_{1}

This study investigates the seasonal-size effect in an emerging market by examining two alternative hypotheses over the period 1995 to the pre-2007 global financial crisis. Empirical results show some evidence. Small firms experience abnormally higher returns than large firms in non-January months, and the size effect in non-January months could be attributed to the consideration of risk compensation for small firms with high risk, especially when the market or firm performance is worse. Once the stock returns are adjusted appropriately for risk, the seasonal-size anomaly disappears, which tends to support the risk mismeasurement hypothesis rather than economic cycle hypothesis.

Banz [

In the Asian-Pacific emerging markets, the Hong Kong market is relatively important, because its economy has grown dramatically from its position as an emerging market in the 1970s and 1980s, and its stock market ranks the second largest after Japan in terms of market capitalization. Researchers have also shown tremendous interest in exploring issues related to the size effect in this market, even though their findings are mixed [

Due to the inconclusive empirical results on the seasonal-size anomaly for Hong Kong, and the fact that little of these studies explore why the seasonal-size pattern may exist in this market, the Hong Kong stock market is still a good place to look for anomalies, and learn why they exist. Because the capital gains from security trading are not taxed in Hong Kong, the tax-loss selling hypothesis is unlikely to be associated with the seasonal-size effect in this market, and thus it does not need to be examined. On the other hand, the culture bonus hypothesis drawn from behavioral biases with regard to mental accounting and house money could also not explain the seasonal-size effect for Hong Kong since this market is composed of mainly institutional investors with fewer behavioral biases. The purpose of this paper is thus to explore the seasonal-size anomaly in the Hong Kong stock market using an out-of-sample period starting 1995 to the pre-2007 global financial crisis, along with examining two alternative hypotheses offered in previous research, namely, the risk mismeasurement hypothesis and the economic cycle hypothesis. This would also be useful to examine the external validity of the results of Chui and Wei [

A review of the extant literature is provided in Section 2. Section 3 describes the data and methodology. Section 4 presents the empirical results and analyses, and the final section concludes this paper.

For the existence of the size effect in Hong Kong, Ho et al. [

The tax-loss selling hypothesis is first frequently been advanced to explain the size effect. The tax-loss selling hypothesis suggests that individual investors tend to take advantage of tax benefits, and thus sell their losing stocks before the year ends, especially the stocks of smaller firms that institutions tend to avoid. The selling pressure in late December is then followed by buying pressure in January [

The second explanation offered for the seasonal-size effect is the risk mismeasurement hypothesis that the size effect in January may be associated to the increased risk for small firms in January [

Krueger and Johnson [

The recent explanation for seasonal-size effect is the culture bonus hypothesis proposed by Chen and Chien [

This study uses a sample period of the pre-2007 global financial crisis, which ranges from January 1995 to December 2006, for the Hong Kong stock market. This sample period is different from the ten-year period of 1984 to 1993 in Chui and Wei [

The Fama and MacBeth [^{1}. The first step is to perform the following cross-sectional regression model [

where R_{it} is the monthly return of firm i at month t, and R_{mt} is the value-weighted market return at month t. R_{it} − R_{mt} represents the excess returns. Size is defined as the logarithm of the i^{th} firm’s market value at the end of the preceding year. The next step is to calculate the time series means of the monthly regression slopes, and then provide standard tests of whether the size effect in January or non-January months exists. On the other hand, this paper uses the Sharpe ratio as the dependent variable to examine the risk mismeasurement hypothesis [^{2}. The Sharpe ratio of each firm is defined as the raw stock return minus the risk-free return and divided by the standard deviation of daily stock returns for a given month.

On the other hand,

Parameters | Parameter estimate | N | R^{2} (Adj R^{2}) |
---|---|---|---|

Panel A: January-December | |||

Intercept | 4.1456^{*} | 98,436 | 0.0161 |

Size | −0.2770^{*} | (0.0145) | |

Panel B: January | |||

Intercept | 9.9340 | 8203 | 0.0269 |

Size | −0.6012 | (0.0253) | |

Panel C: Non-January | |||

Intercept | 3.6194 | 90,233 | 0.0151 |

Size | −0.2475^{*} | (0.0135) |

Note: ^{**} and ^{*} denote 1% and 5% significance level, respectively.

Parameters | January | Non-January | ||||
---|---|---|---|---|---|---|

Parameter estimate | N | R^{2} (Adj R^{2}) | Parameter estimate | N | R^{2} (Adj R^{2}) | |

Intercept | −3.2763 | 8110 | 0.0379 | −2.4487^{**} | 89,238 | 0.0209 |

Size | 0.1061 | (0.0363) | 0.0357 | (0.0193) |

Note: ^{**} and ^{*} denote 1% and 5% significance level, respectively.

