A Trading Strategy for the Indian Stock Market

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Research Articlefocuses on the analysis and reso lution o f managerial issues based on analyt ical and

empirical studies

A Trading Strategy for the Indian Stock Market:Analysis and Implications

Madhusudan Karmakar and Madhumita Chakraborty

Introduction

A curious seasonality reported in finance isthe monthly effect which implies that themean daily return for stock is positive andhigher during the first half of the monththan the second half. Another related

anomaly is the turn-of-the-month effect whichis said to exist when the average daily returnat the turn of the month is significantlyhigher than the daily return on the remaining days of the month. This paper examinesboth the monthly effect and the turn-of-the-month effect in the Indian stock market byapplying two different approaches: calendarday approach and trading day approach.The results of both the approaches revealsignificantly higher return at the first half ofthe month than that of the second half andabnormally high returns at the turn of themonth. Various explanations for the observed anomalies have been consideredincluding the problem of 'data mining,'proxy of other anomalies, etc., but nonecould provide adequate explanations for theobserved intra-month return regularities.However, based on the findings, the studytries to evolve certain trading strategieswhich would benefit in the decision makingof the investors concerned with timing of

stock purchases and sales.

Madhusudan Karmakar is a Senior Lecturer of Finance

at the National Institute of Financial Management,

Faridabad and Madhumita Chakraborty is a Lecturer

of Accounts and Finance at thejagannath International

Management School, New Delhi.

Vol. 25, No. 4, October-December 2000

A curious anomaly in the monthly pattern ofstock market returns was first documented byAriel (1987). He examined the US stock returnsand found that the mean return for stock ispositive only for days immediately before andduring the first half of calendar months, and

indistinguishable from zero for days during thesecond half of the month. Ariel calls thisempirical finding the 'monthly effect,' whichimplies that returns at the beginning of themonth are greater than the returns after the mid-point of the month. Following Ariel's study, Jaffeand Westerfield (1989) examined the stockmarket returns in the UK, Japan, Canada, andAustralia and found a significant US type ofmonthly effect only in Australia. They, however,observed a weak evidence of the anomalyconsistent with Ariel's work in the UK and

Canada and, in fact, a reverse monthly effectfor Japan. The reverse monthly effect is alsoreported by Barone's (1990) study, who inves-tigated the Italian market and found that stockprices fall in the first part of the calendar monthand then rise in the second.

Another seasonality related to this monthlypattern is 'the turn-of-the-month effect' whichimplies that average daily return at the turn ofthe month is significantly positive and higherthan the daily return during the remaining days

of the month. Lakonishok and Smidt (1988)showed that stock returns in the US are sig-nificantly higher on turn-of-the-month tradingdays than on other days. Extending the analysisto nine other countries, Cadsby and Ratner(1992) documented the same findings for Aus-tralia, Canada, Switzerland, UK, and West

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Germany but not for France, Hong Kong, Italy,and Japan. In a recent study, Hensel and Ziemba(1996) investigated the daily return patterns inUS stock market by taking a very long seriesfrom 1928 to 1993 and found that the meanreturns in the stock market were significantly

positive at the turn and in the first half of themonth and significantly negative in the rest ofthe month.

In the studies mentioned above, the day ofthe month anomaly has been reported only fordeveloped capital markets mostly in the west.One's belief regarding this empirical regularitywould be strengthened if it is known to alsooccur in yet another capital market separatedfrom the West by distance, institutional arrange-ments, and culture. Hence, it is of interest tosearch whether such anomalies exist for adeveloping market such as the one in Indiawhich belongs to the east. In this paper, weinvestigate the daily return patterns in a monthin the Indian stock market. More specifically,the study aims to examine the following twoissues :

Whether average daily return at the first halfof the month is significantly different fromthat of the second half (i.e., the monthlyeffect).

Whether average daily return at the turn-of-the-month is significantly different fromthat of the remaining periods of the month(i.e., the turn-of-the-month effect).

On the basis of results of the above twoissues, the study will try to develop the tradingstrategies which will be of potential use indecision-making by institutional investors con-cerned with timing of stock purchases and salesand to long term individual investors who useThe Economic Times Share Price Index or similarbenchmarks for performance measurement of

portfolios.

Sample Data and Time Period

The data used in this study consist of the dailyclosing prices of "The Economic Times IndexNumbers of Ordinary Share Pr ices" for the

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period from January 1981 to December 1995,compiled and published by The Economic Timeson a daily basis.

