Illiquidity premium of expected excess returns
in the Japanese Healthcare sector equity market
by using Fama-MacBeth regression technique
on the Fama-French five factors model.
by
Niccolò Melacarne 11739347
Supervisor : Ms. Yumei Wang
A Dissertation
Submitted to the Faculty of Economics and Business department of Finance
University of Amsterdam
In Partial Fulfilment of the Requirements
For Bsc Business administration specialization in Finance
22 June 2020
Statement of Originality
This document is written by Student Niccolò Melacarne 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.
Abstract
This thesis aims to research the impact of illiquidity on the expected excess return of stocks in the healthcare sector listed on Tokyo stock exchange (TSE). Liquidity is referred as the easiness with which a stock can be bought and sold on the market whereas illiquidity implies the opposite effect. In this paper, the Amihud measure (Amihud, 2002) has been used as a proxy for Illiquidity. Moreover, the Fama-French five factors model (Fama and French (2015)) has been used to estimate the expected excess return of the stocks. By employing the Fama-MacBeth regression analysis, this paper provides an estimate of the risk premium associated with illiquidity for Japanese healthcare stocks for the period between June-2009 and March-2020. The results indicate the existence of a liquidity premium and a negative impact of illiquidity on expected excess returns of the stocks.
TABLE OF CONTENTS
1.INTRODUCTION ... 5
2.1ESTIMATION OF ILLIQUIDITY EFFECT ... 7
2.3FAMA FRENCH ASSET PRICING MODEL ... 9
2.4FAMA-MACBETH CROSS-SECTIONAL REGRESSIONS ... 9
3.1EXCESS RETURNS AND AMIHUD MEASURE ... 11
3.2FAMA-MACBETH PROCEDURE ... 12
3.3.HYPOTHESIS ... 14
4.DATA AND VARIABLES ... 16
4.1DATA COLLECTION ... 16 4.2VARIABLES DEFINITION ... 17 TABLE 1 ... 17 4.4DESCRIPTIVE STATISTICS ... 18 Table 2 ... 19 5.EMPIRICAL RESULTS ... 20
5.1.FM REGRESSIONS ON FAMA-FRENCH 5-FACTORS MODES ... 20
5.1.1. Beta estimates ... 20 5.1.2. Illiquidity premium ... 20 5.1.3 5-factors premia ... 21 5.1.4 Model significance ... 21 Table 3 ... 22 Table 4 ... 23
5.2FURTHER ANALYSIS FF3 AND CAPM ... 24
1.Introduction
Illiquidity premium can be seen as the premium paid to the investor for having their invested capital tied up. In the case of public listed stocks, the market is usually characterized by a considerate level of liquidity, but we can still observe the phenomenon of illiquidity. For instance, in order to better understand how this premium directly affects investors, we can think of illiquidity premium as a trading cost. Bid-ask spread is the difference between ask price at which an investor is willing to sell a security and bid price at which the investor is willing to purchase a security. The bid-ask spread is an immediate cost because it is paid every time an investor executes a trade Choe, H., & Yang, C. W. (2008). This shows how the availability of a security which is directly related to the concept of liquidity requires a premium for the investor. The difference between the true value of the security and its Bid/Ask price is the premium paid/received due to the imperfections in market liquidity.
Researching how this premium can affect the classical models for asset pricing is relevant in order to understand if a portion of what is seen as abnormal return, utilizing CAPM or Fama-French 3 and 5 factors to price securities, is in reality purely a premium paid to the investor due to the exposure to this missing risk factor (Illiquidity). This topic has received substantial attention of researchers in the past years. With this thesis we aim on expanding the existing literature focusing the analysis on the healthcare sector stocks listed on the Tokyo stock exchange.
The healthcare sector has been chosen as these stocks are experiencing unusual volatility and high inflow of investments compared to previous years due to the corona virus outbreak. On the 20st of April in the article “How Has Coronavirus Affected Europe’s Biotech
Stocks?” Labiotech.eu reported how the pandemic affected healthcare stocks and in particular biotech stocks. For instance, The NASDAQ stock price of the German giant BioNTech went up by 60% in the middle of March. De Kerpel, Managing Director of Life Sciences & Healthcare at the Dutch merchant bank Kempen Corporate Finance, stated in the same article that healthcare and pharma are now considered a safer haven than any other industry and that he expects investors to increase their investments exposure in this sector.
Moreover, this research will keep being relevant for the coming years as healthcare stocks will probably keep experiencing great investors’ attention. As reported in a CNBC article and interview to Steve Chiavarone, portfolio manager, equity strategist and vice president at Federated Hermes. “It’s more about what we’re going to do coming out of this crisis, and I
for this… This could boost medical-device, pharmaceutical and biotechnology stocks “on a go-forward basis” as demand grows”.
With respect to the choice of Japan for this study, in which the Japanese stock market and particularly the Tokyo stock exchange have been examined. Being the Tokyo stock exchange the third largest exchange after NASDAQ1 and NYSE2 by market capitalization helps
evaluating the differences with the studies carried out within the U.S. Chan, Hamao and
Lakonishok (1991). Moreover, it allows us to critically assess empirical models of
cross-sectional stocks return proposed in the existing literature.
