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ISSN 2229-6891 International Research Journal of Applied Finance Volume

 Volume.II
Issue.6 June 2011
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Contents

Testing for Seasonality in Option and Calendar Month: An
Empirical Investigation on the US Major Index Components
590 – 608

Rafiqul
Bhuyan

Determinants Influencing the Seasoned Equity Offerings: Private
Placements vs Rights Issue
609 – 621

Norhanim
Dewa & Izani Ibrahim

Effect on Security Prices and Volatility from Cross Listing
within the GCC Markets

622 – 630

Dr.
Abraham, Abraham

Cash Flow-Investment Sensitivity for Manufacturing Firms in
America, Japan and Taiwan

631 – 641

Feng-Li Lin &
Jui-Ying, HungDeterminants
of the ‘Decision to Finance’ in Micro Finance Institutions

Prof.
Fedhila Hassouna & Dr. Mehdi Mejdoub

Cost of equity in
emerging markets. Evidence from Romanian listed companiesCostin Ciora
Corporate Events’ Effect on Stock Returns: Evidence from Athens
Stock Exchange

692 – 715

Aristeidis
Samitas, Dimitris Kenourgios & Ioannis Tsakalos
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International Research Journal of Applied Finance ISSN 2229 –
6891Vol – II Issue – 6 June, 2011

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589

International Research Journal of Applied Finance ISSN 2229 –
6891Vol – II Issue – 6 June, 2011

Testing for
Seasonality in Option and Calendar Month: An Empirical Investigation on the US
Major Index Components

Rafiqul
Bhuyan,
PhD

Associate
Professor of Finance
Dept. of
Accounting & Finance
College
of Business & Public Administration
California State
University

San Bernardino

CA 92407 rbhuyan@csusb.edu

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International Research Journal of Applied Finance ISSN 2229 –
6891Vol – II Issue – 6 June, 2011

Abstract

Using
all securities from Dow 30, S&P 100 and S&P 500 indices respectively we
show that Option month based monthly returns and volatilities are different
from those of calendar month. These differences may explain the worthiness of
options contracts on call and put options when they expire. We conclude the
option expiration effect may explain the differences in return in option month
compared to the calendar month. Our result contributes to the existing
literature by offering evidence of return differences in option month what
support the option expiration effect. When security returns are analyzed based
on calendar month and option month to test for seasonality, our results support
the findings of the existing literature in terms of the calendar month. Our
findings contribute to the literature by adding the result that when security
returns are analyzed based on the option month; it also shows the seasonal
pattern. Our both results could be the added evidence against the weak-form
market efficiency.

I.
Introduction

Seasonality
in financial market is widely investigated in finance literature. It is
addressed by investigating the abnormal returns in the month of January, day of
the week, tax loss selling effect, among other effects. When analyzing the
January effect, it is the calendar month January effect addressed in the
literature. However, there remains to be seen the effect of option month in
return pattern. Option month’s beginning and ending dates are from two calendar
months. The third Friday of a month marks the ending day of the option month
and the Monday after the third Friday marks the First day of the option month.
Trillions of dollar transaction takes place in option markets to profit from
the movement of the underlying assets. That makes the option month a special
case and event for stock market. The intent of this current research is to
analyze the option month effect whether it adds as an additional anomaly in
financial market.

II.
Literature Review

The
January effect has been widely studied to see if a profitable investment
strategy exists. The key explanations for the January effect are: the year-end
tax-loss-selling hypothesis (e.g., Branch (1977), Dyl (1977), and Schultz
(1985)); the window-dressing hypothesis (e.g., Haugen and Lakonishok (1988),
and Ritter and Chopra (1989)); turn-of- the-year ‘liquidity’ hypothesis (e.g.,
Ogden (1990)); accounting information hypothesis (e.g., Rozeff and Kinney
(1976)), and bid-ask spread (e.g., Keim (1989)). However, Bhardwaj and Brooks
(1992) conclude that for typical investors, the January anomaly of low-price
stocks outperforming high-price stocks cannot be used to earn abnormal returns.
Mills and Coutts (1995) report that even if calendar effects are persistent in
their occurrence and magnitude, the costs of implementing trading rules is
prohibitive. Draper and Paudyal (1997) find that although it appears to be
feasible to earn a high nominal return by trading on seasonality, it does not
appear to be feasible to earn excess returns after allowance for transaction
costs. Booth and Keim (2000) also conclude that the January effect is ‘alive’
but difficult to capture.

