Mr USHAD SUBADAR AGATHEE PHONE NUMBER: +230 4541041 AFFILIATION: DEPARTMENT OF FINANCE AND ACCOUNTING, FACULTY LAW AND MANAGEMENT, UNIVERSITY OF MAURITIUS. EMAIL: u.subadar@uom.ac.mu June 24-26, 2009 1 St. Hugh‟s College, Oxford University, Oxford, UK
  2. 2. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 Leverage Effects in the Mauritian’s Stock Market Abstract This paper essentially aims at comparing the GARCH (1,1), T-GARCH and E-GARCH models in the ability to describe volatility on the Stock Exchange of Mauritius (SEM). Daily observations from the SEMDEX for the period July 1989 to December 2007 are used for the study. The results suggest that the SEMDEX series exhibit some non-normal properties and fat tail characteristics. Using the GARCH models, the results indicate that there is no leverage effect in contrast to most developed and emerging markets. Also, the presence of a leverage effect cannot be found when splitting the sample into a non-daily trading regime and a daily regime. Keywords: Leverage effects; Stock markets; African Emerging Stock markets; Efficient market hypothesis; SEMDEX June 24-26, 2009 2 St. Hugh‟s College, Oxford University, Oxford, UK
  3. 3. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 1.0 Introduction Since its inception in 1989, the Stock Exchange of Mauritius (SEM) have experience major developments in terms of market size, trading volume, number of listed companies and contribution to the Mauritian GDP. There have also been significant interests from foreign investors lately. However, published research has been so far very limited. To this effect, it is important to know the behaviour of stock market volatility in this emerging market. There have been a number of models attempting to capture volatility. However, one of the well- known and commonly used models is the so-called Generalised Autoregressive Conditional Heteroskedasticity (GARCH) model suggested by Bollerslev (1986). Specific styles in financial time series call upon the use of GARCH models as they can capture the volatility clustering effect whereby large changes are likely to trail large changes and small changes tend to follow small changes. However, there is usually an asymmetry in the stock return‟s distribution. As such, asymmetric GARCH models such as T-GARCH, proposed by Glosten et al. (1993), and E-GARCH models, proposed by Nelson(1991), are more appropriate. This study is an initial formal attempt to shed some lights on the presence of volatility patterns and leverage effects. Indeed, the use of GARCH models fit in perfectly with the stylized characteristics of financial time series. In this respect, this paper attempts to investigate the leverage effects on the SEM using GARCH models. June 24-26, 2009 3 St. Hugh‟s College, Oxford University, Oxford, UK
  4. 4. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 This paper is organised as follows; Section 2 reviews previous literature, Section 3 provides an overview of the research methodology, Section 4 focuses on the analysis of results while section 5 concludes the paper. 2.0 Prior Research Earlier models in explaining movements of asset prices focus on the methodology developed by Box and Jenkins (1976). In particular, Box and Jenkins developed the Autoregressive Integrated Moving Average (ARIMA) model to predict movement in equity prices. However, ARMIA models are constrained by their assumptions of constant conditional variance over time. Essentially, the ARIMA model cannot be used to capture volatility clustering effects present in financial time series. To this effect, Engle (1982) suggested an ARCH model to explain volatility patterns. However, given some limitations of ARCH models, Bollerslev (1986) extended the ARCH models by introducing a GARCH model. The GARCH model itself is an infinite ARCH process. Another style feature of financial time series is the leverage effect whereby there is an asymmetric reaction of volatility changes in response to positive and negative shocks of the same magnitude. To this effect, Nelson (1991) has developed and exponential GARCH model (E-GARCH) and Glosten et al. (1993) have suggested a T-GARCH model. Stock market volatility has attracted great attention in