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SIZE EFFECT IN INDIAN STOCK MARKET : AN ANOMALY OR A METHODOLOGICAL ARTIFACT.

Introduction

The phenomenon of small size stocks to provide higher returns than big size stocks even after riskadjustment is termed as size effect (anomaly). The recognition of size effect dates back to more than 35 years ago when Banz (1) studied the US stock market, and the same has been confirmed in a number of subsequent studies for different markets. However, literature is rife with conflicting evidences being reported at same point in time and no discreet conclusion can be drawn on the existence of the anomaly. Exacerbating this confusion is literature questioning the authenticity of these reported evidences. Schwert (2) stated:
After they are documented and analyzed in the academic literature,
anomalies often seem to disappear, reverse, or attenuate. This raises
the question of whether profit opportunities existed in the past, but
have since been arbitraged away, or whether the anomalies were simply
statistical aberrations that attracted the attention of academics and
practitioners.


This implies that the reported size effect in literature could be either because the market was inefficient or because there was statistical distortion in the process of analysis. The aim of this paper is to test the potential of both these arguments in explaining the size effect in the Indian stock market. The findings suggest that statistical distortion could be a possible driver of the evidence in India.

Prelude

After identification in the US stock market, the presence of the size effect was confirmed for different stock markets worldwide (*). However, the findings were not consistent. Berk (1996) (20) contended that the size effect was not evident across different measures of size. Dimson and Marsh (21). Horowitz, Loughran and Savin (22) studied the US stock market and reported flat relationship between returns and size. The authors concluded that the size effect could be simply an academic discovery.

Referring to the studies on the Indian stock market, the findings have been comparatively more consistent. The paper aims to test if the size effect is indeed an anomaly that persists in the Indian stock market, or is simply an artifact of the chosen data and methodologies. The findings are more in support of the latter.

Methodology Used

Stretching over a period of twenty years (October 1995 to September 2015, the study is based on the constituent companies of Nifty 500 index whose financial year end in March. As Schwert raised the concern that evidence of anomalies could be influenced by the choice of data and methodology, this paper employs two related datasets and multiple methodologies for calculation of returns. The data is obtained from Ace Equity[R] database.

Dataset I consists of a fixed set of companies which are kept constant over the study period. This sample is selected based on the index composition as on 31 March 2014. Dataset II requires annual revision of companies forming the study sample. This sample is chosen on 31 March 1999 (**) and updated everyyear on 31 March to match the changes in the index constitution. As is the general practice in literature, market capitalization is chosen as the proxy for size. Every year at September end, companies are divided into 10 size sorted portfolios using deciles as the break-points. The portfolios are then held constant for one year and monthly returns are calculated on them from October to next September. The gap of six months is maintained between financial year end and portfolio formation to ensure that the variable is known at the time of portfolio creation.

The returns are calculated as equal-weighted and value-weighted. The equal-weighted returns are first calculated on the whole sample, and then on the trimmed sample. Trimmed sample excludes the extreme one per cent records from both the ends of the dataset. Further, value-weighted returns employ September end sizes as the weights. These returns are calculated in three ways--based on (a) whole sample, (b) trimmed sample where extreme one per cent records are excluded from both the ends and (c) winsorized sample where the highest/lowest 1 per cent records are made equivalent to the next highest/lowest values respectively.

Paired t-test is applied on the returns series of extreme portfolios to test if they are statistically different. The capital asset pricing model (CAPM) is then applied to test the magnitude of excess riskadjusted returns generated by all the portfolios.

The model is defined as follows:

[R.sub.pt] - [R.sub.ft] = [[alpha].sub.p] + [[beta].sub.p] ([R.sub.mt] - [R.sub.ft] + [[epsilon].sub.mt] (1)

Where,[R.sub.pt] is the return on a portfolio p for time t

[R.sub.ft] is the risk-free rate during time t

[[alpha].sub.p] and [[beta].sub.p] are the regression intercept and slope respectively

[R.sub.mt] is the return on market portfolio m for time t

[[epsilon].sub.t] is the error term.

Nifty 500 is used as the proxy for market portfolio. 91-day Treasury bill is used as the proxy for risk-free security. Statistically significant alphas ([alpha]) would signify that the portfolio generates excess returns over the risk-adjusted returns. As a robustness test, the period of study is divided into two phases: phase I (October 1995 to September 2008) and phase II (October 2008 to September 2015) where phase I depicts the pre-recession phase while phase II depicts post-recession phase.

Research Findings

Table 1 summarizes the time-series averages of monthly excess returns on size-sorted portfolios for dataset I. Excess returns are actual returns net of risk-free returns. Portfolio PI contains stocks of the smallest 10 per cent companies while portfolio P10 contains stocks of the largest 10 per cent companies. The Table exhibits persistence of significant negative relationship between returns and size in the Indian stock market. Across all the five methods of calculation of returns, portfolio P1 generates statistically higher returns than portfolio P10. For the equal-weighted returns on whole sample, the difference between extreme portfolios are 2.06 per cent per month on an average, which is statistically significant at one per cent. The corresponding figure for equal-weighted trimmed sample is 1.88 per cent, which again is statistically significant at one per cent. For the cases of value-weighted returns, the differences are 1.90, 1.84 and 1.99 per cent for whole sample, trimmed sample and winsorized sample respectively, all of which are statistically significant at 1 per cent. Further, the differences are significant across all the measures even in the two sub-periods considered--phase I (1995-2008) and phase II (2008-2015).
TABLE 1
AVERAGE MONTHLY EXCESS RETURNS ON SIZE SORTED PORTFOLIOS (DATASET I):
1995-2015

