2008 Oxford Business &Economics Conference Program
ISBN : 978-0-9742114-7-3
TITLE PAGE:
TITLE:
MONTHLY ANOMALIES ON THE MAURITIAN EQUITY MARKET: EVIDENCE
FROM GARCH MODELS
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 22-24, 2008
Oxford, UK
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Monthly Anomalies on the Mauritian Equity Market: Evidence from GARCH models
Abstract
This paper essentially aims at examining the monthly anomalies on the Stock Exchange of
Mauritius (SEM). Daily observations from the SEMDEX for the period July 1989 to
December 2006 are used for the study. As a matter of fact, the implication of this study can
help towards the investment strategies developed to earn excess return on the SEM if the
monthly anomalies are present. The descriptive statistics also suggest the presence of January
and July effect. One plausible explanation for the July effect relates to the fiscal incentives
made available to local stock market investors. Based on the standard GARCH model, the TGARCH model and the E-GARCH model, evidence of monthly effect is found, suggesting
investors to consider the seasonal effects when investing on the SEM. Finally, the results
from the T-GARCH model suggest the presence of a leverage effect on the SEM.
Keywords: Month of the year effects; Stock market anomalies; African Emerging Stock
markets; Efficient market hypothesis; SEMDEX
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1.0 Introduction
Over the last three decades, there have been a number of studiesi considering calendar
anomalies on major developed and emerging markets. Major anomalies relate to the day of
the week and the month of the year effect. This paper concentrates on the second anomaly.
Essentially, the monthly anomalies would relate to the returns being higher on certain specific
months. Undoubtedly, this is in sharp contradiction with the Efficient Market hypothesis as
prices should be random and not be predictable based on certain months.
A significant finding of most empirical researchii is the January effect where returns are
abnormally higher relative to other months. Main reasons suggested relate to the tax-loss
selling argumentiii where investors sell shares on certain months to minimize their tax
liability. There is also the information release hypothesisiv where news are released on
specific dates or months such that this affect the trading behaviour of investors.
In the past decade, the SEM have experience major developments in terms of market size,
trading volume, number of listed companies and contribution to the Mauritian GDP.
However, published research has been so far very limited on monthly anomalies. To my
knowledge, there is no published paper on this topic. Additionally, 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 monthly anomalies on the SEM using GARCH models.
This paper is organised as follows; Section 2 reviews previous literature, Section 3 provides
an overview of the SEM, the research methodology is discussed in section 4, Section 5
focuses on the analysis of results while section 6 concludes the paper.
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2.0 Prior Research
Stock market anomalies have attracted great attention in the last decades and have as such
been widely discussed in several developed and developing capital markets. One of the wellknown anomalies has been the month of the year effect where returns for a particular month
are higher than other months. One of the major findings in several equity markets is the socalled January effect where returns in January tend to be higher relative to other months.
Studies such as Rozeff and Kinney (1976), Keim (1983), Keim and Stambaugh (1984), Fama
(1991) have documented on the January effect on the US markets. Essentially, Rozeff and
Kinney (1976) found an average return of 3.48% for the months of January compared to
0.42% for other months using data from 1904 to 1974 on the NYSE. Keim (1983) employed
data for the period 1963-79 and found that approximately 50% of the risk-adjusted premium
of small firms relative to large firms is attributed to the January abnormal returns while Keim
and Stambaugh (1984) reported that low-quality bonds earn abnormal returns in January.
Fama (1991) used the S&P500 index for the period 1941-81 to report that small firms
averaged a return of 8.06% in January.
Besides the US markets, there is also international evidence of the January in some developed
and emerging markets. For instance, Gultekin and Gultekin (1983), in a study of 17 countries,
found that higher returns occur in January for non US markets. Also, an April effect is
reported for the UK market. Additionally, Choudhry (2001) found evidences that UK returns
are subject to the January effect. Moreover, Cheung and Coutts (1999) documented evidence
of January effect on the Hang Seng Index using daily closing prices from 1985 to 1997.
However, Fountas and Segredakis (2002) in a study of 18 emerging markets did not, on
overall, found evidence of a January effect.
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A number of arguments have been put forward to explain the monthly patterns of the stock
market returns. The first argument relates to the tax-loss selling hypothesis ( Branch (1977)
and Dyl (1977)). Essentially, investors would most likely sell their stocks at the end of the
tax year to realise capital losses and reduce the amount of tax that is due. Hence, if the tax
year ends in December, investors will sell at the end of the year to reduce tax liability and
buy in January such that returns will be higher at the turn of each tax year. Secondly,
researchers such as Rozeff and Kinney (1977) argued for the information release hypothesis
in that firms release their news or make announcements at the end of the fiscal year such that
returns tend to be higher subsequently. Other researchers like Corhay et al. (1995) simply
argued for the positive relationship between risk premium and mean portfolio returns to
explain the abnormal returns in a given month.