For the purpose of this thesis the illiquidity factor which will be included in the statistical analysis has been estimated differently from the bid-ask spread mentioned previously. The Amihud (2002) measure was used. This measure is defined as follows, !"#ℎ%&!,# = $%!,#$
&'()*+!,#× 1
,000,000 where
,-!,#, is the absolute value of the daily return of stock i on day T and ./0%"1!,# is the trading volume of stock i on day T. The large value of the
Amihud measure indicates low liquidity (Amihud 2002). The expected excess returns of securities were estimated through the five factors asset pricing model Fama and French (2015) which is an extension of the classical model proposed by Fama and French (1993). The expected excess return of each security depends on the exposure (3-) to the 5 factors (f): “MKT-rf, HML, SMB, RMW and CMA”.
The technique that has been used in order to assess the premium associated to illiquidity is the Fama, E. F., & MacBeth, J. D. (1973) regressions. This allows to investigate the premium (5̅- =/0∑001/5-) associated with each risk factor f included in the chosen model which for the
case of this paper is the FF3 5 factors plus Amihud for illiquidity. This analysis has been carried
out on panel data composed of 95 stocks observed over a period of 130 months. The results of this analysis disproved the existence of a premium for illiquidity. In fact, the results show a statistically significant negative impact on stocks excess return associated to the Amihud measure for Healthcare stocks in Japan. Meaning that there might be, even if minimal, a liquidity premium instead of an illiquidity premium.
1 National Association of Securities Dealers Automated Quotation 2 New York Stock Exchange
2.Literature review
2.1Estimation of illiquidity effect
Extensive literature about illiquidity and its premium estimation exist. The main literature this thesis will expand on, is the research proposed by Amihud (2002) which uses the same proxy for illiquidity as this paper. The central idea of Amihud (2002) is that over time, expected market illiquidity positively affects ex ante stocks excess return, suggesting that expected stocks excess return partly represents an illiquidity premium. Chan, H. W., & Faff, R. W. (2005) carries out a similar study for Australia using shares turnover to estimate illiquidity. The findings of this paper also support the idea of an existence of an illiquidity premium. Conclusively, we also find support for the existence of an illiquidity premium from Hagströmer, B., Hansson, B., & Nilsson, B. (2013). In this paper, Reversal Measure of Pastor
and Stambaugh (2003) was used to measure illiquidity, the average annual premium is
estimated between 1.74-2.08% for U.S. stocks in the period between 1927 and 2010.
Nevertheless, Asparouhova, et al, (2010) which focuses on the estimation of potential biases that can arise in tests for illiquidity premium. Showed how the positive results of previous researches regarding the existence of an illiquidity premium as a risk factor might be biased. In their analysis, Bid-Ask spread has been used as illiquidity proxy.
Moreover, directly linked to the narrower scope of this thesis is the paper by Fang, J., Sun, Q., & Wang, C. (2010). This paper tried to extend the research on illiquidity proposed by Amihud (2002) on Japan. What is interesting of their research is that firstly, instead of using the pure Fama-French model to price securities, a tailor-made model has been developed based on Japanese specific risk factors such as earnings yield and cash flow yield. Secondly, different subsamples of data have been analyzed in order to be able to assess how the effect of illiquidity varies depending on different market conditions. Mainly, they realized that results that are valid for the NYSE cannot be transferred easily to the TSE as there are embedded differences in how the Japanese stocks are priced relative to the exposure to risk factors.
This concept has also been highlighted by Hodoshima, Garza–Gomez and Kunimura
(2000) which finds that a regression of returns on betas without differentiating positive and
negative market excess returns produces a flat relationship between return and beta in Japan. Moreover, Fang, J., Sun, Q., & Wang, C. (2010) find that the illiquidity in Japan can have a negative impact on expected stock prices if the illiquidity is unexpected even after controlling ups and downs of the market. This disaffirms what was previously stated by Amihud (1986) and Amihud (2002) in the context of U.S. stocks. Whereas, it is in line with the findings of
Hasbrouck (2005) which identify that that the relations proposed by Amihud (1986) between the illiquidity measure and expected stock returns are not robust.
2.2 Amihud measure as Illiquidity proxy
In this section the reasons for which the measure used by Amihud (2002) has been chosen as a proxy for illiquidity are explained. For this purpose, the main source of information has been the paper of Choe, H., & Yang, C. W. (2008) which is a complete guidance and description of all the different liquidity proxies for stocks known in the academic. The Amihud
(2002) measure represents the illiquidity of an individual stock. If a stock’s price moves
considerably in response to little volume, this stock has a high value of Amihud measure, and It means that the stock is illiquid.
There are numerous measures for illiquidity as for example the Bid-Ask spread, Reversal Measure of Pastor and Stambaugh (2003), Kyle (1985)’s Lambda (λ), Amivest Measure and many others. On the other hand, the Amihud (2002) measure provides some advantages such as being easy to estimate, this is because it only requires data which is readily available over long time frames for most existing securities (stock returns and traded volume). Secondly, it allows to measure the impact that daily prices have on the order flow. Thirdly, Amihud (2002) is strongly related to many of the other measures such as Amivest, proportional spread and it entails the same economic concept as the reversal measure of Pastor and
Stambaugh (2003); return scaled by trading volume. Finally, concepts of liquidity and (trading
costs, price impact and quantity) are embedded in the measure as shown by Choe, H., & Yang, C. W. (2008).
