The illiquidity premium in the Japanese textiles, apparel and luxury goods
industry
Abstract
In this paper the existence of an illiquidity premium in the Japanese textiles, apparel and luxury goods industry is researched following the methodology introduced by Amihud et al. (2015). A better insight into the existence of illiquidity premia is essential for the analysis of stock excess returns and to determine whether the excess returns can be explained by the risk of the stock or if it is due to a market inefficiency. The results in this paper show a significantly positive illiquidity premium for stocks with medium and high volatility, implying that illiquid stocks have higher returns compared to liquid stocks with similar volatility. For stocks with a low volatility no significant illiquidity premium is found. Due to a low number of stocks in illiquidity portfolios and a dubious fit of the asset pricing model used, further research is needed to strengthen the conclusions in this paper.
Lars van Alen
11880155
Statement of Originality
This document is written by Student Lars van Alen, who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
1. Introduction
Investors value stock liquidity: part of the excess return of a stock in the U.S.A. is found to be due to expected illiquidity (Amihud, 2002). A stock is considered liquid if it can be sold or bought quickly at low transaction costs at the current market price (Amihud & Mendelson, 1991). Whereas illiquidity is not directly observable, it is intuitive that an asset that can be sold quickly at low transaction costs is more valuable to investors than a similar asset that cannot be sold quickly at low costs. For short-term investors, the excess returns related to illiquidity are mitigated by the higher transaction costs of illiquid assets. However, long-term investors prefer to refrain from frequent transactions and therefore face relatively low transaction costs. Thus, they can profit from an illiquidity premium in the excess returns of an asset (Amihud & Mendelson, 1991). The existence of such an illiquidity premium has been examined across the world and is shown to be positive (Amihud, Hameed, Kang, & Zhang, 2015). This thesis examines the possible illiquidity premium across stocks in the textiles, apparel and luxury goods industry in Japan over the timeframe 2000 until 2020. It shows that, consistent with Amihud et al. (2015), there is a positive illiquidity premium on stocks with medium and high volatility. The illiquidity premium remains positive after taking common risk factors into account.
Where the focus in other papers is on the U.S. stock market over the period 1963 to 1997 (Amihud, 2002), the Korean stock market over the years 1980 to 2012 (Jang, Kang, & Lee 2015), or the global stock market from 1990 to 2011 (Amihud et al., 2015), illiquidity premia in an industry in a country outside of the U.S. are rarely examined. This leaves room for further research of illiquidity premia in individual stock markets outside of the U.S.A., which this paper aims to initiate. Jang, Kang and Lee (2017) find that from July 1962 to December 2010 crises tend to increase the illiquidity premium. Therefore, this paper contributes to the analysis of the effect of the financial crisis of 2008 on the illiquidity premium in the years after the crisis, as data is used over a more extensive period after the 2008 crisis than the Jang et al. (2015; 2017) and Amihud et al. (2015) papers.
The illiquidity measure used in this paper is based on the Amihud (2002) measure and calculates the impact of one yen of trading volume on the absolute fluctuation of daily stock returns. Following Amihud et al. (2015), the first measure of the illiquidity premium is the IML (illiquid-minus-liquid) factor that takes the differential of the returns of high illiquidity and low illiquidity portfolios that contain the 20% most illiquid and 20% most liquid stocks, respectively. These portfolios are obtained monthly by first dividing the sample in three portfolios of equal size based on volatility. Within these volatility terciles, stocks are divided into 5 portfolio of equal size containing stocks with an increasing illiquidity. In other words, the first illiquidity portfolio contains the 20% most liquid stocks and the fifth portfolio contains the 20% most illiquid stocks within each volatility portfolio. IML thus measures the illiquid-minus-liquid portfolio return, corrected for firm volatility.
The portfolio average returns are calculated using equally weighted stock returns in the month after the portfolio formation. Over the sample period the average monthly IML for the least volatile firms is insignificant at 0.47%. For firms with medium volatility, monthly IML is significantly positive with a mean of 1.56%, whilst for the most volatile firms in the sample, average monthly IML equals a significant 2.20%. The second measure for the illiquidity
premium is the risk-adjusted IML illiquidity premium, denoted αIML, which controls for the Fama and French (1993) risk factors: market excess return (MRF), firm size (SMB) and firm book-to-market value (HML). αIML is obtained by regressing IML on the risk factors, using robust standard errors. This results in an insignificant risk-adjusted illiquidity premium of 0.54% per month over the whole sample period for the least volatile firms. The risk-adjusted illiquidity premium increases for stocks with medium and high volatility: a significant αIML of 1.58% and 2.05% are found, respectively. The analysis is repeated for a pre-crisis and post-crisis subsample.
In the existing literature, the illiquidity premium is found to be positive (Amihud, 2002; Amihud et al., 2015). Amihud et al. (2015) found an average IML of 0.80% and αIML of 0.82% for return-weighted stock returns. In line with these results, a positive illiquidity premium of around 1% can be expected. The significant illiquidity premia reported in this paper are 1.56 % and 2.20% for stocks with medium and high volatility, respectively. Thus, in line with preceding literature, the illiquidity premium is found to be positive, whereas it is higher than the premia found by Amihud et al. (2015). Similarly, the illiquidity premium is found to fluctuate across stocks with different volatilities. The financial crisis is not found to significantly increase the illiquidity premium. Therefore, this paper contributes to previous research that in a number of cases illiquidity premia differ with volatility and that the 2008 crisis has not increased the illiquidity premium in the Japanese textiles, apparel and luxury goods industry. However, problems concerning the number of stocks in the illiquidity portfolios and the Fama and French (1993) risk factors that are used to calculate αIML complicate the significance of the results. Thus, further research is needed to ensure the significance of our findings.