3.0 Stock Exchange of Mauritius- An overview
The Stock Exchange of Mauritius (SEM) began its activities in July 1989 and it is also a
member of the World Federation of Exchanges (WFE) since November 2005. It comprises
mainly of the Official Market and Development & Enterprise Market (DEM). It is also
important to note that the Financial Services Commission (FSC) is the regulatory body of the
SEM since the inception of first-mentioned.
Since 1989 to date the SEM has made an immense progress on the Official Market, with only
5 companies at the beginning and is now culminating with 41 companies. Indeed the trading
frequency on the official market has amplified gradually from twice weekly to thrice weekly
in 1994 before moving to daily trading in November 1997. The market capitalization
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increased from 1.44 billion rupees in 1989 to 160, 706,708,929.85 rupees as at November
2007.
However, before a company can be listed on either the DEM or the official Market, there is a
set of rules and procedures that must be respected. Most of the rules are stated in the Listing
Rules, Trading rules, Financial Services Act and the Securities Act. These listed companies
are classified into seven sectors, namely; The Banks and Insurance, Industry, Investments,
Sugar, Commerce, Leisure & Hotels and Transport.
Also, there are eleven stock broking companies in operation. The brokerage fee claimed by a
stock broking company to its client are apportioned among the stock broking company, the
Stock Exchange of Mauritius (SEM), the Financial Services Commission (FSC) and the
Central Depository & Settlement Co. Ltd. (CDS) and it ranges from 0.9% to 1.25%.A Central
Depository and Settlement (CDS) system is operational since January 1997 to speed up share
transfer and settlement operations.
To further improve the facilities/services offered and attract more players on the Official
Market and the DEM, a Central Depository and Settlement Co. Ltd was set up in 1997. It
provides centralised depository, clearing and settlement services. Regarding the regulatory
bodies, the Financial Services Commission (FSC) and the Financial Services Promotion
Agency were set up in 2001, enforcing new listing rules for transparent and precise disclosure
of information to relevant stakeholders.
The Stock Exchange of Mauritius Automated Trading System (SEMATS) was also
established in 2001 replacing the traditional dealing method which had many deficiencies.
The SEMATS is an online trading system that can accommodate shares as well as debt
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instruments. Moreover there exist some market indices on which the SEM based their daily
operations. For the Official market they are SEM-7v and SEMTRI along with the SEMDEXvi
while indices use for the DEM are the DEMTRIvii and DEMEXviii
4.0 Research Methodology
To test for the months of the year effect on the SEM, a GARCH (1,1) specification is used.
According to Brooks (2004), a typical GARCH (1,1) is sufficient for financial time series and
it is very rare to find higher order of GARCH models in the academic finance literature. Also,
daily observations of the SEMDEX are used to calculate returns for the months as from July
1989 to December 2006. 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. Mean returns are subsequently calculated for each months.
Using GARCH models entail several advantages in that they help in capturing the
characteristics of financial time seriesix. For instance, they allow for volatility clustering and
leverage effects. Essentially, many financial time series are subject to a period of subsequent
intense volatility followed by a period of low volatility. In effect, conditional variance is
time-varying. Also, the conditional variance can show some asymmetric behaviour. Thus,
according to Engel (1982), Bollerslev (1986) and Bollerslev et al. (1992), autoregressive
conditional heteroscedasticity models (GARCH) are more appropriate as they are more
flexible in capturing dynamic structures of conditional variance.
Based on the empirical literaturex, the following regression models are used.
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yt   1   2 D2t   3 D3t   4 D4t   5 D5t  .................   12 D12t  MA(1)   t
(1)
 t  1 ~ N (0, ht )
(2)
ht   0  1 2 t 1   2 ht 1
(3)
Where yt is the average monthly stock return and Dt represent dummy variables where Dit = 1
for the ith month and 0 otherwise; ε is an error term which is dependent on past information
and ht is the conditional variance. MA(1) stands for the moving average component to
correct for any serial correlation.
The coefficients of the dummy variables in equation (1) show the difference between January
and the ith month of the year while the intercept stands for the mean returns in January. 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 sensitive to negative shocks. To this effect, the following two asymmetric
GARCH models, namely TGARCH and EGARCH, are employed
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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
 
ht 1
 ht 1
(5)
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, the excess skewness and kurtosis of the
standardized residuals,the ARCH effect and the information criterion are used to assess
which model is more appropriate.
