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Measuring Liquidity Using Daily Stock
Market Returns:
A study of ten quoted companies in dierent
sectors in Nigeria.
Dr. H.O.R Ogwuru1; Dr. John Okey Onoh2,
1. Department of Economics, Abia State University, PMB 2000, Uturu, Nigeria
E-mail: profeca@yahoo.com
2. Department of Banking & Finance, Abia State University, PMB 2000, Uturu, Nigeria
E-mail: johnonoh@gmail.com
Abstract
This is study on measuring liquidity and stock returns of ten quoted companies in the Nigerian stock Exchange. The
problem being studied is that similar studies have being using models without emphasizing on the increasing
importance of standard deviation inclusive models in measuring liquidity of stock market returns which is not
unconnected to the general understanding that there is a need to model risk measures that would capture the effect
of liquidity on returns. The research objective was to examine the impact of liquidity measured by market
capitalization value ratio on stock market returns of the ten quoted companies of different sectors of the Nigerian
Stock Exchange. The data was sourced from the Nigerian Stock Exchange (NSE) official daily report. It was found
that, in all the selected quoted companies, the level of their liquidity significantly impact on the degree or volume of
returns made from stocks and therefore, we concluded that sound liquidity position increases returns on stocks. The
study based on the findings recommends that the Nigerian Securities and Exchange Commission should create
policies that will encourage increases in firms profit after tax and their dividends. Also, recommended is that
investors should make trading volume based strategies to make profits and theoretically this provides evidence of
weak form inefficiency of the Nigerian Stock Exchange.
1.0 Introduction
Because of the vital economic role the capital market plays in any emerging or developed economy, it is important to
study the trend of change in macro economic variables using certain periodic gauges like yearly, monthly, weekly or
daily yardsticks. Many scholars have tested the efficiency of markets and the efficacy of policies, in recent times the
daily data is getting increasing attention in not just testing for liquidity but in measuring volatility of markets.
Investors will always be interested in testing the efficiency of markets especially where there is a chance of earning
abnormal profits. Many studies such as Olowe (2009) have shown that the Nigerian market is far from efficient. An
efficient market is one which does not provide any chance to the potential investors for earning abnormal profit as
all the information is dispersed and absorbed in the market and is quickly and accurately reflected by the prices of
securities thereby opening up the market. Therefore, there will be no undervalued securities offering higher than
expected returns, considering the risk associated with them.
Therefore the investment strategy of an investor will consider the overall risk and return of the portfolio rather than
of an individual security. However, if markets are not efficient, higher returns can be made by correctly picking
winners (Rutterford, 1993). It has been empirically proved that most western equity markets are more efficient in
comparison to their developing countries counterparts (Gupta and Basu, 2007). Like fair game in game theory the
expected return from efficient market is also zero (Fama, 1965). Fama (1970) and (1991) provided the formal
definition of “Market Efficiency”. Fama categorized market efficiency into three classes which are weak form, semi
strong form and strong form. In Weak form of efficiency the stock yields are serially un-correlated and have a
perpetual mean. In other words, a market is considered weak form efficient if current prices completely imitate all
information incorporated in past prices, which means that no investor can toil a plan on the basis of past price
patterns alone with the purpose of earning abnormal returns. Semi strong efficiency suggests that only information
that is not publicly available can benefit investors seeking to earn abnormal returns on investments. All other
information is accounted for in the stock price and, regardless of the amount of fundamental and technical analysis
one performs, above normal returns will not be had. The last of the market efficiency ideology is the strong market
efficiency which implies that profits exceeding normal returns cannot be made, regardless of the amount of research
or information investors have access to, the premise being that all market information public or private is accounted
for in the stock price.
Okpara (2010) opined that stock prices are priced efficiently to reflect all available information about the intrinsic
value of the security. Ajayi, Mehdian and Perry (2004) also of the same opinion, went further to state that efficient
market is one where all unexploited profit opportunities are estimated by arbitrage. In Nigeria not many scholars
have documented several persistent and potentially exploitable daily patterns on stock market anomalies which
present serious challenges to the stock markets around the world, especially emerging economies. An efficient
market is one which does not provide any chance to the potential investors for earning abnormal profit as all the
information is dispersed and absorbed in the market and is quickly and accurately reflected by the prices of
securities thereby opening up the market. Therefore, there will be no undervalued securities offering higher than
expected returns, considering the risk associated with them.
Therefore the investment strategy of an investor will consider the overall risk and return of the portfolio rather than
of an individual security. However, if markets are not efficient, higher returns can be made by correctly picking
winners (Rutterford, 1993). It has been empirically proved that most western equity markets are more efficient in
comparison to their developing countries counterparts (Gupta and Basu, 2007). Like fair game in game theory the
expected return from efficient market is also zero (Fama, 1965). Fama (1970) and (1991) provided the formal
definition of “Market Efficiency”. Fama categorized market efficiency into three classes which are weak form, semi
strong form and strong form. In Weak form of efficiency the stock yields are serially un-correlated and have a
perpetual mean. In other words, a market is considered weak form efficient if current prices completely imitate all
information incorporated in past prices, which means that no investor can toil a plan on the basis of past price
patterns alone with the purpose of earning abnormal returns. Semi strong efficiency suggests that only information
that is not publicly available can benefit investors seeking to earn abnormal returns on investments. All other
information is accounted for in the stock price and, regardless of the amount of fundamental and technical analysis
one performs, above normal returns will not be had. The last of the market efficiency ideology is the strong market
efficiency which implies that profits exceeding normal returns cannot be made, regardless of the amount of research
or information investors have access to, the premise being that all market information public or private is accounted
for in the stock price.