The paper proceeds as follows. In section 2, the theoretical framework of this paper is described. The methodology and construction of the illiquidity premium measures are described in section 3. The estimates of the illiquidity premium over the sample are presented and discussed in section 4. Section 5 provides theoretical context on the performance of the Fama and French (1993) three-factor model in Japan. Section 6 presents concluding remarks and suggestions for further results.
2. Theoretical framework
Markowitz (1952) first proposes the idea that the return of the stock of a firm is related to the risk of that stock. To quantize that risk, Sharpe (1964) and Lintner (1965) propose the CAPM asset pricing model that uses the sensitivity of the returns of a firm to the market excess return – the return of the market in excess of the risk-free rate – as a measure of risk. Whilst the CAPM model does a decent job explaining excess stock returns, Fama and French (1993) find that also other common risk factors, in addition to the market excess returns, affect excess returns. Specifically, they introduce a firm value (HML) and size (SMB) factor that provide a better asset pricing model compared to CAPM. In later papers, the Fama and French (1993) three-factor model is expanded with more factors, such as momentum (Carhart, 1997) and illiquidity (Kubota & Takehara, 2010). In order to further asset pricing model development, research is needed to determine if and how illiquidity influences excess stock returns.
Amihud and Mendelson (1986) first propose a positive relationship between stock excess returns – the returns of a stock in excess of the market – and illiquidity in the U.S.A., based on stock bid-ask spreads as a measure for illiquidity. They find that higher-spread stocks, which are seen as more illiquid, require higher yields. The rationale is that the bid-ask spread decreases as a stock is traded more, i.e. is more liquid. However, microstructure data are needed for precise measures of illiquidity such as the bid-ask spread used by Amihud and Mendelson (1986), the price response to changes in stock order flow (Kyle, 1985), the price response to signed order size and the fixed cost of trading (Brennan & Subrahmanyam, 1996), the amortized effective spread – the absolute differential of the mid-point of the bid-ask spread that is quoted and the following transaction price, divided by the turnover rate – (Chalmers & Kadlec, 1998), and the trading discontinuity measure (Liu, 2006), which are not available for all stock markets. On the other hand, illiquidity measures such as share turnover (Datar, Naik & Radcliffe, 1998; Chan & Faff, 2005) and the Amihud (2002) measure, which will be addressed in more detail in one of the following sections, use more widely accessible stock data.
Constantinides (1986) and French, Schwert and Stambaugh (1987) find that expected excess return of a stock is positively related to the expected volatility of that stock. Constantinides (1986) argues that, as portfolios consisting of more volatile stocks need to be rebalanced more often, the trading costs on these portfolios are higher, which increases the return investors require on more volatile stocks. As illiquidity also has a positive relationship with stock excess returns (Amihud & Mendelson, 1986; Amihud & Mendelson, 1991; Amihud, 2002), stock illiquidity and volatility are likely correlated. Stoll (1978) validates this and finds that illiquidity is positively related to a stock’s volatility, assuming that risk-averse market makers set the bid-ask spread and it thus increases with the stock’s risk. Therefore, the IML factor is controlled for volatility in this paper.
Hagströmer, Hansson and Nilsson (2013) explore the presence of an illiquidity premium in the U.S. stock market over the period 1927 to 2010. They use a different illiquidity measure than the Amihud (2002) measure, namely the Holden (2009) effective tick proxy for the effective spread that assumes that the effective spread is equal to the price increment of the used price cluster that day. The underlying theory is that investors decide every day what price cluster they want to trade in: in pennies, nickels, dimes, quarters or whole dollars. This has the advantage of reducing trading costs, as investors will negotiate a trading price within the price cluster and will refrain from negotiating on negligible price differences. Similarly, price clustering reduces the amount of information that needs to be exchanged in order to trade. A price cluster in pennies has a smaller effective spread, and thus a higher liquidity according to this theory. Hagströmer et al. (2013) use this illiquidity measure to construct illiquidity portfolios and utilize the liquidity adjusted CAPM of Acharya and Pedersen (2005) to examine whether an illiquidity premium is present. They find an annual illiquidity premium of around 2%, which is lower than the premium found by Amihud et al. (2015). Furthermore, the illiquidity premium is found to fluctuate over time, with peaks during crises.
Jang et al. (2017) study the state-dependent illiquidity premium in the U.S. stock market from July 1962 to December 2010 and utilize the Amihud (2002) measure as an illiquidity measure, as well as the Datar et al. (1998) turnover measure and the Liu (2006) trading discontinuity measure. However, their estimations of the illiquidity premium are robust across these illiquidity measures. They find that the premium increases substantially during economic
downturns, but is relatively low in economic expansions, as found by Jang et al. (2015) in Korea. Following the implication of Jang et al. (2017) that the illiquidity premium should be considered conditional on the economic state, pre- and post-crisis subsamples are examined in this paper.
Chan and Faff (2005) look into the Australian stock market over the period 1990 to 1998 to determine whether including liquidity as a factor in the Fama and French (1993) three-factor model improves the performance of the model in asset pricing. They take share turnover as a measure for illiquidity and construct an illiquidity factor similar to IML of Amihud et al. (2015). Chan and Faff (2005) find strong support for their four-factor model that consists of the Fama and French (1993) factors and their illiquidity factor based on stock turnover. Furthermore, they conclude that the turnover factor is significantly positive.
Pástor and Stambaugh (2003) measure liquidity in the U.S. stock market using the monthly average of daily data on multiple liquidity measures of individual stocks. Primarily, the liquidity proxy measures volume-related return reversals and stock order flow, where a liquid stock is expected to generate a smaller return reversal for a given dollar volume of trading compared to a more illiquid stock. Pástor and Stambaugh (2003) construct liquidity portfolios based on this liquidity measure and find an expected return differential of 7.5% annually between illiquid and liquid stocks over the period 1966 to 1999.
