Unique Calendar Effects in the Indian Stock Market: Evidence and Explanations

Abstract

Covering 20 years (1995–2015), the article ascertains the presence of the month-of-the-year effect in the Indian stock market, for the raw returns series as well as after adjusting for non-linearities of the market. Whether the effect is the same for portfolios of different sizes and values is also ascertained. The threshold generalised autoregressive conditionally heteroskedastic (TGARCH) model is employed to address non-linearity. The results suggest the presence of higher returns in November/December at the index level. Further, only firms with a size smaller than the average exhibit seasonality in the form of the April/May and November/December effect. The value-sorted portfolios exhibit weaker evidence of the December effect. Tax-loss selling, window dressing and behavioural aspects seem to provide the explanation.

JEL Classification: C58, G14

Keywords

Market efficiency anomalies calendar effect ARCH models Indian stock market

1. Introduction

Market efficiency measures the ability of a stock market to incorporate the available information and reflect it in the stock prices as quickly as possible (Bodie, Kane, & Marcus, 2014). While the concept of market efficiency originated as early as the 1950s,¹ the dynamic stock market has not let research in this area diminish. Rather, the concept of efficiencies has led to the concept of anomalies, the signs of inefficiencies observed in real practice, and this area of research is still far from maturing. Hawawini and Keim (1998) stated, ‘…Research over the next 100 years will, we hope, settle many of these issues’.

The calendar anomaly (or the calendar effect) refers to the tendency of stock returns to exhibit certain patterns that could be associated with certain times of the calendar (Philpot & Peterson, 2011). The month-of-the-year effect refers to a specific form of the calendar anomaly where the returns exhibit different patterns across different months of the year. Gallagher and Pinnuck (2006) contended that a priori there were reasons to suspect that the calendar anomaly could be associated with size (market capitalisation) and value (price-to-book ratio or P/B ratio) of the stocks. One of the most prominently cited reasons in literature for the explanation of monthly seasonality (the January effect being the most frequent) is the tax-loss selling hypothesis² (Jacobs & Levy, 1988b). Keim (1983) argued that smaller-sized stocks were more likely than larger stocks to undergo tax-loss selling. On a similar line, Gallagher and Pinnuck (2006) argued that value stocks (stocks with low P/B ratios) were more likely to be sold than growth stocks (stocks with high P/B ratios) to undergo tax-loss selling. This article aims to ascertain the behaviour of the month-of-the-year effect across firms of varying sizes and values in the Indian stock market.

The motivations for this study are many. Chang, Faff, and Hwang (2010) and Lam and Tam (2011) stated that studies based on non-US data provided out-of-sample evidences to test anomalies, and this study endeavours to provide the same. Moreover, Truong (2011) and Cakici, Fabozzi, and Tan (2013) acknowledged the growing relevance of Asia-Pacific economies and emerging markets (respectively) at the global level and recommended more studies to be conducted on these markets. National Stock Exchange of India Limited (NSE) (2015) stated that India was heading to become the fastest-growing major economy of the world. The projections by the International Monetary Fund World Economic Outlook (2016) also reflected the growing importance of Indian economy at the global level. The stock market is seen as a barometer of a nation’s economy (Tiwari & Chaudhari, 2014); therefore, testing the level of informational efficiency of the Indian stock market is a topic of global interest. Further, Truong (2011) reported that the presence of foreign investors contributed towards better informational efficiency in stock markets. Therefore, to attract foreign (as well as domestic) investors, an update on the level of efficiency of the market is important. The findings of the study could be relevant for the stock market investors, as it would provide them inputs to design and time their investment activities. Finally, as evident in the section on literature review, the study on the interaction of calendar anomaly with other anomalies is a less-researched area for the Indian stock market. This study aims to fill this gap as well.

For better exposition, the article is divided into four sections. The second section summarises the literature review. Objectives, data and methodology are explained in the third section. The fourth section presents the analysis of the findings, and the conclusion is presented in the fifth section.

2. Literature Review

Studying seasonal patterns has been an area of interest for both practitioners and academicians. Literature on the stock market is inundated with various forms of calendar anomalies studied across economies—turn-of-the-year effect, month-of-the-year effect, turn-of-the-month effect, day-of-the-week effect, holiday effect, Halloween effect, Friday the 13th effect, etc. (Auer & Rottmann, 2014; Carchano & Pardo, 2015; Jacobsen & Visaltanachoti, 2009; Kayacetin & Lekpek, 2016; Ng & Wang, 2004; Raj & Kumari, 2006; Singh, 2014). Seasonal patterns have been reported in other markets and series as well—national businesses and economic series (Cleveland & Devlin, 1980), petrol prices (Mitchell, Ong, & Izan, 2000), money market (Washer, Nippani, & Wingender, 2011), real estate investment trusts (Khaled & Keef, 2012), bonds (Compton, Kunkel, & Kuhlemeyer, 2013), currency market (Kumar & Pathak, 2016) and so on.