In the United States some of these studies have been going on as far as the early 1930s. Fields (1931) observed that
the US stock market consistently experienced significant negative and positive liquidity on Mondays and Fridays
respectively. The observation once again started receiving increasing attention during the 1980's (French, 1980;
Gibbons and Hess, 1981; Lakonishok and Levi, 1982), especially when it was discovered that capital markets of
many other countries also experience similar seasonality (WesterField, 1985; Peiro, 1994; Agarwal and Tandon,
1994). This “day of the week effect”, in sharp contrast to the theories of efficient market, was considered a puzzle
and despite different theories, so far the puzzle has not been satisfactorily resolved. As more and more empirical
evidence are obtained from different stock markets all over the world, the puzzle far from being solved seems to
have increased. Using a long time series data from 1962–1993, Wang et al (1997) found out that the US capital
market enhances liquidity. Also studying liquidity in the US market, Peiro (1994) observed that there were positive
stock market returns. Of late, studies have incorporated volatility of market returns in the framework of analysis (Ho
and Cheung, 1994; Choudhry, 2000). A market is characterized as efficient if stock prices promptly reflect any new
publicly available information and it is called efficient when all available information whether available publicly or
privately affects stock market returns. It is against the concept of how efficient the Nigerian stock market is that,
this study examined the impact of liquidity and volatility on stock market returns of the Nigerian stock market.
Over the years, Economists have been emphasizing the need for effective mobilization of resources as a catalyst for
national development in any economy, which can only be achieved through the effectiveness in the mobilization and
allocation of funds to different sectors of the economy. Basically, the capital market is primarily created to provide
avenues for effective mobilization of idle funds from the surplus economic units and channel them to the deficit
economic units for long-term investment purpose. It, therefore, serves as a linkage or mechanism between the deficit
sector and the surplus sector in any economy. The suppliers of funds are basically individuals and corporate bodies
as government rarely supply funds to the market. The users of funds, by contrasts, consist mainly of corporate
bodies and government. The vital roles played by the capital market in the achievement of economic growth thereby
enables governments, industries and corporate bodies to raise long-term capital for the purpose of financing new
projects and for expanding and modernizing industrial concerns. A unique benefit of the capital market to corporate
entities is the provision of long-term, non-debt financial capital. To determine the impact of stock market on the
Nigeria economy, more funds are needed to meet the rapid development and expansion of the economy. The stock
market serves as a veritable tool in the mobilization and allocation of savings among competing ends which are
critical and necessary for the growth and efficiency of the economy. Therefore, the determination of the overall
growth of an economy depends on how efficiently the stock market performs its allocation functions of capital.
In capital markets, the stock in trade is money which could be raised through various instruments under well-
governed rules and regulations, which are carefully administered and adhered to by different institutions or market
operators. It is, therefore, a fact not disputed that the rate of economic growth of any nation is inextricably linked to
the sophistication of its financial market and specifically its stock market efficiency. The fund required by the
corporate bodies and governments are often huge, sometimes running into billions of naira. It is, however, usually
difficult for these bodies to meet such funding requirements solely from internal source. Hence, they often look up
to the stock market because it is the ideal source as it enables corporate entities and government to pool monies from
a large number of people and institutions.
1.2 Statement of research problem
The problem under investigation is theoretical in nature but with practical consequences to investors, academics and
policy makers. Many studies have questionable methodologies when measuring the impact of certain factors on
stock market returns. Amihud et al (2005) in studying liquidity and asset pricing believes that the increasing
importance of standard deviation inclusive models in measuring volatility and liquidity of stock market returns is not
unconnected to the general understanding that there is a need to model risk measures that would capture the effect of
liquidity and volatility on returns.
Ajayi et al (2004) in studying eastern European markets implies that the validity of certain volatility measures
generally depends upon specific distributional assumptions. Again, the existence of multiple competing models
immediately calls into question the robustness of previous findings, the squared returns of some of the models also
obscured by very noisy volatility indicators. Some research did not perform some tests such as diagnostic/ post
estimation tests, unit root tests or even the granger causality tests making it difficult to place complete reliance on
the inference.
1.3 Research objective
To examine the impact of liquidity measured by market capitalization value ratio on stock market returns of the ten
quoted companies of different sectors of the Nigerian Stock Exchange.
1.4 Research hypothesis
Ho1: Liquidity measured by market capitalization value ratio does not have any significant impact on stock
market returns of the ten quoted companies of different sectors of the Nigerian Stock Exchange.
2.0 Literature review
One of the earliest and most enduring questions of financial economics is whether financial asset prices are
forecastable. The concept of efficient market hypothesis which asserts that the asset price changes are unforecastable
is found in the theoretical contribution and empirical research of Bachelier and May .D (2011). The modern
literature on financial market efficiency begins with Samuelson (1965) who in his landmark article tried to prove
why properly anticipated prices fluctuate randomly. In an informationally efficient market different from an
allocationally or Pareto - efficient market -- price changes must be unforecastable if they are properly anticipated,
i.e., if they fully incorporate the expectations and information of all market participants.
Since the early 1960’s a considerable amount of empirical research has been undertaken on determining whether or
not financial markets are efficient. Market efficiency refers to a condition, in which current prices reflect all the
publicly available information about a security. The basic idea underlying market efficiency is that competition will
drive the price to reflect all information. In the financial market, the maximum price that investors are willing to pay
for a financial asset is actually the current value of future cash payments that are discounted at a higher rate to
compensate for the uncertainty in the cash flow projections. Therefore, investors trade information as a commodity
in financial markets. The Efficient Market Hypothesis (EMH) has been consented as one of the cornerstones of
modern financial economics which proposes that share price fluctuations are random and do not follow any regular
pattern.