All in all, there are numerous studies on the presence of an illiquidity premium, mostly concentrated on the U.S. stock market. In these papers, a positive illiquidity premium is consequently found, regardless of the illiquidity measure that is used. However, since the Amihud (2002) measure is the primary illiquidity proxy in the literature, as stated by Jang et al. (2017), it will be used as the illiquidity measure in this paper.
The illiquidity measure employed by Amihud (2002) uses daily absolute returns and the daily trading volume in dollars to measure the impact of trading one dollar on the price response. This way, illiquidity can be measured over more stock markets and over a longer period of time. Thus, according to Amihud (2002), the usability of this measure places it above other, more precise, illiquidity measures. Utilizing this measure allowed Amihud (2002) to find that from 1963 to 1997 expected stock returns increased with expected illiquidity of the stock market in the U.S.A. and that an illiquidity premium seems to be a part of stock excess returns.
Elaborating on this finding, Amihud et al. (2015) examine the presence of an illiquidity premium globally and the relation between regional and global illiquidity premia over the period 1990 to 2011. Similarly, they present a measure for the illiquidity premium. Based on the HML (high-minus-low book-to-market ratio) and SMB (small-minus-big firms in terms of market capitalization) factors of Fama and French (1993), the illiquid-minus-liquid IML factor is created, which is the differential between the returns of the most illiquid and liquid stocks. The IML factor is calculated for developed and emerging markets, along with the Fama and French (1993) factors RM (market excess return), SMB and HML. IML is then corrected for these common risk factors, resulting in risk-adjusted IML, αIML. Amihud et al. (2015) find that a positive illiquidity premium on excess returns is present across countries, also after controlling for the common risk factors mentioned above. Similarly, they find that there is commonality between the illiquidity premium across countries.
This paper replicates the methodology introduced by Amihud et al. (2015) in order to determine whether an illiquidity premium is present in the textiles, apparel and luxury goods
industry in Japan. Explicitly, an IML factor will be created and adjusted for the Fama and French (1993) common risk factors. Furthermore, the illiquidity premium is tested for robustness over time, specifically over a pre-crisis and post-crisis sub-period. In addition, this study will provide an insight into whether the Fama and French (1993) factors fit Japanese data well, which is contested by Kubota and Takehara (2018). This paper should provide a greater insight into country-specific illiquidity premia outside of the United States, opposed to earlier papers that focus on the U.S. stock markets (Amihud & Mendelson, 1986; Amihud, 2002; Pástor & Stambaugh, 2003; Hagströmer et al., 2013; Jang et al., 2017) or on regional and global illiquidity premiums (Amihud, 2015). If the results in this paper contrast the results found in earlier studies, further research is needed to address differences between the U.S.A. stock market and other stock markets in terms of illiquidity premia.
In short, this paper aims to find empirical support for an illiquidity premium in the Japanese textiles, apparel and luxury goods industry.
3. Data and methodology
The sample in this paper includes daily share data of 108 firms in the textiles, apparel and luxury goods industry, which is narrowed down to 101 firms after correcting for outliers and other irregularities. The procedure is described below. The share data ranges from 2000 to 2019, with December 31st, 2019 as the last observation, and is obtained from the Compustat Global
database. Only shares that fall within the textiles, apparel and luxury goods sector are included in the sample, with no criterium with regard to the stock exchange a stock is traded on. Daily share data will be used to calculate the Amihud (2002) measure, whereas monthly returns are calculated from the daily data in order to measure the illiquidity premium using the IML factor. Monthly Fama and French (1993) factors for Japan over the sample period of January 2000 until December 2019 are obtained from the website of Kenneth French1.
Over the whole sample period, observations without a recorded trading volume are excluded from the dataset, as well as duplicate observations. To avoid further possible data errors, daily returns that exceed 200% are excluded from the dataset (Lee, 2011). Furthermore, if either the return on stock i on day d, 𝑟!,#, or the return on stock i on day d-1, 𝑟!,#$%, is greater than 100%, and "1 + 𝑟!,#% ∗ "1 + 𝑟!,#$%% − 1 ≤ 50%, the daily returns are excluded. These conditions are based on the caution for data errors in Datastream emphasized by Ince & Porter (2006). In absence of a paper disclosing possible data errors in Compustat, the measures proposed for Datastream datasets are applied. Moreover, following Amihud (2002), stocks with an Amihud (2002) measure in the lowest or highest 1% of the sample distribution are excluded.
For every month, data on the three months prior to month t are needed to sort stocks on volatility and illiquidity. Similarly, data on month t+1 is required to calculate the return in month t+1 of a portfolio constructed in month t. Therefore, only stocks in month t that have data on months t-3 to t-1 and month t+1 are included in the sample. Data from the last three months of 1999 are used to sort stocks into volatility and illiquidity portfolio in the first three months of 2000. Data from December 1999 is used to construct the illiquidity portfolios, whose average returns over January 2000 are used in the formation of the IML factor for January 2000. 1http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html#Developed
Stocks are not required to have data on all months in a year or on all years in the sample, as these restrictions do not increase the significance of the results.
Following Amihud (2002) and Amihud et al. (2015), the daily illiquidity measure Illiqdaily is constructed: 𝐼𝑙𝑙𝑖𝑞#&!'( = )*!,#)
+,'-./!,#∗ 1,000,000.
