Table of Content
Chapter 1:- Conceptual Overview
Chapter 2:- Research Methodology
Objective of Study
Scope and Rationale of Study Methodology Limitation of
StudyChapter 3:- Theoretical Background
Chapter 4:- Case Study
Introduction of Company profile and Product
About the work in company done by students
Chapter 5:- Data Analysis Chapter 6:- FindingsBibliography
Annexure CHAPTER - 1Chapter 1:- Conceptual Overview
Recent research has suggested that aggregate market liquidity
varies over time and that the covariance of returns with
innovations in market liquidity is priced. However, liquidity has
multiple dimensions which incorporate key elements of volume, time
and transaction costs. An ideal measure of market-wide liquidity
should therefore incorporate elements of depth, breadth and
resiliency. This paper estimates measures of market-wide liquidity
along each of these dimensions and finds that each measure's
innovations are correlated, that covariance of stock returns and
innovations in each measure is priced, and combining the
information in each measure improves the precision of estimates of
liquidity risk premia. I estimate the liquidity risk premiu to be
approximately 2-5% per year and show that this premium is distinct
from firm size, a securitys individual liquidity, and the
covariance between changes in a security's individual liquidity and
market-wide liquidity. As a byproduct, I also document that the
liquidity risk premium has a strong January seasonal, which is
unrelated to firm size.
Impact of liquidity on various aspects of economy
A very basic definition of liquidity is 'the cash or money in a
system'. Liquidity is measured in terms of the monetary base and
the Reserve Bank of India (RBI) is the sole supplier of liquidity
in the country.
In general, the supply of monetary base by the central bank
depends on the public's demand for currency and the banking
system's need for reserves to settle or discharge payment
obligations.
The RBI monitors the liquidity situation on a daily basis and
attempts to control and moderate liquidity conditions by varying
the supply of bank reserves to meet its macroeconomic objectives of
financial stability.
The periodic liquidity assessment is done by the RBI based on
the bank reserves position, and the expected inflows and outflows
from both domestic operations and foreign flows. Depending on the
liquidity forecast, the RBI decides on a course of action to be
taken to either supplement or withdraw liquidity.
These are some of the factors that influence liquidity
conditions in the economy: Domestic factors An increase in
liquidity is required to cover inflation and GDP growth. Several
instantaneous domestic factors also influence the liquidity in the
system.
Most commonly, quarterly or annual advance tax payments draw
liquidity out of the system as a lot of liquid money gets locked
with the government.
On the other hand, any large payouts by the government or higher
corporate sector spending can increase the liquidity in the
system.
Funds inflows
A strong economic performance and the relative under-performance
in the developed countries attracted the attentions of many large
global investors who were drawn towards investing here ( FDI as
well as portfolio investments).
This resulted in healthy capital inflows in the last few years.
These capital inflows put a lot of pressure on the liquidity
management here as uncontrolled capital flows can result in rising
inflation, currency appreciation, loss of competitiveness and
reduction in monetary control.
Tools to control liquidity
The RBI monitors the liquidity situation periodically and takes
necessary steps to control the situation from time to time. The RBI
uses various direct and indirect policies to control the shortterm
and long-term liquidity position.
These are various instruments used by the RBI to control
liquidity:
Cash reserve ratio: The RBI uses the cash reserve ratio (CRR) as
a tool to control the medium to long-term liquidity issues. An
increase in the CRR results in an increase in the amount of money
that banks have to maintain with the RBI as a percentage of their
deposits.
This reduces the overall liquid funds with the bank and hence
reduces the overall liquidity. Liquidity adjustment factor: The
liquidity adjustment factor (LAF) was introduced a decade ago as a
part of financial reforms.
LAF helps in managing a shortterm liquidity situation resulting
from the large and volatile capital flows (inflows as well as
outflows). Reverse repo rate: The RBI uses the reverse repo rate
for short-term liquidity management and to smoothen interest rates
in the call/money market.
The repos also help in keeping the interest rates in a
predictable range, as provided by the prevailing repo rate and
reverse repo rate.
In times of excess visible liquidity, the call rates hover
around the reverse repo rate, whereas in times of tight liquidity,
the call rate will hover around the repo rate.
Liquidity impacts inflation
An uncontrolled and unmanaged liquidity situation can have a
severe impact on inflation, rates of interest, STOCK MARKETS, and
foreign exchange rates.
Since the conditions in the global markets and foreign fund
flows are quite volatile, the job of the RBI in controlling the
liquidity condition has become more challenging.
The RBI has taken small steps in changing the monetary policy
since the beginning of this year. These steps have shown good
results in terms of maintaining interest rates, liquidity and GDP
growth.
The inflation rate is still ruling high due to various factors
and analysts believe that further monetary actions from the RBI
along with a good rainfall and base effect will moderate it in the
next couple of quarters.DEFINITION
Market CapitalizationThe total dollar market value of all of a
company's outstanding shares. Market capitalization is calculated
by multiplying a company's shares outstanding by the current market
price of one share. The investment community uses this figure to
determine a company's size, as opposed to sales or total asset
figures.EXPLAINS 'Market Capitalization'
If a company has 35 million shares outstanding, each with a
market value of $100, the company's market capitalization is $3.5
billion (35,000,000 x $100 per share).
Company size is a basic determinant of asset allocation and
risk-return parameters for stocks and stock mutual funds. The term
should not be confused with a company's "capitalization," which is
a financial statement term that refers to the sum of a company's
shareholders' equity plus long-term debt.
The stocks of large, medium and small companies are referred to
as large-cap, mid-cap, and small-cap, respectively. Investment
professionals differ on their exact definitions, but the current
approximate categories of market capitalization are:
Large Cap: $10 billion plus and include the companies with the
largest market capitalization.Mid Cap: $2 billion to $10
billion
Small Cap: Less than $2 billionMarket capitalizationTheNew York
Stock ExchangeonWall Street, the world's largeststock exchangeper
totalmarket capitalizationof its listed companies.[1]Market
capitalizationormarket capis the total dollar market value of the
shares outstanding of apublicly traded company; it is equal to
theshare pricetimes the number ofshares outstanding.[2]
HYPERLINK "https://en.wikipedia.org/wiki/Market_capitalization"
\l "cite_note-3" [3]As outstandingstockis bought and sold in public
markets, capitalization could be used as aproxyfor the public
opinion of a company'snet worthand is a determining factor in some
forms ofstock valuation. The investment community uses this figure
to determine a company's size, as opposed to sales or total asset
figures.