                                                  P1    P2    P3

equal-weighted  whole       Whole (1995-2015)     2.67  2.51  2.38
                            Phase I (1995-2008)   2.85  2.90  2.99
                            Phase II (2008-2015)  2.34  1.78  1.25
                trimmed     Whole (1995-2015)     2.54  2.77  2.32
                            Phase I (1995-2008)   2.64  3.31  2.86
                            Phase II (2008-2015)  2.36  1.77  1.30
value-weighted  whole       Whole (1995-2015)     2.47  2.52  2.34
                            Phase I (1995-2008)   2.64  2.91  2.92
                            Phase II (2008-2015)  2.14  1.79  1.27
                trimmed     Whole (1995-2015)     2.45  2.84  2.33
                            Phase I (1995-2008)   2.61  3.41  2.87
                            Phase II (2008-2015)  2.16  1.79  1.32
                winsorized  Whole (1995-2015)     2.56  2.52  2.34
                            Phase I (1995-2008)   2.78  2.91  2.92
                            Phase II (2008-2015)  2.14  1.79  1.27

                                                  P4    P5    P6

equal-weighted  whole       Whole (1995-2015)     2.03  1.37  1.35
                            Phase I (1995-2008)   2.42  1.56  1.71
                            Phase II (2008-2015)  1.30  1.01  0.69
                trimmed     Whole (1995-2015)     1.78  1.29  1.35
                            Phase I (1995-2008)   1.99  1.47  1.73
                            Phase II (2008-2015)  1.40  0.94  0.63
value-weighted  whole       Whole (1995-2015)     1.96  1.35  1.31
                            Phase I (1995-2008)   2.33  1.54  1.66
                            Phase II (2008-2015)  1.26  1.00  0.67
                trimmed     Whole (1995-2015)     1.77  1.24  1.29
                            Phase I (1995-2008)   1.98  1.39  1.66
                            Phase II (2008-2015)  1.40  0.%   0.61
                winsorized  Whole (1995-2015)     1.96  1.35  1.31
                            Phase I (1995-2008)   2.33  1.54  1.66
                            Phase II (2008-2015)  1.26  1.00  0.67

                                                  P7    P8    P9

equal-weighted  whole       Whole (1995-2015)     2.04  1.00  1.07
                            Phase I (1995-2008)   2.61  0.96  1.17
                            Phase II (2008-2015)  0.97  1.08  0.88
                trimmed     Whole (1995-2015)     2.11  0.92  1.07
                            Phase I (1995-2008)   2.74  0.82  1.13
                            Phase II (2008-2015)  0.94  1.10  0.94
value-weighted  whole       Whole (1995-2015)     2.19  0.98  1.07
                            Phase I (1995-2008)   2.83  0.94  1.19
                            Phase II (2008-2015)  0.99  1.05  0.84
                trimmed     Whole (1995-2015)     2.23  0.91  1.06
                            Phase I (1995-2008)   2.92  0.81  1.13
                            Phase II (2008-2015)  0.96  1.08  0.94
                winsorized  Whole (1995-2015)     2.19  0.98  1.07
                            Phase I (1995-2008)   2.83  0.94  1.19
                            Phase II (2008-2015)  0.99  1.05  0.84

                                                  P10   P1-P10

equal-weighted  whole       Whole (1995-2015)     0.61  2.06 (***)
                            Phase I (1995-2008)   0.72  2.13 (***)
                            Phase II (2008-2015)  0.41  1.93 (***)
                trimmed     Whole (1995-2015)     0.66  1.88 (***)
                            Phase I (1995-2008)   0.75  1.88 (***)
                            Phase II (2008-2015)  0.48  1.88 (***)
value-weighted  whole       Whole (1995-2015)     0.56  1.90 (***)
                            Phase I (1995-2008)   0.71  1.93 (**)
                            Phase II (2008-2015)  0.30  1.85 (***)
                trimmed     Whole (1995-2015)     0.61  1.84 (***)
                            Phase I (1995-2008)   0.67  1.94 (***)
                            Phase II (2008-2015)  0.51  1.65 (***)
                winsorized  Whole (1995-2015)     0.57  1.99 (***)
                            Phase I (1995-2008)   0.69  2.09 (***)
                            Phase II (2008-2015)  0.35  1.79 (***)

Notes: All the figures are in per cent; (***) indicates significance at
1 per cent; (**) indicates significance at 5 per cent level.


Table 2 is analogous to Table 1 and reports the same findings, but for dataset II of the study. Contrary to the findings of Table 1, no negative relationship between returns and size is evident in this Table. Looking at the difference in returns of extreme portfolios, while portfolio P1 consistently generates higher returns than portfolio P10 across all the five return measures, none of them are statistically significant. For equal-weighted returns, the average difference is 0.58 per cent per month for whole sample and 0.26 per cent per month for trimmed sample. For value-weighted returns, the figures of whole sample, trimmed sample and winsorized sample are 0.57 per cent, 0.35 per cent and 0.63 per cent respectively. Similar findings are evident across the two study phases. The findings imply that the size effect reported in literature on the Indian stock market is not robust to changing the dataset. When the study sample is revised annually to include only the latest Nifty 500 stocks, no significant relationship between returns and size could be seen. This could mean that the stocks which qualify the requirements of the index do not exhibit size-based return differential.
TABLE 2
AVERAGE MONTHLY EXCESS RETURNS ON SIZE SORTED PORTFOLIOS (DATASET II):
1999-2015