However, Amihud highlights some drawbacks in his research paper. Firstly, the measure misses the concept of trading speed which can lead to biased estimation as it does not take into account the effect of non-trading days. Secondly, the effect of outliers, pose a threat to the estimation of reliable results. For this reason, as suggested by Choe, H., & Yang, C. W. (2008), winsorization of the Amihud measure estimated in this paper has been applied in the statistical analysis.
2.3Fama French asset pricing model
The expected excess return of the stocks have been estimated through the Fama and French five factors model. This model has been presented in the paper: “five-factor asset pricing model (2015)” and it is an extension of Fama and French (1993). The main idea is that expected returns are due to the exposure of an individual asset to five common risk factors. The first three factors which come from Fama and French (1993) capture the exposure of average excess returns to 1.exceess Market returns (Rm-rf), as proposed by the CAPM model Sharpe, W. F. (1964), 2. Size (SMB), considered as market capitalization of the stock and 3. to the B/M book to market price ratio (HML). The final two risk factors added in 2015 are (RMW) which tries to capture the exposure a stock to a well-diversified portfolio of stocks with robust and weak profitability. And (CMA) which represents a well-diversified portfolio of stocks of low (conservative) and high (aggressive) investment firms. According to Fama and French (2015) the expected excess return of a given security can be estimated through a linear model which has expected excess return as dependent variable and the exposure of the stock to the five factors as independent variables. On the other hand, further research showed how this model should be adapted depending on the context the security we are analyzing will find itself in.
Moreover, in Kubota, Takehara (2018) it is shown how the robust-weak (RMW) and conservative-aggressive (CMA) factors, mentioned in the previous paragraph, are not statistically relevant to explain expected excess returns in Japan. A second suggestion of the misspecification of the model for Japanese stocks can be found in Fang, J., Sun, Q., & Wang, C. (2010) which as mentioned previously substituted few factors of the regular Fama-French five factors model with risk factors that work better for Japanese stocks. For example cash flow yield ( i CPy−1), which is the ratio of earnings plus depreciation.
2.4 Fama-MacBeth cross-sectional regressions
In order to statistically estimate if illiquidity premium is priced in Japanese healthcare stocks, the approach used in this thesis is the two-steps Fama-MacBeth regressions. In the field of asset pricing, when dealing with panel data of i entities (stocks) and t time periods (months) FM4 method has shown to be statistically relevant to measure the cross-sectional dispersion in
expected equity returns beyond what is explained by a factor asset pricing model. The
stochastic model proposed in the paper of Fama and MacBeth (1973) which allowed them to estimate the risk premium !"! associated with a risk factor f is the following: ##$#! = %%+ !!,%'(',# + )# where '(! is the exposure (factor loading) of stock i to the risk factor f estimated through the Fama-French asset pricing model explained in the previous section.
In plain words, the two steps of the regression consist of the following: In the first step, for each time period, linear regressions are used to obtain estimates of the '(! for each stock. The second step consists of time series cross-sectional regressions of these estimates which are used to obtain final estimates for the parameters and standard errors so that the risk premium !"! and its p-value can be computed Skoulakis, G. (2008). This paper also highlights how to
deal with one of the main concerns regarding the validity of the results estimated through the FM method. Which stands in the computation of standard errors and relates to the cross-sectional and serial correlation of the residuals and/or the independent variables in the panel regressions.
Skoulakis, G. (2008) showed that in the case of large t with generic serial dependence the FM method produces accurate asymptotic approximations. Moreover, it has also been tested that the use of econometric tools for dealing with serial correlation, namely heteroscedasticity and autocorrelation consistent (HAC) estimators Newey-West (1987), estimate reliable T-statistics. For this reason, Newey-West (1987) standard errors have been used in the process of this analysis.
Furthermore, the FM regression entails some implicit assumptions which might not hold in reality. For instance, Pasquariello. P. (1999) highlights the two main problems which might weaken the conclusions drawn using FM regressions.
1. Errors-In-Variable Problem: the cross-sectional regressions of step-2 assume that the resulting betas of step-1 correspond to the true and unobservable sensitivity of stock i to the factor considered. This structural bias, due to the fact that we can only estimate the true exposure to the risk factor, affects the precision with which the parameters of the cross-sectional regressions are then estimated, and therefore, the validity of the conclusions.
2. The Roll Critique: the final concern raised in the paper of Pasquariello. P. (1999) refers to the fact that the true market portfolio is unobservable, and the proxy used for the market return is not necessarily mean-variance efficient. In fact, Roll (1977) and Roll and Ross
(1994), reported that the reason for the low or even lack of a relation between expected
wrong market portfolio as a proxy. The threat posed by adopting the incorrect market proxy are relative to the fact that if the true market portfolio is mean-variance efficient, even a slight difference between the true portfolio and the adopted proxy will impact cross-sectional relationship between expected returns and betas.
3.Methodology
In this section, it is presented how the data has been processed and the technicalities of the FM procedure together with the hypothesis which will be tested.
