Size Effect In China

The size effect refers to the negative relationship between firm size and expected returns.On average,small firms tend to have higher risk-adjusted returns than large firms.Banz（1981）first reports the size effect.Fama and French（1993）use the longshort portfolio to construct the size factor（SMB）which is one of the most widely used factors.The size effect is important for both academic research and investment practice.With the development of quantitative investment in China,the Smart Beta strategies have been prevalent recently and investors are optimizing the weighting and stock selection of their portfolios to capture the size effect.However,the existing researches mainly focus on the US market.Researches on size effect in China are relatively few.The Chinese equity market is the second-largest in the world and finances an economy which may become the world’s largest within one or two decades.This market ought not to be overlooked.Moreover,the China equity market has a relatively short history and exhibits several unique characteristics,which significantly explains the size premium as shown in our research.This paper is intended to fill this gap.We focus on size effect and its causes.More recent researches debated over whether the size effect still exists.Schwert（2003）notes that “it seems that the small-firm anomaly has disappeared since the initial publication of the papers that discovered it”.Similar results are obtained by Israel ＆Moskowitz（2013）.Asness et al.（2018）show that if quality is controlled for,the size effect still matters.Hou and van Dijk（2019）report that even though the size effect has disappeared from ex post realized returns,the size effect in ex ante expected return is robust.Most of previous studies focus on the size effect measured by market value.The size effect measured by other operating characteristics and the influence of different measures on the size effect are less explored.In existing research since the size effect was first proposed by Banz（1981）,many financial economists have examined and attempted to explain it from different perspectives（Van Dijk,2011）.The first explanation is the theory of risk premia.Berk（1995）argues that the reason why size can predict returns is not correlated with the operating characteristics it measures but is due to its market characteristics.Market value can capture risk premia.Firms with low market value are generally riskier than those with higher market value,and in turn require higher returns to compensate for risk.According to Berk’s argument,the other non-market-based measures cannot produce a significant size premium.The second possible explanation is the theory of liquidity.Amihud（2002）uses the illiquidity premium to explain the size effect and argues that size is a proxy for liquidity.Acharya and Pedersen（2005）provide evidence that liquidity risk can affect asset pricing and the pricing model containing liquidity risk has a better performance explaining the size effect than the standard CAPM.Asness et al.（2018）use an illiquidity factor to explain the size premium and prove that the size factor has a significantly positive exposure on the illiquidity factor.The third potential explanation is information uncertainty.Statistically,compared with large listed companies,small caps tend to have a shorter traceable history,attract less attention from analysts,and have less strict mandatory disclosure requirements,and in turn,have a higher level of information uncertainty on average.Merton（1987）suggests that firms which lack popularity and have a smaller investor base command higher returns.Hou and Moskowitz（2005）show that the price delay to information,for which investor recognition are responsible,can explain part of the size effect.Existing researches also show evidences that the amount of information available is related to firm size and the level of information uncertainty has an impact on subsequent returns.Insufficient information of small firms limits investors’ diversification and attributes to higher returns（Banz,1981）.Firm size and age are regarded as useful measures of information uncertainty（Jiang,Lee,＆ zhang,2005;Zhang,2006）.Besides these three explanations we mentioned above,there are also other market-specific explanations.Liu,Stambaugh,and Yuan（2019）have shown that the strict IPO regulation and the large proportion of retail investors significantly enhance the size effect.In these researches on the causes of size effect,the following issues particularly interest us,which may be also main contributions to the literature.First,we find that the size effect measured by market value is significant in China equity market.Sorting into quintile portfolio by market value,the monthly return on the smallest portfolio is significantly higher than the monthly return on the largest portfolio.The result is not affected by the frequency of rebalance and whether the sample contains ST or PT stocks.Further,the full sample is divided into two parts on the basis of different periods.We show that the size effect in the early period is weaker than that in the recent period,and the size effect in the bull market is weaker than that in the bear market.Although the January effect is empirically supported in the European and American markets,the size effect in China is not significant in January.The returns on the size effect are mainly concentrated in February,March,May and August.The performance of the size effect varies in different industries.Financial stocks did not show a significant size effect,while the size effect of non-financial stocks was more significant.The most significant size effect was among public utility stocks.Secondly,idiosyncratic volatility has an important influence on the size effect in China capital market.We calculate the size effect controlling idiosyncratic volatility through the 5×5 two-dimensional grouping method,and find that the size effect is significantly enhanced.In particular,the size effect measured by fundamental variables such as total assets,net assets,and total income becomes significant after controlling for the idiosyncratic volatility.The idiosyncratic volatility of small firms is obviously higher than that of large firms.Firms with high idiosyncratic volatility tend to get lower returns.This negative correlation between idiosyncratic volatility and expected returns has become a puzzle in academia.The negative correlation between firm size and idiosyncratic volatility weakens the significance of the size effect,resulting in an insignificant size effect measured by fundamentals.Thirdly,quality does not have an important influence on the size effect,although some foreign scholars have found that the size effect that disappeared in developed markets resurrects after controlling quality.This article examines the relationship between firm size and quality by investigating four single quality variables,that is profitability,investment level,cash dividends and accrual,as well as F-Score,a comprehensive quality variable,and find that there is no obvious relationship between quality and firm size,so it is concluded that quality have no significant impact on the（1）The existence of size effect.size effect in Chinese capital market.