This study aims at analyzing the Weekend effects and the Calendar effects on the volatility and returns of the Bombay Stock Exchange’s BSE-100 Index after the number of days for settlement changed to 2 days.

1. NATIONAL INSTITUTE OF TECHNOLOGY, DURGAPUR
Analytical study of Weekend and Calendar Effects on the
Volatility of BSE-100 Index
Project Report
(2006-2007)
| Mohammed Zishan Ansari
04/351
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2. Objective
This study aims at analyzing the Weekend effects and the Calendar effects on the volatility and
returns of the Bombay Stock Exchange’s BSE-100 Index after the number of days for settlement
changed to 2 days.
Introduction
The anomalies of Stock markets have been studied widely and almost all the effects and the
volatile nature of the stock prices are widely known. The investors today are well informed of
the ways in which the stock market operates and the risks associated with their investments.
The various factors which affect the stock prices and hence the BSE-100 Index are related to the
happenings in the country, its economy, happenings across the other markets of the world and
also to the performance of companies, sectors etc. The factors contributing to the volatility of
stock prices are numerous and hence the risk associated with them varies.
The presence of Seasonality or Calendar effects in the returns has been observed in many
markets of the world including the markets in the emerging countries. Any change in market’s
way of operation can possibly change the investing habits of the investors. The studies of
Weekend effects on the other markets of the world have shown interesting results. The
average daily return is not same across all the days which should be in the ideal case. In
general, the Mondays are expected to behave differently from the entire week because of the
Weekend effect. Weekend effect can be explained as the increased volatility when the market
reopens on Monday (The first working day of the week) after the weekend due to any
happenings over the weekend. This is generally observed as low trade volumes on Fridays
(which is the last working day of the week). The general tendency of the investor is to reduce
the risk associated to his/her investment and gain maximum returns. Keeping the funds parked
for the weekend at a safe place such as bank and investing it on Monday offers more safer
option than remaining invested over the weekend and bearing the losses (if any) due to
happenings over weekend.
Moreover this behavior varies from Investor to Investor and from Portfolio to Portfolio.
Generally regular investors and the major players are quite apprehensive of the weekend
volatility, and hence refrain from entering into riskier investments. The investor is also choosy
about selecting the months which have maximum yield, although uncertainty still plays its role,
but the investors plan their investment days and expected returns well in advance. Holidays in
stock markets also play a role in the volatility of the stock market. All such factors have been
analyzed in this study in the context of Indian stock markets.
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3. Background
With the introduction of electronic trading of shares in the country, the settlement dates and
means also observed a change. In the year 1999 SEBI (Securities and Exchange Board of India)
established trading in dematerialized from (electronic trading of shares). The rolling settlement
mechanism was introduced in 2000, allowing a settlement time of five days to the investors and
traders. In the year 2002, the number of days for settlement was changed to three days, only to
be modified again in 2003 and is finally at two days. This reduction in number of days for
settlement is certainly to reduce the risk associated with the number of days of settlement. In
order to overcome any effects due to change in the number of settlement days, the data will be
considered from April 2003- March 2006, because the fiscal year ends in March in India.
The stock market is operational for around 250 days out of 365 in a year, which along with
weekends includes holidays too. The investors are well apprised of the days in which the
market is operating and hence take the investment decisions accordingly to minimize the risk
and maximize the returns. So the investment decisions are expected to be based on the day of
the week to a certain extent, incorporating the effect due to a holiday. The holidays add to the
change in investors’ behavior and expectations, and if those are coupled with the weekends,
people are even more careful.
Volatility in general represents the standard deviation of returns. A histogram of returns, to a
first approximation will appear ‘normal’ but cannot be, because the return R>= -1, hence in
order to consider a normal distribution of the returns, we take the log normal values over a
period. The method of calculating log normal returns is described later and is a widely practiced
method.