However, results are far from the consensus. Coutts and Sheikh (2002) reported instances of the non-existence of calendar patterns. Doyle and Chen (2009) reported that seasonal patterns in returns were not consistent over time. Evidence of decline as well as reversal of seasonal patterns was reported by Dubois and Louvet (1996), Tan and Tat (1998), Kohers, Kohers, Pandey, and Kohers (2004), Chong, Hudson, Keasey, and Littler (2005) and Worthington (2010). Urquhart and Hudson (2013) argued that the markets were adaptive and the level of efficiency changed over time. The change in the nature of calendar anomaly due to events like the financial crisis was reported by Hui (2005) and Vasileiou and Samitas (2015).

In addition to the diverse findings of researchers in the past, the methodologies employed for these findings are equally diverse. While the ordinary least square (OLS)-based dummy variable regression equation was initially the conventional methodology in the literature on anomalies (Arsad & Coutts, 1997), several methodologies have been tested over time—the analysis of variance (ANOVA) (Mittal & Jain, 2009; Rogalski, 1984), the autoregressive conditionally heteroskedastic (ARCH) model and its variants (Abalala & Sollis, 2015; Akyol, 2011; Baker, Rahman, & Saadi, 2008; Jaisinghani, 2016; Kayacetin & Lekpek, 2016; Zhang & Li, 2006), event study (Bialkowski, Etebari, & Wisniewski, 2012), non-parametric tests (Carchano & Pardo, 2015; Elango & Macki, 2008; Mitchell et al., 2000), stochastic dominance (Al-Khazali, 2008) and so on. Zhang and Li (2006) reported that calendar anomaly was subject to sample selection and the methodology utilised. Baker et al. (2008) reported that findings were subject to the distributional assumptions of the underlying data.

Another area of interest was the interaction of calendar anomalies with other identified anomalies. One of the earliest occurrences of monthly calendar anomaly in the literature was in the form of ‘small firm in January effect’ (Blume & Stambaugh, 1983; Keim, 1983; Reinganum, 1983)—the January effect was construed as an explanation to the contemporarily existing size effect.³ Ever since, there have been several studies on the interaction of calendar anomalies with other anomalies. Jacobs and Levy (1988a) provided a review of literature on the studies that addressed the interrelationships of different anomalies. Table 1 presents a summary of such papers.

Table 1.
Studies on the Interaction of Calendar Effect with Other Anomalies

Author(s) Year Region Period Studied Issue Studied

Rogalski 1984 USA 1963–1982 Size and Monday/January/holiday effect

Wahlroos and Berglund 1984 Finland 1970–1981 Size and turn-of-the-year effect

Kato and Schallheim 1985 Japan 1964–1980 Size and January effect

Jacobs and Levy 1988a USA 1978–1986 Size, value, January effect and other anomalies

Jaffe, Keim, and Westerfield 1989 USA 1951–1986 Size, value and January effect

Fortin 1990 USA 1973–1985 Size and day-of-the-week effect

Cadsby 1992 USA 1963–1985 Beta and January effect

Hawawini and Keim 1998 USA and others 1962–1994 Size, value, momentum and January effect

Mills, Siriopoulos, Markellos, and Harizanis 2000 Greece 1986–1997 Size and calendar effect

Jacobsen, Mamum, and Visaltanachoti 2005 USA 1926–2004 Size, value, January effects and other anomalies

Haug and Hirschey 2006 USA 1802–2004 Size and January effect

Cao, Premachandra, Bhabra, and Tang 2008 New Zealand 1967–2006 Size and pre-holiday effect