The total capitalization ofstock marketsoreconomic regionsmay be
compared to othereconomic indicators. The total market
capitalization of all publiclyTRADED COMPANIESin the world was
US$51.2 trillion in January 2007[4]and rose as high as US$57.5
trillion in May 2008[5]before dropping below US$50 trillion in
August 2008 and slightly above US$40 trillion in September
2008.[5]Since 2009, whenBitcoinbecame the first decentralized
cryptocurrency and numerous cryptocurrencies (altcoins) have been
created, the 'market cap' term has also come into common use to
describe the total dollar market value of the total amount
ofcryptocurrencyin circulation (available supply).[6]
HYPERLINK "https://en.wikipedia.org/wiki/Market_capitalization"
\l "cite_note-7" [7]The term sometimes can refer to the estimated
market value of the total amount of cryptocurrency that will ever
be in circulation (total supply).[8]Calculation Market cap is given
by the formula, where MC is the market capitalization, N is the
number of shares outstanding, and P is the price per share.
For example, if some company has 4 million shares outstanding
and the price per share is $20, its market cap is then $80 million.
If the price per share rises to $21, the market cap becomes $84
million. If it drops to $19 per share, the market cap falls to $76
million.
Market cap terms Traditionally, companies were divided
intolarge-cap,mid-cap, andsmall-cap.[2]The
termsmega-capandmicro-caphave also since come into common
use,[9]
HYPERLINK "https://en.wikipedia.org/wiki/Market_capitalization"
\l "cite_note-10" [10]andnano-capis sometimes heard. Different
numbers are used by different indexes;[11]there is no official
definition of, or full consensus agreement about, the exact cutoff
values. The cutoffs may be defined as percentiles rather than
innominal dollars. The definitions expressed in nominal dollars
need to be adjusted over the decades due to inflation, population
change, and overall market valuation (for example, $1 billion was a
large market cap in 1950, but it is not very large now), and they
may be different for different countries.
Related measures Market cap reflects only theequityvalue of
acompany. It is important to note that a firm's choice of capital
structure has a significant impact on how the total value of a
company is allocated between equity and debt. A more comprehensive
measure isenterprise value(EV), which gives effect to outstanding
debt, preferred stock, and other factors. For insurance firms, a
value called theembedded value(EV) has been used.
CHAPTER - 2
Chapter 2:- Research Methodology
Objective of Study
Scope and Rationale of Study
Methodology
Limitation of Study
CHAPTER - 3
Chapter 3:- Theoretical Background
Asset liquidity occupies an important, but elusive, position in
the study of asset pricing. Market microstructure research has made
it clear that liquidity providers offer a real service. Buyers and
sellers may not arrive in the market simultaneously, creating a
role for liquidity providers to transact and hold securities on a
temporary basis1 . Liquidity providers are compensated for their
expense and risk exposure via the bid/ask spread. This cost of
liquidity may be viewed as an added transaction cost and investors
might require a higher expected gross return to compensate for this
added cost.At the level of individual securities, Amihud and
Mendelson (1986), Brennan and Subrahmanyam (1996), Brennan,
Chordia, and Subrahmanyam (1998), and Datar, Nail, and Radcliffe
(1998) have all found a negative relationship between a security's
characteristic liquidity and its average gross return2 . Other
researchers have established that the characteristic liquidity of
individual stocks covary with one another (Chordia, Roll, and
Subrahmanyam (2000), Hasbrouck and Seppi (2001) and Huberman and
Halka (2001)). Commonality in characteristic liquidity raises the
question of whether shocks to aggregate or market-wide liquidity
comprise a source of nondiversifiable risk that is compensated with
expected return. When market-wide liquidity is low the probability
of a seller completing a large transaction in a timely manner
without making a significant price concession is low relative to
times of high market liquidity. However, the definition of terms
such as "large", "timely", and "significant" tend to be subjective.
Fernandez (1999) points out that "liquidity, as Keynes noted, is
not defined or measured as an absolute standard but on a scale,
which incorporates key elements of volume, time and transaction
costs. Liquidity then may be defined by three dimensions which
incorporate these elements: depth, breadth (or tightness) and
resiliency." Standard asset pricing theory says that covariance
between stock returns and any state variable that investors care
about in aggregate should be priced. If the market-wide liquidity
is 1 NYSE specialists and NASDAQ market makers perform this
function, however individual investors may also provide liquidity
via limit orders. 2 Amihud and Mendelson use the bid-ask spread as
a proxy for liquidity, Brennan and Subrahmanyman use fixed and
variable components of transactions costs estimated from
microstructure data, Brennan, Chordia and Subrahmanyam use trading
volume, and Datar, Naik, and Radcliffe use share turnover. such a
state variable and securities differ in their return covariances
with market liquidity, then liquidity betas should be priced. One
natural approach to investigating this question is to follow the
majority of the characteristic stock liquidity literature and
estimate measures of systemic liquidity by aggregating
microstructure data, but this approach suffers from at least two
practical problems. First, the large volume of data per unit of
time makes it difficult to compute even the most basic aggregate
liquidity measure. Second, even the longest time series of
transaction data is short compared to the availability of lower
frequency data. Pastor and Stambaugh (2002) devise a measure of the
price reversal (resiliency) dimension of market-wide liquidity
utilizing daily returns over a long time period (1962-1999).
Controlling for the usual risk factors, they find a positive
relationship between stock returns and the covariance of return
with their measure of market-wide liquidity. Using other dimensions
of liquidity such as depth and breadth to construct market-wide
liquidity measures appears to remain an unexplored area of
research. This study asks three questions. First, are measures of
aggregate liquidity using depth and breadth priced, as Pastor and
Stambaugh (2002) find for their resiliency measure? In addition, is
it possible to aggregate exposure to measures derived using the
three dimensions of liquidity to derive an estimate of the price of
liquidity risk? Second, is it possible for investors who do not
care about return sensitivity to liquidity shocks to invest in a
portfolio that is sensitive to liquidity shocks but hedged against
other common sources of systematic risk, using only prior
information, and earn a liquidity risk premium? Finally, does the
premium associated with high liquidity beta stocks survive after
controlling for market capitalization, the covariance of a stock's
characteristic liquidity with changes in aggregate liquidity, and
the level of the stock's characteristic liquidity? To preview, I
find that estimates of the liquidity risk premium of approximately
2-5% per year are not sensitive to the approach used for measuring
market-wide liquidity, that a feasible investment strategy earns
approximately this return before transaction costs, and that the
result survives after controlling for the three alternatives listed
above. I investigate the pricing of alternative liquidity measures
by first calculating two variations of each of three types of
aggregate liquidity measures based on market resiliency, depth, and
breadth. The resiliency measure relies on the principle that order
flow induces greater return 4 reversals when market-wide liquidity
is low, as in Pastor and Stambaugh (2002). The second type of
liquidity measure attempts to capture the depth of the market and
reflects the average price impact per unit of trading volume. This
measure is closely related to that used by Amihud (2002). The third
type reflects the breadth of the market and is derived from
microstructure data on individual stock bid/ask spreads. Although
this measure is available for only part of the sample period
(1983-2001) and is computationally intensive, it is important to
understand how breadth measures derived from transaction level data
compare to the two alternative approaches that are estimated using
daily frequency data. The innovations in each time series of
market-wide liquidity measures are highly correlated with each
other and reflect periods of especially low measured liquidity
corresponding to commonly accepted low liquidity periods in recent
U.S. history. I find that return covariance with shocks to
aggregate liquidity is priced for all three types of liquidity
measures. The estimated risk premium is positive, however there is
a significant negative January seasonal in the liquidity premium
that is not related to firm size. A feasible investment strategy
constructed to have positive exposure to systemic liquidity shocks
but hedged against other common risk factors earns positive returns
on average and negative returns when there is a shock to liquidity.