Data and Tools
The data gathered is the Open, Close, High, Low and Volume figures of BSE-100 index (also
called the SENSEX) for each day in which the Bombay Stock Exchange was functional during
January 2003 – March 2007. The data is easily available through http://finance.yahoo.com/ and
www.google.com/finance . Tool used for the purpose is the basic spreadsheet software Microsoft Excel.
Freely available tools such as Open office spreadsheet can also be used for the purpose.
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4. Methodology
In order to analyze the calendar effects on the returns of investment during any particular
month, we calculate the return on monthly investment on BSE-100 index as per the formula -
Rm = ln(Pm end/Pd)
Where,
Pd = Price of the stock on any given day.
Pmend = Price of the stock at the end of the month.
Rm = Log normal return calculated at the month end on the investment done on any given day
of the month. In case the two prices are same the return will be zero.
The value of Rm is calculated for every day of the month except the end of the month and the
average of lognormal returns for each of the twelve months are plotted for all the four years
i.e. from 2003-2006. But before we proceed with such analysis, we need to check the
applicability of Gaussian distribution on the lognormal returns calculated for each year
separately. Separate graphs are plotted for each year using the Scatter plot feature in the MS
Excel.
The annualized volatility σ is the standard deviation σ of the instrument's logarithmic returns in
a year. The generalized volatility σT for time horizon T in years is expressed as:
Therefore, if the daily logarithmic returns of a stock have a standard deviation of σSD and the
time period of returns is P, the annualized volatility is
A common assumption is that P = 1 / 252 (there are 252 trading days in any given year). Then,
if σSD = 0.01 the annualized volatility is
In order to analyze the Weekend effect, we will calculate the log-normal returns using the
closing price of each day of the week and compare it with the opening price of the first day of
the next week. We will also consider the effect of holidays on various days of the week.
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5. Results
Analysis of daily log-normal returns of the BSE-100 Index in the year 2003, 2004, 2005 and 2006
shows that all these curves are bell shaped in general and hence can be considered to follow a
normal distribution in case of 2003, 2005 and 2006 as is indicated by low Kurtosis value for
these series, whereas, year 2004 observes exceptionally high Kurtosis value.
100
80
Frequency
60
40
20
0
2003
Annualized
Observations Std Dev Average Kurtosis Skewness
Volatility
250 0.01164 0.00219 0.075937 -0.144412 18.40%
140
120
100
Frequency
80
60
40
20
0
2004
Annualized
Observations Std Dev Average Kurtosis Skewness
Volatility
250 0.016277 0.000443 13.3222 -1.5017422 25.74%
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6. 120
100
80
Frequency 60
40
20
0
2005
Annualized
Observations Std Dev Average Kurtosis Skewness
Volatility
249 0.01086476 0.0014177 0.36737067 -0.4354632 17.14%
120
100
80
Frequency
60
40
20
0
2006
Annualized
Observations Std Dev Average Kurtosis Skewness
Volatility
247 0.016414 0.001552 2.895088 -0.45890727 25.80%
All these curves resemble bell shaped curves, as there are fairly less number of data points
(around 250 every year), the shape of the curves is not that of a perfect bell shaped curve. But
the population distribution very well confirms the applicability of the Gaussian rule.
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7. Calendar effect: After validating the applicability of Normal distribution to the log normal
returns of the BSE-100 index, we plot the monthly average value of log normal returns in these
years in order to know the months which are in safe for short term investments.
0.1
Average monthly return
0.05
Average Lognormal Returns
0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
-0.05
-0.1 2003 2004 2005 2006
-0.15
The graph shows months with all time positive returns in all the four years. The months safe for
investments as per the graphs are July, August, September, November and December as the
return is positive in all these months, whereas, in all the other months behavior keeps on
changing, from year to year. The average daily volume traded every month also shows the
investor habits. The graph below shows, the most favorable months in terms of high trade
volume. Very clearly April observes the least trading volume and is very much owed to the
beginning of new Fiscal year in India.