Parameters | January | Non-January | ||||
---|---|---|---|---|---|---|

Parameter estimate | N | R^{2} (Adj R^{2}) | Parameter estimate | N | R^{2} (Adj R^{2}) | |

Panel A: A market is defined as bullish in the month if the index return was higher than the return of the preceding month | ||||||

Intercept | −1.1753 | 3169 | 0.0107 | −3.5574 | 43,960 | 0.0136 |

Size | 0.3181 | (0.0093) | 0.1386 | (0.0120) | ||

Panel B: A market is defined as bearish in the month if the index return was lower than the return of the preceding month | ||||||

Intercept | 15.4886 | 5034 | 0.0350 | 10.5819^{**} | 46,273 | 0.0166 |

Size | −1.0609 | (0.0334) | −0.6222^{**} | (0.0150) |

Note: ^{**} and ^{*} denote 1% and 5% significance level, respectively.

bullish rather than bearish market. Panel A shows that the coefficients on firm size are positive and insignificant in January and non-January months under the bullish market. However, Panel B shows that the coefficient of firm size is negative when the market is bearish, especially is significant at a 5% level in non-January months. This thus shows that the small firm anomaly in non-January months for Hong Kong should be not due to the expansion or bullish phase of the economic cycle. Specifically, this finding that the small firms tend to have higher stock performance only in a bearish market is more likely to imply the high risk-compensation for small firms that generally have higher risk than larger ones, especially when economic conditions are bad.

To explore whether the apparent seasonal-size anomaly in a bearish market is related to the risk factor, this study divides data into five sub-samples based on the stock risk defined as the standard deviation of daily stock returns in the preceding year and reports the analyses for the five volatility portfolios in

Parameters | January | Non-January | ||||
---|---|---|---|---|---|---|

Parameter estimate | N | R^{2} (Adj R^{2}) | Parameter estimate | N | R^{2} (Adj R^{2}) | |

Panel A: A market is defined as bullish in the month if the index return was higher than the return of the preceding month | ||||||

Panel A1: The firms with the lowest volatility (RISK1) | ||||||

Intercept | −9.5985 | 644 | 0.0424 | −9.0890^{**} | 8756 | 0.0283 |

Size | 0.6629 | (0.0357) | 0.4591^{**} | (0.0201) | ||

Panel A2: The firms with RISK2 | ||||||

Intercept | −9.5710 | 661 | 0.0195 | −7.0915^{*} | 9011 | 0.0228 |

Size | 0.9590 | (0.0127) | 0.3622 | (0.0149) | ||

Panel A3: The firms with RISK3 | ||||||

Intercept | −19.5927 | 642 | 0.0323 | −4.1338 | 8957 | 0.0238 |

Size | 1.7932^{*} | (0.0255) | 0.2101 | (0.0159) | ||

Panel A4: The firms with RISK4 | ||||||

Intercept | −12.1543 | 632 | 0.0090 | −2.3566 | 8847 | 0.0178 |

Size | 1.3587 | (0.0020) | 0.0558 | (0.0099) | ||

Panel A5: The firms with the highest volatility (RISK5) | ||||||

Intercept | 11.0479 | 590 | 0.0092 | 6.1181 | 8389 | 0.0111 |

Size | −0.6765 | (0.0017) | −0.5996^{*} | (0.0028) | ||

Panel B: A market is defined as bearish in the month if the index return was lower than the return of the preceding month | ||||||

Panel B1: The firms with the lowest volatility (RISK1) | ||||||

Intercept | 12.7491 | 990 | 0.0346 | 7.8110^{**} | 9218 | 0.0239 |

Size | −0.7817 | (0.0261) | −0.3438^{**} | (0.0160) | ||

Panel B2: The firms with RISK2 | ||||||

Intercept | 20.2523 | 1019 | 0.0534 | 10.3001^{**} | 9469 | 0.0293 |

Size | −1.2925 | (0.0453) | −0.5657^{**} | (0.0217) | ||

Panel B3: The firms with RISK3 | ||||||

Intercept | 15.9281 | 1027 | 0.0321 | 13.2938^{**} | 9402 | 0.0275 |

Size | −1.1049 | (0.0239) | −0.8656^{**} | (0.0198) | ||

Panel B4: The firms with RISK4 | ||||||

Intercept | 28.8828 | 1018 | 0.0401 | 13.1765^{**} | 9303 | 0.0213 |

Size | −2.1690 | (0.0320) | −0.8661^{**} | (0.0136) | ||

Panel B5: The firms with the highest volatility (RISK5) | ||||||

Intercept | 25.0918 | 980 | 0.0369 | 20.8609^{**} | 8881 | 0.0191 |

Size | −1.9707 | (0.0285) | −1.4832^{**} | (0.0111) |

Note: ^{**} and ^{*} denote 1% and 5% significance level, respectively.