Volumei,t measures the trading volume of stock i on day t in yen, which is calculated by multiplying the closing price of stock i on day t by the number of traded shares on that day. |ri,t| is the absolute return over day t of stock i. The measure is multiplied by 1,000,000 to ensure more intuitive illiquidity values. Illiqdaily measures the impact of one yen of trading on the price of a stock. According to this measure, one yen of trading should impact the price of an illiquid stock more than a more liquid stock. This follows the illiquidity concept of Kyle (1985), that measures illiquidity as the price response to changes in the order flow of a stock. According to Kyle (1985), a liquid market provides a narrow spread between bid and ask prices of stocks. Thus, in a liquid market one dollar – or, in this case, yen – of trading should influence the current market price less than it would in an illiquid market. Whilst there are more accurate illiquidity estimates based on microstructure data, the Amihud (2002) measure is based on widely accessible stock data. Furthermore, the Amihud (2002) measure and illiquidity measures that use less accessible microstructure data are strongly positively related (Amihud, 2002). Therefore, it makes sense to estimate illiquidity with the Amihud (2002) measure. The daily estimate of illiquidity Illiqdaily will from now on be referred to as the Amihud (2002) measure. The effect of illiquidity on returns is estimated by the IML factor, which is constructed by taking the difference in returns between a portfolio of illiquid stocks and a portfolio of liquid stocks. The formation of these illiquidity portfolios is based on the portfolio formation described by Amihud et al. (2015). To control for volatility, stocks are pre-sorted on volatility before sorting them into illiquidity portfolios.
In each month t, stocks are sorted into three portfolios by the standard deviation of their daily returns in month t-3, t-2 and t-1, with thresholds on the 33th and 66th percentile. For every
stock i, the mean of the Amihud (2002) measure over a rolling window from months t-3 to t-1 is assigned to stock i in month t. Within the volatility terciles, stocks are then sorted into five portfolios by their average Amihud (2002) measure over months t-3 to t-1, with thresholds on the 20th, 40th, 60th and 80th percentile. Thus, in each month t, stocks are sorted into a total of 15
portfolios. The portfolios are visualized in panel D of Table 1 below.
The portfolio returns in month t+1 of a portfolio constructed in month t are calculated by taking the equally weighted average of monthly returns of the stocks in the portfolio over month t+1. According to Da, Liu and Schaumburg (2013), liquidity shocks are subject to short-term return reversals. Therefore, the month t in which the portfolios are constructed is not taken into account in the calculation of portfolio returns.
IML for month t is then calculated as the return differential in month t between the most illiquid and most liquid stocks in month t-1, which represents the excess return premium on illiquid stocks. Specifically, in each month, within each volatility portfolio, the average return of the least illiquid portfolio is subtracted from the average return of the most illiquid portfolio, where both portfolios are constructed in the previous month. Therefore, only the first and fifth quintile portfolio are used. Since each illiquidity portfolio consists of in between four and six stocks, this can be problematic for the significance of the IML factor. A low number of stocks
Table 1
Descriptive statistics.
Panel A presents descriptive statistics for each illiquidity portfolio. “N” is the total of valid observations that are in each portfolio over the sample period. “Illiq mean” is the average Amihud (2002) measure in month t, rolling every month over the three months prior to month t over the whole sample period. “Average monthly portfolio return” is the equally weighted average monthly return of stocks in each illiquidity portfolio, that is constructed in month t-1, over the whole sample period, which is tested for significance using the Student’s t-test with the null hypothesis: H0: average portfolio return = 0. “Standard Deviation” is the standard deviation of the monthly returns of each portfolio over the whole sample period. “Average number of stocks per month per illiquidity portfolio” is the average number of stocks per month in the concerning illiquidity portfolio within the volatility portfolio.
Panel B presents the descriptive statistics over the whole sample period of IML and the Fama and French (1993) risk factors. “Number of months” is the number of months that provided valid IML and risk factor values over the sample period. “Factor average” is the average monthly value of each factor, which is tested for significance using the Student’s t-test with the null hypothesis: H0: factor average = 0. “Standard deviation” is the monthly standard deviation of each factor.
Panel C presents the number of stocks that are available each month for sorting into volatility portfolios and, within the volatility portfolios, for sorting into illiquidity portfolios. “Average number of stocks” is the average number of stocks that are available for sorting into the aforementioned portfolios each month over the whole sample. “Minimum number of stocks” is the minimum number of stocks that is available each month. “Maximum number of stocks” is the maximum number of stocks that is available each month.
Panel D presents the illiquidity portfolio construction. Panel A: Descriptive statistics per portfolio
Portfolio N Illiq mean Average monthly portfolio return
Standard deviation
Average number of stocks per month per
illiquidity portfolio
Low Volatility Low Illiquidity
1260 0.0002 0.3267% 0.0545 5.2292
Low Volatility High Illiquidity 1048 0.0200 0.7957%** 0.0509 4.3458 Medium Volatility Low Illiquidity 1252 0.0002 1.1364%* 0.1025 5.1958 Medium Volatility High Illiquidity 1039 0.0304 2.6939%*** 0.1531 4.3083
High Volatility Low Illiquidity
1242 0.0007 -0.0349% 0.1005 5.1542
High Volatility High Illiquidity
1029 0.0408 2.1620%*** 0.1279 4.2667
Panel B: Descriptive statistics of IML and Fama and French (1993) factors over the sample period
Factor Number of months Factor average Standard Deviation
Fama-French factors MktRF 240 0.1270 4.5675
SMB 240 0.3052* 2.5640
HML 240 0.5169*** 2.9461
Low Volatility Portfolio IML 240 0.4690 5.5053
Medium Volatility Portfolio IML 240 1.5575* 12.5729
Table 1 (continued)
Panel C: Number of stocks available for sorting into each portfolio each month
Number of stocks available for Average number of stocks Minimum number of stocks Maximum number of stocks Sorting on volatility 71.2282 57 84
Sorting within low illiquidity portfolio 24.0833 19 28
Sorting within medium illiquidity portfolio 23.7458 19 28
Sorting within high illiquidity portfolio 23.3750 19 28
Panel D: Illiquidity Portfolio Construction
Volatility tercile
Illiquidity quintile Low Medium High
Q1 (0%-20%) Liquid Low Volatility Liquid Medium Volatility Liquid High Volatility
Q2 (20%-40%) … … …
Q3 (40%-60%) … … …
Q4 (60%-80%) … … …
Q5 (80%-100%) Illiquid Low Volatility Illiquid Medium Volatility Illiquid High Volatility *p<0.1; **p<0.05; ***p<0.01
in each portfolio results in a greater influence of firm-specific factors on portfolio returns, which can deteriorate the estimated illiquidity premium.