The relationship between liquidity beta and return remains after
controlling for market capitalization, the covariance between stock
liquidity and market-wide liquidity, and the liquidity level of the
individual stocks. In other words, the higher return earned by
stocks with large liquidity betas is not due to these stocks being
small, being themselves illiquid, or becoming particularly illiquid
when there is a market-wide liquidity shock. The rest of this paper
is organized as follows. Section II describes each of the measures
of aggregate liquidity examined in this paper. Section III tests
whether liquidity risk as measured by return covariance with shocks
to the aggregate liquidity measures is priced. Section IV
investigates the relationship between liquidity betas and the
covariance of individual stock liquidity with aggregate liquidity,
stock's characteristic liquidity, and firm size. Section V
concludes. II. Measures of Aggregate Liquidity This section defines
two versions for each of three types of market liquidity measure. I
show that each of the measures is correlated with the others, with
market returns, and with the size and book-to-market factor returns
of Fama and French.A. The Price Reversal Measure Pastor and
Stambaugh estimate a liquidity measure based on the idea that price
changes accompanying large volume tend to be reversed when
market-wide liquidity is low. This view of volume related return
reversals arising from liquidity effects is motivated by Campbell,
Grossman, and Wang (1993), where risk-averse market makers (in the
sense of Grossman and Miller (1988)) accommodate order flow from
liquidity motivated traders and are compensated with higher
expected return. For this type of measure, low market-wide
liquidity refers to those states where market makers require a
higher expected return to accommodate a given order flow. The
ordinary least squares estimate of , PRV i t is a proxy for stock
i's liquidity in month t. Superscripts on liquidity measures are
used to differentiate between the various measures used. An upper
case X denotes a generic liquidity measure. 6 Following Pastor and
Stambaugh (2002), a stock's liquidity is computed in a given month
only if there are more than 15 observations from which to estimate
the regression (2.1), it is not the first or last month that the
stock appears on CRSP, and the share price at the end of the
previous month is between $5 and $1000. The market-wide liquidity
measure is then constructed from the individual stock measures by
averaging all of the individual measures during the month and
inflating by the ratio of total market capitalization at the end of
month t-1 to total market capitalization at month 0. See Pastor and
Stambaugh (2002) for a detailed discussion of their measure. The
rational for inflating the average liquidity measure by the ratio
of market capitalizations may not be clear. Pastor and Stambaugh
(2002) argue that , PRV i t can be viewed as "the liquidity cost,
in terms of return reversal, of trading $1 million of stock i,
averaged across all stocks." Since $1 million was a relatively
larger trade in the 1960s than in the 1990s, the simple average
coefficient will fall through time. Inflating the coefficient
adjusts for this condition. One drawback of the PRV liquidity
measure is the use of dollar volume since equal size trades may
have different impact due to differences in, for example, the
number of shares outstanding, differences in float, and differences
in the number and types of shareholders. One possible alternative
is to substitute turnover (dollar volume divided by end of previous
month market capitalization) for dollar volume although, as Pastor
and Stambaugh point out, this is similar to simply value weighting
their measure. However even this measure would miss variation in
return impact of order flow due to, for example, differences in
float. A second alternative, unexplored in previous studies, is to
substitute turnover scaled by average daily turnover during the
previous month for dollar volume in equation (2.1).
This measure of order flow will capture any unusual volume at
the expense of ease of interpretation but without the need to
inflate the average coefficient by total market capitalization.
Figure 1a plots the time series of scaled , PRV i t and Figure 1b
plots , mPRV i t . The series are very similar with large negative
liquidity levels in months where liquidity is generally considered
to be low including October of 1987 (the crash, which is the
largest negative value in both series), November of 1973 (the Arab
oil embargo, 2nd and 12th largest negative levels respectively),
September of 1998 (the Russian debt and LTCM crisis, 4th and 2nd),
and October of 1997 (the height of the Asian financial crisis, 13th
and 9th). The overall correlation between the two series is 0.713 .
Table 1 reports that both series display significant
autocorrelation (0.21 and 0.16 for PRV and mPRV respectively). B.
The Price Impact Measure Amihud (2002) estimates a liquidity
measure based on price impact. Kyle (1985) argues that spreads are
an increasing function of the probability of facing an informed
trader, and since the market-maker cannot distinguish between order
flow from informed traders and order flow from noise traders, she
sets prices that are an increasing function of the order imbalance
that may indicate informed trading. This implies an inverse
relationship between price impact and liquidity. Alternatively,
price impact measures for a particular stock may be large for
reasons unrelated to asymmetric information issues or liquidity.
For example, when there is a news 3 Omitting October of 1987 from
both series reduces the estimated correlation to 0.67. Although
influential, omitting this observation does not have a large impact
on the reported correlations of the levels or innovations of the
liquidity measures. 8 release which impacts firm value but about
which there is little disagreement, price change can be large and
volume small resulting in a large estimated price impact. My use of
the price impact measure follows the spirit of Amihud but is
different from the individual stock or characteristic liquidity
approach. When market-wide liquidity is low, price concessions
required from Grossman-Miller market makers are larger per unit of
volume than when market-wide liquidity is high. By averaging price
impact measures across all stocks the idiosyncratic effects should
diversify leaving only systematic liquidity. Whether this is
measurable in practice is an empirical issue. The measure is
defined as the negative of the daily average so that large negative
values signify 'low liquidity' consistent with the interpretation
of the PRV and mPRV measures. The marketwide measure is the simple
average of the individual stock measures. The resulting time series
is then inflated by the ratio of total market capitalization at the
end of month t-1 to total market capitalization at the end of month
0. The same criticisms that apply to the use of dollar volume in
the PRV measure also apply here; therefore I also examine a
modified version of the price impact measure: ( ) , , , 1 , , 1 1
Dn mPI idt i t d n idt r D STO = = + (2.4) The aggregate measure is
the simple average of the individual stock measures and is not
rescaled by market capitalization. 9 Figure 1c plots the time
series of scaled , PI i t and Figure 1d plots , mPI i t . Scaled ,
PI i t is highly serially correlated (first order serial
correlation, 1=0.89) with periods of especially low liquidity in
the early 1970s and again in 1999-2000. , mPI i t also shows
similar periods of illiquidity although not as severe as , PI i t .