But since 1980's it is well appreciated that lack of linear dependence (i.e., serial correlation) does not rule out
nonlinear dependence which, if present, would contradict the EMH and may aid in forecasting, especially over short
time intervals. Sakai and Tokumaru (1980) have shown that simple nonlinear models exhibit no serial correlation
while containing strong nonlinear dependence. This has, in fact, led several researchers like Hinich and Patterson
(1985) and Scheikman and LeBaron (1989) to look for nonlinear structures in stock returns. It may be noted in this
context that one of the most important and useful tests available in the literature for detecting nonlinear patterns i.e .,
the existence of potentially forecastable structures, is due to Brock et al. (1987, revised 1996), to be henceforth
denoted as BDS test.
With increasing power of computers coupled with advances in both nonlinear dynamics and chaos, the volume of
research into the re-examination of the behaviour of security returns from the standpoint of market-efficiency has
increased considerably, and most of these (see Hsieh, 1991; Willey, 1992;) have cast doubt on the conclusion of
market efficiency based only on the lack of serial correlation in returns.
Apart from complicated nonlinear dependence/dynamics, there are two well known reasons as to why stock prices
may deviate from the random walk model. First, conditional variance of stock returns is not constant over time. This
fact has led to the development of autoregressive conditional heteroscedasticity (ARCH) and generalised ARCH
(GARCH) models (Engle, 1982). Returns based on equity prices/indices are most often found to have time
dependent conditional variance and hence ARCH/GARCH models are used to take care of the volatility observed in
the time series of returns. Some of the tests for (linear) autocorrelation mentioned earlier perform poorly in presence
of conditional heteroscedasticity in the returns. In fact, Diebold (1986), Silvapulle and Evans (1993), and others
have noted that in the presence of ARCH, the serial correlation tests, if not corrected, can result in misleading
inferences.
Further, Silvapulle and Evans (1993) have suggested a simple volatility based specification test, called variance ratio
test, to test random walk hypothesis. The Variance Ratios as test statistics are intutively appealing and are known to
have optimal properties under certain circumstances. But researchers have now noted that the test's performance
critically depends on 'lag truncation point' which is often chosen arbitrarily by most researchers. Very recently Choi
(1999)'s has suggested calculating variance ratio test by using optimal data dependent method, so that this
shortcoming could be overcome. This modified test is now known in the literature as Automatic Variance Ratio test.
A few more recent tests for serial correlation are available (Choi, 1999), but the optimality of some of these tests
was not yet clearly established.
The other reason for stock returns to deviate from random walk model is due to what is known as calendar
anomalies/effects. Many authors like French (1980), Engle et al. (1987) have found that returns differ by small yet
statistically significant amounts during different periods of time i.e., day-of-the-week, week-of-the month and
month-of-the-year. These effects, if present in returns, indicate that stock prices have a predictable pattern in their
movements leading to the conclusion that the stock market is inefficient.
Additionally, there may be predictable component in stock returns in the form of significant time-varying risk factor
which obviously goes against EMH. In view of this many experts incorporate conditional risk component in the
model in testing for volatility. An important point to be noted at this stage is that in all the studies on efficiency the
underlying models are assumed to have correctly specified conditional mean. It is now too well-known that
inferences based on models suffering from misspecification due to inappropriate conditional mean could very well
be misleading and incorrect. It is worth mentioning that in the context of studies on efficiency in the framework of
ARCH/GARCH, Lumsdaine and Ng (1999) (Tong, 1990; Giles et al., 1993) have shown that in general the popular
Lagrange Multiplier (Rao's score) test for testing the null of homoscedasticity leads to overrejection of the null
hypothesis of conditional homoscedasticity if there is misspecification of conditional mean. It thus becomes
important to test for ARCH in the general context of a possibly misspecified conditional mean and then take
appropriate steps for guarding against misspecification in the mean function in case the test rejects the null
hypothesis of no misspecification of conditional mean.
As stated by Lumsdaine and Ng, the misspecification problem referred to here can arise if the functional form and/or
conditioning information set is misspecified. For linear dynamic models, notable cases of such misspecifications are
omitted shifts in the trend function, selecting a lag length in an autoregression that is lower than the true order,
failure to account for parameter instability, residual autocorrelation and omitted variables. They have also proposed
a method based on use of recursive residuals for adjusting the standard ARCH test to allow for possible
misspecification of unknown form. In this context it is also relevant to note that incorrectly specified conditional
mean might as well lead to misspecification of conditional variance. In fact, GARCH model would be correctly
specified if only there is no serial correlation. As a way out for this problem in the context of studying serial
correlation, Robinson (1991) and Woolridge (1991a, b) have suggested ways of robustifying tests for serial
correlation to allow for possible misspecification of conditional variance.
When predicting the future prices of Stock Market securities, there are several theories available. In EMH, it is
assumed that the price of a security reflects all of the information available and that everyone has some degree of
access to the information. Fama’s theory further breaks EMH into three forms: Weak, Semi-Strong, and Strong. In
Weak EMH, only historical information is embedded in the current price. The Semi-Strong form goes a step further
by incorporating all historical and currently public information into the price. The Strong form includes historical,
public, and private information, such as insider information, in the share price. From the tenets of EMH, it is
believed that the market reacts instantaneously to any given news and that it is impossible to consistently outperform
the market
A different perspective on prediction comes from Random Walk Theory (Malkiel 1992). In this theory, Stock Market
prediction is believed to be impossible where prices are determined randomly and outperforming the market is
infeasible. Random Walk Theory has similar theoretical underpinnings to Semi-Strong EMH where all public
information is assumed to be available to everyone. However, Random Walk Theory declares that even with such
information, future prediction is ineffective It is from these theories that two distinct trading philosophies emerged;
the fundamentalists and the technicalists. In a fundamentalist trading philosophy, the price of a security can be
determined through the nuts and bolts of financial numbers. These numbers are derived from the overall economy,
the particular industry’s sector, or most typically, from the company itself. Figures such as inflation, joblessness,
industry return on equity (ROE), debt levels, and individual Price to Earnings (PE) ratios can all play a part in
determining the price of a stock.