                                                  P1    P2    P3

equal-weighted  whole       Whole (1999-2015)     1.27  1.19  1.33
                            Phase I (1999-2008)   1.66  1.34  1.53
                            Phase II (2008-2015)  0.77  1.01  1.07
                trimmed     Whole (1999-2015)     1.00  1.10  1.39
                            Phase I (1999-2008)   1.16  1.19  1.64
                            Phase II (2008-2015)  0.79  0.99  1.06
value-weighted  whole       Whole (1999-2015)     1.21  1.18  1.32
                            Phase I (1999-2008)   1.45  1.36  1.51
                            Phase II (2008-2015)  0.90  0.94  1.08
                trimmed     Whole (1999-2015)     1.08  1.07  1.35
                            Phase I (1999-2008)   1.18  1.18  1.57
                            Phase II (2008-2015)  0.93  0.92  1.06
                winsorized  Whole (1999-2015)     1.29  1.18  1.32
                            Phase I (1999-2008)   1.59  1.36  1.51
                            Phase II (2008-2015)  0.90  0.94  1.08

                                                  P4    P5    P6

equal-weighted  whole       Whole (1999-2015)     1.48  1.43  0.82
                            Phase I (1999-2008)   1.81  1.92  0.93
                            Phase II (2008-2015)  1.06  0.80  0.69
                trimmed     Whole (1999-2015)     1.64  1.31  0.80
                            Phase I (1999-2008)   2.05  1.76  0.83
                            Phase II (2008-2015)  1.11  0.73  0.76
value-weighted  whole       Whole (1999-2015)     1.48  1.42  0.81
                            Phase I (1999-2008)   1.80  1.90  0.93
                            Phase II (2008-2015)  1.06  0.81  0.66
                trimmed     Whole (1999-2015)     1.64  1.32  0.80
                            Phase I (1999-2008)   2.04  1.77  0.87
                            Phase II (2008-2015)  1.13  0.73  0.73
                winsorized  Whole (1999-2015)     1.48  1.42  0.81
                            Phase I (1999-2008)   1.80  1.90  0.93
                            Phase II (2008-2015)  1.06  0.81  0.66

                                                  P7    P8    P9

equal-weighted  whole       Whole (1999-2015)     1.16  1.62  1.09
                            Phase I (1999-2008)   1.44  2.03  1.26
                            Phase II (2008-2015)  0.80  1.08  0.87
                trimmed     Whole (1999-2015)     1.13  1.56  1.11
                            Phase I (1999-2008)   1.39  1.92  1.30
                            Phase II (2008-2015)  0.80  1.10  0.87
value-weighted  whole       Whole (1999-2015)     1.21  1.64  1.11
                            Phase I (1999-2008)   1.49  2.09  1.34
                            Phase II (2008-2015)  0.84  1.05  0.82
                trimmed     Whole (1999-2015)     1.17  1.56  1.11
                            Phase I (1999-2008)   1.42  1.91  1.29
                            Phase II (2008-2015)  0.85  1.12  0.88
                winsorized  Whole (1999-2015)     1.21  1.64  1.11
                            Phase I (1999-2008)   1.49  2.09  1.34
                            Phase II (2008-2015)  0.84  1.05  0.82

                                                  P10   P1-P10

equal-weighted  whole       Whole (1999-2015)     0.68  0.58
                            Phase I (1999-2008)   0.81  0.85
                            Phase II (2008-2015)  0.52  0.25
                trimmed     Whole (1999-2015)     0.74  0.26
                            Phase I (1999-2008)   0.86  0.30
                            Phase II (2008-2015)  0.59  0.20
value-weighted  whole       Whole (1999-2015)     0.64  0.57
                            Phase I (1999-2008)   0.85  0.60
                            Phase II (2008-2015)  0.37  0.53
                trimmed     Whole (1999-2015)     0.73  0.35
                            Phase I (1999-2008)   0.80  0.38
                            Phase II (2008-2015)  0.63  0.30
                winsorized  Whole (1999-2015)     0.66  0.63
                            Phase I (1999-2008)   0.83  0.76
                            Phase II (2008-2015)  0.43  0.47

Notes : All the figures are in per cent.