Descriptive statistics of the sample are presented in Table 1 above. In panel A, the number of observations, the average value of the Illiq measure, the equally weighted average monthly returns, the standard deviation of the monthly returns and the average number of stocks per month are described for each illiquidity portfolio that is used to construct the IML factor over the whole sample period. The mean of the Illiq measure in each illiquidity portfolio increases with the volatility portfolios, primarily in the high illiquidity portfolios, in line with the positive relationship between illiquidity and volatility proposed by Stoll (1978). The equally weighted average return of the illiquid portfolio is higher than that of the liquid portfolio in each volatility portfolio, which implies that an illiquidity premium is present. This is in line with preceding literature described in the theoretical framework. The Student’s t-test is used to test the null hypothesis that average monthly portfolio return equals 0. The low illiquidity portfolio returns are found to be significantly different from 0 for stocks with medium volatility at the 10% level. The average monthly returns for the high illiquidity portfolios are all significantly positive, regardless of the volatility. In the medium and high volatility portfolios, the standard deviation of monthly returns is higher for illiquid stocks, which is again in line with Stoll (1978). However, this is not the case for the lowest volatility portfolio, which shows a negative relationship between volatility and illiquidity.
Descriptive statistics of the Fama and French (1993) common risk factors and the IML factor for each volatility portfolio are presented in panel B. The common risk factors used by Fama and French (1993) are MktRF, SMB and HML, where MktRF is the market excess return, SMB is the size factor return and HML is the value factor return. SMB is calculated as the return differential of small and big firms in terms of market capitalization, whilst HML is calculated
as the return differential of high and low value firms in terms of their book-to-market equity ratio. All factors have data over 240 months (January 2000 until December 2019). Using Student’s t-test, IML is found to be significantly different from 0 at the 10% and 5% level for the medium and high volatility portfolio, respectively, whereas IML is insignificant for the low volatility portfolio. Similarly, HML is significant at the 1% level over the whole sample period, SMB is significant at the 10% level and MktRF is insignificant.
The number of stocks that is available per month for portfolios sorting is presented in panel C of Table 1. Each illiquidity portfolio consists of between 1029 and 1260 valid observations over the whole sample period. Per month, between 57 and 84 firms are sorted into three volatility portfolios, which is far lower than the 2176 stocks that were sorted on average per month in Japan in the Amihud et al. (2015) paper. This is due to the focus in this paper on the textiles, apparel and luxury goods industry, which naturally contains less stocks than the whole Japanese stock market. Within the volatility portfolios, there are between 19 and 28 stocks that are sorted into the five illiquidity portfolios. This amounts to a portfolio consisting of between 3 and 6 stocks. There is a clear difference in the number of stocks in each illiquidity portfolio: the low illiquidity portfolios consist of a higher number of stocks compared to the high illiquidity portfolios. Each month, within each volatility portfolio, the stocks are sorted based on their illiquidity in five portfolios, each consisting of 20% of the observations within the volatility portfolio. When the number of observations within a volatility portfolio in a certain month is not dividable by 5, the stocks in the lower illiquidity portfolios are filled first and the highest illiquidity portfolio is filled with the remaining stocks. Thus, if the low volatility portfolio in month t consists of 24 stocks, the first four illiquidity portfolios consist of 5 stocks, whilst the fifth illiquidity portfolio, i.e. the highest illiquidity portfolio, consists of 4 stocks. This explains the difference in the average number of firms in the high and low illiquidity portfolios. The same reasoning applies for the average number of stocks per month in each volatility portfolio, which is also decreases from the lowest to the highest volatility portfolio.
Panel D presents a visualization of the formation of the illiquidity portfolios. 4. Results
The results of the regression of IML on the common risk factors is presented in panel A in Table 2. The regression follows the formula:
𝐼𝑀𝐿0,1 = 𝛼234,0+ 𝛽%,0∗ 𝑀𝑘𝑡𝑅𝐹1+ 𝛽5,0∗ 𝑆𝑀𝐵1+ 𝛽6,0∗ 𝐻𝑀𝐿1+ 𝑒0,1
The subscript v denotes the volatility portfolio (low, medium or high) and the subscript t refers to the month each factor value belongs to.
In order to examine whether the illiquidity premium in the Japanese textiles, apparel and luxury goods industry is robust over time or was influenced by the financial crisis of 2008, a pre-crisis and post-crisis subsample is created. The collapse of Lehman Brothers on September 14th, 2008 is chosen as the starting date of the crisis, as this bankruptcy can be seen as a
catalysator for the crisis in the global financial system (Fernando, May, & Megginson, 2012). Following Katada (2013), we take January 2013 as the first month of the post-crisis period, as the recovery of the Japanese economy began at that time. September 2001 is chosen as the starting date of the pre-crisis period to ensure that the subsamples are of equal size (84 months). Thus, the pre-crisis subsample consists of observations over the period September 2001 to
Table 2
The illiquidity return premium, measured by IML and αIML.