The selection of the period is basicallyguided by the following argument. Before the80s, the Indian capital market traditionally

played a marginal role in allocating productiveresources in its national economy. The situation,however, started changing gradually when thecapital market witnessed significant develop-ment mostly in quantitative terms since the early80s. The quantitative development along withthe qualitative change brought about by marketreforms initiated in 1992 has made Indianbourse a mature one which deserves a studyof this nature.

The sample data consist of price index of

3404 trading days from January 1981 to Decem-ber 1995 excluding the index of the trading daysin December 1994 which are not available tous.

With this data set, we have computed thedaily returns as follows :

where R(is the continuously compounded dailypercentage change of the share price index forthe day t, P t is the price index at the day t,and Ptj is the same for the preceding day, andInis the natural logarithm.

Empirical Evidence

In this section, we examine both the monthlyeffect and the turn-of-the-month effect followingtwo different approaches: calendar day ap-proach and trading day approach. In calendarday approach, we investigate the regularitiesusing the mean returns of calendar days of themonth. In trading day method, investigation is

made measuring mean return of trading daysof the month.

Table 1 presents sample values of averagereturns for 31 calendar days. The sample dataused for this purpose conventionally excludesthe holiday return and contains 31 17 observa-tions.

1The highest mean calendar day return

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is on the 30th day, which is almost six timesthe global mean return. In fact, gross return onthis day alone accounts for more than 16 percent of the total return over the 15 year period.Figure 1 displays histograms of the arithmeticmean returns for 31 calendar days. It appears

from Figure 1 that half of the daily returns ofthe first half of the month starting from the 30thday of the previous month to the 14th day ofthe current month (30, 31, 1, ............14) areabove the global mean return whereas majorityof the daily return of the second half (1.5, 16,

.29) of the calendar month fall below the overall mean.

2

Following Ariel (1987), we use the tradingday approach to investigate whether any monthlypattern of stock returns exists in the Indianmarket/

1 Table 2 shows the mean returns of the

seven trading days before and after the start ofeach month (-7 to -1 and 1 to 7),

4 where +1

is the first trading day of each month and -1is the last trading day of the previous month.The days that do not fall in the intervals (1 to7) and (-7 to -1) are ignored. Each daily mean

Table 1: Means, Standard Deviations and t-statistics of Per cent Returns by CalendarDay of the Month*

Statistics 7 2 3 4 5 6 7

Mean

S D (ajNo of Observation

t-statistic

0.05955

1.1165976

0.46187

0.33082

1.34467 852.25492b

0.07508

1.33274104

0.57173

-0.07478

1.19139101 -

0.62767

0.05544

0.98598106

0.57622

-0.00861

1.11462108 -

0.07990

0.06883

1.12124107

0.63202

8 9 10 77 72 13 14

MeanS D (a)

No of Observation

t-statistic

0.31178

1.08945

110

2.98783C

0.21603

1.07616

104

2.03731b

0.23490

1.10979

106

0.04856

1.12174

113

0.46018

0.11918

0.91850

109

1.34846

0.02394

0.80767

107

0.30517

-0.08479

0.84863

99 -

0.98909

15 16 77 18 19 20 27

Mean

S D (oj

No of observation

t-statistic

-0.02435

1.09411

95 -

0.21577

-0.11215

0.96618

104 -1.17803

-0.00478

0.95143

105 -0.05123

0.12284

1.08585

108

1.17021

0.03625

1.07901

112

0.35395

-0.00992

0.99841

111 -

0.10421

0.01057

1.04557

109

0.10506

22 23 24 25 26 27 28

Mean

S D (a)

No of Observation

t-statistic

0.04956

0.87016

108

0.58915

0.12211

0.83329

107

1.50870

-0.05247

1.11408

108 -

0.48718

0.18179

1.13204

101

1.60585

0.08121

1.12891 86

0.66322

0.13997

0.99821

94

1.35224

-0.08234

1.07917

104 -

0.77436

29 30 31

Mean 0.02566

S D (oj 1.14908

No of Observation 96

t-statistic 0.21765

0.45181

1.38451 85

2.99087'

0.16137

0.88581

491.26212

'Returns for periods including a holiday are omitted. These returns are defined as: R(=are the E.T. Share Price Index on day t and t- 1 successively.

The underlined figures are significantly different from zero at 5% level (one-tail test)P(t > 1.645/D = oo) = 0.05 (one tail).

'The underlined figures are significantly different from zero at 1% level (one-tail test)

P(t > 2.326/u = oo) = 0.01 (one tail).