Table 3 & 4 report the CAPM results on dataset I of the study. Looking at the results on equalweighted returns on whole sample for the whole study period, significant alphas are generated for 8 out of 10 portfolios. They range from 0.55 for P8 (significant at 10 per cent) to 2.42 for P2 (significant at 1 per cent). This implies that these portfolios generate significantly higher returns than those warranted as per CAPM. Further, the alphas of small size portfolios (PI to P4) are significantly larger in magnitude than the alphas of large size portfolios (P5 to P10). This is evidence favoring the presence of size effect - small size portfolios provide higher risk-adjusted returns than big size portfolios. The adjusted R-squares range from 53 per cent for P2 to 92 per cent for P10, and are also comparatively lower for smaller size portfolios than bigger size portfolios. However, these findings are not robust across sub-period analysis. While phase I exhibits findings that are similar to whole period, the magnitude of size effect weakens in phase II. For phase I, 7 out of 10 portfolios exhibit significant alphas (ranging from 0.71 for P9, significant at 10 per cent to 3.54 for P2, significant at 1 per cent) and their magnitude are statistically higher for smaller portfolios (PI to P4) than larger portfolios (P5 to P10). The adjusted R-squares are also comparatively lower towards the lower end of the portfolio (ranging from 41 per cent for P2 to 89 per cent for P10). These findings reinforce the findings of overall period. However, phase II generates slightly different results--significant alphas are reported only for 3 out of 10 portfolios (small portfolios P1 and P2 and big portfolio P10). while PI generates an alpha of 1.61 (significant at 5 per cent), P10 generates a significantly negative alpha (-0.21, significant at 10 per cent). This implies that the returns on smaller portfolio are significantly higher on risk-adjusted basis than returns on larger portfolio, which again is an evidence of size effect. However, returns on almost all the remaining portfolios conform to risk-adjusted returns. The adjusted R-squares are also higher in this phase that the previous phase I. These can be taken as evidence of weaker size effect in the phase II of the study. The findings are similar to those reported by Banz (1), Schwert (2) and Jiang and Yamada (23) that the size effect did not persist over different sample period and its magnitude varied over sub-periods. The weakening of size effect was reported by Shum and Tang (24) for other Asian markets (Hong Kong, Singapore, and Taiwan). Similar to the results of phase II, Banz (1) reported that the effect was mainly evident in very small firms and there was little difference between returns of remaining firms. The results of CAPM on the remaining four methods of returns calculation exhibit similar pattern and thus reinforce the aforementioned observations.
TABLE 3
CAPM EXCESS RETURNS (JENSEN'S ALPHA) AND GOODNESS OF FIT (ADJUSTED
[R.sup.2]) for DATASET I (EQUAL-WEIGHTED RETURNS): 1999-2015

                P1          P2          P3          P4
equal-weighted
whole sample

                Jensen's alpha

1999-2015       2.39 (***)  2.42 (***)  1.13 (***)  1.69 (***)
                4.35        3.93        2.71        3.25
Phase I         3.00 (***)  3.54 (***)  1.63 (**)   2.60 (***)
(1999-2008)     3.55        3.53        2.56        3.09
Phase II        1.61 (**)   0.99 (*)    0.49        0.52
(2008-2015)     2.63        1.97        1.13        1.33

                Adjusted [R.sup.2]

1999-2015       0.56        0.53        0.69        0.59
Phase I         0.48        0.41        0.60        0.44
Phase II        0.72        0.82        0.85        0.88
equal-weighted
trimmed sample

                Jensen's alpha

1999-2015       2.23 (***)  2.26 (***)  1.53 (***)  1.44 (***)
                4.38        3.62        2.76        3.78
Phase I         2.70 (***)  3.26 (***)  2.29 (**)   2.09 (***)
(1999-2008)     3.58        3.21        2.50        3.74
Phase II        1.63 (***)  0.98 (*)    0.55        0.62
(2008-2015)     2.64        1.92        1.29        1.58

                Adjusted [R.sup.2]

1999-2015       0.59        0.52        0.57        0.71
Phase I         0.51        0.39        0.45        0.62
Phase II        0.72        0.82        0.85        0.88

                P5        P6     P7         P8        P9
equal-weighted
whole sample

                Jensen's alpha

1999-2015       0.92 (*)   0.32  1.01 (**)  0.55 (*)  0.49 (**)
                1.78       0.84  2.07       1.90      2.02
Phase I         1.48 (*)   0.64  1.64 (**)  0.67      0.71 (*)
(1999-2008)     1.79       1.13  2.04       1.57      1.94
Phase II        0.20      -0.09  0.20       0.40      0.21
(2008-2015)     0.55      -0.25  0.62       1.26      0.83

                Adjusted [R.sup.2]

1999-2015       0.57       0.73  0.61       0.79      0.85
Phase I         0.41       0.63  0.46       0.74      0.81
Phase II        0.90       0.89  0.91       0.90      0.93
equal-weighted
trimmed sample

                Jensen's alpha

1999-2015       0.83       0.29  1.02 (**)  0.51 (*)  0.49 (**)
                1.54       0.77  2.11       1.70      1.99
Phase I         1.38       0.66  1.68 (**)  0.59      0.65 (*)
(1999-2008)     1.59       1.17  2.10       1.31      1.78
Phase II        0.13      -0.17  0.18       0.41      0.28
(2008-2015)     0.34      -0.45  0.58       1.31      1.04

                Adjusted [R.sup.2]

1999-2015       0.56       0.73  0.61       0.78      0.85
Phase I         0.39       0.64  0.46       0.72      0.81
Phase II        0.90       0.89  0.91       0.90      0.92

                P10
equal-weighted
whole sample

                Jensen's alpha

1999-2015        0.05
                 0.28
Phase I          0.25
(1999-2008)      0.94
Phase II        -0.21 (*)
(2008-2015)     -1.69

                Adjusted [R.sup.2]

1999-2015        0.92
Phase I          0.89
Phase II         0.98
equal-weighted
trimmed sample

                Jensen's alpha

1999-2015        0.08
                 0.46
Phase I          0.29
(1999-2008)      1.06
Phase II        -0.17
(2008-2015)     -1.06

                Adjusted [R.sup.2]

1999-2015        0.91
Phase I          0.88
Phase II         0.97

Notes: Figures in italics indicate the t-stats; (***) indicates
significance at 1 per cent level; (**) indicates significance at 5 per
cent level; (*) indicates significance at 10per cent level.