5.0 Analysis of Data and Results
The basic statistics are presented in Table 1 for return series on SEMDEX for the period
July1989 to December 2006.
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[INSERT TABLE 1 ABOUT HERE]
Table 1 shows the descriptive statistics for the whole sample period. At first notice, the
returns are positively skewed and have significant kurtosis. The large kurtosis value suggests
that the series follow a fat tail distribution. The mean return is found to statistically
significant but is not normally distributed as the Jarque-Bera statistics is significant at 1%
level.
Additionally, the returns are stratified according to their months and the results are reported
below in Table 2.
[INSERT TABLE 2 AROUND HERE]
Based on Table 2, most of the monthly returns (10 out of 12) do not follow a normal
distribution. Significant kurtosis (greater than 3) is found for all months except for the month
of December. Also, returns are, in general, positively skewed for all months except for April
and September. The highest return is found in the months of July while the lowest return is in
September. Interestingly, the tax period in Mauritius starts from July and ends in June next
year. Therefore, consistent with the tax-loss selling hypothesis, the SEM is expected to have a
July effect as investors sell their shares in June to avoid taxes and bounce back in July to buy
those shares. However, in Mauritius there is no capital gains tax. Nevertheless, the tax
structure in Mauritius prior to the year 2006, allow investor to benefit from tax deductions if
they invest on the SEM. Thus, it may be plausible to assume that investors enter in the market
at the start of the tax year (July), hold the investment for one whole tax year and thereby
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benefit from the tax deductions. Furthermore, a possible January effect may be observed as
the month of January experienced the second highest mean return. This finding is consistent
with other studiesxi in developed and emerging markets.
Table 3 shows the results from the different GARCH models for the stock market returns for
the period 1989 to 2006.
[INSERT TABLE 3 AROUND HERE]
From table 3, the result shows that the T-GARCH model has the highest log-likelihood value
as well as the lowest AIC and SBIC values. Also, most coefficient on the T-GARCH model
seems to statistically significant. Also, based on the Ljung-Box statistics, there is no problem
of serial autocorrelation for all the three models. Furthermore, if GARCH models are
properly specified, they should reduce the excess skewness and kurtosis in normal returns.
From Table 3, it is observed that the T-GARCH model has the lowest excess skewness and
kurtosis value. Moreover, ARCH test shows conditional homocesdasticity in all the three
models. Finally, it is observed that all restrictions imposed on the T-GARCH’s parameters
are met while one non-negativity constraint in GARCH (1,1) model is violated. Thus, in light
of the above, the T-GARCH is considered as the best model.
To this effect, the T-GARCH model is mainly considered for the testing of monthly
anomalies on the SEM. 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 GARCH
(1,1) model and E-GARCH model, this is not the case for T-GARCH model. Essentially,
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shocks to the conditional variance are highly persistent under the T-GARCH model while the
shocks to volatility decay over few lags for the standard GARCH and E-GARCH models.
From the T-GARCH model, a significant asymmetry coefficient, B3 , is found, suggesting the
presence of a leverage effect. Essentially, negative news on the SEM causes volatility to
increase more than positive news of the same magnitude.
Turning to the mean equation, it is observed that intercept term measures the average return
for January. From table 3, based on the T-GARCH model, the intercept term, 1 , is
statistically positively significant at 1% level. The dummy variables measure the difference
in the mean returns for the months of February-December and the average return of January.
The T-GARCH model shows that the average January returns are higher relative to most of
the months, thereby suggesting evidence in favour of a seasonal effect on the SEM. To test
for the existence of monthly anomalies, the Wald Test is used with the null hypothesis being
that all the months have same means. In all three GARCH models, the Wald statistic shows
that there are significant differences in returns across the months. Finally, the July effect is
not present in the T-GARCH model but is detected in the E-GARCH model.
6.0 Conclusion
This paper has investigated the monthly anomalies present on the SEM using three different
GARCH models. The descriptive statistics shows that the mean returns exhibit some nonnormal characteristics. Also, the high returns in January and July suggest the presence of a
monthly seasonality on the SEM. One plausible explanation for the July effect relates to the
tax incentives available to stock market investors.
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With regards to the regression models,
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the results show that the T-GARCH model is the most properly specified. The T-GARCH
model suggests the existence of a leverage effect on the SEM. Furthermore, a January effect
is detected with the Wald statistic confirming the presence of monthly effect on the SEM for
all three GARCH models. As a concluding note, it may be suggested that investors should
start considering the monthly anomalies when investing on the SEM.