Presented below are the regression results for the regression: 𝐼𝑀𝐿!,#= 𝛼$%&,!+ 𝛽',!∗ 𝑀𝑘𝑡𝑅𝐹#+ 𝛽(,!∗ 𝑆𝑀𝐵#+ 𝛽),!∗
𝐻𝑀𝐿#+ 𝑒!,#, where IML is the illiquid-minus-liquid illiquidity factor, αIML is the regression intercept and serves as the risk-adjusted IML, MktRF is the excess market return, SMB is the small-minus-big size factor, HML is the high-minus-low book-to-market ratio value factor and e is the error term. The subscript v denotes the volatility portfolio (low, medium or high) and the subscript t refers to the month each factor value belongs to. For all regressions, the number of observations, R2, adjusted R2
and the percentage of risk-adjusted IML, αIML, over IML is disclosed. Panel A presents the results for the three volatility portfolios over the full sample. Panel B present the results for the volatility portfolios over the pre-crisis subsample. Panel C presents the results for the volatility portfolios over the post-crisis subsample. Panel D presents the results of the regression for each (sub)sample using IML factors that are not controlled for volatility. Panel E presents the portfolio characteristics of the illiquidity portfolios when portfolios are not controlled for volatility, but sorted directly into illiquidity portfolios. For each sample, IML is tested for significance using Student’s t-test with the null hypothesis H0: mean IML = 0.
Panel A: Full Sample
Portfolio:
Low Volatility Medium Volatility High Volatility
MktRF -0.1670** -0.4273** 0.1419 SMB 0.2481** 0.8729*** 0.1500 HML -0.2437** -0.4464 0.1594 αIML 0.5405 1.5762* 2.0508** Number of observations 240 240 240 R2 4.76% 6.66% 0.32% Adjusted R2 3.55% 5.47% -0.94%
αIML over IML 115.25% 101.20% 93.35%
IML 0.4690 1.5575* 2.1969**
Panel B: Pre-Crisis
Portfolio:
Low Volatility Medium Volatility High Volatility
MktRF 0.0304 -0.2605 0.3231 SMB 0.2898* 1.1534*** 0.0036 HML 0.2294 0.6735* 0.9092** αIML 0.5940 0.3519 1.4612 Number of observations 84 84 84 R2 4.81% 19.35% 6.11% Adjusted R2 1.24% 16.32% 2.59%
αIML over IML 76.54% 43.51% 66.91
IML 0.7761* 0.8088 2.1837**
Panel C: Post-Crisis
Portfolio:
Low Volatility Medium Volatility High Volatility
MktRF -0.2570 -0.7972 0.3208
SMB 0.0445 -0.4480 0.1716
Table 2 (continued)
Panel C: Post-Crisis
Portfolio:
Low Volatility Medium Volatility High Volatility
αIML -0.5368 3.0826 1.9047
Number of observations 84 84 84
R2 3.94 % 6.70% 2.95%
Adjusted R2 0.34% 3.20% -0.69%
αIML over IML 85.38% 111.04% 77.19%
IML -0.6287 2.7762 2.4674
Panel D: Regression results using IML without controlling for volatility
Sample:
Full Sample Pre-Crisis Post-Crisis
MktRF -0.0258 0.0991 -0.2675 SMB 0.5512*** 0.8045*** -0.1366 HML -0.1741 0.6197** -1.0175*** αIML 1.2212*** 0.6206 1.3326* Number of observations 240 84 84 R2 6.62% 20.82% 17.37% Adjusted R2 5.43% 17.85% 14.27%
αIML over IML 94.22% 55.50% 95.49%
IML 1.2961*** 1.1181* 1.3956*
Panel E: Portfolio characteristics
Average number of stocks Minimum number of stocks Maximum number of stocks
Low Illiquidity Portfolio 14.6292 12 17
High Illiquidity Portfolio 13.7958 11 16
*p < 0.10; **p < 0.05; ***p < 0.01
September 2008, whereas the post-crisis subsample contains observations over the period January 2013 to December 2019. The results of the regressions on the subsamples are presented in panel B and C of Table 2. To control for heteroskedasticity, robust standard errors are used in the regressions. To improve the readability, the (adjusted) R2 and α
IML over IML are presented
as percentages rather than decimals, i.e. 0.0662 becomes 6.62%.
Over the three samples, αIML is significant for stocks in the medium and high volatility
portfolios over the whole sample period at the 10% and 5% level, respectively, but for none of the stocks in the pre- and post-crisis subsamples. IML is tested for significance using a Student’s t-test, testing the null hypothesis that the illiquidity premium equals 0. The IML values found for the medium and high volatility portfolios – 1.56% and 2.20%, respectively – are significant at the 10% and 5% level, respectively. The IML value for stocks with a high volatility is higher than the corresponding αIML of 2.05%, whereas the IML value for stocks with medium volatility
than the illiquidity premia of around 1% found by Amihud et al. (2015) in developed markets. Adjusting IML for the Fama and French (1993) common risk factors does not change the significance of the illiquidity premium over the whole sample period, which is in accordance with Amihud et al. (2015). However, in the pre-crisis subsample, the illiquidity premium found for low and high volatility stocks lose their significance when they are adjusted for the risk factors. For the medium and high volatility portfolios in over the full sample, where both IML and αIML are significant, αIML is 101.20% and 93.35% of the value of IML for stocks,
respectively. Thus, for these values, adjusting IML for the Fama and French (1993) risk factors barely reduces IML or even increases it, which is in line with Amihud et al. (2015), who also obtain an αIML that is higher or almost equal to IML. This suggests that the Fama and French
(1993) factors do not explain a big part of the illiquidity premium, which implies that the illiquidity premium is a separate risk factor.