TABLE 4
CAPM EXCESS RETURNS (JENSEN'S ALPHA) AND GOODNESS OF FIT (ADJUSTED
[R.sup.2]) for DATASET I (VALUE-WEIGHTED RETURNS): 1999-2015

                    P1           P2           P3           P4
value-weighted
whole sample

                    Jensen's alpha

1999-2015           2.13 (***)   2.48 (***)   1.24 (***)   1.61 (***)
                    4.09         3.91         2.74         3.26
Phase I             2.68 (***)   3.64 (***)   1.63 (**)    249 (***)
(1999-2008)         3.35         3.50         2.59         3.17
Phase II            1.43 (**)    1.00 (**)    0.51         0.48
(2008-2015)         2.46         2.03         1.15         1.21

                    Adjusted [R.sup.2]

1999-2015           0.58         0.51         0.69         0.61
Phase I             0.49         0.38         0.61         0.47
Phase II            0.74         0.82         0.84         0.88
value-weighted
trimmed sample

                    Jensen's alpha

1999-2015           2.12 (***)   2.27 (***)   1.53 (***)   1.42 (***)
                    4.23         3.64         2.75         3.69
Phase I             2.65 (***)   2.27 (***)   2.28 (**)    2.04 (***)
(1999-2008)         3.51         3.23         2.48         3.66
Phase II            1.45 (**)    0.99 (*)     0.57         0.62
(2008-2015)         2.47         1.96         1.32         1.54

                    Adjusted [R.sup.2]

1999-2015           0.59         0.52         0.57         0.71
Phase I             0.51         0.38         0.45         0.62
Phase II            0.73         0.82         0.85         0.87
value-weighted
winsorized sample

                    Jensen's alpha

1999-2015           2.24 (***)   2.48 (***)   2.24 (***)   1.61 (***)
                    4.13         3.91         2.74         3.26
Phase I             2.87 (***)   3.64 (***)   1.63 (**)    2.49 (***)
(1999-2008)         3.41         3.50         2.59         3.17
Phase II            1.43 (**)    1.00 (**)    0.51         0.48
(2008-2015)         2.46         2.03         1.15         1.21

                    Adjusted [R.sup.2]

1999-2015           0.57         0.51         0.69         0.61
Phase I             0.48         0.38         0.61         0.47
Phase II            0.74         0.82         0.84         0.88

                    P5         P6      P7          P8         P9
value-weighted
whole sample

                    Jensen's alpha

1999-2015           0.86 (*)    0.31   1.07 (**)   0.54 (*)   0.47 (*)
                    1.70        0.84   2.00        1.88       1.88
Phase I             1.38 (*)    0.64   1.73 (*)    0.66       0.70 (*)
(1999-2008)         1.72        1.14   1.94        7.55       1.85
Phase II            0.19       -0.11   0.22        0.38       0.17
(2008-2015)         0.51       -0.29   0.68        7.23       0.67

                    Adjusted [R.sup.2]

1999-2015           0.59        0.73   0.56        0.79       0.84
Phase I             0.43        0.63   0.40        0.73       0.80
Phase II            0.90        0.90   0.91        0.90       0.93
value-weighted
trimmed sample

                    Jensen's alpha

1999-2015           0.73        0.29   1.08 (**)   0.50 (*)   0.46 (*)
                    1.49        0.77   2.04        1.68       1.82
Phase I             1.20        0.67   1.78 (**)   0.58       0.61
(1999-2008)         1.52        1.19   2.00        1.30       1.60
Phase II            0.15       -0.19   0.20        0.40       0.27
(2008-2015)         0.39       -0.50   0.63        1.29       0.99

                    Adjusted [R.sup.2]

1999-2015           0.60        0.74   0.56        0.78       0.84
Phase I             0.44        0.65   0.41        0.71       0.80
Phase II            0.90        0.89   0.91        0.90       0.92
value-weighted
winsorized sample

                    Jensen's alpha

1999-2015           0.86 (*)    0.31   1.07 (**)   0.54 (*)   0.47 (*)
                    1.70        0.84   2.00        1.88       1.88
Phase I             1.38 (*)    0.64   1.73 (*)    0.66       0.70 (*)
(1999-2008)         1.72        1.14   1.94        7.55       7.55
Phase II            0.19       -0.11   0.22        0.38       0.17
(2008-2015)         0.51       -0.29   0.68        1.23       0.67

                    Adjusted [R.sup.2]

1999-2015           0.59        0.73   0.56        0.79       0.84
Phase I             0.43        0.63   0.40        0.73       0.80
Phase II            0.90        0.90   0.91        0.90       0.93

                    P10
value-weighted
whole sample

                    Jensen's alpha

1999-2015           -0.01
                    -0.09
Phase I              0.19
(1999-2008)          0.90
Phase II            -0.27 (**)
(2008-2015)         -2.34

                    Adjusted [R.sup.2]

1999-2015            0.95
Phase I              0.94
Phase II             0.98
value-weighted
trimmed sample

                    Jensen's alpha

1999-2015            0.01
                     0.07
Phase I              0.12
(1999-2008)          0.55
Phase II            -0.13
(2008-2015)         -0.76

                    Adjusted [R.sup.2]

1999-2015            0.95
Phase I              0.94
Phase II             0.97
value-weighted
winsorized sample

                    Jensen's alpha

1999-2015           -0.01
                    -0.06
Phase I              0.16
(1999-2008)          0.79
Phase II            -0.23 (**)
(2008-2015)         -2.07

                    Adjusted [R.sup.2]

1999-2015            0.95
Phase I              0.94
Phase II             0.98

Notes : Figures in italics indicate the t-stats; (***) indicates
significance at 1 per cent level; (**) indicates significance at 5 per
cent level; (*) indicates significance at 10per cent level.