In contrast, technical analysis depends on historical and time-series data. These strategists believe that market timing
is critical and opportunities can be found through the careful averaging of historical price and volume movements
and comparing them against current prices. Technicians also believe that there are certain high/low psychological
price barriers such as support and resistance levels where opportunities may exist. They further reason that price
movements are not totally random, however, technical analysis is considered to be more of an art form rather than a
science and subject to interpretation. Both fundamentalists and technicalists have developed certain techniques to
predict prices from financial news articles.
Financial markets deviate, to varying degrees, from the perfect-market ideal in which there are no impediments to
trade. Trade impediments reduce the liquidity that markets offer. In theory lack of market liquidity is often attributed
to underlying market imperfections such as asymmetric information, different forms of trading costs, and funding
constraints. Dimitri .V and Jiang .W (2012) studied how these impefections affect expected asset return across
markets by empirical estimating measures of liquidity using theoretical models relating them to asset characteristics
and asset returns.
Theoretically, researches are conducted studying a variety of market impefections, relying on different modeling
assumptions. For example Nilsson (2002) in his study of Nordic stock return characteristics assumed the life-cycle
and risk sharing motives to trade and relating them to trading costs. The findings of Najand (1991) also using
liquidity models consolidated positions taken by Mestel et al (2003) that asymmetric information often rely on noise
trading.
Some scholars who worked on the assumptions of asymmetric information mostly assume risk-neutral market
makers who can take unlimited positions, while others studying imperfections typically assume risk aversion or
position limits. In the attempts to link empirical methodologies and findings with theory Dimitri and Jiang (2012)
considered six imperfections affecting measures of liquidity; they are participation costs, transaction costs,
asymmetric information, imperfect competition, funding constraints and search to measure the effect of price
volumes on price and also measure price reversal using auto-covariance of returns.. Some of the liquidity measures
used in finance are derived from theoretical models while other measures are intuitive or heuristic especially useful
in interpreting existing results and suggesting new tests and analysis.
Imperfection affects price reversals and expected returns in a unified model hence delivers new insights by
improving on existing literature. These imperfections where accurately measured can indicate the existence and to
what extent of price impact per unit trade and trade size per period measured. Again imperfections do not always
raise expected returns and the validity of the assumption has been put to test on a number of occasions and many
scholars are in agreement that this assumption are likely to hold in certain conditions than others. Some liquidity
impact measures such as price reversal are motivated by theory but others like bid-ask spread, market depth,
turnover and trade size are more intuitive or heuristic. Other ways of measuring liquidity could be as an aggregate
asset, single asset, variations across assets overtime, relationship to asset characteristics such as supply and volatility
and expected asset returns.
Emphasis has been placed in literature reviews on links to theory of empirical measures of liquidity reflecting
underlying market imperfections by trying to find out the role of theory in accounting for the variation of liquidity
measures and asset characteristics such as expected returns. Theory in most cases has been proven to shed new light
on existing empirical results and suggest new tests and analysis. Huang, Jennifer and Jiang (2009) opines in theory
that effectiveness of a particular measure of illiquidity, in terms of reflecting the underlying market imperfection,
depends on the imperfection. This is why some measures are more successful than others in capturing liquidity and
its relationship with expected asset returns in some markets. Using those measures, and controlling for additional
factors suggested by theory, would yield sharper empirical tests.
Liquidity effects can manifest themselves over different time horizons. The market microstructure literature focuses
on short horizons, from minutes or hours to days or weeks. At the same time, recent work on the limits of arbitrage
finds that flows can affect returns even at the longer horizons used in asset-pricing analysis, e.g., months, quarters or
years. Most of the theoretical literature considers one imperfection at a time and thus does not allow for interactions.
Again the underlying economic causes of the imperfections and the ways in which imperfections are linked is also
contentious. Huberman et al (2001) attributed the linkage problem to some imperfections being a consequence of
other more fundamental ones. For example, some types of transaction costs viewed as a consequence of
participation costs or asymmetric information, then costly participation could be linked to asymmetric information.
Asymmetric information could underlie the contracting frictions that give rise to funding constraints.
Endogenizing some market imperfections from more fundamental frictions could further streamline, clarify and
deepen the study of market liquidity. In particular, various forms of informational problems could be the underlying
economic cause for various forms of imperfections. Geert and Guojun (1997) wrote that a large fraction of trading
activity in financial markets is generated by specialized financial institutions, and these institutions can be important
suppliers or demanders of liquidity. In the models a common friction unfortunately often underestimated or ignored
in studies of this nature is funding constraints. The importance of financial institutions in affecting asset prices is
emphasized in a rapidly growing literature on the limits of arbitrage.
Related to the institutional context is the issue of market design. While some researches consider ways in which
markets deviate from the Walrasian ideal, the have not studied market design in depth observed Huberman et al
(2001). The market microstructure literature studies various dimensions of market design and shows that they can
affect market performance. Such dimensions include whether liquidity is supplied by dedicated market makers or an
open limit-order book, whether limit orders are visible to all traders, whether transactions are disclosed to all traders
after they are executed, etc. It is vital for any analysis to be conducted at a more aggregate level with more market
detail, so that an attempt can be made to derive some key effects within a tractable unified model is in computing
empirical measures of market depth and resiliency at such horizons.