3.1 Excess returns and Amihud measure
The first step of the data analysis was to calculate the monthly returns of each stock in the sample. From the monthly stock price *#,% , where i correspond to the entity and t to the month analyzed, monthly return ##,% of i at time t is calculated as the percentage change between *#,% and *#,%('.
##,% = *#,%('− *#,% *#,%
At this point, after plotting the dataframe containing the returns of each stock
(appendix1), it was clear that a few outliers might have caused a bias in the subsequent steps
of the analysis. Therefore, the double side winsorization at the 5% level has been used to correct returns in order to have finite fourth moments. This is important to be done, as ##,% will be the main component of the dependent variable during the whole FM procedure and by assumption of the OLS regression, the dependent variable Y and the independent variables X need to have finite fourth moments. Finally, the last step to be done in order to have the final dependent variable Y is to subtract the corresponding risk-free rate at time t from the winsorized value of ##,% obtaining the excess return of stock i at time t.
- = ##,%− #.
Where #. has been proxied with the risk-free returns for Japan of the Fama-French factors website for the relevant period and ##,% is the return of the stock observed in our sample.
The second data processing needed before implementing the FM procedure was the estimation of the measure for illiquidity Amihud (2002). The Amihud measure is defined as follows:
/01ℎ34#,% = )*!,#) +,-./0!,#× 1
10001000
where 8##,28 is the absolute value of the monthly return of stock i on day t, 9:;30<#,2 represents the trading volume of stock i on day T. The large value of the Amihud measure indicates the low liquidity Amihud (2002). It is important to notice that time t utilized for the calculation of the monthly returns ##,% is different from T used in the calculation of the Amihud measure. This is due to the fact that Amihud measure is a daily measure and therefore, obtained from daily values of returns ##,2 and volume 9:;30<#,2 . Only afterwards, the daily values of Amihud measure are averaged by month in order to compute the monthly measure of illiquidity =>#,%.
=>#,% = 3'∑3 /01ℎ34#,2
24'
where T represents the day and N is the number of days T in a specific month t.
3.2 Fama-MacBeth procedure
The goal of this analysis is to find the expected premium !"! associated with the exposure '(! to factors f. In the first step, each asset return is regressed against the return of one or more factor time series to determine the sensitivity of each asset to the chosen factors. In the second step, the asset returns are regressed cross-sectionally against the '(! estimated in the previous step. The insight of Fama-MacBeth is to then average the coefficients !!,% , for each factor, which yields the expected premium for a unit of exposure to each risk factor over time.
1. first step.
In order to estimate the expected excess return of the stocks time series regressions on the Fama-French 5 factors model has been employed. The time series-equation of this model is formulated as follows.
Where @AB%, C@>%, D@E%, F@G% , H@/% are the given returns of the FF five factors for Japan at time t. From this model we were able to estimate 5 coefficients (betas) and a constant (alpha) for each stock i. The mathematical procedure for the estimation of the coefficients and the constant is the following.
'( = ∑ J% K%− 1L ∑ J% ∑ K% ∑ J5 %−'9 (∑ J%)5 = H:O[J, K] 9R#[J] %" = KS − '(J̅
Where x represents the independent variables (risk factors f). n is number of regressors. For the purpose of this regression, Heteroscedasticity-consistent standard errors (HC3) have been used to calculate t-statics.
CH3 DVW'(X = <#,%5 (1 − ℎ#,%5)
Where e are the residuals and h are the leverage values (i.e. the diagonal elements of the OLS hat matrix).
Y = '( DV('()
'( is the coefficient estimated through the regression and the SE is the Heteroscedasticity-consistent standard error (HC3).
2. second step.
The second step of the FamaMacBeth regression consists in t cross sectional regressions This process allows us to obtain t estimations of g for each factor in the regression. The second stage regression model is shown below.
Where the dependent variable y is the same as from step-1. Whereas, the independent variables in this case are substituted with the coefficients estimated from step-1 in addition to the monthly Amihud measure (IL) for illiquidity.
From these estimations of gammas, we can calculate the illiquidity premium simply taking the average of all the coefficients !̅; attributed to illiquidity.
!̅; = '6<' ∑'6<!";,% %4' .
Where t goes from 1 to 130 as the number of months in our sample is 130 and !";,% is the coefficient for illiquidity of the second regression estimated for month t.
The t-statistic for the second step of the regression is expressed through the following formula.
Y − ZYRY = [!! =! √B
Where !! is the coefficient of factor f estimated with the cross-sectional regression and [=! is the standard deviation of !!
In order to avoid issues related to serial correlation, heteroscedasticity and autocorrelation consistent (HAC) estimators Newey-West (1987) have been used for the estimation of the coefficients in the second step of the FM regression.
]∗ = 1 B ^ <%5J% 2 %4' J%1 +1 B^ ^ <-<%<%$-(J% 2 %4-(' J1 %$-+ J%$-J′%) ? -4' `- = ; > + 1
where Q* is the matrix of sums of squares and cross products that involves [#,@ and the rows of X. Whereas <# is the residual. and `- is the weight to be given to each component depending on the distance between the disturbances. The further apart the observations are the lower the weight will be. Same subscript (meaning no distance) will receive a weight of 1. This is to ensure that the second term will converge to a finite matrix Greene, W. H. (2003).