TABLE 5
CAPM EXCESS RETURNS (JENSEN'S ALPHA) AND GOODNESS OF FIT (ADJUSTED
[R.sup.2]) for DATASET II (EQUAL-WEIGHTED RETURNS): 1999-2015

                P1     P2     P3     P4          P5          P6
equal-weighted
whole sample

                Jensen's alpha

1999-2015       0.41   0.40   0.54   0.73 (*)     0.67 (*)    0.05
                0.61   0.74   1.22   1.80         1.77        0.14
Phase I         0.73   0.51   0.74   1.04 (*)     1.15 (**)   0.21
(1999-2008)     0.67   0.60   1.09   1.65         2.01        0.40
Phase II        0.00   0.25   0.30   0.33         0.05       -0.14
(2008-2015)     0.00   0.48   0.62   0.83         0.13       -0.35

                Adjusted [R.sup.2]

1999-2015       0.50   0.58   0.66   0.69         0.72        0.72
Phase I         0.40   0.48   0.57   0.59         0.63        0.64
Phase II        0.73   0.79   0.82   0.86         0.88        0.88

equal-weighted
trimmed sample

                Jensen's alpha

1999-2015       0.19   0.31   0.60   0.87 (**)    0.56        0.02
                0.30   0.61   1.34   2.08         1.51        0.07
Phase I         0.33   0.37   0.84   1.26 (*)     1.02 (*)    0.10
(1999-2008)     0.33   0.48   1.24   1.92         1.84        0.18
Phase II        0.02   0.23   0.29   0.38        -0.03       -0.06
(2008-2015)     0.03   0.43   0.61   0.92        -0.07       -0.15

                Adjusted [R.sup.2]

1999-2015       0.50   0.61   0.66   0.67         0.72        0.73
Phase I         0.39   0.52   0.57   0.58         0.63        0.65
Phase II        0.73   0.79   0.83   0.85         0.88        0.88

                P7     P8          P9         P10
equal-weighted
whole sample

                Jensen's alpha

1999-2015       0.38   0.88 (**)   0.37 (*)   -0.02
                1.15   2.06        1.79       -0.12
Phase I         0.65   1.30 (*)    0.48        0.04
(1999-2008)     1.37   1.87        1.58        0.17
Phase II        0.03   0.34        0.22       -0.09
(2008-2015)     0.08   1.12        0.95       -0.74

                Adjusted [R.sup.2]

1999-2015       0.78   0.65        0.89        0.93
Phase I         0.72   0.52        0.87        0.90
Phase II        0.90   0.92        0.93        0.98

equal-weighted
trimmed sample

                Jensen's alpha

1999-2015       0.35   0.81 (**)   0.39 (*)    0.02
                1.07   1.94        1.81        0.12
Phase I         0.61   1.19 (*)    0.52        0.08
(1999-2008)     1.31   1.76        1.62        0.31
Phase II        0.02   0.34        0.23       -0.05
(2008-2015)     0.04   1.08        0.91       -0.34

                Adjusted [R.sup.2]

1999-2015       0.79   0.66        0.88        0.92
Phase I         0.73   0.53        0.85        0.90
Phase II        0.90   0.91        0.92        0.97

Notes: Figures in italics indicate the t-stats; (***) indicates
significance at 1 per cent level; (**) indicates significance at 5 per
cent level; (*) indicates significance at 10 per cent level.

TABLE 6
CAPM EXCESS RETURNS (JENSEN'S ALPHA) AND GOODNESS OF FIT (ADJUSTED
[R.sup.2]) FOR DATASET II (VALUE-WEIGHTED RETURNS) : 1999-2015

                    P1     P2     P3     P4          P5          P6
value-weighted
whole sample

                    Jensen's alpha

1999-2015           0.39   0.37   0.54   0.72 (*)     0.66 (*)    0.04
                    0.63   0.70   1.21   1.80         1.74        0.70
Phase I             0.57   0.52   0.72   1.03 (*)     1.13 (**)   0.20
(1999-2008)         0.57   0.61   1.08   1.65         1.99        0.39
Phase II            0.16   0.20   0.30   0.33         0.05       -0.17
(2008-2015)         0.27   0.37   0.63   0.84         0.14       -0.40

                    Adjusted [R.sup.2]

1999-2015           0.53   0.59   0.66   0.69         0.72        0.72
Phase I             0.42   0.49   0.57   0.59         0.63        0.64
Phase II            0.75   0.79   0.83   0.86         0.88        0.88

value-weighted
trimmed sample

                    Jensen's alpha

1999-2015           0.29   0.28   0.57   0.87 (**)    0.57        0.03
                    0.48   0.56   1.28   2.09         7.53        0.07
Phase I             0.37   0.36   0.79   1.25 (*)     1.04 (*)    0.12
(1999-2008)         0.39   0.47   1.16   1.92         1.87        0.23
Phase II            0.19   0.17   0.29   0.39        -0.03       -0.09
(2008-2015)         0.33   0.32   0.61   0.94        -0.07       -0.23

                    Adjusted [R.sup.2]

1999-2015           0.52   0.61   0.66   0.68         0.71        0.73
Phase I             0.40   0.52   0.57   0.59         0.63        0.65
Phase II            0.75   0.78   0.83   0.85         0.88        0.88

value-weighted
winsorized sample

                    Jensen's alpha

1999-2015           0.46   0.37   0.54   0.72 (*)     0.66 (*)    0.04
                    0.72   0.70   1.21   1.80         1.74        0.70
Phase I             0.70   0.52   0.72   1.03 (*)     1.13 (**)   0.20
(1999-2008)         0.67   0.61   1.08   1.65         7.99        0.39
Phase II            0.16   0.20   0.30   0.33         0.05       -0.17
(2008-2015)         0.27   0.37   0.63   0.84         0.14       -0.40