Liquidity measures applied in certain models at the microeconomic structure are strong indicators on how
imperfections can measure policy actions on welfare, asset returns. Amihud, Mendelson and Pedersen (2005)
focused mainly on transaction costs while Huang et al (2009) concentrated their study on imperfections attributed to
limits of arbitrage and how ex-ante expected returns are affect by imperfections. Huang and Wang (2009) study how
participation costs affect both the demand for immediacy, which Grossman and Miller (1988) treat as exogenous,
and the supply. They assume that liquidity shocks are opposite across agents and do not affect the price in the
absence of participation costs. Participation costs lower the price because sellers are more willing to participate than
buyers. The intuition is that sellers receive a larger risky endowment, and are hence more concerned about the risk
that an additional shock will leave them with a large risk exposure.
In addition to costs of market participation, agents typically pay costs when executing transactions. Transaction costs
drive a wedge between the buying and selling price of an asset. They come in many types, e.g., brokerage
commissions, exchange fees, transactions costs can be viewed as a consequence of other market imperfections.
Costly participation can generate price-impact costs. The difference between transaction costs and participation cost
is that the decision whether or not to incur the transaction costs is contingent on the price. The effect of transaction
costs on the price depends on the relative measures of liquidity suppliers and demanders since transaction costs
impact the liquidity measures and the expected return.
Vayanos (2004) explores time variation in investor horizons, assuming constant transaction costs. He assumes that
investors are fund managers subject to withdrawals when their performance drops below a threshold, and the
volatility of asset dividends is time-varying. During volatile times, fund managers’ horizon shorten because their
performance is more likely to drop below the threshold. This causes liquidity premium per unit of transaction costs
to increase precisely during the times when the market is the most risk averse. In researching on time varying
transaction costs and liquidity premium Vayanos (2004) further supports pricing factors related to aggregate
liquidity augments traditional pricing models like CAPM.
There is a very significant correlation between money supply, deflated for changes in the consumer price index, and
the general level of stock prices. Increases in the money supply provide liquidity, however increases in the consumer
price index decreases liquidity. Evidence have been provided in the studies of many stock market models by
academics ranging from rigorous analytical frameworks to questionable intuitive reasoning suggesting that liquidity
plays a significant role in explaining the cross-sectional variation in stock returns. According to Mazumdar, (2004),
changes in liquidity measured by increase in market capitalization are also a casual factor producing immediate
changes in stock returns.
Adequate market liquidity motivates investors to adjust their wealth portfolios in such a manner as to yield
predictable movements in the prices of securities. Liquidity considerations correspond to the individual’s attitude to
risk, the risk preference of the investor influences the individual’s choice for precautionary-liquid balances.
Generally as the size of an individual’s portfolio increases the smaller will be the portion of highly liquid assets held.
Demand pressure, exogenous trading costs, inventory risk, search frictions, and asymmetric information are
common denominators affecting liquidity in the market. There is increased cost to the investor who holds assets that
are less than perfectly liquid hence there is a positive relationship between stock returns and illiquidity, conversely,
the relationship between stock returns and liquidity should be negative. Patient investors who make long term
investments in assets that are sensitive to liquidity expect higher returns as a compensation for additional risks. That
is why there should be liquidity risk premium in stock pricing (Amihud, 2002).
Amihud et al (2005) studied the implications of liquidity on stock returns defining the degree of market liquidity as
the cost of immediate execution. They also indicated that the bid-ask spread contains a premium for immediate
purchase or sale, and also that the spread between supply and demand is a natural measure of liquidity. Amihud et al
(2005) proved that in an equilibrium context there is an increasing and concave relationship between required return
rate and the degree of liquidity of financial assets. They also show that financial assets spreads are negatively
correlated with certain measures of liquidity such as trading volume.
Amihud et al (2005) indicate that measuring the degree of liquidity compared to bid-ask spread is critical since the
spread contains an information asymmetry component. In other words the effects of liquidity with information
asymmetry may often be measured by the variable component of transaction costs. As anticipated return increases
expectedly market liquidity reduces but time forecast return excess compensates market’s anticipated liquidity.
Amihud (2002) proves that anticipated market illiquidity has a positive and significant effect, while non-anticipated
illiquidity has a negative and significant effect. Market-wide liquidity is a factor for pricing common stocks.
Expected stock returns are related cross-sectionally to the sensitiveness of stock returns to innovations in aggregate
liquidity. Stocks that are more sensitive to aggregate liquidity have substantially higher expected returns, even after
accounting for exposures to the market return as well as size, value, and momentum factors.
Dimitri and Jiang (2012) used liquidity measures capturing dimensions associated with the strength of volume-
related return reversals. Liquidity measures are characterized by significant commonality across stocks, supporting
the notion of aggregate liquidity as a priced state variable. Smaller stock are less liquid, according to our measure,
and the smallest stocks have high sensitiveness to aggregate liquidity.
Empirical research across financial markets has noted regularities in intraday behavior of volume and volatility.
Typically, both the volatility of returns and volume of trading is found to be “U-shaped”, i.e., more at the beginning
and at the close of trading as compared to rest of the trading hours. In some markets, the increase towards the close
of trading is less pronounced resulting in so called “reverse J” shaped pattern or even “L shaped” intraday pattern.
Researchers have also explored the role of information flow and of the microstructure variables as determinants of
intraday volatility.