3.3. Hypothesis
Different hypothesis will be tested in order to draw conclusions about the existence of an illiquidity premium.
H0: !̅#- = 0 (no illiquidity premium)
H1: !̅#- ≠ 0 positive coefficient means that illiquidity has a positive impact on the expected excess return of the stock (illiquidity is priced in). If the coefficient is negative, illiquidity negatively affects stocks expected returns (liquidity premium)
What we expect to find is a positive coefficient for !̅#- in the case of an existing illiquidity premium as proposed by Amihud (1986) and by the majority of the existing literature for U.S. equities. Whereas we expect to find a negative coefficient for !̅#- in the case of unexpected illiquidity as explained by Fang, J., Sun, Q., & Wang, C. (2010).
Furthermore, outside the main scope of this thesis we explore how the choice of the model for expected returns could affect our results. FF 3-factors and CAPM are analyzed to test if one of these two models have higher explanatory power compared to the Fama-French 5-factors.
Fama-French 3-factors model.
##$#! = %" + '('@AB%+ '(5C@>%+ '(6D@E%+ )#
CAPM model.
4.Data and variables
This section dives deeper into the details of the data utilized for the analysis.
4.1 Data collection
The function UniverseScreen of FactSet Database has been used in order to create a universe containing only stocks with the required characteristics. This function allows to screen stocks by country, sector and stock exchange providing the list of tickers for all the (TSE) listed stocks which are in the healthcare sector. From this first screen the sample had 165 tickers of companies. For this sample, we retrieved daily adjusted close prices and volume as well as monthly adjusted close prices for a period of 130 months which goes from 06-2009 to 01-03-2020. Since not all the stocks existing in the initial list had available data for 130 months the number of stocks in the sample has been reduced from 165 to 95. This allowed the analysis to be performed on a balanced panel data. The Data mentioned above has been collected from
Yahoo Finance which utilizes data provided by Thomson Reuters for historical time-series of
(monthly and daily) stock prices and (monthly) volume for each stock.
Nevertheless, technically the Fama-MacBeth regression is able to be performed on unbalanced data. On the other Hand, the specific tool used to perform this analysis in this paper is the Fama-MacBeth method from Linearmodels library for Python which, can create errors if the data provided is not balanced. Finally, the remaining data required for the analysis was the returns of the Fama-French 5-factors for Japan relative to the same period of which the stocks prices are being analyzed. This data could easily be collected from the Fama-French factors website5.
4.2 Variables definition
Table 1
This table shows the source, abbreviation and description of each variable needed for the FM analysis.
Source Abbreviation Description
Individual daily stock return Calculated from prices provided by Yahoo Finance
2!,# The daily individual stock
return
Individual monthly stock return
Calculated from prices provided by Yahoo Finance
2!,$ The monthly individual stock
return
Market return Fama-French website 2%,$ Monthly market index return
Risk-Free rate Fama-French website 23$ Return provided by risk-free
asset in Japan
Stock excess return --- 2!,$− 23$ --
Market excess return --- 2%,$− 23$ --
Small – Big Fama-French website 567$ The monthly market Small
minus Big factor of three-factor model
High-Low Fama-French website 869$ The monthly market High
minus Low factor of three-factor model
Robust-weak Fama-French website :6;$ The monthly market Robust
minus Weak factor of three-factor model
Conservative-aggressive Fama-French website <6=$ The monthly market
conservative minus aggressive factor of three-factor model
Amihud measure Calculated from daily prices
and volume provided by Yahoo Finance
=>?ℎAB!,$ Amihud measure of illiquidty
4.4 Descriptive statistics
As shown in Table 2 excess returns of the stocks have a low negative average -0.03, which means that during the 130 months analyzed the overall Japan Healthcare stocks have not outperformed the market in pure terms of returns. On the other hand, the standard deviation 0.08 of these returns is extremely low. If we consider std. deviation as the right risk measure for stocks and compare Healthcare stocks to the overall market excess return which has std. deviation of 3.68, then we can see that the market is extensively more volatile (riskier) than the Healthcare sector per se. The second important consideration about the descriptive statistics is in regard to the illiquidity factor which has a mean of 0.76. this value can be considered quite low compared for instance to the dataset used by Asparouhova, E., Bessembinder, H., & Kalcheva, I. (2010) which found average illiquidity in NASDAQ/AMEX stocks to be 0.971 for the period between 1926-2006. This difference is even more relevant considering that, as explained by Cooper, S. K., Groth, J. C., & Avera, W. E. (1985), AMEX and NASDAQ indexes are found to be the indexes containing the most liquid stocks.
Table 2
this table provides the descriptive statistics (number of observations, mean, standard deviation, minimum value, 25th percentile, median, 75th percentile
and maximum value) for the final variables needed in the FM regressions. Excess returns statistics are calculated on the mean of each stock’s return for the entire period. Illiquidity statistics, (monthly Amihud (2002) measure) are also calculated on the mean of each stock’s illiquidity for the entire period. The number of observations for exc. Returns and illiquidity refer to the entities (stocks). Whereas, the number of observations for all the remaining variables refer to the time-periods (months).