Swinkels and Vliet 2010 USA 1963–2008 Size, value and five calendar effects

Chou, Das, and Rao 2011 USA 1926–2004 Size, value and January effect

Sharma and Narayan 2012 USA 2000–2008 Size and day-of-the-week effect

Author(s)	Year	Region	Period Studied	Issue Studied
Rogalski	1984	USA	1963–1982	Size and Monday/January/holiday effect
Wahlroos and Berglund	1984	Finland	1970–1981	Size and turn-of-the-year effect
Kato and Schallheim	1985	Japan	1964–1980	Size and January effect
Jacobs and Levy	1988a	USA	1978–1986	Size, value, January effect and other anomalies
Jaffe, Keim, and Westerfield	1989	USA	1951–1986	Size, value and January effect
Fortin	1990	USA	1973–1985	Size and day-of-the-week effect
Cadsby	1992	USA	1963–1985	Beta and January effect
Hawawini and Keim	1998	USA and others	1962–1994	Size, value, momentum and January effect
Mills, Siriopoulos, Markellos, and Harizanis	2000	Greece	1986–1997	Size and calendar effect
Jacobsen, Mamum, and Visaltanachoti	2005	USA	1926–2004	Size, value, January effects and other anomalies
Haug and Hirschey	2006	USA	1802–2004	Size and January effect
Cao, Premachandra, Bhabra, and Tang	2008	New Zealand	1967–2006	Size and pre-holiday effect
Swinkels and Vliet	2010	USA	1963–2008	Size, value and five calendar effects
Chou, Das, and Rao	2011	USA	1926–2004	Size, value and January effect
Sharma and Narayan	2012	USA	2000–2008	Size and day-of-the-week effect

Source: Authors’ compilation.

There are two points worth highlighting with reference to the Indian stock market: there are very limited studies which take care of non-linear aspects of the stock market and accordingly employ sophisticated tools and second, while the interaction of calendar anomaly with other anomalies is studied for other stock markets, little attention has been paid to this aspect of the Indian stock market. This study is an attempt to enrich the literature by addressing these gaps.

3. Objectives, Data and Methodology

3.1 Objectives

The primary objective of the article is to examine the presence of month-of-the-year effect in returns of the Indian stock market. First, the article ascertains if monthly seasonality exists at the market level. Then, the article tests if this seasonality is the same across portfolios with different inherent characteristics—market capitalisation and P/B ratio.

3.2 Data

The study is based on the Nifty 500 Index and its constituent companies. The date of sample selection is 31 March 2014. The study covers a period of 20 years, from October 1995 to September 2015.⁴ The variables involved are as follows:

Returns: Monthly returns are calculated using closing prices.

Market capitalisation: It is taken as the measure of size.

P/B ratio: It is taken as the measure of value.

The data are taken from Ace Equity^®, a financial database for Indian companies.

3.3 Methodology

First, monthly returns for the NSE 500 Index series is calculated as follows:

R_{t} = [\frac{P_{t} - P_{t - 1}}{P_{t - 1}}] * 100,

(1)

where R_t is the return at time t and P_t and P_t_-1 are prices at time t and t−1, respectively.

To test seasonality at the index level, the regression equation with 12 dummies (1 for each month of the year) is employed. No constant term is included in the equation to avoid the dummy variable trap (Brooks, 2014).

\begin{matrix} R_{t} = γ_{1} J A N D U M_{t} + γ_{2} F E B D U M_{t} + γ_{3} M A R D U M_{t} + \\ γ_{4} A P R D U M_{t} + γ_{5} M A Y D U M_{t} + γ_{6} J U N D U M_{t} + \\ γ_{7} J U L D U M_{t} + γ_{8} A U G D U M_{t} + γ_{9} S E P D U M_{t} + \\ γ_{10} O C T D U M_{t} + γ_{11} N O V D U M_{t} + γ_{12} D E C D U M_{t} + u_{t} \end{matrix}

(2)

where JANDUM_t to DECDUM_t are dummy variables for each month (from January to December), taking the value of 1 if the returns pertain to that month and 0 otherwise; γ₁ to γ₁₂ are coefficients for corresponding months; and u_t is the error term, $u_{t} \sim N (0, σ_{t}^{2}) .$

To test the presence of monthly seasonality across firms varying in sizes and values, the constituent companies of the index are divided into portfolios—10 size-sorted and 10 value-sorted portfolios are constructed.

For the purpose of portfolio creation, only the firms whose accounting years span from April to March are included. This captures around 88 per cent of the records. The process of portfolio creation is as follows:

Size-sorted portfolios: Every year in September end, firms are sorted on the basis of September-end market capitalisation. Following the literature (Agarwalla, Jacob, & Varma, 2013; Fama & French, 1993), portfolios are created after 6 months from the accounting year end. This is to ensure that the accounting data are available publicly at the time of portfolio formation. Extreme 5 per cent of the data is trimmed from both ends to lessen the influence of outliers in driving the results. For the resulting cases, 10 portfolios are formed using deciles as the break points.

Value-sorted portfolios: Every year in September end, firms are sorted on the basis of March-end P/B ratios. To lessen the influence of outliers in driving the results, cases with P/B ratios <1 are excluded. Further, following the approach of Singh, Jain, and Yadav (2016), cases with P/B ratios >5 are also considered as outliers and excluded. Similar to size-sorted portfolios, 10 value-sorted portfolios are formed using deciles as break-points.

