Leverage Effects In The Mauritian's Stock Market

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: [email protected]

June 24-26, 2009St. Hugh’s College, Oxford University, Oxford, UK

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mailto:[email protected]


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


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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.


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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,


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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

i The SEMDEX is the market index on the official market, comprising all stocks on the official market. June 24-26, 2009St. Hugh’s College, Oxford University, Oxford, UK

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(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.

(1)

(2)

(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:

In general, the ARCH and GARCH terms, and 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


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sensitive to negative shocks. To this effect, the following two asymmetric GARCH models, namely

TGARCH and EGARCH, are employed

TGARCH:

(4)

Where =1 if , or zero otherwise

EGARCH:

(5)

For the TGARCH model, the leverage effect parameter, , 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, , 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]


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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


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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, , 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.



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

effects on the SEM as the coefficient is positive though insignificant. In fact, a coefficient which is


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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-

Day, 1976.


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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


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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


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LIST OF TABLES:

Table 1: Descriptive statistics for SEMDEX returns

Period Mean Std. Dev. Skewness Kurtosis Jarque-

Bera

P-Value

19890.006396 0.020392 0.054026 1.952512 1.155111 0.56127

19900.00741 0.016196 -0.73256 3.903369 6.295627 0.04295

1991-0.0021 0.008095 -0.22425 2.495465 0.9494 0.62207

19920.001742 0.006716 0.546948 4.105234 9.974867 0.00682

19930.005176 0.00936 0.518875 3.941684 7.936589 0.01891

19940.003104 0.00825 0.459189 4.080463 12.23246 0.00221

1995-0.00228 0.010135 -0.01359 7.552003 122.602 0.00000

19960.000175 0.008792 -1.87144 19.55013 1775.482 0.00000

19970.000633 0.005183 0.199473 3.610731 3.547673 0.16968

19980.0007 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

20020.000637 0.004066 0.406741 4.729487 37.74641 0.00000

20030.001268 0.005942 0.26814 11.31762 729.4384 0.00000

20040.001013 0.003357 0.329357 6.794036 156.9362 0.00000

20050.000495 0.004078 0.519162 10.16587 543.9384 0.00000

20060.00161 0.007684 0.624211 11.29317 735.59 0.00000

20070.001705 0.009451 0.737439 14.28066 1342.822 0.00000

All Sample

[89-07]0.000853 0.006922 0.506192 14.16385

17893.08 0.00000


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Table 2: GARCH MODEL (1989-2007)

Coefficient GARCH(1,1) P-value TGARCH P-value EGARCH P-value0.000378 0.0000 0.000427 0.0000 0.000609 0.0000

0.393481 0.0000 0.400311 0.0000 0.348677 0.0000

5.37E-06 0.0000 5.21E-06 0.0000 -1.255971 0.0000

0.314019 0.0000 0.355528 0.0000 0.378340 0.0000

0.566946 0.0000 0.582654 0.0000 0.904904 0.0000

-0.120705 0.0000 0.026103 0.0020

LBQ2(12) 1.6673 1.000 1.5734 1.000 2.5448 0.998Log-likelihood function value 13114.51

13120.0213134.70

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



0.312496 0.0000 0.313831 0.0000 0.295464 0.0000

7.89E-07 0.0000 8.54E-07 0.0000 -1.209301 0.0000

0.143323 0.0000 0.176021 0.0000 0.355157 0.0000

0.839631 0.0000 0.834078 0.0000 0.910862 0.0000

-0.063057 0.0000 0.045906 0.0000

LBQ2(12) 34.713 0.001 32.902 0.001 13.990 0.301Log-likelihood function value 10040.75 10046.41 10024.80

AIC -8.038250 -8.041982 -8.024668

SBIC -8.026590 -8.027990 -8.010676



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0.560087 0.0000 0.560475 0.0000 0.532883 0.0000

1.24E-05 0.0000 1.25E-05 0.0000 -2.367505 0.0000

0.260199 0.0000 0.349568 0.0000 0.393887 0.0000

0.565982 0.0000 0.565580 0.0000 0.786341 0.0000

-0.191066 0.0024 0.052265 0.1207

LBQ2(12) 0.2980 1.000 0.2941 1.000 0.1716 1.000Log-likelihood function value 3193.755 3197.445 3188.352

AIC -6.954755 -6.960622 -6.940790

SBIC -6.928468 -6.929077 -6.909246


List of Footnotes:

ii Pagan (1996)


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