Cross-listed stocks, where the foreign listing is in a market in different time-zone, present a case where the trading
continues much after it has stopped for other stocks. Since these stocks are traded overnight (in foreign market),
relatively more recent price quotes are available and hence variance of price at opening should be low for these
stocks, assuming that information can flow freely (Amihud and Mendelson 1991). Amihud and Mendelson (1987)
observe that pricing errors at open are lower for cross-listed stocks vis-à-vis other stocks and conclude that available
sequence of transaction prices from the trading day in other markets facilitates faster price discovery for cross-listed
stocks.
Another phenomenon of empirical interest in the context of intraday dynamics is the effect of expiry of derivative
contracts on prices, volume and volatility. Alkeback and Hagelin (2004) find high volumes but no price distortions
in Swedish market. Vipul (2005), based on low-frequency data from Indian stock market, notes that the price and
volatility are sometimes distorted near expiration day in the Indian market due to unwinding of cash positions by
arbitrageurs in cash markets.
3.0 Research methodology
This research adopts the ex-post facto research design. In the context of social and educational research the phrase
‘after the fact’ or ‘retrospectively’ refers to those studies which investigate possible cause-and-effect relationships by
observing an existing condition or state of affairs and searching back in time for plausible causal factors.
Secondary data is data which has been collected by individuals or agencies for purposes other than those of our
particular research study (Onwumere, 2005). The justification for the use of secondary data in this research is that; it
is available and is entirely appropriate and wholly adequate to draw conclusions and answer the question or solve
the problem. Thus, the data used for this research was generated from the NSE official daily report from January
2016 to December 2016.
In the process of developing of the model the first step is to identify the linear regression model requiring the
inclusion of the dependent and independent variable and the attendant coefficient weights identified by using
statistical method called Ordinary Least Squares (OLS). These coefficient weights measure the strength of the
relationship between independent and dependent variables. The two dimensions of the coefficients are direction and
magnitude. The direction indicates whether variations in the dependent variable are caused by changes in the
independent variable. Generally, the magnitude of coefficients can be compared only if two independent variables
have the same unit of measurement. Otherwise the variables need to be normalized to a standard scale to be
compared to measure the strength of the relationship across different independent
variables.
To test for the impact of liquidity and volatility on stock returns of the Nigerian stock market, we adopted the linear
regression model in line with existing studies in this area of finance, for instance, the works of Arumugam (1997),
Berument and Kiymaz (2001) and Rahman (2009), Guha Deb and Mukherjee (2008), Chaudhury (1991), Goswami
and Anshuman (2000), Lumsdaine and Ng (1999) and Woolridge (1991), etc. According to Onwumere (2009),
regression is a statistical technique used in measuring the impact of one or more variables (otherwise known as
independent variables or regressors) on another variable (the dependent variable or the regressand). The general
linear regression model according to Koutsoyiannis (2006) and Onwumere (2009), is:
Y = α0+ α 1X + µ - - - - - - (i)
Where Y is a function of X independent variable and µ is the error term, a 0 being the constant and a1 being the
coefficient of the independent variable.
The model for this study was expressed in line with the hypotheses stated as follows
Ho1: Liquidity measured by market capitalization value ratio does not have any significant impact on stock
market returns of the ten quoted companies of different sectors of the Nigerian Stock Exchange.
Log ASI = α0 + α 1MCVr + µ ..………………………………… (i)
where;
Log ASI = Log of All Share Index (a proxy for Stock Market Returns)
MCVr =Market Capitalization Value ratio ( a proxy for Liquidity measured by Market Capitalization
divided by Value of Transactions)
α0 = Equation constant
α 1 = Coefficient of independent variable
µ = Error Term
Variables
The variables used in the models are the Dependent and Independent, the former represents the output or effects
while the latter represents the inputs or causes. And since the models are statistical the dependent variable is studied
to see if and how much it varies as the independent variable varies.
Stock Return (SR)
This study adopted the daily All Shares Index (ASI) of the Nigerian Stock Market (NSE) as a measure of stock
market returns in line with the works of Arumugam (1997), Berument and Kiymaz (2001) and Rahman (2009). The
NSE all shares index is a composite index calculated from prices of all common stocks traded on the NSE.
Specifically, the Index is a market capitalization weighted price index which compares the current market value of
all listed common shares to the value on the base date of 4th January 1999 when the first session was traded on the
market. The NSE-Index was primarily set at 100 points. The data was obtained over the period from January 2016
to December 31st 2016. This is the dependent variable.
Market Capitalization Value Ratio
Market Capitalization Value ratio measures attempts to differentiate between price movement due to the degree of
liquidity from other factors such as general market conditions or arrival of new information to measure both
elements of resilience and speed of price recovery. This measure uses the residuals of a regression of the asset’s
return on the return of the market thus purging it from its systemic risk to determine the intrinsic liquidity of the
assets. This is in line with Sarr and Lybek (2002) and was measured by value of shares traded divided by market
capitalization multiplied by 100. This is the independent variable.
Techniques of Analysis
The hypothesis earlier specified in the model was tested using the Least Square (LS) regression analysis. While
regression analysis is concerned with the study of the dependence of one variable, the dependent variable, on one or
more other variables, the explanatory variables, with a view to estimating and/or predicting the population mean or
average value of the former in terms of the known or fixed (in repeated sampling) values of the latter (Gujarati and
Porter, 2009). In statistics and econometrics, regression analysis is used in modeling and analyzing several variables,
when the focus is on the relationship between a dependent variable and one or more independent variables
(Onwumere, 2005). Most commonly, regression analysis estimates the conditional expectation of the dependent
variable given the independent variables that is, the average value of the dependent variable when the independent
variables are held fixed. Less commonly, the focus is on a quartile, or other location parameter of the conditional
distribution of the dependent variable given the independent variables (Brooks 2002). In all cases, the estimation
target is a function of the independent variables called the regression function. In regression analysis, it is also of
interest to characterize the variation of the dependent variable around the regression function, which can be
described by a probability (Gujarati and Porter 2009).