P1 represents the portfolio of the firms with the smallest market capitalisation or lowest P/B ratios, while P10 represents the portfolio of the firms with the largest market capitalisation or highest P/B ratios. Value-weighted monthly returns are calculated for each portfolio using market capitalisation as the weights. The regression equation with 12 dummies (Equation [2]) is then applied on these portfolios individually.

However, the Indian stock market has been reported to exhibit non-linearity in the form of leptokurtosis, volatility clustering, and leverage effect⁵ (Singh et al., 2016). Tsay (2005) contended the employment of volatility models to account for non-linearity. Therefore, the article evaluates the seasonal pattern in returns for both the index and the sorted portfolios (both size and value) using the Glosten, Jagannathan, and Runkle (GJR) (1993) volatility model, also known as the threshold generalised autoregressive conditionally heteroskedastic (TGARCH) model.

Under the GJR model, the conditional mean equation (Equation [2]) is further augmented with a second equation on conditional variance (Equation [3]). The conditional variance equation is:

σ_{t}^{2} = α_{0} + α_{1} u_{t - 1}^{2} + β σ_{t - 1}^{2} + γ u_{t - 1}^{2} I_{t - 1},

(3)

where

$σ_{t}^{2}$ and $σ_{t - 1}^{2}$ are conditional variances of u_t and u_t_-1, respectively.

u_t and u_t_-1 are the error terms at time t and t−1, respectively.

α₀, α_1, β and γ are the parameters of the equation.

I_t_-1 takes the value 1 when u_t_-1 < 0, 0 otherwise.

As is evident in Equation (3), in this model, the conditional variance of the error term ( $σ_{t}^{2}$ ) is allowed to depend on the lagged value of the error term ( $u_{t - 1}^{2}$ ) as well as its own lagged value ( $σ_{t - 1}^{2}$ ). This takes care of leptokurtosis and volatility clustering. The term that switches values between 0 and 1 takes care of the leverage effect. The parameters are estimated using maximum likelihood estimates. A log-likelihood function (LLF) is formed and the parameter values that maximise it are obtained using an iterative process. The Marquardt algorithm is employed for the iteration.

4. Analysis

Table 2 and Figure 1 summarise the time series average of the monthly returns for the Nifty 500 Index across different months of the year. The data reveal that over the past 16 years, December, on an average, offered the highest return, of 4.91 per cent, per month. It was followed by November that offered an average return of 4.06 per cent per month.

Table 2.
Time Series Average of Returns in Different Months of the Year (1999–2015)

Month Average of Returns

January −0.23

February 0.55

March −1.13

April 1.14

May 1.26

June 0.89

July 1.64

August 2.30

September 1.50

October −0.14

November 4.06

December 4.91

Month	Average of Returns
January	−0.23
February	0.55
March	−1.13
April	1.14
May	1.26
June	0.89
July	1.64
August	2.30
September	1.50
October	−0.14
November	4.06
December	4.91

Source: Authors’ computation.

Note: Figures are in per cent per month.

Figure 1.

Source: Authors’ computation.

The time series average of monthly returns for the 10 size-sorted portfolios is summarised in Table 3 and Figure 2. For the 10 value-sorted portfolios, similar data are presented in Table 4 and Figure 3.

Table 3 and Figure 2 depict that on an average, portfolios have a general tendency to generate higher returns in April and December. Returns for January are negative for all the portfolios. For all the portfolios, returns increase from March to April. Returns also increase from October to November and are further higher in December.

Table 3.

Time Series Average of Returns in Different Months of the Year Across Size-sorted Portfolios (1995–2015)

Month	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10
January	−1.55	−1.25	−0.79	−1.10	−1.59	−1.25	−1.20	−1.20	−0.74	−0.46
February	−0.44	0.05	0.01	0.61	0.48	0.37	0.63	0.90	1.56	1.75
March	−1.00	0.83	−1.02	0.51	0.25	−0.22	4.57	0.24	−0.43	0.19
April	8.48	6.09	7.12	5.94	4.58	5.23	5.08	4.44	3.60	3.73
May	4.61	4.30	6.58	5.10	3.35	5.52	4.67	2.53	2.33	1.99
June	2.36	1.79	1.95	0.79	−0.47	0.13	0.14	0.42	0.04	0.90
July	3.55	3.71	2.52	2.29	2.52	0.91	2.54	1.37	1.54	1.32
August	3.54	2.74	4.94	3.51	2.53	2.37	1.93	1.69	0.72	1.16
September	1.12	1.23	1.67	0.81	0.31	0.95	1.36	1.51	2.21	1.01
October	0.03	−0.65	−0.62	0.09	−1.39	−0.75	−0.76	−0.30	−0.67	−0.34
November	3.21	1.54	2.87	1.33	0.96	1.72	2.45	2.14	2.22	1.65
December	8.71	7.56	7.69	5.98	7.92	5.60	7.72	5.59	5.86	4.64

Source: Authors’ computation.