The correlation between the two measures is 0.54. The correlation
matrix for all of the aggregate liquidity measures is shown in
Table 1. All of the measures are positively correlated with each
other and we can reject the null that each correlation is zero
although the correlation between scaled , PRV i t and scaled , PI i
t is only 0.09. C. Measures Based on Bid/Ask Spread Amihud and
Mendelson (1986), Chordia, Roll, and Subrahmanyam (2000), Hasbrouck
and Seppi (2001), Huberman and Halka (2001), Jones (2001), Baker
and Stein (2002) and many others examine the bid-ask spread as a
measure of the characteristic liquidity of individual stocks. An
investor wishing to trade immediately may always sell (buy) at the
quoted bid (ask) price that includes a concession (premium) for
immediate execution. Therefore the spread between the bid and the
ask prices, which is the sum of the concession and premium, divided
by the midpoint of the spread, is a natural measure of liquidity.
Using ISSM data from 1983-1992 and TAC data from 1993-2001, I
calculate aggregate liquidity measures using all NYSE/AMEX stocks
as follows.4 First, define RQSi,d,t as the daily average relative
quoted spread for stock i on day d in month t. RQSi,d,t is the
average of every best bid and offer (BBO) eligible quote from the
open until just prior to the market close divided by the quote
midpoint. RESi,d,t is defined as the daily average relative
effective spread and is the average of the absolute value of the
difference between each transaction price and the midpoint of the
most recent quote, which is at least five seconds prior to the
trade, divided by the quote midpoint. The aggregate liquidity level
during month t is: Dt i,d,t 1 d=1 t 1 RQS D = = RQS Nt t i Nt (2.5)
4 I am grateful to M. Nimalendran for providing the quote and
effective spread data. 10 Dt i,d,t 1 d=1 t 1 RES D = = RES Nt t i
Nt (2.6) where Nt is the number of firms in month t and Dt is the
number of days in month t. Increasing spreads are associated with
decreasing liquidity, therefore the leading negative sign is added
so that smaller values of are associated with lower liquidity,
consistent with the other measures. Figure 1e plots the time series
of RQS t and Figure 1f plots RES t for the period 1983-2001. Both
plots show an upward trend reflecting the falling quoted and
effective spreads during the period. There are also large negative
changes in the liquidity measure in October of 1987 and September
of 1998. Consistent with the positive time trend, both series are
strongly positively serially correlated. D. Innovations in
Aggregate Liquidity For asset pricing purposes it is the covariance
of asset returns with innovations in the aggregate liquidity
measure that is important. This is in contrast to characteristic
liquidity where the difference in liquidity levels implies
differences in transaction costs that must be compensated with
expected return. To estimate innovations from levels, I calculate
the first difference of each liquidity measure as: ( ) , ,1 1 1 . =
= Nt X X XX t t it it i t M N (2.7) where X Mt = (mt-1 /m0), the
ratio of total market capitalization at time t-1 and time zero, for
X = PRV and X=PI and Mt X =1 for all others. I then regress t on
its lag as well as the lagged value of the scaled series: 1 1 ,1 .
X X XX X t t j it t a b cM u = + + + (2.8) Thus, the predicted
change depends on the lag level and the lag change. The innovation
in aggregate liquidity is X t u . To ease comparison of results
between liquidity measures in later sections, I rescale X t u so
that the standard deviation of the innovations is of the same order
of magnitude for each measure. 11 100 0.10 10 100 100 PRV PRV mPRV
mPRV PI PI tt t t t t mPI mPI RQS RQS RES RES t tt t t t Lu L u L u
L uL u L u = = = = = = (2.9) Table 2 shows that (2.8) yields
innovations that are serially uncorrelated for all measures in the
full sample and in both subperiods. If the three dimensions of
market-wide liquidity are related, then we might expect the
innovations to be correlated. Panel A of Table 2 shows the
correlation matrix of the innovations over the full sample period.
All of the innovations are significantly positively correlated,
both in the full sample and in each subperiod. The only exception
is the correlation between the PRV and PI measures in the second
subperiod, which is a statistically insignificant 0.06. The
significant correlations for the later subperiod in Panel B between
the breadth measures estimated from microstructure data and the
resiliency and depth measures estimated from daily data are
particularly encouraging. If market-wide liquidity measures can be
estimated using low frequency data then the cost of estimation is
greatly reduced and the measures can be estimated over much longer
time periods and for markets for which transaction level data is
not available. Figure 2 plots the time series of the innovations in
aggregate liquidity. All show large negative values on similar
dates, October of 1987 in particular, although the magnitude of
these shocks varies. Panel B of Table 2 shows us that the LmPI
measure is highly correlated with each of the microstructure based
measures with an estimated correlation of 0.74 with each. The LPRV,
LmPRV, and LPI measures are also significantly correlated with LRQS
and LRES. The correlation matrices in Table 2 suggest a similarity
among proxies but do not by themselves imply that market liquidity
is a priced state variable. E. Empirical Features of the Liquidity
Measures Pastor and Stambaugh (2002) describe a "flight to quality"
effect when their measure of market liquidity is low. Months in
which liquidity is exceptionally low tend to be months in which
stock returns and bond returns move in opposite directions. Table 3
reports the correlation between the value-weighted CRSP index of
NYSE-AMEX stocks and three fixed income variables: minus the change
in the rate on one-month Treasury bills, the return on the thirty
year 12 government bond, and the return on a portfolio of long term
corporate bonds5 . Over the full sample period 1962-2001, the
correlation between minus the change in the rate on one-month
Treasury bills and the market return is near zero and between the
market return and the bond returns is positive. In months of low
liquidity, defined as a liquidity shock more than two standard
deviations below the mean, the correlation between the market
return and both minus the treasury bill return and the government
bond return is negative, regardless of the liquidity measure used
to identify months of low liquidity. The correlation between the
corporate bond return and the market return is near zero when low
liquidity is defined using LPRV or LmPRV and negative when using
LPI or LmPI. Panel B reports similar figures for the 1983-2001
period and include the spread based (breadth) measures of
liquidity. The results are very similar to those in Panel A. Also
shown in Table 3 is the correlation between the market return and
the equally weighted average percentage change in monthly dollar
volume for NYSE-AMEX stocks. The unconditional correlation between
volume changes and market returns is positive; however, regardless
of the measure used to identify months of low liquidity, when
liquidity is low, market returns and changes in volume are
negatively correlated. Table 4 reports correlations between
innovations in each liquidity measure and the valueweighted CRSP
index, the equal-weighted CRSP index, and the Fama French factors
SMB and HML. Each measure is positively correlated with both CRSP
indices; however the correlation is driven by months in which the
market falls. For example, the LPRV measure has a correlation of
0.29 with the value-weighted index, but the correlation is 0.02 in
months in which the index return is positive and 0.44 when
negative. Each of the measures is positively correlated with SMB