                    Adjusted [R.sup.2]

1999-2015           0.51   0.59   0.66   0.69         0.72        0.72
Phase I             0.41   0.49   0.57   0.59         0.63        0.64
Phase II            0.75   0.79   0.83   0.86         0.88        0.88

                    P7     P8          P9         P10
value-weighted
whole sample

                    Jensen's alpha

1999-2015           0.42   0.90 (**)   0.38 (*)   -0.07
                    7.30   2.12        1.83       -0.52
Phase I             0.70   1.36 (**)   0.54 (*)    0.01
(1999-2008)         1.49   1.96        1.78        0.06
Phase II            0.07   0.32        0.17       -0.18
(2008-2015)         0.79   7.05        0.70       -1.58

                    Adjusted [R.sup.2]

1999-2015           0.79   0.66        0.89        0.94
Phase I             0.73   0.52        0.87        0.93
Phase II            0.90   0.92        0.93        0.98

value-weighted
trimmed sample

                    Jensen's alpha

1999-2015           0.39   0.82 (**)   0.38 (*)   -0.02
                    1.23   7.97        1.76       -0.14
Phase I             0.64   1.18 (*)    0.50       -0.05
(1999-2008)         1.40   7.76        1.58       -0.23
Phase II            0.08   0.36        0.23        0.02
(2008-2015)         0.22   7.75        0.88        0.16

                    Adjusted [R.sup.2]

1999-2015           0.79   0.67        0.88        0.95
Phase I             0.74   0.54        0.86        0.93
Phase II            0.90   0.91        0.92        0.97

value-weighted
winsorized sample

                    Jensen's alpha

1999-2015           0.42   0.90 (**)   0.38 (*)   -0.06
                    1.30   2.12        1.83       -0.42
Phase I             0.70   1.36 (**)   0.54 (*)   -0.01
(1999-2008)         1.49   1.96        1.78       -0.03
Phase II            0.07   0.32        0.17       -0.12
(2008-2015)         0.79   1.05        0.70       -7.73

                    Adjusted [R.sup.2]

1999-2015           0.79   0.66        0.89        0.95
Phase I             0.73   0.52        0.87        0.93
Phase II            0.90   0.92        0.93        0.98

Notes : Figures in italics indicate the t-stats; (***) indicates
significance at 1 per cent level; (**) indicates significance at 5 per
cent level; (*) indicates significance at 10per cent level.


Thus, the findings imply that in the Indian stock market, results are not driven by extreme observations and changing the methods of returns calculation does not alter the findings. These findings are unlike the findings reported by Blume and Stambaugh (24) who reported that altering the method of returns calculation nearly halved the magnitude of size effect reported in literature, Knez and Ready (25) and Garza-Gomez, et.al. (26) who reported that the evidence of anomalies could be driven by extreme observations, or De Moor and Sercu (27) who reported that the average returns calculations could be biased by extreme observations.

Analogous to Tables 3 & 4, Tables 5 & 6 report the results of CAPM on dataset II of the study. Unlike the results on dataset I, few of the alphas are significant when dataset II is considered. For the equal-weighted returns based on whole sample and whole period, 4 of the 10 portfolios are significant (ranging from 0.37 for P9 significant at 10 per cent to 0.88 for P8 significant at 5 per cent). Rest of the 6 portfolios generate insignificant alphas (ranging from -0.02 for P10 to 0.54 for P3). This implies that most of the portfolios generate returns as expected by CAPM. This finding is an evidence against the presence of size effect in Indian stock market. However, similar to the results based on dataset I, the adjusted R-squares are comparatively higher for big size portfolios suggesting that the explanatory power of the model is higher for these portfolios. Nevertheless, in statistical sense, the model is able to explain the returns for most of the portfolios. When the results for phase I are considered, findings are similar to those for whole study period. 7 of the 10 portfolios generate insignificant alphas ranging from 0.04 for P10 to 0.74 for P3. The adjusted R-squares also increase, in general, from smaller to bigger size portfolios. Findings are different when dataset II is considered--ranging from -0.14 for P6 to 0.33 for P4, none of the portfolios return significant alphas. This implies that, on an average, the portfolio returns are in accordance with CAPM expected returns. This is evidence against the size effect. Similar to the results observed for dataset I, the results of CAPM on the remaining four methods of returns calculation on dataset II exhibit similar pattern and thus reinforce the aforementioned observations.

Summarizing the overall findings, when a fixed set of stocks are analyzed over 20 years, there are evidences of size effect. This explains the persistent size effect documented in literature for the Indian stock market. However, the size effect seems to lose its significance when the stocks are picked and dropped from the dataset to match their pick and drop from the Nifty 500 index. There is a probable explanation to it. The Nifty 500 index is rebalanced periodically to ensure that the top 500 stocks form part of it and market capitalization is an important eligibility criteria for inclusion of stocks in the index (National Stock Exchange (28)). Thus, it does not include the smallest stocks of the market. There are evidences in literature that size effect was driven largely by the smallest of the stocks (De Moor and Sercu (29)) and smallest stocks were the problem for asset pricing model (Fama and French (30)). Therefore, excluding the smallest stocks reduces the significance of the size effect from the findings. Further, the tests for robustness reveal that irrespective of the dataset, the size effect is not consistent over time and is weaker in the post-2008 phase than the pre-2008 phase. The findings are congruent with the title of paper by Annaert, Holle, Crombez and Spinel (31), "...size effect: now you see it, now you don't". Comparing the possibility of size effect being an anomaly vs an artifact, the latter seems more plausible.