Exc.returns illiquidity Mkt-RF SMB HML RMW CMA
count 95 95 130 130 130 130 130.0 mean -0.032815 0.761530 0.510769 0.340923 -0.167231 0.275923 -0.031385 std 0.008769 1.126294 3.680312 2.123966 2.541863 1.467610 1.421439 min -0.054871 0.005025 -10.090000 -6.240000 -6.190000 -4.570000 -4.190000 25% -0.037363 0.055571 -1.410000 -0.950000 -1.887500 -0.575000 -0.847500 50% -0.033210 0.202036 0.790000 0.430000 -0.175000 0.290000 -0.065000 75% -0.027496 0.818541 2.837500 1.850000 1.140000 1.155000 0.897500 max -0.005555 4.767793 9.260000 5.670000 7.070000 3.530000 4.250000
5.Empirical results
5.1. FM regressions on Fama-French 5-factors modes
This part of the paper analyzes the results of the Fama-MacBeth regressions.
5.1.1. Beta estimates
Table 3 exhibits the coefficients of the time series regressions run between the FF 5-factors and the observed excess returns of the stocks. Looking at the average of the betas which are all between 0 and 0.01 we do not expect great explanatory power given by these factors for the analyzed stocks. As a matter of fact, the stocks excess returns appear to be neutral on average to the Fama-French 5 factors
5.1.2. Illiquidity premium
As shown in Table 4 the g coefficient relative to the illiquidity factor is -0.0013with a p-value of 0.0342 implies that we can reject H0. Hence, there is no statistical evidence to assume that illiquidity has no impact on expected excess returns. On the other hand, we find statistical support at the 5% level for H1, which states that if !̅! is negative illiquidity has a negative impact on expected excess returns (liquidity premium). The effect is considerably small as the change in 1 unit the scale of the monthly Amihud measure will lead to an average -0.13% change in expected excess return for a healthcare stock in listed in the Tokyo Stock Exchange.
As mentioned in the paper of Fang, J., Sun, Q., & Wang, C. (2010) this unusual results compared to previous results of existing literature can be explained by the fact that illiquidity is unexpected. Moreover, they also state that the relationship between illiquidity and excess expected returns is sensitive to the direction of the market “up or down”. For these reasons, it reasonable to further research if the implications that the high volatility of the markets in Japan in recent years, which meant many changes in market direction, had an influence on the estimates of this paper and what is the direct impact of this effect on asset pricing models.
5.1.3 5-factors premia
Moreover, analyzing the regression results of table 4 for the FF 5-factors we can immediately observe that the coefficient for the Market factor (Mkt-rf) is insignificant with a p-value of 0.1482. the main takeaway from this fact, is that as stated by Pasquariello. P. (1999) and Roll and Ross (1994) the insignificant cross-sectional relation between excess expected
returns and the market factor can be due to the choice of a wrong proxy for the factor Mkt-rf. In this paper, the market proxy chosen for this research is the factor provided by the Fama-French website for the country of Japan. This proxy might not be the best choice for Japanese healthcare stocks and further investigation with different portfolios is required before stating that there is not a significant relation between the market factor and the expected excess return of healthcare stocks in Japan.
Furthermore, between the remaining 4 factors the only significant factor found is the robust-weak (RMW), which appears to have high positive impact (premium) on Japanese healthcare stocks with a coefficient of 0.6723 and P-value of 0.0002 (statistically significant even below the 1% level). Small-Big and High-low factors are both insignificant and the issues related with applying the FF 5 factors model to Japan are also highlighted in Fang, J., Sun, Q., & Wang, C. (2010).
5.1.4 Model significance
Overall the model is significant at the 1% level as shown by the robust F-statistic value of 2.8515 which has a P-value of 0.0089. the F-statistic refers to the test of joint significance of all the factors included in the model. Moreover, the #" which is the fraction of variance explained by the model over the overall variance of expected excess returns is divided in three parts. #" (between) shows the explained variance across entities compared, #" (within) is the average explained variance within an entity and the #" (Overall) which is simply the weighted average of #" (between) and #" (within).
#" (between) is 0.2387 this means that 23.87% of the variance observed in expected excess returns can be explained using the variables included in the model. #" (within) is negative -0.0008 meaning that the model does not have enough explanatory power to estimate the variance in expected excess returns for a single entity across time and therefore, simply computing the average of expected excess returns would lead to a more precise estimate of expected excess returns in this case. A negative #" can also be due to the low number of
observations which can lead to biased results. #" (Overall) is positive 0.0008 meaning that this model is a better estimate then the simple average of expected excess returns for the variance across and within entities. On the other hand, this value is relatively low. Therefore, even though the model is economically meaningful it is advisable to find more variables to include in the model in order to enhance the explanatory power of the model.
Table 3
Results of the first step FM regression
n. observation mean stdandard deviation
b (Mkt-RF) 95 0.002383 0.005336
b (SMB) 95 0.004783 -0.002841
b (HML) 95 0.003896 -0.005483
b (RMW) 95 0.006572 -0.016654
b (CMA) 95 0.004927 -0.008089
Table 3 shows the results concerning the first step of the FM regression. Number of observations, mean and standard deviation of the estimated b coefficients are reported. Coefficients are calculated with Heteroscedasticity-consistent standard error (HC3).