4.0 Data analysis and discussion of results
OKOMU OIL
Dependent Variable: CAPITALIZATION
Method: Least Squares
Date: 04/10/18 Time: 08:12
Sample (adjusted): 2 261
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
VALUE 33.39397 1.187367 28.12438 0.0000
C 21819004 15816198 1.379535 0.1691
R-squared 0.778539 Mean dependent var 2.42E+08
Adjusted R-squared 0.777555 S.D. dependent var 4.39E+08
S.E. of regression 2.07E+08 Akaike info criterion 41.14224
Sum squared resid 9.63E+18 Schwarz criterion 41.17242
Log likelihood -4667.645 Hannan-Quinn criter. 41.15442
F-statistic 790.9809 Durbin-Watson stat 2.188953
Prob(F-statistic) 0.000000
UACN Plc
Dependent Variable: CAPITALIZATION
Method: Least Squares
Date: 04/10/18 Time: 08:14
Sample (adjusted): 2 261
Included observations: 225 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
VALUE 20.10694 0.073122 274.9762 0.0000
C -6203734. 2082021. -2.979670 0.0032
R-squared 0.997059 Mean dependent var 2.68E+08
Adjusted R-squared 0.997046 S.D. dependent var 5.04E+08
S.E. of regression 27402655 Akaike info criterion 37.09903
Sum squared resid 1.67E+17 Schwarz criterion 37.12939
Log likelihood -4171.641 Hannan-Quinn criter. 37.11128
F-statistic 75611.89 Durbin-Watson stat 1.426003
Prob(F-statistic) 0.000000
Julius Berger
Dependent Variable: CAPITALIZATION
Method: Least Squares
Date: 04/10/18 Time: 08:26
Sample (adjusted): 2 261
Included observations: 219 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
VALUE 42.47973 0.397748 106.8006 0.0000
C 5385450. 6615380. 0.814080 0.4165
R-squared 0.981331 Mean dependent var 1.83E+08
Adjusted R-squared 0.981245 S.D. dependent var 6.92E+08
S.E. of regression 94739047 Akaike info criterion 39.58024
Sum squared resid 1.95E+18 Schwarz criterion 39.61119
Log likelihood -4332.036 Hannan-Quinn criter. 39.59274
F-statistic 11406.38 Durbin-Watson stat 2.295908
Prob(F-statistic) 0.000000
Nestle Plc
Dependent Variable: CAPITALIZATION
Method: Least Squares
Date: 04/10/18 Time: 08:28
Sample (adjusted): 2 261
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
VALUE 804.0600 3.518512 228.5227 0.0000
C -3.24E+09 1.11E+09 -2.910712 0.0040
R-squared 0.995710 Mean dependent var 1.14E+11
Adjusted R-squared 0.995691 S.D. dependent var 2.27E+11
S.E. of regression 1.49E+10 Akaike info criterion 49.69346
Sum squared resid 4.98E+22 Schwarz criterion 49.72363
Log likelihood -5638.208 Hannan-Quinn criter. 49.70564
F-statistic 52222.63 Durbin-Watson stat 1.217601
Prob(F-statistic) 0.000000
Zenith Bank Plc
Dependent Variable: CAPITALIZATION
Method: Least Squares
Date: 04/10/18 Time: 08:31
Sample (adjusted): 2 261
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
VALUE 14.36373 0.601355 23.88560 0.0000
C 1.67E+08 2.67E+08 0.626573 0.5316
R-squared 0.717167 Mean dependent var 4.45E+09
Adjusted R-squared 0.715910 S.D. dependent var 5.60E+09
S.E. of regression 2.99E+09 Akaike info criterion 46.48106
Sum squared resid 2.01E+21 Schwarz criterion 46.51124
Log likelihood -5273.601 Hannan-Quinn criter. 46.49324
F-statistic 570.5217 Durbin-Watson stat 2.009175
Prob(F-statistic) 0.000000
Glaxo pharmaceuticals Plc
Dependent Variable: CAPITALIZATION
Method: Least Squares
Date: 04/10/18 Time: 08:33
Sample (adjusted): 2 261
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
VALUE 25.86482 0.237238 109.0250 0.0000
C -59606682 18713548 -3.185215 0.0017
R-squared 0.981423 Mean dependent var 3.30E+08
Adjusted R-squared 0.981340 S.D. dependent var 2.03E+09
S.E. of regression 2.77E+08 Akaike info criterion 41.72387
Sum squared resid 1.72E+19 Schwarz criterion 41.75405
Log likelihood -4733.659 Hannan-Quinn criter. 41.73605
F-statistic 11886.44 Durbin-Watson stat 1.226049
Prob(F-statistic) 0.000000
NCR Plc
Dependent Variable: CAPITALIZATION
Method: Least Squares
Date: 04/10/18 Time: 08:37
Sample (adjusted): 2 252
Included observations: 62 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
VALUE 9.671866 0.109068 88.67734 0.0000
C -12854.43 28865.33 -0.445324 0.6577
R-squared 0.992428 Mean dependent var 943594.4
Adjusted R-squared 0.992302 S.D. dependent var 2402791.