100%
Dec
90%
Nov
80% Oct
Average Volume Traded
70% Sep
60% Aug
Jul
50%
Jun
40% May
30% Apr
20% Mar
10% Feb
Jan
0%
2004 2005 2006
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8. Weekend effect: The daily lognormal return on various weekdays calculated as the natural
logarithm of ratio of stock index of next day to that of current day is as shown below. This
clearly shows that Monday as expected are very volatile in nature, where as the behavior on
Fridays is fairly stable across all the four years.
Average Daily log normal returns 0.005
0.004
0.003
0.002
0.001
0
Monday Tuesday Wednesday Thursday Friday
-0.001
-0.002
2003 2004 2005 2006
Gap effect: The plot between ‘the number of days’ till the next working day is referred as Gap
and the graphs below shows the effect of more number of gaps on the returns as well as the
trade volume in those days. Consecutive trading days i.e. all weekdays except Fridays have zero
gaps in case of no holiday, whereas Friday has two day gap in case of no holiday.
Average daily lognormal returns (2003-2006)
0.02
0.015
Average Log normal return
0
0.01
1
0.005 2
3
0
4
Monday Tuesday Wednesday Thursday Friday
-0.005
-0.01
The graph indicates that the Friday coupled with a holiday on Monday gives lesser returns as
compared to one with no holiday on Monday. Also Thursday with a holiday on Friday, gives a
gap of 3 days and shows negative return on the day the market opens. Monday with holiday on
next two days has similar effect. The settlement time of two days when added to these gaps
gives the total risk period.
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9. The graph below shows the average volume traded on various days of the week during 2003-
2006, along with the gap associated with that day.
Average volume traded (2003-2006)
Average Volume traded 100%
90%
80%
70% 4
60%
50% 3
40%
30% 2
20% 1
10%
0% 0
The graph clearly shows lesser trade volume on the days coupled with a holiday. Monday with a
two day gap and Wednesday with a four day gap have very fairly less volume than that of the
same day with no holiday. Also any day without a gap has lesser volume than normal day with
some gap except Tuesday.
Conclusion
The analysis carried out gives the results which are in accordance with the expectations and are
very well explainable on the basis of investor behavior in the Indian Market.
 The log-normal returns of BSE-100 index follow Gaussian distribution.
 Investor behavior changes on certain months of the year where as remains constant
during some months as is visible by the traded volume on certain months.
 Returns on some of the months are constantly positive, where as the market is highly
volatile across the years in consideration.
 Various weekdays behave differently in terms of the average daily returns. Although
none of them is consistent but still some are more profitable than the others.
 The investor behavior is different on different days. Fridays observe a lesser trading
volume as compared to the other days of the week.
 Holiday occurring on any day of the week has different effect on the index. With more
the number of gaps in between two trading days the risk associated increases and hence
a lesser trade volume is observed in those days.
All these results and conclusions are based on the result of the four years of data (2003-2006)
and after the T+2 days for settlement rule was established in the BSE.
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10. References
I. Weekends Can Be Rough: Revisiting the Weekend Effect in Stock Prices -Peter Fortune,
Federal Reserve Bank of Boston.
II. Dyl, Edward. 1988. $A Possible Explanation of the Weekend Effect, # Financial Analysts
Journal, May/June, pp. 83-84.
III. Groth, J., W. Lewellen, G. Schlarbaum, and R. Lease. 1979. “An Analysis of Brokerage
House Security Recommendations,” Financial Analysts Journal, pp. 32-40.
IV. Rogalski, Richard. 1984. “New Findings Regarding Day of the Week Returns Over Trading
and Non-Trading Periods,” Journal of Finance 39, pp. 1603-1614.
V. Miller, Edward. 1988. “Why a Weekend Effect?” Journal of Portfolio Management, 14-
Summer, pp. 42-48.
VI. www.investopedia.com
VII. Statistics for Management – Richard I. Levin, David S. Rubin
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