7.0 References
Aggarwal, A., and K. Tandon, (1994). Anomalies or Illusions? Evidence from Stock Markets
in Eighteen Countries. Journal of International Money and Finance, 83-106
Ariel, Robert A. (1987). A Monthly Effect in Stock Returns. Journal of Financial Economics,
Vol.18, 161-174.
Black, F. (1976). Studies of Stock Price Volatility Changes. Proceeding of the meetings of
the American Statistics Association, Business and Economics Section, 177-181.
Branch, B. (1977) .A tax-loss trading rule. Journal of Business, 50, 198-207.
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, 14372.
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Brooks C. (2004). Introductory Econometrics for Finance. Cambridge University Press
Brooks, C. and Persand, G. (2001). Seasonality in Southeast Asian Stock Markets: Some
New Evidence on Day-of-the-Week Effects. Applied Economic Letters, Vol 8, 155-158.
Cheung, K.C. and Coutts, J.A. (1999). The January effect and monthly seasonality in the
Hang Seng index: 1985-1997. Applied Economics Letters, 6, 121-123.
Christie, A. (1982). The Stochastic Behaviour of Common Stock variances: Value, Leverage
and Interest Rate Effects. Journal of Financial Economics, 10, 407-432.
Choudhry, T. (2001). Month of the Year Effect and January Effect in Pre-WW1 Stock
Returns: Evidence from A Nonlinear GARCH Model. International Journal of Finance and
Economics, 6, 1-11.
Corhay, A., Hawaini, P. and Michel, P. (1995). Seasonality in the risk-return relationship:
some international evidence. Journal of Finance, 42, 49-86.
Dyl, E. (1977). Capital gains taxation and year-end stock market behaviour. Journal of
Finance, 32, 165-175.
Engle, R.F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of
Variables of UK Inflation. Econometrica, 50, 987-1008.
Fama, E. (1991). Efficient capital markets:II. Journal of Finance, 46, 1575-617.
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French, K.,(1980). Stock Returns and the Weekend Effect. Journal of Financial Economics,
55-69.
Fountas, Stilianos, and Konstantinos N. Segredakis, (2002). Emerging stock markets returns
seasonalities: the January effect and the tax-loss selling hypothesis. Applied Financial
Economics, 12 (4):291-300.
Gibbons, M., and P. Hess, (1981). Day of the Week Effects and Asset Returns. Journal of
Business, 579-596.
Gültekin, M. and Gültekin, N. B. (1983). Stock Market Seasonality: International Evidence.
Journal of Financial Economics, 12,469-81.
Jaffe, Jeffery and Randolph Westerfield. (1989). Is there a Monthly Effect in Stock Market
Returns? Evidence from Foreign Countries. Journal of Banking and Finance, Vol.13, 237244.
Jaffe, J., and R. Westerfield. (1985). The Weekend Effect in Common Stock Returns: The
International Evidence. Journal of Finance, 433-454.
Keim, D. (1983). Size Related Anomalies and Stock Market Seasonality; Further Empirical
Evidence. Journal of Financial Economics, 12, 12-32.
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Keim, D., and R. Stambaugh, (1984). A Further Investigation of the Weekend Effect in Stock
Returns. Journal of Finance, 819-835.
Lakonishok, J., and Levi. M. (1982). Weekend Effects on Stock Returns: A Note. Journal of
Finance, 883-889.
Mahhayereh, A. (2003). Seasonality and January effect anomalies in an emerging capital
market. The Arab Bank Review,5, 25 –32.
Reinganum, M. R. (1983). The Anomalous Stock Market Behavior of Small Firms in
January: Empirical Tests for Tax-Loss Selling Effects. Journal of Financial Economics, 12,
89-104.
Rozeff, M. and Kinney, W.(1976). Capital Market Seasonality: The Case of Stock Market
Returns. Journal of Financial Economics, 3, 379-402.
Pagan, A.(1996). The Econometrics of financial markets. Journal of Empirical Finance, 3, 15102.
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LIST OF TABLES:
Table 1: Descriptive statistics for stock returns
Returns
Mean
Std.
Skewness
Kurtosis Jarque-Bera
Dev.
SEMDEX 0.002329** 0.015399
2.519821
22.78351
3685.78*
Note: * significant at 1% level; ** significant at 5% level; *** significant at 10% level
Table 2: Descriptive Statistics for stock returns on monthly basis
Returns
Mean
Std.
Skewness Kurtosis Jarque-Bera
Dev.