and negatively correlated with HML. When liquidity is low, large
stocks outperform small stocks and value outperforms growth. The
correlations are larger in magnitude and significance for the price
impact and spread based measures than for the reversal-based
measures. It is remarkable is that the six liquidity measures that
address the three separate dimensions of liquidity appear so
similar. Months of low liquidity are months in which stock market
returns fall, large stocks outperform small stocks, and value
outperforms growth. The next step is to 5 The corporate bond data
is from Ibbotson Associates. 13 examine the pricing implications of
a stock's return covariance with each of these measures,
controlling for other commonly used sources of risk. III. The
Liquidity Risk Premium This section investigates whether a stock's
expected return is related to the covariance of its return with
innovations in each of the liquidity measures after controlling for
other variables that have been found to be important in asset
pricing. To accomplish this I use a portfolio-based approach where
the portfolios are formed on the basis of predicted sensitivity to
liquidity shocks. Each month, the universe of available stocks is
sorted into ten portfolios by predicted liquidity beta and held for
one month. The portfolio returns are linked through time to form a
single return series for each decile portfolio. These post
formation returns are then regressed on return based factors that
are commonly used in empirical asset pricing studies. To the extent
that the intercepts are different from zero, liquidity sensitivity
explains a component of returns not captured by exposure to other
factors. Specifically, for each month t, I regress the excess stock
return on the liquidity innovation, LX, in a regression that also
includes the Fama and French (1993) factors: 0 , M S H XX it i i t
i t i t i t t r RMRF SMB HML L =+ + + + + (3.1) where X Lt is the
innovation calculated using one of the six methods described above.
For every month t between December 1965 and December 2001, the
regression is run for every stock whose end of month price at month
t-1 is between $5 and $1000 and which has valid return data in at
least 36 months between t-1 and t-60. Although it seems natural to
use the estimated regression coefficient l X i to sort stocks into
portfolios, it is well known that sorting on regression
coefficients in this manner is problematic, especially when the
standard errors of the regression coefficients are large. This is
of particular concern for the regression (3.1) since the standard
errors of l X i for individual stocks are very large and therefore
sorting on l X i , in effect, leads to sorting on estimation
errors. 14 To mitigate this problem I use a Bayesian approach to
form the estimates of X i then sort into portfolios based on these
estimates. The Bayesian estimates of X i are only used to sort
stocks into portfolios, all point estimates reported in the tables
are the result of classical econometric techniques. Specifically, I
estimate (3.1) for every stock at month t, then treat each estimate
of the vector = [0 , M, S , H, X] as a draw from a multivariate
normal distribution with estimated covariance . The Bayesian
estimate of , lbi , is then estimated as: l ( ) ( ) ( ) l ( ) = + +
1 1 1 2 2 ' ' i i b XX XX i s s i (3.2) where ( ) 1 2 ' s i X X is
the estimated covariance matrix of l i . The Bayesian estimate of
is a weighted average of the OLS estimate of i and the average of
across all stocks at time t where the weight on i is the inverse of
the covariance matrix of i. This estimator "shrinks" the estimate
of the coefficient vector for each stock towards the population
average with the amount of shrinkage an inverse function of the
precision of the estimate for the individual stock. Pastor and
Stambaugh (PS) use a similar approach to infer that their liquidity
measure is priced, although they use a different method of sorting
stocks into portfolios. They model the time variation in X i
explicitly using the full sample up to time t to estimate the
parameters. I prefer my method for sorting into portfolios for
three reasons. First, although PS model time variation in the
liquidity beta, they assume the other factor loadings and the
parameters of the model for time variation in liquidity beta do not
change over a sample period of up to 35 years. Second, the model of
time variation proposed by PS captures very little of the variation
in liquidity betas as measured by R2 , and the coefficients are
unstable through time. Third, the insample loadings on innovations
in liquidity are not as the model predicts. Appendix A discusses
the PS methodology, elaborates on the above points, and compares it
to the method used in this paper. A. Asset Pricing Tests I test for
the existence of a liquidity risk premium in two ways. First I
estimate the abnormal return to each predicted liquidity beta
sorted decile portfolio using the three-factor model of Fama and
French and examine the intercepts. The difference in abnormal
return between the 15 extreme deciles provides information about a
component of expected returns not captured by the three-factor
model. The second test uses the information in all ten decile
return series to estimate the liquidity risk premium directly. 1.
Fama French Alphas The time series returns for each liquidity beta
decile portfolio are regressed on the three Fama-French factors
that are commonly used in empirical asset pricing studies6 . To the
extent that the regression intercepts, or alphas, differ from zero,
X explains a component of expected returns not captured by exposure
to the other factors. Table 5, panel A shows the alphas from
Fama-French regressions of the excess return on each equal-weighted
decile portfolio for each liquidity measure. The intercepts are
generally negative for the portfolio of those stocks with the least
sensitivity to liquidity shocks and increasing as we move to
portfolios with a greater sensitivity. The spread in intercepts
between the most and least sensitive portfolios is positive,
ranging from 0.32 to 3.11 percent per year. None of the spreads
differs significantly from zero. Panel B reports results from
value-weighting the decile portfolios. The pattern in intercepts in
Panel A repeats although the pattern is less apparent. Five of the
six spreads in intercept are positive and none of the spreads are
statistically significant. Since there is a size component to
liquidity, smaller firms are concentrated in the extreme deciles,
it seems appropriate to check for a January seasonal in order to
verify that the "liquidity premium" is not a rediscovery of the
size/January effect7 . To isolate the seasonal effect in the
intercepts I estimate (3.1) and (3.2) separately for Januaries and
for all other months. The portfolio returns are the same as those
above. Table 6 reports the results. When the portfolios are
equal-weighted, the spread in annualized intercepts for non-January
months ranges from 0.93 to 2.67 percent. Few of the individual
portfolio intercepts differ significantly from zero, but both price
reversal measures and one of the two price impact 6 For each
liquidity measure, the ten equations are stacked and estimated
using GMM. The point estimates will be identical to those from
equation by equation OLS but the standard errors are corrected for
autocorrelation and conditional heteroskedasticity. This method
makes tests of cross-equation restrictions simple. 7 Unreported
tests fail to identify a January seasonal in any of the six
market-wide liquidity measures. 16 measures' portfolio intercept
spreads are statistically significant. Although the spread in
intercepts for the microstructure based measures are of similar
magnitude (annualized spreads of 2.65 and 1.87), the shorter time
series results in an inability to reject that the spreads are zero.