（2）An important finding of this article is the important role of profitability shocks.We define the profitability shock as the difference between realized profitability and expected profitability.Profitability shocks significantly affect contemporaneous returns.Firms experiencing positive shocks will have higher contemporaneous returns,while firms experiencing negative shocks tend to have low returns.Large firms often experience positive shocks,while small firms often experience negative shocks.The different performance of firms with different size in shocks has an important impact on the size effect in China capital market.When we eliminate the impact of profitability shocks on realized returns,we can get more accurate expected returns.We use this data to calculate the size effect,we find that the size effect is more significant.This improvement is more significant in total assets,book equity,and total revenue,making the insignificant size effect significant.（3）The performance of the size effects measured by different metrics.As for the theory of risk premium,the original Berk（1995）and a large number of follow-up studies argue that the fact that firm size can predict returns has nothing to do with the fundamental characteristics it measures,but because of the market characteristics it represents.However,the theory of information uncertainty explains the size anomaly in a completely different way.The latter is more inclined to agree that the important thing is firm size,rather than a specific measure of firm size.As we have seen,in the existing literature,the role of size measures in the size effect is relatively less explored.It is necessary to conduct a comprehensive study on the influence of size measures on the size effect.We find that the size effect measured by market capitalization are indeed significantly greater than that measured by fundamentals such as total assets,book equity and total revenue.We further find that there are two reasons which may explain this phenomenon: First,while the two different size measures are used to sort firms into quintile portfolios,the variation of the book-to-market ratios are significantly different.If size is measured by the market value,the ratio is 40.74% for the small portfolio and45.09% for the big portfolio,the difference between them is 4.35% with a t-value of1.97,which has just passed the significance test at the 5% level.If you use fundamental metrics,the results are quite different.For total assets,the resulting difference in the book-to-market ratio is 30.35%,with a t-value of 9.96;for book equity,the difference is 31.24%,with a t-value of 10.71;for total revenue,the differenc is 23.61%,and the tvalue is 8.12.In short,there is a significant monotonic increasing relationship between firm size measured by fundamentals and the valuation ratio.While firm size is increasing,the valuation ratio is also increasing.According to the significant positive correlation between the valuation ratio and expected returns,that is,the value effect,we find that after controlling for the value effect,the performance of the size effect measured by fundamentals has increased.The gap is decreasing.Second,the size effect measured by market value unintentionally captures the reversal effect.This is another major reason why the size effect measured by market value is more significant than the size effect measured by fundamentals.By comparing the contemporaneous returns on long-short portfolios,we find that the performance of long-short portfolios measured by market capitalization are far inferior to that constructed based on fundamentals.The contemporaneous returns of the former are significantly negative,and the contemporaneous returns of the latter are positive,though not significantly.This shows that while sorting by market capitalization,small stocks perform poorly in the previous period,which we can call losers,and large stocks perform better in the last period,which we can call winners.According to the reversal effect,stock portfolios that performed poorly in the previous period will perform better in the next period;stocks that performed well in the previous period will perform poorly in the next period.Constructing long-short portfolios on the basis of market value can not only capture the size effect,but also capture the reversal effect.The combination of the two effects leads to a significant increase in the returns on the long-short portfolio.However,the fundamental variables cannot capture this reversal effect,so the return on the long-short portfolio is not as good as that constructed by market value.We explained why different measurements have attributed to huge differences in size effects.In order to prove the reliability of our conclusion,we used a three-factor model including market factor,value factor and reversal factor to do a robustness test.The result again proves that the size effect measured by market value is more significant.Once we control these two factors,the difference in abnormal returns produced by the two different measurements is decreasing.（4）Finally,we use a multi-factor model that includes market factors,value factors,profit factors,growth factors,turnover factors,and liquidity factors to test the reasons for the existence of size effects in China capital market.We found that the size effect has a significant positive exposure to the turnover factor,indicating that investor sentiment is helpful to explain the size effect in China.Individual investors are a major feature of China capital market.These individual investors prefer small-cap stocks and have great enthusiasm for speculating on small-cap stocks,which makes the price of small-cap stocks suddenly rise during speculation and then fall sharply.Small-cap stock prices severely fluctuate with investor sentiment.Second,the size effect has a significant exposure to the liquidity factor.After adding the liquidity factor,the alpha is no longer significant.To a certain extent,firm size is a proxy for liquidity.This proves why a profitable strategy in theory cannot make money in practice.Because the size strategy requires to buy small stocks,and these stocks have poor liquidity and the large amounts of funds may lead to a rapid increase in transaction costs.The huge transaction costs are likely to lose most of the profits,making the strategy ultimately unprofitable.In addition,in order to control the shell value,we exclude 30% of the smallest stocks,confirming the impact of shell value on the size effect.After removing the shell value,the size effect is significantly reduced.