the last decades and has as such been widely discussed in several developed and developing capital markets. Among the pioneering studies, Black (1975), using a sample of 30 industrial equities, considered the relationship between stock market returns and volatility for the period 1962-1975. He found that changes in stock prices are negatively related to changes in stock market volatility (leverage effects). Similarly, Christie (1982), using quarterly data for the period 1962-1978 with a sample size of 379 firms, found that the average regression coefficient between stock market prices and volatility to be negative. Additionally, June 24-26, 2009 4 St. Hugh‟s College, Oxford University, Oxford, UK
  5. 5. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 Christie (1982) found that the debt to equity ratio could be a possible explanation for the negative relationship between stock market returns and changes in volatility. Moreover, Koutmos and Saidi (1995) and Henry (1998) support the claim of a leverage effect. Other authors such as Haroutounian and Price (2001), Glimore and McManus (2001), Poshakwale and Murinde (2001) have found significant high volatility persistence in Central and Eastern European stock markets. There are also studies which consider volatility in periods around financial crises. For instance, Schwert (1990) considered the stock market volatility before the October 1987 crash and after the crash. He found that stock market volatility was higher during the crash and after that. Similarly, Kaminsky and Reinhart (2001) reported high volatility persistence in a post-crisis period. 3.0 Research Methodology According to Brooks (2004), a typical GARCH (1,1) is adequate for financial time series and it is very uncommon to find advanced order of GARCH models in the academic finance literature. Daily observations of the SEMDEXi are used to calculate returns for the months as from July 1989 to December 2007. Daily stock returns are calculated as follows; Rt= Ln(Pt)-Ln(Pt-1) where Pt is the index number at time t and Pt-1 is the index in the preceding day. Using GARCH models involve a number of advantages in that they assist in capturing the features of financial time seriesii as they cater for volatility clustering and leverage effects. In particular, several financial time series are subject to a period of successive strong volatility followed by a period of low volatility. As a consequence, conditional variance is time-varying. However, the conditional variance can exhibit a mixture of asymmetric behaviour. Thus, according to Engel (1982), Bollerslev June 24-26, 2009 5 St. Hugh‟s College, Oxford University, Oxford, UK
  6. 6. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 (1986) and Bollerslev et al. (1992), autoregressive conditional heteroscedasticity models (GARCH) are more suitable as they are more flexible in capturing dynamic structures of conditional variance. Based on the empirical literature, the following regression models are used. yt    yt 1   t (1)  t  1 ~ N (0, ht ) (2) ht   0  1 2 t 1   2 ht 1 (3) Where in equation (1), daily stock return, y, is regressed on a constant, μ and a time-lagged value of return, y t −1 ; ε is an error term which is dependent on past information and ht is the conditional variance. According to Zhang and Wirjanto (2006), “the purpose of using the AR(1) process is to capture time dependence of the return series and to smooth the series of possible structural shifts over the sample period”. For the conditional variance, ht, to be nonnegative and positive, the following conditions must be met:  0  0; 1  0;  2  0and1   2  1 In general, the ARCH and GARCH terms, 1 and  2 indicate short run and long run shocks persistence respectively. Furthermore, based on the studies Black (1976) and Christie (1982), positive and negative shocks do not have the effect on volatility. Essentially, shocks are asymmetric such that volatility is more June 24-26, 2009 6 St. Hugh‟s College, Oxford University, Oxford, UK