Interestingly, the spreads in January are negative for five of the
six measures. Only the RQS measure, which is based on quoted
spreads and does not include transaction prices, has a positive
spread in January. Panel B of Table 6 reports value-weighted
results similar to the equalweighted results. Five of six measures
have positive intercept spreads in non-January months although none
are statistically significant. Only the RQS measure is associated
with a positive intercept spread in January. The difference in
intercept spreads in Januaries vs. Non-Januaries presents an
interesting puzzle. Even after including the SMB factor, the model
of Fama and French does not fully explain the January effect. Since
small firms are concentrated in the lowest and highest liquidity
beta sorted deciles, we might be tempted to argue that the
inability of the three factor model to explain the January effect
in small stock returns is confounding any liquidity effects.
However, as I will show later, the negative January seasonal in the
liquidity premium is not confined to small stocks but exists across
all size quintiles. 2. Direct Estimation of the Liquidity Risk
Premium The previous section infers the existence of a liquidity
risk premium from the spread in abnormal returns between the
highest and lowest decile of predicted liquidity sensitivity. It is
also possible to estimate the liquidity risk premium directly using
information from all ten portfolios. For each measure of aggregate
liquidity X, define the time series regression: 0 X X t t tt r BF L
e =+ + + (3.3) where rt is a 10x1 vector of excess returns on the
decile portfolios, Ft is a 3x1 vector containing the realizations
of the Fama-French factors RMRF, SMB, and HML, B is a 10x3 matrix
of factor loadings, X is a 10x1 vector of liquidity betas, and X Lt
is the innovation in aggregate liquidity measure X. Assume the
portfolios are priced by: ( ) , F XX Er B t = + (3.4) 17 where E (
)i denotes the unconditional expectation, and i is the risk premium
for factor i. Since F are returns on portfolios, let ( ) F = E F T
. Taking expectations of both sides of (3.3), substituting (3.4),
and solving for 0 gives: 0 ( ) ( ) XX X = E Lt (3.5) I estimate the
vector of parameters b = [0 B x X] using the General Method of
Moments of Hansen (1982). The GMM estimator of b minimizes g(b)'
W-1g(b) where g(b) is the sample average of ft(b), ( ) ( ) ( ) ' '
0 1 , t t t X X t t X t tt X X tt t t h e f b L EL h FL e r BF L =
= = (3.6) and W is a consistent estimator of the spectral density
of ft 8 . The estimates of the liquidity risk premium X for each of
the liquidity measures as well as the associated t-statistics for
both equal-weighted and value-weighted portfolios are reported in
Table 7. The magnitude of X depends on the arbitrary scaling of LX,
but the scaling does not affect the t-statistics or the product ,
therefore Table 7 also reports (10-1) for each of the liquidity
measures. The first column uses the full time series of predicted
liquidity beta portfolio returns and ignores the January seasonal,
and is comparable to Table 5. The second column uses the same time
series but drops all January observations from the sample and is
comparable to Table 6. When portfolios are equal-weighted and the
full sample is used, the estimated liquidity risk premium is
positive for all six measures and is statistically significant for
four of six. When Januaries are dropped from the sample, five of
six are significant, and the point estimates are generally larger.
(10-1) is always positive, ranging from 0.40 to 4.29 percent per
year using the full sample and 1.17 to 4.30 percent per year using
only non-January months. All of the 8 I use an iterated GMM
estimator where the moment conditions are equally weighted in the
first step and the value of b that minimizes the objective function
used with the QS kernel to estimate the spectral density of ft. 18
values of (10-1) are statistically significant with the exception
of the modified price impact measure, mPI. Splitting the sample
shows the price of liquidity to be approximately constant through
time. Panel B of Table 7 reports results using value-weighted
portfolios. The results are similar to the equal-weighted results.
Estimates of the return for bearing systematic liquidity risk as
measured by (10-1) in non-Januaries ranges from 1.72 to 5.02
percent per year. B. Hedged Portfolio Returns If a portfolio
constructed to have a positive sensitivity to liquidity risk earns
a risk premium then we would expect the portfolio to do well on
average and to do poorly when there is a market liquidity shock. To
test whether this is in fact the case, I form a feasible portfolio
for each liquidity measure that is long decile 10 (high predicted
liquidity beta) and short decile 1 (low liquidity beta). The
returns to this portfolio are then hedged for the usual Fama-French
risk factor exposure using factor loadings estimated using data
from months t-1 through t-60. Table 8 reports the results. When the
Fama-French factor-neutral portfolios are equalweighted, the
liquidity trading strategy earns from 14 to 42 basis points (1.68%
and 5.04% annualized) per month. The profits from portfolios formed
on the four non-microstructure data based measures that are
available for the full sample period are all statistically
significant. Five of the six portfolios have negative returns in
months when liquidity is low, and all six have smaller returns in
low liquidity months than in other months. The last three columns
drop Januaries from the sample with little effect. When the
feasible Fama-French factor-neutral portfolios are value weighted,
all six earn positive returns, four of six are negative in low
liquidity months and five of six earn lower returns on average when
liquidity is low than in other months. Statistical significance is
generally lower than when portfolios are equal-weighted. C.
Combining Liquidity Measures If the three dimensions of liquidity
are related, then it should be possible to combine the information
contained in each variable to improve our estimates of liquidity
risk factor exposures and liquidity premia. To this end I form a
new set of decile portfolios based on the sum of the 19 portfolio
assignments from each of the six individual liquidity measures. For
each stock that has a portfolio assignment for each of the six
measures (four prior to 1987), I sum the portfolio numbers to which
each is assigned then sort this summary statistic into deciles. I
then repeat the experiment outlined in Section A using the summary
deciles as test assets. Table 9 presents the results. The spread in
annualized intercepts is a statistically significant 2.64% when
portfolios are equal-weighted and 2.11% when portfolios are value
weighted. We are unable to reject that the spread in intercepts is
zero when portfolios are value-weighted. Both point estimates are
within the range of those estimated in Table 5 using the individual
liquidity measures. An inspection of the t-statistics associated
with the individual intercepts shows that the estimation error
associated with the intercepts is much smaller with the aggregate
measure than with individual measures. The annualized spread in
intercepts is a statistically significant 3.13% when portfolios are
equalweighted and Januaries are omitted and 2.65% when
value-weighted. Direct estimation of the liquidity risk premia
using the method of Table 8 is difficult since the portfolios have
been formed based on information contained in all six liquidity
measures. However, it is possible to estimate the returns to an
investment strategy long decile 10 and short decile 1 formed using
the aggregate measure and hedged against any exposure to the
FamaFrench risk factors. The results to such a strategy are
reported in Panel B of Table 9. The strategy using equal-weighted
portfolios earns a statistically significant return of 43 basis
points per month (5.16% annualized), larger than the return earned
by any of the six individual liquidity measure based strategies in
Table 8. When the portfolio is value-weighted, the investment
strategy earns a statistically significant 50 basis points per
month, again larger than that earned by the feasible investment
strategy based on any of the six individual liquidity measures. If
a "low liquidity" month is defined as a month in which all
available liquidity measures are greater than two standard
deviations below their mean, the equal weighted strategy earns an
average 242 basis points in low liquidity months and the value
weighted strategy an average of +33 basis points per month.