Note: Figures are in per cent per month.

Figure 2.

Source: Authors’ computation.

Table 4 and Figure 3 depict seasonality across value-sorted portfolios. While no specific trend persists across portfolios across all the months, returns in general demonstrate a rising trend from October to November and further until December. It then demonstrates a fall in January. April experiences an increase in returns when compared from March across all portfolios.

Table 4.

Time Series Average of Returns in Different Months of the Year Across Value-sorted Portfolios (1995–2015)

Month	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10
January	−1.45	−0.08	−1.05	0.27	−2.61	−0.70	−0.41	−0.56	−0.77	0.77
February	−0.75	2.70	1.07	3.47	1.02	0.45	2.16	2.75	0.07	1.01
March	0.68	−2.57	3.69	−1.26	−0.66	0.78	−1.01	0.96	−0.48	−0.06
April	3.45	3.69	4.28	1.70	1.96	3.80	6.54	2.80	3.22	3.58
May	5.62	0.05	3.12	1.16	1.69	3.82	3.44	3.01	3.35	1.45
June	0.12	0.92	−0.54	0.63	0.81	−1.12	1.81	−0.12	0.35	−0.76
July	0.21	2.92	0.03	3.04	1.78	1.96	1.19	1.49	3.66	1.27
August	−1.21	−1.45	0.69	0.68	2.49	1.08	0.27	0.17	3.10	2.17
September	2.13	−0.27	0.71	1.19	2.63	−0.19	2.50	2.17	1.16	2.50
October	−1.28	0.66	−0.51	−0.54	−0.13	−1.61	0.36	−0.19	0.28	−0.90
November	2.22	1.40	4.35	0.92	1.32	2.79	2.48	−0.11	1.91	3.79
December	2.62	4.66	7.42	6.27	7.89	7.28	4.99	4.22	4.13	6.20

Source: Authors’ computation.

Note: Figures are in per cent per month.

Figure 3.

Source: Authors’ computation.

The results so far exhibit that there indeed is variation in returns across different months of the year, and the pattern is almost similar for size-sorted portfolios and value-sorted portfolios. However, the above results are based on the raw return series, without taking into consideration the non-linear aspects prevalent in the stock market.

Tables 5–7 summarise the results based on the GJR model.

Table 5 summarises the result of the application of the model on the Nifty 500 Index’s monthly returns. Unlike the results of Table 3 where the highest returns were recorded in December followed by November, after adjusting for the underlying non-linearity in the data, November offers the highest returns, of 3.74 per cent per month, followed by December, with an average of 3.29 per cent per month. While January continues to record negative returns along with February, the magnitudes are statistically insignificant. None of the months except November and December offer statistically significant returns.

Table 5.

Application of TGARCH Model on Nifty 500 Index (1999–2015)

Variable	Coefficient	p-Value
Mean equation
JANDUM	−0.15	0.93
FEBDUM	−0.19	0.93
MARDUM	0.06	0.97
APRDUM	0.20	0.93
MAYDUM	1.36	0.28
JUNDUM	1.52	0.49
JULDUM	0.70	0.76
AUGDUM	0.93	0.57
SEPDUM	2.79	0.06
OCTDUM	1.34	0.39
NOVDUM	3.74**	0.05
DECDUM	3.29*	0.09
Variance equation
α₀	3.43	0.23
α₁	0.18**	0.05
γ	−0.02	0.81
β	0.78***	0.00

Source: Authors’ computation.

Note: ***, ** and * depict significance at 1%, 5% and 10% levels, respectively.

Table 6 summarises the results of the model for size-sorted portfolios. The most consistent seasonal pattern is the high returns of December. December returns are positive and statistically significant for portfolios P1–P9 (ranging from 4.83 per cent per month for P9 to 8.61 per cent per month for P1). However, though positive (3.63 per cent per month), it is statistically insignificant for the portfolio with firms having the highest market capitalisation (P10). Besides, portfolios P1–P8 exhibit statistically significant returns in April and/or May (ranging from 2.99 per cent per month for P3 in April to 6.32 per cent per month for P1 in April). This pattern is again not evident in portfolios with higher market capitalisation firms—P9 and P10.