Vol. 25, No. 4, October-December 2000 29 Vikalpa

^ (P/P, ,)-100, where Prand


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Note: The global mean (0.07503) is est imated from

return in the table is estimated from 172 dailyobservations.5The table reveals that the highestmean return is on the last trading day of theprevious month, having as much as 0.24681 percent which is 2.2 times the global mean. Thegross return on this day alone contributes almost16 per cent of the total return of all 14 tradingdays over the 15-year period. Figure 2 exhibits

the returns to all trading days in the 15-year period.

the histogram of arithmetic mean return for 1trading days. The figure shows that most of thmean trading days' return of the first half othe month starting from last trading day of thprevious month to six trading days (-1 to 6) arabove the global mean return while majoritof the daily return of the second half (7 to -2of the month fall below the overall mean.6

Table 2: Means, Standard

of the Month"

Deviations and t-statistics of Per cent Returns by Trading Day

Trading Days Mean S D (aj No of Observations t-statistics

-7 0.09896 0.88793 172 1.45738-6 0.05844 1.16287 172 0.65716

-5 0.14112 1.02691 172 1.797051'

-4 0.01221 0.94039 172 0.16978

-3 -0.00686 1.08890 172 -0.08238

-2 0.22076 1.02954 172 2.80399*

-1 0.24681 0.99153 172 3.25501'

1 0.22375 1.46778 172 1.99342

2 0.08500 1.14537 172 0.97044

3 0.09739 1.02858 172 1.238164 0.00743 1.03146 172 0.09419

5 0.19171 1.11966 172 2.23901h

6 0.12645 1.13564 172 1.45605

7 0.05795 0.87829 172 0.86281

Returns are defined as Rt= IJP/PJ.100,Holiday returns have not been excluded bThe underlined figures are significantly0The underlined figures are significantly

where P(and Pttare the E.T. Share Price Index on day t and t-1 successively,in this trading day approach.

different from zero at 5% level (one-tail test).

different from zero at 1% level (one-tail test).

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Figure 2: Mean Return in Trading Day of the Month

Note: The global mean (0.1115099) is estimated from the re turns to all 14 trading days in the 15-year period.

Test of Monthly Effect

To investigate the monthly effect, we test thefollowing null hypothesis applying both calen-dar day and trading day approaches:

"Mean daily return in the first half ofthe month is equal to the mean daily

return in the second half of the month."As mentioned earlier, the first and second

halves of each month consist of 30th and 31st of last month, and 1, ...., 14 and 15, ........, 29calendar days in calendar day approach and-1, ..........., +6 and +7, -7, .........., -2 trading daysin trading day approach respectively. We presentthe sample values across the first half as wellas the second half of all months for eachapproach separately in two panels in Table 3.Panel A of the table displays the mean andstandard deviations of calendar day returns ofthe two halves, along with the t-statistic to testthe difference of the two mean returns. Simi-larly, Panel B exhibits the mean and standarddeviations of trading day returns of the twohalves along with the associated t-statistic.

The t-statistic of Panel A indicates that theaverage calendar days' return in the first half

of the month is significantly higher than thatof the second half at 5 per cent level ofsignificance. According to this approach, thereis a strong monthly effect in the Indian stockmarket. While this effect is corroborated by t-statistic in Panel B, the statistic is, however,significant only at 10 per cent level for thetrading day approach. Thus, both the ap-

proaches reveal that there is a monthly effectin the Indian stock market.

Test of Turn-of-the Month Effect

Investment advisers have argued that US stocksexperience substantial price rises at the turn ofthe month.

7 As noted in the introduction,

different researchers also demonstrate anoma-lous returns at the turn of each month, vindi-cating the claims of practitioners. A cursoryreading of Tables 1 and 2 in the present study

apparently suggests a turn-of-the-month effect inour market too. Table 1 reveals that the returnson 30th and 2nd calendar days are the largestand the second largest respectively and alsosignificantly different from zero. Similarly, Table2 shows that the largest, second largest and thirdlargest daily returns fall on -1, +1, and -2 tradingdays respectively.

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Table 3: Difference of Means Test Comparing Returns at the First Half of Month withReturns at the Second Half of the Month

Panel A: Calendar Day Approach

Average Return

Across Calendar Days

(30, 31, 1....14)"

Average Return Across

Calendar Days (15 to

29)

Mean (X) 0.11835 0.03113

S D (a)'

1.11157 1.03999

No of Observations 1569 1548t-statistic 2.26134

Panel B: Trading DayApproach


Trading Days (-1 to

+6)b


Trading Days (7 to -2)

A Trading Strategy for the Indian Stock Market

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