  7. 7. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 sensitive to negative shocks. To this effect, the following two asymmetric GARCH models, namely TGARCH and EGARCH, are employed TGARCH: ht   0  1 2 t 1   2 ht 1  3 2 t 1 I t 1 (4) Where I t 1 =1 if  t 1  0 , or zero otherwise EGARCH:   t 1 2  ln(ht )   0   1      2 ln(ht 1 )   3 t 1 (5)  ht 1   ht 1 For the TGARCH model, the leverage effect parameter,  3 , should be greater than zero. However, restrictions are imposed on the parameters in that they must all be greater than zero for the conditional variance to be non-negative. For the EGARCH model, there is no need for non-negativity constraints on the parameters and the leverage effect is accounted for if the relationship between volatility and returns is negative such that,  3 , will be negative. Finally, to assess the validity of the model, the Ljung-Box Q statistics on the squared standardized residuals is used while the log- likelyhood value and the information criterion are used to assess which model is more appropriate. 4.0 Analysis of Data and Results The basic statistics are presented in Table 1 for return series on SEMDEX for the period July1989 to December 2007. [INSERT TABLE 1 ABOUT HERE] June 24-26, 2009 7 St. Hugh‟s College, Oxford University, Oxford, UK
  8. 8. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 Table 1 shows the descriptive statistics for the whole sample period and on a year to year basis. At first glance, most of the mean returns are positively skewed and have significant kurtosis. However, from 1989 to 2007, there are six years where the returns have been negatively skewed and two years where the kurtosis value has been lower than 3. On overall, for the whole sample, there is large kurtosis value, suggesting that the series follow a fat tail distribution, and a positively skewed series. With the exception of 3 years, the mean returns are found to be non-normal as the Jarque-Bera statistics is significant at 1% level. In general, the series present some of the stylized facts of financial series in that they are non-normal and exhibit fat tails, supporting the claim that GARCH models appear to most appropriate. Table 2 shows the results from the different GARCH models for the stock market returns for the period 1989 to 2007. [INSERT TABLE 2 AROUND HERE] From table 2, the result shows that the E-GARCH model has the highest log-likelihood value as well as the lowest AIC and SBIC values. Also, all coefficients on the E-GARCH model are statistically significant. Also, based on the Ljung-Box statistics, there is no problem of autocorrelation for all the three models. Finally, it is observed that all restrictions imposed on the GARCH models are met while one non-negativity constraint on T-GARCH model is violated. Thus, in light of the above, the E-GARCH is considered as the best model. The ARCH and GARCH effects are significant in all three models. However, while the sum of ARCH and GARCH coefficients are less than one for all the models, except for the E-GARCH June 24-26, 2009 8 St. Hugh‟s College, Oxford University, Oxford, UK
  9. 9. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 model. Essentially, while there is shocks persistence for the E-GARCH model, the shocks to volatility decay over few lags for the standard GARCH and T-GARCH models. From the E-GARCH model, a significant asymmetry coefficient, B3 , is found. However, the leverage effect is accounted if the coefficient is less than zero, where a negative surprises seem to increase volatility more than a positive surprises. Contrary to the expectations, there seem to be no leverage effects on the SEM as the coefficient is statistically positive. As such, negative news on the SEM cause volatility to increase less than positive news of the same magnitude. However, the Stock Exchange of Mauritius has been trading at irregular intervals since its inception. It only starts to trade on a daily basis for the full year in 1998. As such, structure of volatility could have been different under the regime of non-daily trading relative to daily trading. To this effect, the sample is segregated into two periods, namely, 1989-1997 and 1998-2007. The results are reported below. [INSERT TABLE 3 AROUND HERE] [INSERT TABLE 4 AROUND HERE] From Table 3, based on the Ljung-Box statistics, the T-GARCH and the standard GARCH models seem to suffer from autocorrelation while the E-GARCH is valid model. As such, the E-GARCH model is considered. It is observed that there is no leverage effect on the SEM for the period 1998- 2007. As such, the results are in line with the earlier predictions. Considering Table 4, the E- GARCH model is recommended for comparison purposes though results from T-GARCH and GARCH models are reported. Considering the period 1989-1997, there seems to be no leverage June 24-26, 2009 9 St. Hugh‟s College, Oxford University, Oxford, UK