Thus, the results signify that monthly seasonality in returns is not consistent across firms of all sizes. Agarwalla et al. (2013) stated that the mean market capitalisation of Indian firms was close to the ninth decile value. Thus, it can be concluded that while the firms with sizes less than the average market capitalisation exhibited higher returns in April and/or May and December, no seasonal pattern was evident in firms that are more than the average size.

A possible explanation for the presence of the April/May effect at the portfolio-level data, when the pattern is not evident at the index level, is that the strength of the coefficients are not consistently high across all the portfolios for any particular month. Thus, high coefficients for some portfolios might be mellowed down by not-so-high coefficients for the remaining portfolios.

Table 6.

Application of the GJR Model on Size-sorted Portfolios (1995–2015)

(a) Mean Equation
Variable	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10
JANDUM	−0.11	0.08	0.41	−0.05	−1.09	−0.51	−1.66	−1.37	−1.48	−0.80
	0.97	0.97	0.86	0.98	0.63	0.81	0.62	0.50	0.38	0.60
FEBDUM	−0.19	0.03	−0.75	0.44	−0.43	−0.63	1.00	0.86	0.73	0.62
	0.95	0.99	0.73	0.83	0.85	0.70	0.81	0.73	0.70	0.76
MARDUM	−1.22	1.04	−1.78	−1.01	−0.78	−1.19	4.67**	0.86	0.00	0.33
	0.52	0.58	0.28	0.56	0.64	0.34	0.05	0.67	1.00	0.84
APRDUM	6.32***	5.23**	2.99*	2.83	1.18	1.01	4.61	4.86**	2.13	2.97
	0.01	0.02	0.09	0.12	0.60	0.62	0.15	0.02	0.30	0.15
MAYDUM	2.88	3.11*	4.47**	3.87**	2.46	4.00**	5.35**	1.09	0.29	−0.29
	0.15	0.06	0.02	0.04	0.18	0.03	0.03	0.48	0.86	0.84
JUNDUM	1.96	1.26	1.39	0.63	−0.85	−0.65	−0.21	0.77	1.24	1.11
	0.29	0.55	0.39	0.73	0.69	0.75	0.94	0.66	0.43	0.54
JULDUM	2.80	4.84***	2.78	2.53	2.41	0.77	3.12	2.00	0.73	0.05
	0.18	0.01	0.28	0.35	0.24	0.76	0.31	0.31	0.69	0.98
AUGDUM	3.54	3.24*	5.03**	3.75*	2.91	1.33	2.36	2.35	−0.43	0.38
	0.20	0.10	0.02	0.07	0.20	0.54	0.53	0.22	0.84	0.84
SEPDUM	2.49	2.16	2.61	1.85	1.94	1.80	0.74	3.08	3.01*	1.65
	0.22	0.30	0.15	0.38	0.32	0.33	0.84	0.12	0.09	0.27
OCTDUM	−0.25	−0.53	−0.65	0.28	−0.11	0.16	−1.29	0.77	−0.24	0.89
	0.93	0.85	0.78	0.91	0.97	0.95	0.68	0.71	0.90	0.59
NOVDUM	2.67	0.98	3.41*	1.76	1.75	2.64	1.36	3.27	−0.02	1.36
	0.20	0.62	0.06	0.28	0.31	0.12	0.64	0.13	0.99	0.47
DECDUM	8.61***	7.28***	7.54***	5.93*	7.09***	5.11**	8.48***	5.83***	4.83**	3.63
	0.00	0.00	0.00	0.06	0.01	0.02	0.01	0.01	0.02	0.14
(b) Variance Equation
Variable	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10
α₀	76.10***	84.65***	47.84***	59.10***	50.24***	38.28***	44.47	12.23***	0.61	4.40
	0.01	0.00	0.00	0.00	0.01	0.00	0.20	0.00	0.47	0.17
α₁	0.46***	0.39**	0.64***	0.52***	0.49***	0.59***	−0.01	−0.05***	−0.08***	0.06
	0.01	0.02	0.00	0.00	0.00	0.00	0.32	0.00	0.00	0.27
γ	−0.37**	−0.29	−0.50***	−0.37**	−0.28	−0.32	−0.07	0.17***	0.11***	0.15
	0.03	0.11	0.01	0.05	0.11	0.12	0.42	0.00	0.00	0.13
β	0.05	−0.10	0.15	0.08	0.17	0.20	0.68***	0.80***	1.02***	0.81***
	0.83	0.53	0.32	0.46	0.40	0.25	0.01	0.00	0.00	0.00

Source: Authors’ computation.