On
the other

hand,
Ko (1998) gives
some favorable evidence
on the economic

exploitation of

seasonalities.
Specifically, he investigates the effects of international

diversification on the
stock market monthly seasonality from an economic point of view. He finds that
the strategy using monthly seasonality outperforms a buy-and-hold strategy. De
Bondt, Thaler and Bernstein (1985), found that investors over-reacted to
unexpected news. Stocks that performed well in the previous periods (winners),
and stocks that performed poorly in the

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International Research Journal of Applied Finance ISSN 2229 –
6891Vol – II Issue – 6 June, 2011

previous
periods (losers), both tended to revert back to their mean value in the
subsequent periods. In a psychological study, Kahneman and Tversky (1982)
document individuals over-reacting to new information, whether good or bad. If
over-reaction behavior occurs, profitable contrarian trading strategies, buying
past losers and selling past winners can be formed. Smirlock and Starks (1986)
report the negative Monday effect in stock returns has been “moving
up” in time. Johnston, Kracaw, and McConnell find similar results (for
GNMAs, this effect occurs after December 1984. For T-bonds, the negative
Wednesday occurs before January 1981) of Gay and Kim (1987) and Chang and Kim
(1988), who document the disappearance of Monday effects in the commodities
futures index.

III.
Data and Methodology

The
data in this research is taken from PC QUOTES for stocks of three US indices:
Dow Jones Industrial Average, S&P 100, and S&P 500 respectively. Stocks
of each of these indices are analyzed from the period beginning 1970 to the end
of 2001. We sort the stock price data for each stock based on calendar month
and option months and estimate two different monthly returns and standard
deviations respectively. We then organize times series of monthly returns and
standard deviation of each stock according to month. For example, we pool all
monthly returns of January (only) from 1970 to 2001 and averaged over this
period to estimate mean January return for a stock. Similarly mean monthly
return for all other months are estimated. This process is followed to estimate
mean monthly return for both calendar month and option month. Then a cross
section of all stocks’ monthly returns are pooled together to conduct different
econometric analysis.

Once
the data are processed and pooled, we first test for the equality of mean
return and volatility for calendar month and option month, i.e., for return, if
the mean calendar month January returns is equal to mean option month January
return and so on. Our hypothesis is that there is no difference between the
return and volatilities of these two types of months. Second, we also test if
there is any seasonality in monthly return. We conduct the seasonality test on
both calendar month and option month returns. Our test hypothesis would be that
there is no difference between returns in different option months. Using the F
test we investigate if the seasonality persists in return pattern of the option
months. If the calendar month and option month returns are not the same then
the second issue is of our importance. Third, if seasonality exists in options
month then we investigate if one can capture abnormal returns from the
seasonality in options month by applying some trading rules.

IV.
Econometric Analysis:

We propose that the
mean return of the calendar month return and option month return are equal. So
our formal hypothesis is:

H0:µOM

= µCM

(1)

Ha:µOM

? µCM

Here,
µOM indicates the mean option month return, andµCM indicates the calendar month mean

return. This hypothesis is tested under
two different circumstances: when the variance of calendar month and option
month are same and when they are different. Similarly, the equality

592

International Research Journal of Applied Finance ISSN 2229 –
6891Vol – II Issue – 6 June, 2011

of monthly variance is
tested to see if the variance based on option month is equal to that of
calendar month. So, our test hypothesis is of the following form:

H0:?OM2

=?CM2

(2)

Ha:?OM2

? ?CM2

Next we investigate the
seasonality in monthly returns on both calendar month return and on option
month return. The regression equation that addresses this issue is as follows:

Rt =?+?1D1t+?2 D2t+?3 D3t+?4 D4t+???????+?11D11t+?t (3)

The
dependent variable, Rt is the stock’s monthly return at time t,?t is the white noise error

term.
? ,
the constant, in the right hand side of the equation identifies the monthly
return for the

month
of January. The

seasonal dummy variables are defined
by the D1t
,………, D12,t where

1,

for

the

ith

month

Di
t =

otherwise

and month
begins from the second month ( February) of the

0,

year and hence

i =

2, ——,12,
indicates the difference in return between January and the ith

month
of the year.