S.E. of regression 210822.8 Akaike info criterion 27.38715
Sum squared resid 2.67E+12 Schwarz criterion 27.45577
Log likelihood -847.0017 Hannan-Quinn criter. 27.41409
F-statistic 7863.670 Durbin-Watson stat 1.625009
Prob(F-statistic) 0.000000
Dangote cement plc
Dependent Variable: CAPITALIZATION
Method: Least Squares
Date: 04/10/18 Time: 08:39
Sample (adjusted): 2 261
Included observations: 227 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
VALUE 177.2224 1.067476 166.0200 0.0000
C -7.61E+08 2.03E+08 -3.756021 0.0002
R-squared 0.991903 Mean dependent var 1.60E+10
Adjusted R-squared 0.991867 S.D. dependent var 2.93E+10
S.E. of regression 2.65E+09 Akaike info criterion 46.23948
Sum squared resid 1.58E+21 Schwarz criterion 46.26965
Log likelihood -5246.181 Hannan-Quinn criter. 46.25165
F-statistic 27562.65 Durbin-Watson stat 1.072690
Prob(F-statistic) 0.000000
Mobil Plc
Dependent Variable: CAPITALIZATION
Method: Least Squares
Date: 04/10/18 Time: 08:41
Sample (adjusted): 2 261
Included observations: 224 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
VALUE 243.4496 4.494590 54.16503 0.0000
C -5.25E+08 2.96E+08 -1.773989 0.0774
R-squared 0.929654 Mean dependent var 4.91E+09
Adjusted R-squared 0.929338 S.D. dependent var 1.57E+10
S.E. of regression 4.16E+09 Akaike info criterion 47.14667
Sum squared resid 3.85E+21 Schwarz criterion 47.17713
Log likelihood -5278.427 Hannan-Quinn criter. 47.15896
F-statistic 2933.850 Durbin-Watson stat 1.420506
Prob(F-statistic) 0.000000
NAHCO Plc
Dependent Variable: CAPITALIZATION
Method: Least Squares
Date: 04/10/18 Time: 08:43
Sample (adjusted): 2 261
Included observations: 226 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
VALUE 556.8265 19.24783 28.92931 0.0000
C -6.13E+08 72216765 -8.490834 0.0000
R-squared 0.788860 Mean dependent var 1.50E+08
Adjusted R-squared 0.787917 S.D. dependent var 2.19E+09
S.E. of regression 1.01E+09 Akaike info criterion 44.31416
Sum squared resid 2.29E+20 Schwarz criterion 44.34443
Log likelihood -5005.500 Hannan-Quinn criter. 44.32638
F-statistic 836.9050 Durbin-Watson stat 1.816539
Prob(F-statistic) 0.000000
5.0 Discussion of findings and conclusions
The findings indicate different scenarios for the different quoted companies analyzed have sufficient goodness of fit.
The goodness of fit of the model can be seen in the coefficient of determination (R-square). Which means that the R2
measures how well variations in the dependent variable are explained by the independent variables on a trading day
basis for one financial year. The adjusted R2 moderates the R2 indicating that there may be other variables other than
our explanatory variables that might have an impact on the dependent variable but not represented in the equation.
The Durbin Watson statistics is meant to reveal if there are signs of serial correlation and to what extent. The AIC, or
Schwarz criterion, shows that the difference between the two is very negligible, an indicator of a near perfect model
convergence near zero. The smaller they are the better the fit of a model is (from a statistical perspective) as they
reflect a trade-off between the lack of fit and the number of parameters in the model. That the differences between
the R2 and adjusted R2 are negligible is an indicator that the regression line approximates the real data points and so
is a very good fit and also shows how well observed outcomes in the analyses are replicated in the model.
The R2 and adjusted R2 for the companies like Okomu oil plc (77.7% & 77.8%), UACN (99.7% & 99.7%), Julius
Berger (98.1% & 98.1%), Nestle plc (99.5 & 99.5%), Zenith bank plc (71.7% & 71.5%), Glaxo pharmaceutical plc
(98.1% & 98.1%), NCR plc (99.2% & 99.2%) Dangote cement plc (99.1% & 99.1%), Mobil oil plc (92.9%
&92.9%), NAHCO plc (78.8% & 78.7%). For most of the companies under study it was evident that there were
significant relationship between their liquidity measured by market capitalization ratio and their respective stock
market returns. Companys such as Okomu oil in the Agricultural sector had its R2 analyzed at 77.7% NAHCO plc of
the aviation industry grouped under the ‘services sector’ of the Nigerian stock market had the lowest R2 at 78.8%
which indicates that liquidity had a positive and significant impact on stock market returns for the company shares
but was much lower than the other quoted companies which could be attributed to lower stock trading in line with
the works of Raghbendra (2003) and Ekanem (2003). However, Zenith bank with an R2 of 71.5% cannot be said to
be because of low trading since the number of deals and the fact that the banking sector has the highest trading in the
exchange. It is believed that the level of competition in the banking sub-sector of the exchange for the year under
study may have reduced the returns average growth rate. The converse can also be said of the other companies such
as Julius Berger, Dangote cement and NCR with higher average returns being dominant in their various sectors.
Again theory supports that investor misspecification about future earnings or illiquidity of low volume stocks like
NCR may be responsible for the high variations seen in it’s analysis according to Khan S.U and Rizwan F (2008).
6.0 Policy Recommendations
1. Thus, this study recommends that the Nigerian Securities and Exchange Commission should create policies
that will encourage increases in firms profit after tax and their dividends as these variables have been
statistically proven to have strong significances on the changes in the company’s performance and the value
of stock returns.
2. Thus, this study recommends that investors should make trading volume based strategies to make profits.
Strategies need to be designed toward reaping abnormal returns by exploiting information and actions that
enhance inefficiency in stock markets thus, firms and individuals should be encouraged to buy or sell
securities outside their face values, as a means of encouraging business or economic activities in the
economy this is due to large volatilities in some markets.
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