Although the average monthly return for the value weighted strategy
is positive, it is the average of only three observations. The
median return of these three observations is -324 basis points and
the average return is below that of the other months. If 20 "low
liquidity" is defined as any liquidity measure being more than two
standard deviations below is average, then both equal and
value-weighted strategies earn negative returns in low liquidity
months and significantly positive returns in other months. IV.
Individual Stock Liquidity The previous sections ask whether stocks
whose return covaries with each of several marketwide liquidity
measures earn higher returns. This section asks whether the
covariance between stock return and market-wide liquidity shocks
(liquidity return beta) is a proxy for the covariance between
changes in a stock's characteristic liquidity and market-wide
liquidity shocks (liquidity spread betas), or a proxy for the
stock's characteristic liquidity level, or simply a proxy for
market capitalization. A. Liquidity Spread Beta Amihud and
Mendelson (1986) develop a model in which expected returns are an
increasing function of the bid/ask spread. Because illiquid stocks
are more expensive to trade, investors must be compensated with
higher expected returns. The question examined here is similar to
that of Amihud and Mendelson, stocks that become relatively more
illiquid when aggregate liquidity falls are particularly
unattractive members of a portfolio. To see why this might be the
case recall that aggregate liquidity, regardless of which measure
is used, and market returns covary strongly when returns are
negative, therefore a mutual fund manager selling to meet
redemption requests or an investor selling to meet a margin call
would incur a particularly large transaction cost associated with
liquidity for holding stocks which become particularly illiquid
when market liquidity falls. This was of particular importance
during the Long Term Capital Management (LTCM) experience of 1998.
(See Lowenstein (2000) for a description of events surrounding the
takeover of LTCM by a consortium orchestrated by the New York
Federal Reserve.) The hedge fund was very highly levered in often
very illiquid securities. When the Russian debt crisis precipitated
a fall in market liquidity, the value of the fund's portfolio value
dropped triggering a need to liquidate positions to meet margin
calls. The anticipation of LTCM's need to liquidate further eroded
the value of the fund's positions. Prior to 1998, did LTCM earn a
liquidity premium for 21 holding illiquid securities9 , holding
securities whose returns were sensitive to liquidity shocks, or
both? To investigate whether the covariance of individual stock
liquidity with aggregate liquidity is priced, each month I regress
changes in individual stock liquidity measures on lag changes in
individual stock liquidity measures, the lag level of the
individual stock's liquidity, and shocks to aggregate liquidity: ,
,1 ,1 , . X X X XX it it it t it a b c dL u = + + + + (4.1) where ,
X i t : The change in characteristic liquidity of stock i from
month t-1 to t using liquidity measure X. , 1 X i t : The
characteristic liquidity of stock i using liquidity measure X. X Lt
: The shock to market-wide liquidity at time t using liquidity
measure X. and X corresponds to one of the six liquidity measures:
PRV, mPRV, PI, mPI, RQS, or RES. The coefficient vector =[a b c d]
is adjusted using the Bayesian technique described in section III.
I then sort the stocks into deciles by the Bayesian estimate of the
coefficient on aggregate liquidity shocks, LX. I refer to this
coefficient as a "liquidity spread beta" and refer to the liquidity
beta discussed in the first three sections as a "liquidity return
beta". The resulting decile portfolios are then regressed on the
Fama-French risk factors and the difference in annualized
intercepts between deciles 10 and 1 is examined for evidence of
variation in alpha across the decile portfolios in a manner similar
to Tables 5 and 6. Table 10 reports the results. For brevity the
individual decile intercepts have been omitted and only the
annualized difference in the extreme deciles is reported. The first
three columns represent the difference in alphas for equal-weighted
portfolios for the full sample and for the sample split by January
vs. Non-January. Examining the Non-January column there is some
evidence, particularly for the mPI (modified price impact) measure
and the RQS (relative quoted 9 This argument applies to long
positions. Many of LTCM's trading strategies involved the
simultaneous purchase of long and short positions in similar
securities whose prices were expected to converge. 22 spread)
measure that stocks which become relatively more illiquid when the
market becomes more illiquid, conditional on the previous months
change in liquidity and liquidity level, earn negative abnormal
returns, precisely the opposite of what we might expect. These
results must be interpreted with caution. Sorting on the
sensitivity of changes in individual stock liquidity to changes in
aggregate liquidity is also a sort on market capitalization. For
example, the ratio of the average market capitalization of decile 1
to decile 10 for the mPI measure reported in the first six columns
of Table 10 is 4.20 and market capitalization decreases nearly
monotonically between decile 1 and decile 10. The size relative for
the RQS measure is much larger (38.70) and market capitalization is
also monotonically decreasing across deciles10. B. Characteristic
Liquidity To investigate the role of the level of characteristic
liquidity, each month I sort all stocks with available data into
ten portfolios by the average of their characteristic liquidity
over months t-2 to t-4. I skip month t-1 to avoid issues associated
with bid/ask bounce. The deciles are then linked through time,
regressed on the Fama-French risk factors, and the difference in
intercepts between the extreme portfolios examined. The results are
reported in the right six columns of Table 10. There is some
evidence that the most liquid stocks in decile 10 earn higher risk
adjusted returns than the less liquid stocks in decile 1,
especially when the mPI (modified price impact ) or the RES
(relative effective spread) measures are used as a measure of
liquidity. Again, we must interpret the results with caution since
sorting on characteristic liquidity is similar to a sort on market
capitalization with the most illiquid stocks in decile 1 also being
the smallest stocks. Table 10 provides weak evidence that more
liquid stocks have higher risk adjusted returns than illiquid
stocks. Although this result contradicts Amihud and Mendelson
(1986), it is consistent with Eleswarapu and Reinganum (1993). In
particular, Eleswarapu and Reinganum find stocks that are
particularly illiquid as measured by relative quoted bid/ask spread
earn higher size-adjusted average returns in January and lower
size-adjusted returns in non-Januaries, consistent with Table 10.