Table 4
results of the second step of the FM regression including the illiquidity measure for the FF 5-factors model.
variable Coef. Standard Errors T-stat P-value Lower C.I. Upper C.I.
const -0.0237 0.0178 -1.3337 0.1823 -0.0586 0.0111 ILL -0.0013** 0.0006 -2.1181 0.0342 -0.0025 -9.674e-05 Mkt-RF -0.7167 0.4956 -1.4459 0.1482 -1.6882 0.2549 SMB -0.1094 0.1954 -0.5597 0.5757 -0.4925 0.2737 HML -0.4025 0.3061 -1.3150 0.1885 -1.0024 0.1975 RMW 0.6723*** 0.1790 3.7552 0.0002 0.3214 1.0233 CMA -0.1859 0.1708 -1.0883 0.2765 -0.5207 0.1489
F-stat. (robust) P-value !! (between) !! (overall) !! (within)
Avg. Time-periods
Avg. entities
2.8515*** 0.0089 0.2387 0.0008 -0.0008 130 95
Significance at the 1%,5%,10% level is respectively represented by ***,**,* in the table above
Table 4 provides the estimates of the ! coefficients for the FM regression for the FF 5-factors model. The standard errors provided are calculated with the Newey-West (1987) method.
5.2 Further analysis FF3 and CAPM
Outside the specific scope of this thesis it has been decided to perform two more analysis to understand how a change in the specification of the model would affect the results of the Fama-MacBeth regression. The decision for the inclusion of the FF 3-factor model and the CAPM has been driven mainly by the fact that Kubota, Takehara (2018) stated that the FF 5-factors model is not statistically more relevant then the FF 3-factors model to explain Japanese asset returns.
The first thing we can notice from table 5 is that overall, both models provide worse results compared to the FF 5-factors in explaining the variance of expected excess returns. This can be seen by the fact that the overall #" of both FF 3-factors and CAPM respectively (0.0002 and -0.0001) are lower than the one found with the FF 5-factors. Moreover, none of the two added models has a significant F-statistic at the 5% level which means that they cannot be used to predict stocks excess returns.
Finally, as visible from the P-values in parenthesis of the T-tests, none of the Fama-French factors is significant which means that they do not present a statistically relevant effect on the dependent even taken singularly. For the reasons mentioned above we can state that for the case of our sample FF 5-factors model is statistically more relevant than the FF 3-factor model and CAPM to explain expected excess returns of the stocks.
Table 5
This table shows the results for the second step of the FM regression on 2 models: FF 3-factors and CAPM
FF-3 factors CAPM const (0.3022) -0.0197 (0.2414) -0.0235 IL2 (0.0661) -0.0011 (0.0626) -0.0011 Mkt-RF (0.0896) -0.8513 (0.1057) -0.8609 SMB (0.1502) -0.2908 HML -0.3297 (0.2675) f-stat (robust 1.882 2.4762 p-value 0.1095 0.0841 R2 Between 0.1203 0.0773 R2 Overall 0.0002 -0.0001 R2 within -0.0006 -0.0006 p-values in parenthesis
Table 5 provides the estimates of the coefficients for the FM regression for the FF 3-factors model and CAPM. The standard errors used to calculate the t-statistics and p-values are calculated with the Newey-West (1987) method.
6.Conclusion
The purpose of this thesis is to validate if the research proposed by Amihud (2002), which shows that illiquidity of a stock positively impacts its expected excess returns (illiquidity premium), can be applied to the setting of Japanese healthcare stocks.
In order to develop this study, we proxied illiquidity through the Amihud measure of illiquidity and utilized Fama-French 5-factors asset pricing model to estimate the relation between expected excess returns and illiquidity. Moreover, the main statistical tool which this paper has made used of is the Fama-MacBeth regression, which allows to estimate the risk-premium across entities associated with each risk factor included in the model.
The results of this analysis did not match what found in the related literature for different contexts. Nevertheless, statistical evidence of a liquidity premium instead of an illiquidity premium has been detected. Even though it has been shown how this particular result can be due to unexpected illiquidity, it advisable to further research the different settings in the market which might lead to a positive premium for liquidity on stocks excess returns.
Furthermore, a final extra analysis with two different models (FF 3-factor and CAPM) has been carried out. Since there is extensive literature debating which asset pricing model should be used to explain the expected excess returns of Japanese stocks the three most famous settings have been tried. The results showed that for the case of this research paper the initial model (FF 5-factor) appeared to be the most efficient and reliable between the three analyzed. On the other hand, it has yet not been as efficient as expected. Therefore, as also shown by Fang, J., Sun, Q., & Wang, C. (2010) it is advisable to further analyze what impact would have carrying out the same analysis utilizing specific country-related risk factors instead of one of the Fama-French models.
References
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Appendix
1.
Plot of returns before winsorization
Boxplot of returns before winsorization
2.
Rf interests returns
(the raise in interest rate was due to the end of the post financial crisis policies which kept it low in order to boost the economy)
Winsorized excess returns
Excess returns overlap of each stock analyzed over the entire sample period.
(notice how the decline in excess return is linked to the raise in rf interest rates)
3.
The illiquidity measure for the following graph has been plotted taking the average over stocks of the monthly illiquidity measure.