A number of sensitivity tests confirm the robustness of the findings. First, this study employs different definitions of the bullish/bearish market, such as whether the index return was higher than the median return of the sample period or the same year, and whether the index return was positive. The results shown in

Parameters | January | Non-January | ||||
---|---|---|---|---|---|---|

Parameter estimate | N | R^{2} (Adj R^{2}) | Parameter estimate | N | R^{2} (Adj R^{2}) | |

Panel A1: A market is defined as bullish in the month if the index return was higher than the median return of the sample period | ||||||

Intercept | −5.6075 | 3011 | 0.0150 | −1.3072 | 52,744 | 0.0139 |

Size | 0.4712 | (0.0136) | 0.0317 | (0.0123) | ||

Panel A2: A market is defined as bearish in the month if the index return was lower than the median return of the sample month | ||||||

Intercept | 17.7047 | 5192 | 0.0328 | 10.1017^{**} | 37,489 | 0.0167 |

Size | −1.1374 | (0.0312) | −0.6150^{**} | (0.0151) | ||

Panel B1: A market is defined as bullish in the month if the index return was higher than the median return in the same year | ||||||

Intercept | −5.6075 | 3011 | 0.0150 | −0.7111 | 50,764 | 0.0137 |

Size | 0.4712 | (0.0136) | −0.0036 | (0.0121) | ||

Panel B2: A market is defined as bearish in the month if the index return was lower than the median return in the same year | ||||||

Intercept | 17.7047 | 5192 | 0.0328 | 9.1445^{**} | 39,469 | 0.0169 |

Size | −1.1374 | (0.0312) | −0.5587^{**} | (0.0153) | ||

Panel C1: A market is defined as bullish in the month if the index return was positive | ||||||

Intercept | −5.6075 | 3011 | 0.0150 | −0.7795 | 55,970 | 0.0132 |

Size | 0.4712 | (0.0136) | 0.0028 | (0.0116) | ||

Panel C2: A market is defined as bearish in the month if the index return was negative | ||||||

Intercept | 17.7047 | 5192 | 0.0328 | 10.6058^{**} | 34,263 | 0.0182 |

Size | −1.1374 | (0.0312) | −0.6451^{**} | (0.0166) |

Note: ^{**} and ^{*} denote 1% and 5% significance level, respectively.

Parameters | January | Non-January | ||||
---|---|---|---|---|---|---|

Parameter estimate | N | R^{2} (Adj R^{2}) | Parameter estimate | N | R^{2} (Adj R^{2}) | |

Panel A: The sub-period in which the sum of earnings before tax per employee of all firms in the preceding year was higher than the year before last | ||||||

Intercept | 22.0810 | 3483 | 0.0489 | −0.7737 | 38,313 | 0.0157 |

Size | −1.4613 | (0.0474) | −0.0067 | (0.0142) | ||

Panel B: The sub-period in which the sum of earnings before tax per employee of all firms in the preceding year was lower than the year before last | ||||||

Intercept | 1.1352 | 4720 | 0.0112 | 6.6507^{*} | 51,920 | 0.0147 |

Size | 0.0191 | (0.0096) | −0.4133^{*} | (0.0131) |

Note: ^{**} and ^{*} denote 1% and 5% significance level, respectively.

Parameters | January | Non-January | ||||
---|---|---|---|---|---|---|

Parameter estimate | N | R^{2} (Adj R^{2}) | Parameter estimate | N | R^{2} (Adj R^{2}) | |

Panel A: The sub-sample in which the amount and growth rate of earnings before tax were both positive in the preceding year | ||||||

Intercept | 12.2442 | 2940 | 0.1055 | 2.5808 | 32,340 | 0.0584 |

Size | −0.7680 | (0.0709) | −0.1572 | (0.0038) | ||

Panel B: The sub-sample in which the amount and growth rate of earnings before tax were not both positive in the preceding year | ||||||

Intercept | 8.3725 | 3475 | 0.0511 | 4.9335 | 38,225 | 0.0451 |

Size | −0.4587 | (0.0256) | −0.3948^{*} | (0.0217) |

Note: ^{**} and ^{*} denote 1% and 5% significance level, respectively.

This is a comprehensive study using Hong Kong stock market to explore the seasonal-size anomaly in this emerging international market along with a comparison of alternative hypotheses. This study utilizes the Fama- MacBeth regression method and finds several results. First, the Hong Kong stock market does not exhibit an apparent size effect in January, but exhibits a significant small firm anomaly in non-January months. This supports the finding reported earlier by Chui and Wei [

The findings suggest that a relationship exists between the seasonal-size anomaly and the risk compensation explanation. Once the stock returns are adjusted appropriately for individual risk by using the Sharpe ratio, the seasonal-size anomaly disappears, which tends to support the risk mismeasurement hypothesis. In addition, the seasonal-size effect in Hong Kong should be not attributed to the economic cycle hypothesis or the tax-loss selling hypothesis offered in prior literature, because that the small firms do not significantly outperform large firms in the bullish market and there are no capital gain tax or loss offsets in Hong Kong, respectively. The culture bonus hypothesis seems to be also not associated with the anomaly in Hong Kong with mainly institutional investors since they are less likely to have behavioral biases drawn from culture bonus, and the non-January size effect could not be due to the Lunar New Year bonuses. The findings give important economic implications of capital market behavior, and should be helpful in financial decision making.

Chieh-ShuoChen, (2016) Assessing the Impact of Risk Mismeasurement and Economic Cycle on the Seasonal-Size Anomaly in Hong Kong. Modern Economy,07,1-9. doi: 10.4236/me.2016.71001