IML of low and high volatility stocks in the pre-crisis subsample are the only significant premia in the crisis subsamples. The risk-adjusted liquidity premium αIML is insignificant for all
volatility portfolios over the pre- and post-crisis period. Thus, whereas Hagströmer et al. (2013) and Jang et al. (2017) find that in the U.S. illiquidity premia increase during crises, the financial crisis of 2008 does not seem to have a similar effect on the illiquidity premium in the Japanese textiles, apparel and luxury goods industry.
We do not find a significant illiquidity premium for stocks in the low volatility portfolio over the whole sample period. As low volatility stocks are less risky, investors might not acknowledge illiquidity risk for these stocks, whereas higher volatility stocks are riskier, which can force investors to analyse risk factors more extensively. Moreover, as stated by Constantinides (1986), holders of more volatile portfolios need to rebalance their portfolio more often. Therefore, investors that hold high volatility stocks should value liquidity highly in order to sell stocks quickly and at low costs when they need to rebalance their portfolio. In other words, it is logical that stocks with a higher volatility have a higher illiquidity premium, which is shown by the higher significant values of IML and αIML of high volatility stocks in this sample
compared to medium and low volatility stocks. However, further research could be determined to whether an illiquidity premium is indeed completely absent for stocks with a low volatility. The Fama and French (1993) common risk factors are predominantly significant. MktRF is significant for low and medium volatility stocks over the whole sample. The SMB factor is significantly positive over the whole sample period and the pre-crisis period for stocks with low and medium volatility. HML is significant for the whole sample in the low volatility portfolio and for highly volatile stocks in the pre-crisis and post-crisis subsamples. In addition, HML is significant for stocks with medium volatility in the pre-crisis period. The adjusted R2 fluctuates
heavily with 0.34% in the low volatility portfolio over the post-crisis period as the lowest value – meaning that only 0.34% of IML is explained by the Fama and French (1993) factors – but 16.32% for medium volatility stocks in the pre-crisis period as the highest value. However, the adjusted R2 is mostly below 4% and the R2 is mostly below 6%. In contrast, Amihud et al.
(2015) find an R2 of around 20% for the regression of IML on regional and global Fama and
French (1993) risk factors. This suggests that the Fama and French (1993) factors do not explain the illiquidity premium measured by IML as well in our sample compared to the Amihud et al. (2015) paper, which is explored further in the next section.
In order to increase the number of stocks in each illiquidity portfolio, the same regressions are also run using an IML factor that is not controlled for volatility. In this case, stocks are not sorted into three volatility portfolios each month, but immediately into five illiquidity portfolios. Hence, each month on average 71 stocks are sorted into five illiquidity portfolios, as opposed to 24 stocks, increasing the number of stocks in each illiquidity portfolio to on average 14.63 and 13.80 stocks for the liquid and illiquid portfolio, respectively, which improves the diversification in each portfolio. The results and characteristics of the illiquidity portfolios are presented in panel D and panel E of Table 2. The main results will be described succinctly. IML and αIML are 1.30% and 1.22%, respectively, and highly significant at the 1% level over the
whole sample period. IML equals 1.12% and 1.40% for the pre- and post-crisis subsamples, respectively, and is significant at the 10% level for both subsamples. The illiquidity premium in the pre-crisis subsample become insignificant after controlling for the Fama and French (1993) risk factors, but the premium in the post-crisis subsample remains significant with a value of 1.33%, suggesting that the financial crisis of 2008 might have increased the illiquidity premium. The Fama and French (1993) common risk factors do not explain IML very well for the full sample, as only SMB is significant and the adjusted R2 is 5.43%. On the other hand,
SMB and HML are both significant for the pre-crisis period, with an adjusted R2 of 17.85%.
Only HML is significant over the post-crisis subsample, but the adjusted R2 is amongst the
highest found in this paper, at 14.27%. Thus, the common risk factors explain IML better in the pre- and post-crisis period, but the resulting αIML becomes significant in the pre-crisis sample.
In conclusion, an illiquidity premium seems to be required by investors in Japanese stocks with medium and high volatility in the textiles, apparel and luxury goods industry. However, due to crucial flaws in portfolio size and a questionable performance of the Fama and French (1993) factors in adjusting IML for common risk factors, further research with improved portfolio size and another asset pricing model that might better fit Japanese stock returns is needed to solidify this conclusion.
5. Literature on the performance of the Fama and French (1993) three-factor model in Japan
Multiple articles are written on the performance of the Fama and French (1993) three-factor model in Japan (Jagannathan, Kubota, & Takehara, 1998; Kubota & Takehara, 2010; Kubota & Takehara, 2018). Kubota and Takehara (2018) focus primarily on the Fama and French (2015) five-factor model over the period January 1978 to December 2014, but use the three-factor model as a benchmark, which provides seven years of updated data on the three-three-factor model performance in Japan compared to the Kubota and Takehara (2010) paper, where share data from January 1977 to December 2007 is used.
Whereas Jagannathan et al. (1998) find that the cross-sectional excess stock returns in Japan are explained rather well by the Fama and French (1993) three-factor model, the results of Kubota and Takehara (2018) are less convincing. They find that MktRF is insignificant for the three-factor model, as well as the SMB factor. HML is significant and positive.
Kubota and Takehara (2010) find that the Fama and French (1993) three-factor model adequately explains the risk-return relationship of stock data in Japan, but reject the model on the basis of a mean-variance efficiency test in favour of a five-factor model that expands the
Fama and French (1993) three-factor model with an LMW (losers-minus-winners) reversed momentum factor and an IML illiquidity factor. However, the illiquidity portfolios used in the formation of the IML factor used by Kubota and Takehara (2010) are based on the equally weighted average of illiquidity measures for a single stock, which differs from the Amihud (2002) measure employed in this study. Therefore, further research is needed to determine the comparability of these different IML factors.