Note: Figures in italics represent p-values. ***, ** and * depict significance at 1%, 5% and 10% levels, respectively.

Table 7 summarises the results of the model for the value-sorted portfolios. Unlike the results of size-sorted portfolios, no consistent seasonal pattern is evident across all value-sorted portfolios. However, returns in December are positive across all the portfolios (ranging from 2.41 per cent per month for P1 to 6.03 per cent per month for P6) and are statistically significant for six of them (P3, P4, P5, P6, P9 and P10). No other month exhibits consistent seasonality.

Thus, the results imply that for firms with a P/B ratio ranging from 1 to 5, higher returns are evident in December to some extent. However, returns of these firms exhibit no other monthly seasonality.

A possible explanation for the disappearance or weakening of seasonal patterns in value-sorted portfolios, which was evident in previous tables, is that seasonality might be primarily concentrated in firms with very high or very low P/B ratios (i.e., less than 1 or more than 5). Hence, excluding those cases from portfolios results in a weaker anomalous pattern.

In India, November/December is the season of festivals; investors are in bullish mood and have surplus money in hand at their disposal (Parikh, 2009). While Jacobsen and Visaltanachoti (2009) contended that the stock market behaviour could be influenced by the moods of investors, Bley and Saad (2010) contended that culture/religion could affect seasonal patterns in stock market returns. Besides, Kato and Schallheim (1985) contended that the months which experienced higher returns in the stock market coincided with the months when bonuses were generally declared by the employers. The presence of the November/December effect in the Indian stock market could be attributed to these behavioural biases of the investors. Behavioural explanations as the driving forces behind calendar anomalies were also put forth by Jacobs and Levy (1988b) and Haug and Hirschey (2006).

For the limited but evident April/May effect, probable explanations could be the tax-loss selling hypothesis (refer to Note 2) and the window-dressing hypothesis.⁶ For tax purposes, the financial year of India spans from April to March. Therefore, the April/May effect seems to be a turn-of-the-financial-year effect, which is corollary to the January effect reported in literature for the countries where the financial year spans from January to December (Chen & Singal, 2004; Dyl, 1977; Ligon, 1997; Sias & Starks, 1997). While the tax-loss selling hypothesis primarily pertains to individual investors, the window-dressing hypothesis pertains to the institutional investors. These arguments are similar to the findings of Poterba and Weisbenner (2001), Chen and Singal (2004), Ng and Wang (2004), Chou, Das, and Rao (2011) and Sharma and Narayan (2014). These findings also support the argument by Keim (1983) that smaller-sized stocks are more prone to tax-loss selling than larger-sized stocks. The findings are also congruent to the findings of Mills, Siriopoulos, Markellos, and Harizanis (2000) who reported that the calendar effect weakened with the increase in the capitalisation.

Table 7.

Application of the GJR Model on Value-sorted Portfolios (1995–2015)