10 This is in contrast to the liquidity return beta deciles from
Section III that have smaller firms concentrated in the lower and
higher deciles with larger firms in the middle deciles. 23 C.
Two-Way Sorts To disentangle liquidity effects from pure size
effects, I first sort all stocks into size quintiles using NYSE
derived breakpoints, then within each size quintile I sort into
quintiles by liquidity measure, either liquidity return beta,
liquidity spread beta, or characteristic liquidity, to form 25
portfolios. These portfolios are linked through time and regressed
on the Fama-French risk factors and, as before, the difference in
alphas is examined for evidence of abnormal return associated with
liquidity while controlling for market capitalization. I also
examine the relationship between liquidity return betas and both
liquidity spread betas and characteristic liquidity by first
sorting into quintiles by either spread beta or characteristic
liquidity and then sorting on liquidity return beta within each
quintile. In the interest of brevity, the results reported in Table
11 are only for equal-weighted portfolios and only report the
difference in alpha by control variable quintile. Examining the
spread in alphas from liquidity return betas while controlling for
market capitalization, there is no obvious relationship between
size quintile and spread in abnormal return. The quintile with the
largest spread in intercepts varies by measure with the quintile of
the largest stocks having the biggest spread in intercepts (in
non-Januaries) for three of six measures. The most surprising
result comes from the January months. The negative spread in
abnormal returns is not confined to the smallest stocks, indeed the
biggest negative spread in intercepts is always in one of the
biggest three of the five quintiles. While the classic January
effect is closely related to market capitalization, the relative
underperformance of high liquidity return beta stocks in January is
not limited to smaller firms. Consistent with Table 10, when using
the reversal-based liquidity measures PRV and mPRV, there is no
evidence that liquidity spread betas or characteristic liquidity is
priced after controlling for market capitalization. The price
impact measure mPI's significant negative spread in alphas when
sorted by liquidity spread beta continues when controlling for size
although the effect is larger for the smaller quintiles. The
similar results using the spread based measure RQS also persists
across size deciles. The significant positive spread in alphas
between a portfolio of stocks with low characteristic liquidity as
measured by mPI and high characteristic liquidity is largest among
the smallest stocks and virtually disappears by the largest
quintile 24 because there is little variability in the measure for
larger stocks. The significant positive spread using the
spread-based RQS as a measure of characteristic liquidity almost
disappears after controlling for size. To verify that liquidity
return betas are not proxies for characteristic liquidity or
liquidity spread betas, I use the latter variables as control
variables and sort stocks into quintiles by the control variable
before sorting by liquidity return beta. For each liquidity
measure, sorting first by liquidity spread beta or characteristic
liquidity then by liquidity return beta has little effect. The
point estimates by quintile are similar to those of the univariate
sort in Table 5 and Table 6. In summary, there is weak evidence
that liquidity spread beta and characteristic liquidity are priced,
but the risk premia do not have the expected sign. Stocks with a
high covariance between changes in individual liquidity and shocks
to market-wide liquidity (after controlling for the lagged level
and lagged change in characteristic liquidity) earn lower risk
adjusted returns than those with a low covariance. There is also
weak evidence that stocks which are relatively liquid earn higher
average risk adjusted returns than stocks which are relatively
illiquid in non-January months. There is strong evidence that
illiquid stocks (as measured by characteristic liquidity) do earn
larger abnormal returns in January, but the effect is concentrated
in the smallest two size quintiles. Most important, there does not
appear to be any relationship between the higher abnormal returns
earned by high liquidity return beta stocks and either liquidity
spread betas or the stock's characteristic liquidity. V. Conclusion
Numerous authors have found that illiquid stocks earn higher
average returns, presumably to compensate for the higher costs of
transacting. This paper addresses the related but separate issue of
market-wide liquidity. If the ability to transact a given volume
with minimal price concession varies through time and there exist
cross sectional differences in a stocks return covariance with
measures of market-wide liquidity, then this covariance should
carry with it a higher expected return. Measures of market-wide
liquidity designed to capture three related, but separate
dimensions of liquidity yield similar results, namely that
covariance with market-wide measures 25 of liquidity carries a risk
premium. This risk premium varies from approximately 2 to 5% per
year depending on the measure. This estimate of the liquidity risk
premium associated with covariance with market-wide liquidity
shocks is much lower than that estimated by Pastor and Stambaugh
(2002) but is still statistically significant. Four of the six
measures used do not require transaction level data and thus can be
constructed over much long time spans and in markets for which
transaction level data is unavailable. Covariance of return with
market-wide liquidity does not appear related to the covariance
between changes in a stocks characteristic liquidity and
market-wide liquidity. In other words, stocks whose price is
sensitive to market-wide liquidity shocks do not necessarily become
themselves more illiquid when market liquidity is low. This is
consistent with fund managers selling more liquid stocks to meet
margin calls or redemption requests when market-wide liquidity is
low. Several surprising results provide avenues for future
research. First, there is a strong January seasonal in the
liquidity risk premia but not in the liquidity measures themselves.
Although high liquidity beta stocks earn higher risk-adjusted
returns on average, they earn lower returns in January. This
January effect in liquidity is not related to firm size, rather it
exists across all size quintiles. Second, liquidity spread betas,
or the covariance between changes in a stock's own characteristic
liquidity and shocks to market-wide liquidity, is associated with
lower average returns. In other words, stocks that become
particularly illiquid when markets become illiquid earn below
average returns, a counterintuitive result. The negative average
return associated with liquidity spread betas is particularly
surprising because one might have expected that an individual
stock's liquidity is particularly important when the market is less
liquid overall. If aggregate liquidity falls when market returns
are large and negative, then investors who must sell will sell
those investments that have the best individual characteristic
liquidity so as to minimize the transaction costs associated with
liquidity. This reasoning is consistent with the financing of
margin investors by uninformed outside lenders who react to losses
by cutting lending (see Shleifer and Vishny (1997) and Xiong
(1999)). This would result in a high covariance between the return
of stocks whose individual liquidity is high and the aggregate
liquidity state variable. Why then should investors demand a 26
premium for holding these stocks? Why do investors not require a
premium for holding stocks whose characteristic liquidity worsens
when aggregate liquidity falls? These questions provide an
interesting avenue for further research.CHAPTER - 4
Chapter 4:- Case Study
Introduction of Company profile and Product
About the work in company done by students
CHAPTER - 5
Chapter 5:- Data Analysis
CHAPTER - 6
Chapter 6:- Findings
Bibliography
Annexure
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