  10. 10. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 effects on the SEM as the coefficient is positive though insignificant. In fact, a coefficient which is statistically equal to zero will imply that the positive surprise will have the same effect on volatility as the negative surprise of the same magnitude. As such, there are no leverage effects on the SEM both under the regime of non-daily trading and daily trading. 5.0 Conclusion This paper has investigated three GARCH models on the SEM. The descriptive statistics shows that the mean returns exhibit some non-normal characteristics and excess kurtosis for most of the years as well as for the whole sample period. With regards to the regression models, the results show that the E-GARCH model is the most properly specified. The E-GARCH model suggests the absence of a leverage effect on the SEM. Furthermore, the absence of a leverage effect is confirmed when segregating the sample periods into two different regimes of daily and non-daily trading. As a concluding note, it is suggested that negative news on the SEM cause volatility to increase less than positive news of the same magnitude. 6.0 References Black, F. (1976). Studies of Stock Price Volatility Changes. Proceeding of the meetings of the American Statistics Association, Business and Economics Section, 177-181. Bollerslev, T. (1986). Generalised Autoregressive Conditional Heteroscedasticity. Journal of Econometrics, 31, 307-27. Bollerslev, T. and Wooldridge, J. (1992). Quasi-maximum likelihood estimation and inference in dynamic models with time varying covariances. Econometric Reviews,11, 143-72. Box, G. E. P. and G. M. Jenkins, Time Series Analysis: Forecasting and Control, Holden- June 24-26, 2009 10 St. Hugh‟s College, Oxford University, Oxford, UK
  11. 11. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 Day, 1976. Brooks C. (2004). Introductory Econometrics for Finance. Cambridge University Press Christie, A. (1982). The Stochastic Behaviour of Common Stock variances: Value, Leverage and Interest Rate Effects. Journal of Financial Economics, 10, 407-432. Engle, R.F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of Variables of UK Inflation. Econometrica, 50, 987-1008. Glimore, C.G. and McManus, G. M., (2001) “Random-Walk and Efficiency of Central European Equity Markets”, Presentation at the 2001 European Financial Management Association, Annual Conference, Lugano, Switzerland. Glosten, L., R. Jagannathan, and D. Runkle (1993): “On the Relation between Expected Return on Stocks,” Journal of Finance, 48, 1779-1801. Haroutounian, M. and S. Price, (2001) "Volatility in transition market of Central Europe”, Applied Financial Economics (11), pp 93-105 Henry, O., (1998) “Modelling the asymmetry of stock market volatility”, Applied Financial Economics (8), pp 145-153 Kaminsky, G.L. and C.M. Reinhart, (2001) “Financial markets in times of stress”, NBER Working paper 8569, www.nber.org/papers/w8569 June 24-26, 2009 11 St. Hugh‟s College, Oxford University, Oxford, UK
  12. 12. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 Koutmos, G. and R. Saidi, (1995) “The leverage effect in individual stocks and the debt to equity ratio”, Journal of Business Finance and Accounting (22), pp 1063-1073 Nelson, D. (1991): “Conditional Heteroskedasticity in Asset Returns: A New Approach,” Econometrica, 59, 349-370 Pagan, A.(1996). The Econometrics of financial markets. Journal of Empirical Finance, 3, 15-102. Pashakwale, S. and Murinde, V., (2001) “Modelling the Volatility in East European Emerging Stock Markets: Evidence on Hungary and Poland”, Applied Financial Economic (11), pp 445-456 Schwert, G.W., (1990) “Stock Volatility and the Crash of „87”, Review of Financial Studies (3), pp 77-102 June 24-26, 2009 12 St. Hugh‟s College, Oxford University, Oxford, UK