(a) Mean Equation
Variable	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10
JANDUM	−1.21	−0.49	−2.20	0.88	−1.76	−0.47	−0.26	−0.79	−0.84	0.01
	0.65	0.86	0.54	0.75	0.43	0.81	0.89	0.74	0.59	1.00
FEBDUM	−0.39	2.99	1.49	2.73	−0.07	1.10	0.83	2.47	0.94	0.12
	0.88	0.24	0.69	0.28	0.98	0.78	0.76	0.29	0.67	0.94
MARDUM	−1.39	−2.20	3.77***	−0.74	−0.91	1.22	−0.99	0.94	0.05	−0.64
	0.50	0.36	0.01	0.74	0.63	0.49	0.58	0.71	0.97	0.66
APRDUM	0.90	3.37	2.95	0.88	1.13	3.11	5.07**	3.23	1.54	2.68
	0.74	0.27	0.33	0.74	0.64	0.34	0.04	0.24	0.35	0.26
MAYDUM	3.19**	−0.48	4.33	0.24	0.20	0.84	1.77	3.83*	1.83	0.21
	0.05	0.80	0.08	0.88	0.91	0.63	0.22	0.09	0.21	0.90
JUNDUM	0.66	1.39	1.83	0.10	0.70	−0.24	1.60	−2.53	−1.89	−0.75
	0.77	0.49	0.37	0.96	0.71	0.92	0.55	0.38	0.29	0.55
JULDUM	0.56	2.24	2.68	2.42	1.19	1.10	−0.27	1.77	1.41	0.02
	0.84	0.37	0.41	0.20	0.67	0.58	0.91	0.53	0.42	0.99
AUGDUM	−1.02	−1.46	1.47	0.48	2.24	−0.10	−0.21	0.02	2.64	2.08
	0.65	0.57	0.71	0.82	0.23	0.97	0.94	0.99	0.13	0.27
SEPDUM	1.96	0.34	−0.76	1.68	3.63	1.47	4.44***	2.45	2.81*	4.21***
	0.36	0.89	0.79	0.35	0.19	0.44	0.01	0.37	0.09	0.01
OCTDUM	−1.62	1.29	−1.08	−0.80	0.55	0.24	0.99	−0.18	2.21	1.39
	0.47	0.55	0.76	0.74	0.78	0.91	0.71	0.93	0.26	0.47
NOVDUM	2.24	0.93	2.16	0.96	2.72	2.68	4.14**	−0.25	3.05*	4.06**
	0.17	0.69	0.38	0.68	0.20	0.15	0.02	0.93	0.07	0.04
DECDUM	2.41	4.41	5.09*	4.98**	5.14**	6.03***	4.49	3.86	5.23***	4.87**
	0.50	0.11	0.07	0.03	0.02	0.01	0.17	0.22	0.01	0.03
(b) Variance Equation
Variable	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10
α₀	22.35*	13.77	76.87*	11.42	10.68*	9.45**	8.58	47.49	44.16***	3.73
	0.10	0.23	0.02	0.23	0.08	0.04	0.12	0.50	0.00	0.13
α₁	0.27**	0.00	−0.01	0.10	0.03	0.07	0.10**	−0.04	0.61***	0.16**
	0.04	0.95	0.41	0.15	0.48	0.22	0.03	0.20	0.00	0.02
γ	0.07	0.09	−0.24***	0.00	0.09	0.14	0.10	0.08	−0.24	0.02
	0.68	0.28	0.00	0.99	0.32	0.13	0.38	0.28	0.23	0.82
β	0.54***	0.83***	0.57***	0.78***	0.80***	0.78***	0.77***	0.54	0.01	0.79***
	0.00	0.00	0.01	0.00	0.00	0.00	0.00	0.41	0.94	0.00

Source: Authors’ computation.

Note: Figures in italics represent p-values. ***, ** and * depict significance at 1%, 5% and 10% levels, respectively.

5. Conclusion

The article studies the Indian stock market for a period of 20 years (1995–2015) and ascertains the monthly seasonality in the returns, both at the index level and across size-sorted portfolios and value-sorted portfolios. The TGARCH model is employed to take into consideration the non-linear aspects of the market—leptokurtosis, volatility clustering and leverage effect. At the portfolio level, the data set is trimmed to reduce the influence of outliers.

The results suggest the presence of the November/December effect at the index level. On grouping these constituent firms on the basis of market capitalisation, the December effect is evident only in those firms with sizes smaller than the average. In addition, these firms also exhibit the April/May effect. The results are different for value-sorted portfolios. Excluding firms with P/B ratios less than 1 or more than 5, while the December effect weakens, no other month exhibits significantly higher returns on a consistent basis. The behavioural aspects of market participants, tax-loss selling and window dressing seem to be the probable explanations behind the evident patterns.

By studying the Indian stock market, the article provides an out-of-sample evidence to the literature on anomalies. Besides, India being an emerging market, the article contributes to a budding area of research. The objective of the study and employed methodology attempt to fill the existing gap in the literature with respect to the Indian stock market.

As Jacobs and Levy (1988b) stated, ‘… planned trades can be scheduled to take advantage of calendar-based return patterns’, the findings of the study can form an important input for stock market investors who can time their investments and choose their holdings in accordance with the evident calendar patterns.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The corresponding author, Harshita, received fellowship from the University Grants Commission during her PhD. This article is an outcome of her doctoral work.

Notes

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Unique Calendar Effects in the Indian Stock Market: Evidence and Explanations

Abstract

Keywords

1. Introduction

2. Literature Review

3.1 Objectives

3.2 Data

3.3 Methodology

Table 2. Time Series Average of Returns in Different Months of the Year (1999–2015) Month Average of Returns January −0.23 February 0.55 March −1.13 April 1.14 May 1.26 June 0.89 July 1.64 August 2.30 September 1.50 October −0.14 November 4.06 December 4.91

Footnotes

Declaration of Conflicting Interests

Funding

Notes

References

Table 2.
Time Series Average of Returns in Different Months of the Year (1999–2015)

Month Average of Returns

January −0.23

February 0.55

March −1.13

April 1.14

May 1.26

June 0.89

July 1.64

August 2.30

September 1.50

October −0.14

November 4.06

December 4.91