Monthly illiquidity over time
(notice the high illiquidity before 2012 due to the post financial crisis markets illiquidity)
4.
Python code.
import pandas as pd
import matplotlib.pyplot as plt import datetime as dt
from datetime import datetime import numpy as np
import linearmodels as lm
from linearmodels.panel.model import FamaMacBeth as fm import statsmodels.api as sm
from scipy import stats
df = pd.read_csv("/Users/niccolo.melacarne/Desktop/stocks prices.csv",index_col='Date',)
df.dropna(axis =1,inplace= True)
df.drop(df.tail(2).index,inplace=True) df.index = pd.to_datetime(df.index) df.head()
returns1 = df.pct_change()
returns1.drop(returns1.index[0],inplace=True)
returns = scipy.stats.mstats.winsorize(returns1, limits=[0.05,0.05]) returns = pd.DataFrame(returns) returns.columns = returns1.columns returns.index = returns1.index returns.index = pd.to_datetime(returns.index) returns.tail() ff_factors = pd.read_csv("/Users/niccolo.melacarne/Desktop/Japan_5_Factors.csv",index_co l =0) ff_factors.drop(ff_factors.index[0],inplace=True) rf = pd.DataFrame(ff_factors['RF'])
ff_factors.drop('RF',axis =1,inplace = True) ff_factors.index = pd.to_datetime(returns.index) rf.index = pd.to_datetime(returns.index) ff_factors.head() returns = np.subtract(returns, rf) returns.head() plt.plot(returns) plt.plot(rf) def get_betas(stock): x = ff_factors[['Mkt-RF','SMB','HML','RMW','CMA']] #x = ff_factors[['Mkt-RF','SMB','HML']] #x = ff_factors['Mkt-RF'] y = returns[stock] x = sm.add_constant(x)
predictions = reg1.predict(x)
## Get beta and remove intercept beta = reg1.params
beta = beta[1:] return beta betas_list = []
for company in returns.columns:
company_betas = get_betas(company) betas_list.append(company_betas) dataframe = pd.DataFrame(betas_list) dataframe.head() dates = [] dt = returns.index.values.tolist() for x in dt: for i in range(95): i = x dates.append(i) stocks = [] for x in returns.columns: stocks.append(x) stocks2 = stocks *130
lista = [dataframe for x in range(130)]
df_beta = pd.concat(lista, axis=0,ignore_index= True) RET = returns.values.tolist() RET2 = [] for x in RET: for y in x: RET2.append(y) finaldf = pd.DataFrame() finaldf['returns'] = RET2 finaldf['dates'] = pd.to_datetime(dates) finaldf['stocks'] = stocks2 df_beta_final = [finaldf,df_beta] finaldf = pd.concat(df_beta_final,axis=1) finaldf.set_index(['stocks','dates'],inplace= True)
finaldf.sort_index(inplace = True) finaldf.head()
illiquidity_daily =
pd.read_excel('NYD3D2NC.xlsx',sheet_name='Sheet2',index_col ='Date') #df.dropna(axis =0,inplace= True)
illiquidity_daily.index = pd.to_datetime(illiquidity_daily.index) illiquidity_m = illiquidity_daily.groupby(pd.Grouper(freq='M')).mean() illiquidity_monthly = illiquidity_m[returns.columns]
illiquidity_monthly.drop(illiquidity_monthly.index[0],inplace=True) #agg2.drop(['4282.T','7743.T'],axis =1,inplace = True)
illiquidity_monthly.index = returns.index #agg2.fillna(0) illiquidity_monthly = scipy.stats.mstats.winsorize(illiquidity_monthly, limits=[0.05,0.05]) illiquidity_monthly = pd.DataFrame(illiquidity_monthly) illiquidity_monthly.columns = returns.columns illiquidity_monthly.index = pd.to_datetime(returns.index) illiquidity_monthly.head() IL_d = illiquidity_monthly.values.tolist() IL_d2 = [] for x in IL_d: for y in x: IL_d2.append(y) finaldf['IL2'] = IL_d2 finaldf.head() res = fm(finaldf['returns'],sm.add_constant(finaldf[['IL2','Mkt-RF','SMB','HML','RMW','CMA']])).fit(cov_type='kernel',kernel='newey-west') #res = fm(finaldf['returns'],sm.add_constant(finaldf[['IL2','Mkt-RF','SMB','HML']])).fit(cov_type='kernel',kernel='newey-west') #res = fm(finaldf['returns'],sm.add_constant(finaldf[['IL2','Mkt-RF']])).fit(cov_type='kernel',kernel='newey-west') res desc_ret = returns.mean()
desc_ret = pd.DataFrame(desc_ret, columns= ['returns']).describe() desc_ill = illiquidity_monthly.mean()
desc_beta = dataframe.describe() desc_beta.columns = ['B mkt-rf','B smb','B hml','B rmw','B cma'] descriptives = pd.concat([desc_ret,desc_ill,ff_factors_descriptives,desc_beta],axis=1) descriptives import seaborn as sns sns.boxplot(x=returns) illiquidity_a = illiquidity_monthly.groupby(pd.Grouper(freq='Y')).mean() illiquidity_a = illiquidity_a.transpose() plt.plot(illiquidity_a.mean()) plt.plot(returns1)