January
0.005001
0.024212
1.601656
9.029419
33.01904*
February
0.003314
0.018807
3.148069
12.76842
95.66997*
March
0.001727
0.007579
1.801459
6.70597
18.92329*
April
-0.00154
0.007172
-2.17817
8.366286
33.84037*
May
0.000817
0.005686
0.947638
4.518732
4.178189
June
0.004532
0.018333
3.576289
14.30041
126.6916*
July
0.005847
0.027772
2.378772
9.87168
52.39066*
August
0.003641
0.015651
3.49796
14.19663
130.7305*
September
-0.00211
0.019126
-3.50674
14.38375
134.0841*
October
0.002985
0.009618
3.559371
14.47686
136.7961*
November
0.001232
0.004728
2.038418
8.250154
33.13853*
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December
0.002494
0.00406
0.29569
ISBN : 978-0-9742114-7-3
1.804615
1.334007
Note: * significant at 1% level; ** significant at 5% level; *** significant at 10% level
Table 3: Month of the year effect- GARCH MODEL (1989-2006)
Coefficient
1
2
3
4
5
6
7
8
9
 10
11
 12

B0
B1
B2
B3
LBQ2(12)
GARCH(1,1) P-value
TGARCH
P-value
EGARCH
P-value
0.009213
0.0137
0.013047
0.0000
0.001739
0.0540
-0.006074
0.4361
-0.014422
0.0000
0.001411
0.0711
-0.007418
0.1654
-0.002484
0.3159
-0.001530
0.2833
-0.011128
0.0578
-0.012534
0.0000
-0.004097
0.0000
-0.005691
0.1909
-0.008786
0.0000
-0.002423
0.0003
-0.004310
0.2950
0.029459
0.0000
0.002067
0.0052
-0.007030
0.1499
-0.013996
0.0000
0.001557
0.0092
-0.004889
0.2650
-0.001889
0.1090
0.001766
0.0397
-0.018044
0.0000
-0.031813
0.0000
-0.005037
0.0000
-0.005850
0.2340
-0.012924
0.0000
0.001802
0.0359
-0.008219
0.2658
-0.012675
0.0000
0.002254
0.0088
-0.007338
0.3689
-0.012618
0.0000
0.002286
0.0299
0.033578
0.4870
-0.057548
0.4064
-0.191700
0.0000
0.000139
0.0000
4.21E-06
0.0000
-7.471065
0.0000
0.459816
0.0000
1.187157
0.0022
-0.812283
0.0000
-0.107535
0.0033
0.153386
0.0002
0.115811
0.0012
0.822424
0.1892
1.412730
0.0000
8.3704
0.680
2.5946
0.995
2.4537
0.996
Log-likelihood function
value
620.0267
653.1082
640.2556
AIC
SBIC
Skewness
Kurtosis
ARCH (6)-LM
-5.752635
-5.497617
2.266790
19.20733
0.907924
-6.058173
-5.787217
1.165895
6.824011
4.525771
-5.935768
-5.664812
1.952729
14.81461
1.989764
Wald Test
(  2 =  3 =…=  12 )
10.46725
0.988863
0.000000
32.91765
0.605904
0.000000
90.31393
0.920638
0.000000
Note: *,**,*** imply significant at 1%,5% and 10% while 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, ARCH (6) of the
order of 6 lags is used as test for conditional heterocedasticity
June 22-24, 2008
Oxford, UK
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2008 Oxford Business &Economics Conference Program
ISBN : 978-0-9742114-7-3
List of Footnotes:
i French (1980), Gibbons and Hess (1981), Keim and Stambaugh (1984); Jaffe and Westerfield (1985); Lakonishok, J., and M. Levi (1988);
Aggarwal and Tandon (1994); Brooks and Persand (2001) amongst others
ii E.g Rozeff and Kiney (1976); Keim (1983); Reinganum (1983); Gulketin and Gulketin (1983); Ariel (1987)
iii Branch (1977) and Dyl (1977)
iv Rozeff and Kinney (1976)
v The SEM-7 consists of the largest 7 Mauritian companies by market value
vi The SEMDEX is the all shares index. It reflects capitalisation based on each listed stock which is weighted according to its shares in the
total market.
vii The Development & Enterprise Market Total Return Index
viii The price index of DEM
ix Pagan (1996)
x Keim (1983); Gultekin and Gultekin (1983); Fountas and Segredakis (2002); Maghayereh(2003)
xi Rozeff and Kiney (1976); Keim (1983); Reinganum (1983); Gulketin and Gulketin (1983); Ariel (1987)
June 22-24, 2008
Oxford, UK
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