  13. 13. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 LIST OF TABLES: Table 1: Descriptive statistics for SEMDEX returns Period Mean Std. Dev. Skewness Kurtosis Jarque- P-Value Bera 1989 0.006396 0.020392 0.054026 1.952512 1.155111 0.56127 1990 0.00741 0.016196 -0.73256 3.903369 6.295627 0.04295 1991 -0.0021 0.008095 -0.22425 2.495465 0.9494 0.62207 1992 0.001742 0.006716 0.546948 4.105234 9.974867 0.00682 1993 0.005176 0.00936 0.518875 3.941684 7.936589 0.01891 1994 0.003104 0.00825 0.459189 4.080463 12.23246 0.00221 1995 -0.00228 0.010135 -0.01359 7.552003 122.602 0.00000 1996 0.000175 0.008792 -1.87144 19.55013 1775.482 0.00000 1997 0.000633 0.005183 0.199473 3.610731 3.547673 0.16968 1998 0.0007 0.006143 0.874326 11.20818 730.7312 0.00000 1999 -0.00027 0.003926 -0.0196 4.252316 16.3524 0.00028 2000 -0.00044 0.002275 -1.09035 8.100459 319.24 0.00000 2001 -0.00055 0.004035 0.572336 15.6869 1663.243 0.00000 2002 0.000637 0.004066 0.406741 4.729487 37.74641 0.00000 2003 0.001268 0.005942 0.26814 11.31762 729.4384 0.00000 2004 0.001013 0.003357 0.329357 6.794036 156.9362 0.00000 2005 0.000495 0.004078 0.519162 10.16587 543.9384 0.00000 2006 0.00161 0.007684 0.624211 11.29317 735.59 0.00000 2007 0.001705 0.009451 0.737439 14.28066 1342.822 0.00000 All Sample 17893.08 0.00000 0.000853 0.006922 0.506192 14.16385 [89-07] June 24-26, 2009 13 St. Hugh‟s College, Oxford University, Oxford, UK
  14. 14. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 Table 2: GARCH MODEL (1989-2007) Coefficient GARCH(1,1) P-value TGARCH P-value EGARCH P-value  0.000378 0.0000 0.000427 0.0000 0.000609 0.0000  0.393481 0.0000 0.400311 0.0000 0.348677 0.0000 B0 5.37E-06 0.0000 5.21E-06 0.0000 -1.255971 0.0000 B1 0.314019 0.0000 0.355528 0.0000 0.378340 0.0000 B2 0.566946 0.0000 0.582654 0.0000 0.904904 0.0000 B3 -0.120705 0.0000 0.026103 0.0020 LBQ2(12) 1.6673 1.000 1.5734 1.000 2.5448 0.998 Log-likelihood function 13120.02 value 13114.51 13134.70 AIC -7.679856 -7.682494 -7.691095 SBIC -7.670870 -7.671710 -7.680312 Note: AIC is Akaike Information Criterion, SBIC is the Schwarz criterion, LBQ2(12) is the Ljung-Box statistics for serial correlation on squared standardized residuals at the 5% level of the order 12 lags respectively Table 3: GARCH MODEL (1998-2007) Coefficient GARCH(1,1) P-value TGARCH P-value EGARCH P-value  0.000222 0.0020 0.000277 0.0003 0.000425 0.0000  0.312496 0.0000 0.313831 0.0000 0.295464 0.0000 B0 7.89E-07 0.0000 8.54E-07 0.0000 -1.209301 0.0000 B1 0.143323 0.0000 0.176021 0.0000 0.355157 0.0000 B2 0.839631 0.0000 0.834078 0.0000 0.910862 0.0000 B3 -0.063057 0.0000 0.045906 0.0000 LBQ2(12) 34.713 0.001 32.902 0.001 13.990 0.301 Log-likelihood function value 10040.75 10046.41 10024.80 AIC -8.038250 -8.041982 -8.024668 SBIC -8.026590 -8.027990 -8.010676 Note: AIC is Akaike Information Criterion, SBIC is the Schwarz criterion, LBQ2(12) is the Ljung-Box statistics for serial correlation on squared standardized residuals at the 5% level of the order 12 lags respectively June 24-26, 2009 14 St. Hugh‟s College, Oxford University, Oxford, UK
  15. 15. 2009 Oxford Business & Economics Conference Program ISBN : 978-0-9742114-1-9 Table 4: GARCH MODEL (1989-1997) Coefficient GARCH(1,1) P-value TGARCH P-value EGARCH P-value  0.000399 0.1213 0.000553 0.0367 0.000927 0.0006  0.560087 0.0000 0.560475 0.0000 0.532883 0.0000 B0 1.24E-05 0.0000 1.25E-05 0.0000 -2.367505 0.0000 B1 0.260199 0.0000 0.349568 0.0000 0.393887 0.0000 B2 0.565982 0.0000 0.565580 0.0000 0.786341 0.0000 B3 -0.191066 0.0024 0.052265 0.1207 LBQ2(12) 0.2980 1.000 0.2941 1.000 0.1716 1.000 Log-likelihood function value 3193.755 3197.445 3188.352 AIC -6.954755 -6.960622 -6.940790 SBIC -6.928468 -6.929077 -6.909246 Note: AIC is Akaike Information Criterion, SBIC is the Schwarz criterion, LBQ2(12) is the Ljung-Box statistics for serial correlation on squared standardized residuals at the 5% level of the order 12 lags respectively List of Footnotes: i The SEMDEX is the market index on the official market, comprising all stocks on the official market. ii Pagan (1996) June 24-26, 2009 15 St. Hugh‟s College, Oxford University, Oxford, UK

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