V.
Results:

V.1
Summary Statistics:

We
calculate returns on calendar month and option month and is presented in Table
1. Table 1A shows the calendar month based monthly returns for the 30 DOW
components from period 1970-2001. Results are pooled by the month. It is shown
in the table that on an average the DOW components offer the lowest return of
-0.686% in the month of September and highest return of 2.89% in the month of
January.
Please
insert Table 1A and 1B about here

Looking at the results one would presume
that historically, September and August are the two worst months for DOW
components and January, December, and November are the best months. In Table 1B
it is observed that option period average monthly returns offer different
returns. The worst average return for the DOW components comes in October
option month with -0.118% and the highest average return comes in January
option month with 2.602%. Historically, October and September offer the worst
returns and January, November, December, and February offer the best returns.

Table
2A offers the summary statistics of historical returns for S&P 100
components based on the calendar month. Results show that S&P 100
components offer worst return in the month of April with average return of
-3.747% and best return in the month of January with average return of 3.268%.

Please insert
Table 2A and 2B about here

Table 2B shows the
summary statistics of historical returns for S&P 100 components based on
the option month. On average, S&P 100 components offer worst return in the
option month of October with average return of -0.051% and best return in the
option month of January with average return of 2.823%.

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International Research Journal of Applied Finance ISSN 2229 –
6891Vol – II Issue – 6 June, 2011

Table 3A presents the
summary results of historical average returns for S&P 500 components based
on calendar month. It shows that April calendar month offers the worst average
ret urn of – 6.937% and January calendar month offers the highest average
return of 3.449%.
Please
Insert Table 3A and 3B about here

When
data are arranged based on option months, the summary results are shown in
Table 3B. It shows that the lowest return comes in the October option month
with average return of 0.102% and the highest return comes in the option month
of January with average return of 4.078%.

V.2
Results for Mean-Variance Equality Test

Table
4-6 shows the test results on S&P 100 components. When the mean returns,
based on calendar month and option months, are tested they are done under two
different assumptions: once it is tested assuming the variances (based on
calendar month and option month respectively) are equal and next when assumed
that variances are not equal.
Please
Insert Table 4, 5, and 6 about here
In
both cases our test results show that the null hypothesis is rejected implying
that the mean return based on calendar month and that of option month are
different. Next we conduct a variance equality test and result indicates that
even variance calculated based on calendar month and on option month is
different.

We conduct the similar
tests on the DOW 30 components. Table 7, 8, and 9 show the test results. When
assumed that the variance calculated based on calendar month and option month
are equal, our mean equality test indicate the similar result that we find in
S&P 100 components: the means are not equal.

Please Insert
Table 7, 8, and 9 About Here

Also, when assumed the
variances are not equal, the mean returns turn out to be different. The tests
for variance equality also show that the variances are not equal either.
Please Insert
Table 10, 11, and 12 About Here

Finally,
we conduct the similar tests on S&P 500 components. The test results are
identical to those of S&P 100 and DOW 30 Components.
The main conclusion we
can draw from our findings is that monthly returns show a pattern when they are
estimated based on the option period. Outstanding options contracts, whose
value depend on the third Friday’s closing price, whether they are worthless or
not and hence exercised or not may have some impact on the closing price of the
Third Friday and that may make the monthly return and variances to be different
from calendar month.

V. 3
Results for Seasonality Test

Seasonality tests are
done both on calendar month return and on option month returns. Table 13 shows
the seasonality test results conducted on S&P 500 components.
Please Insert
Table 13 and 14 About Here

Results
indicate that there is a seasonal pattern exists in the calendar month returns.
Table 14 shows the seasonality test results of option month returns. It is
quite clear that there is a seasonal pattern in return structure of the option
month as well. One difference we like to include is the T statistics for the
month of December. Calendar month show that it is insignificant where as the
Option month based T statistics shows that it is significant.

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