Amihud et al. (2015) employ a more extensive regression that regresses IML on both global and regional Fama and French (1993) factors, whereas in this paper IML is only regressed on regional common risk factors, namely those of Japan. Amihud et al. (2015) observe significant regional MktRF and SMB factors, but insignificant HML factors, which contradicts the results of Kubota and Takehara (2018), who only found a significant HML value. All in all, the Fama and French (1993) common risk factors seem to fit the data used by Amihud et al. (2015) quite well, but they only provide average values of the risk factors over all countries, not specifically for Japan. Thus, the three-factor model might not have produced significant results in Japan. Amihud et al. (2015) do not mention whether the Fama and French (1993) factors are more significant in certain countries compared to others.
MktRF is significant for low and medium volatility stocks in the full sample and it is found to be negative, which is in line with Amihud et al. (2015). All significant values found of SMB in this paper, for low and medium volatility stocks over the whole sample and in the pre-crisis period, are positive, which is in accordance to the values found of SMB by Amihud et al. (2015). HML is significant and positive for the medium and high volatility portfolio in the pre-crisis subsample, which is in accordance with Kubota and Takehara (2018). However, HML is significant and negative in the high volatility portfolio over the post-crisis subsample and in the low volatility portfolio over the whole sample. In the sample that ignores controlling for volatility, MktRF is insignificant for the full sample and both subsamples. SMB is positive and highly significant over the full sample period and the pre-crisis subsample. In the pre-crisis subsample, HML is positive and significant, whereas HML becomes negative and significant in the post-crisis subsample. Over the whole sample period, HML is insignificant.
In summary, there is no clear consensus on the performance of the Fama and French (1993) common risk factors in explaining stock excess returns in Japan. Earlier studies (Jagannathan et al., 1998; Kubota & Takehara, 2010) find that the Fama and French (1993) three-factor model explains excess returns in Japan well, whereas a newer study by Kubota and Takehara (2018) finds that the risk factors are mostly insignificant when applied to Japanese stock data. This study shows contrasting values of the HML factor, which could be explained if the Fama and French (1993) factors, or HML specifically, are indeed unsuitable to explain stock excess returns in Japan. Amihud et al. (2015) found insignificant values of HML, which would suggest that HML does not explain the illiquidity premium. Another possible explanation would be if HML indeed has a different effect on the illiquidity premium across stock with different volatilities and over different time periods in Japan. Therefore, future research could expand the research on the effect of the Fama and French (1993) risk factors on the illiquidity premium IML and the HML factor specifically. Another avenue for future research would be to control IML for another common risk factor than the HML factor, which could improve the measure for the risk-adjusted illiquidity premium, αIML.
6. Conclusion
Over the whole sample period, an illiquidity premium in excess stock returns is present for stocks with medium and high volatility in the Japanese textiles, apparel and luxury goods industry. Both IML and the risk-adjusted illiquidity premium αIML have significant values at the
5% or 10% level. The premium is highest for stocks with the highest volatility. Whereas the Fama and French (1993) risk factors are predominantly significant in the regressions, the value of the HML factor fluctuates heavily. Similarly, the proportion of IML is explained by the risk factors is quite low: the proportion of αIML over IML, when both αIML and IML are significant,
is between 93.35% and 101.20%, suggesting that the risk factors do not explain IML well. However, this is in line with Amihud et al. (2015), which implies that the illiquidity premium could be a separate risk factor that is mostly unrelated to the Fama and French (1993) factors. On the other hand, Kubota and Takehara (2018) find that the three-factor model proposed by Fama and French (1993) does a poor job explaining Japanese stock excess returns. Thus, further research could use another asset pricing model in the analysis of the illiquidity premium and excess returns to examine whether the illiquidity premium is indeed a separate risk factor. Kubota and Takehara (2010) propose a five-factor model that adds an LMW and IML factor, which differs from the IML factor utilized in this paper. Therefore, future research could examine the performance of a five-factor model that employs the IML measure used in this paper on Japanese stocks.
The illiquidity premium cannot be concluded to be robust over time, as IML only has significant values in the pre-crisis subperiod, whilst αIML has insignificant values in both the
pre-crisis and post-crisis period. However, the textiles, apparel and luxury goods industry can be expected to suffer relatively more from a financial crisis than other industries, as luxury goods are plausibly among the first goods that are consumed less during a financial crisis. Moreover, Hagströmer et al. (2013) and Jang et al. (2017) find that the illiquidity premium increases during financial crises. Thus, additional research is needed to establish that the financial crisis indeed did not have a significant effect on the illiquidity premium in this industry or other industries in Japan.
As the number of stocks inside the illiquidity portfolios is only four on average, additional regressions are performed using illiquidity portfolios that consist of more stocks but are not controlled for volatility. The results of these regressions are mostly similar to those of the regressions that are controlled for volatility. IML is positive and significant over the whole sample, pre-crisis and post-crisis period. However, IML becomes insignificant when it is adjusted for the Fama and French (1993) risk factors in the pre-crisis subsample. Over the whole sample and the post-crisis period, the illiquidity premium remains significantly positive after adjusting for risk factors. This would suggest that the illiquidity premium did become significant after the crisis, in line with the expectation of Hagströmer et al. (2013) and Jang et al. (2017). However, as the illiquidity portfolios are not controlled for volatility in these regressions, the resulting values of IML and αIML are likely biased. Therefore, future research
should repeat the portfolio construction employed in this paper that does control for volatility to examine the illiquidity premium in the whole Japanese stock market. Studying the whole stock market results in more stocks in each illiquidity portfolio and leaving out the sorting on volatility to improve the number of stocks in each illiquidity portfolio will be unnecessary.
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