Conclusions

The paper studies the Indian stock market for a period of twenty years (1995 to 2015) to test if the documented size effect in literature on Indian stock market is evidence of an anomaly or is a mere artifact of chosen data and methodology. Based on two related datasets, five ways of calculating returns and two sub-periods of study, the findings can be stated as follows: (a) the size effect is not robust to changing datasets - while it is evident in one dataset, it disappears in the other, (b) the findings on size effect are not altered by method of returns calculation and all the five methods result in similar conclusion, (c) the size effect is not robust to sub-period analysis--it is weaker in the latter sub-period than the former. The findings suggest that the effect could be a result of data and methodological artifact--changing with change in dataset and study periods. The findings reiterate the possibility highlighted by Schwert (2) that anomalies could be "more apparent than real". The findings also caution the practitioners before employing size anomaly while designing their investment strategies, as Dimson and Marsh (21) contended that trying to capitalize on market anomalies would usually lead to losses and quoted Murphy's Law, "bread always falls with the buttered side down".

REFERENCES

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(6.) Glezakos, M. & Mylonas, P., Size effect still present in the Athens stock exchange, European Research Studies (7: 2004).

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(15.) Garza-Gomez, X., Hodoshima, J. & Kunimura, M., Reexamining the robustness of the market value of equity, Asia-Pacific Financial Markets (8: 2001)

(16.) De Moor, L. & Sercu, P., The smallest firm effect: An international study, Journal of International Money and Finance (32: 2013)

(17.) National Stock Exchange of India Limited (2015), IISL methodology document: Nifty broad market indices. Retrieved from https://www.nseindia.com/products/content/equities/indices/broad_indices.htm (accessed 17 February, 2016)

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(19.) Fama, E. F. & French, K. R., A five-factor asset pricing model, Journal of Financial Economics (116: 2015)

(20.) Annaert, J., Holle, F. V., Crombez, J. & Spinel, B., Value and size effect: Now you see it, now you don't (working paper No. 2002/146), (Belgium, 2002)

(21.) Dimson, E. & Marsh, P.,Murphy's law and market anomalies,The Journal of Portfolio Management (25: 1999)

(22.) Horowitz, J. L., Loughran, T. & Savin, N. E., Three analyses of the firm size premium, Journal of Empirical Finance (7: 2000)

(23.) Jiang, H. & Yamada, T., The Impact of International Institutional Investors on Local Equity Prices: Reversal of the Size Premium, Financial Analysts Journal (67: 2011)

(24.) Shum, W. C. & Tang, G. Y.N.,Common risk factors in returns in Asian emerging stock markets, International Business Review (14: 2005)

(25.) Knez, P. J. & Ready, M. J., On the robustness of size and book-to-market in cross-sectional regressions, The Journal of Finance (52: 1997)

(26.) Garza-Gomez, X., Hodoshima, J. & Kunimura, M.,Reexamining the robustness of the market value of equity, Asia-Pacific Financial Markets (8: 2001)

(27.) De Moor, L. & Sercu, P.,The smallest firm effect: An international study, Journal of International Money and Finance (32: 2013)

(28.) National Stock Exchange of India Limited (2015), IISL methodology document: Nifty broad market indices. Retrieved from https://www.nseindia.com/products/content/equities/indices/broad_indices.htm (accessed accessed 17 February 2016)

(29.) De Moor, L. & Sercu, P., Measuring the impact of extreme observations on CAPM alphas : Some methodological issues, Finance Research Letters (November 2015)

(30.) Fama, E. F. & French, K. R., A five-factor asset pricing model, Journal of Financial Economics (116: 2015)

(31.) Annaert, J., Holle, F. V, Crombez, J. & Spinel, B., Value and size effect: Now you see it, now you don't (working paper No. 2002/146), (Belgium, 2002)

HARSHITA, M.Com.

Research Scholar

email : harshita@dmsiitd.org

SHVETA SINGH, M.Com., M.B.A., Ph.D.

Associate Professor

email: shvetasingh@dms.iitd.ac.in

Professor SURENDRA S. YADAV M.B.A., Ph. D.

Professor of Finance

email: ssyadav@dms.iitd.ac.in

Department of Management Studies

Indian Institute of Technology Delhi

New Delhi, INDIA

(*) China (Wang and Iorio (3); Guo, W. Zhang, Y. Zhang and H. Zhang (4)), 16 European countries (Bauer, Cosemans and Schotman (5)), Greece (Glezakos and Mylonas (6)), Hong Kong (Chui and Wei (7)), Korea (Chui and Wei (7); de Groot and Verschoor (8)), Malaysia (Chui and Wei (7); de Groot and Verschoor (8); Drew and Veeraraghavan (9); Lau, Lee and Mclnish (10)), New Zealand (Gillan (11)), Poland (Lischewski and Voronkova (12)), Singapore (Lau et. al. (10)), Taiwan (de Groot and Verschoor (8)); Thailand (Chui and Wei (7); de Groot and Verschoor (8)), US (Keim (13); Reinganum (14); Fama and French (15), (16); Elfakhani and Zaher (17); van Dijk (18)), UK (Hwang, Gao and Owen (19)).

(**) Because of the unavailability of older data on Nifty 500 index and its constituents, some parts of the analysis begin in 1999.
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