WPS5318
Policy Research Working Paper 5318
Liquidity Clienteles
Transaction Costs and Investment Decisions
of Individual Investors
Deniz Anginer
The World Bank
Development Research Group
Finance and Private Sector Development Team
May 2010
Policy Research Working Paper 5318
Abstract
Theoretical papers link the liquidity premium to the among more sophisticated investors. Households with
optimal trading decisions of investors facing transaction longer holding periods earn significantly higher returns
costs. In particular, investors' holding periods determine after amortized transaction costs, and households that
how transaction costs are amortized and priced in asset have holding periods that are positively related to
returns. Using a unique data set containing two million transaction costs earn both higher gross and net returns.
trades, this paper investigates the relationship between The author shows that there is correlation in the demand
holding periods and transaction costs for 66,000 for liquid assets across households and, consistent with
households from a large discount brokerage. The author the notion of flight to liquidity, this demand increases
finds that transaction costs are an important determinant during times of low market liquidity. Households with
of investors' holding periods, after controlling for higher incomes and with higher wealth invested in the
household and stock characteristics. The relationship stock market supply liquidity when market liquidity is
between holding periods and transaction costs is stronger low.
This paper--a product of the Finance and Private Sector Development Team, Development Research Group--is part of
a larger effort in the department to understand liquidity risk in equity markets. Policy Research Working Papers are also
posted on the Web at http://econ.worldbank.org. The author may be contacted at danginer@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Liquidity Clienteles:
Transaction Costs and Investment Decisions
of Individual Investors*
Deniz Anginer
May, 2010
ABSTRACT
Theoretical papers link the liquidity premium to the optimal trading decisions of
investors facing transaction costs. In particular, investors holding periods
determine how transaction costs are amortized and priced in asset returns. Using
a unique dataset containing two million trades, this paper investigates the
relationship between holding periods and transaction costs for 66,000 households
from a large discount brokerage. I find that transaction costs are an important
determinant of investors holding periods, after controlling for household and
stock characteristics. The relationship between holding periods and transaction
costs is stronger among more sophisticated investors. Households with longer
holding periods earn significantly higher returns after amortized transaction
costs, and households that have holding periods that are positively related to
transaction costs earn both higher gross and net returns. I show that there is
correlation in the demand for liquid assets across households and, consistent with
the notion of flight to liquidity, this demand increases during times of low market
liquidity. Households with higher incomes and with higher wealth invested in
the stock market supply liquidity when market liquidity is low.
Keywords: Transaction costs; Liquidity; Individual investor
JEL Classification Codes: G10, G11, G12
*
I thank Yakov Amihud, Mario Macis, Paolo Pasquariello, Uday Rajan, Nejat Seyhun, Tyler Shumway,
Jeffrey Smith, Noah Stoffman, Joe Warburton, Celim Yildizhan, and seminar participants at the University
of Michigan and the World Bank Research Group for helpful comments. I thank Terrance Odean for
providing the data used in this study. All errors are mine.
Economist, World Bank Research Group. Please send correspondence to danginer@worldbank.org.
1. Introduction
Theoretical papers link the liquidity premium to the optimal trading decisions of investors
facing transaction costs. An investors required return on a stock subject to transaction
costs will equal her required return in the absence of transaction costs plus these costs
amortized over the investors expected holding period. In a seminal paper, Amihud and
Mendelson (1986) show that transaction costs cause a clientele effect, whereby investors
with longer holding periods select to hold stocks with higher transaction costs in
equilibrium. These liquidity clienteles drive how transaction costs are amortized and
priced in asset returns. In theoretical models where the holding period is determined
endogenously, the frequency with which investors trade illiquid securities subject to high
transaction costs determine the holding period over which these transaction costs are
amortized. If investors significantly reduce their trading of illiquid securities (Vayanos
1998, Constantinides 1988, Heaton and Lucas 1996) then amortized transaction costs will
be low and investors will demand only a small liquidity premium to hold illiquid assets.
If, on the other hand, investors have frequent trading needs because of income shocks
(Lynch and Tan 2007), exogenous liquidity shocks (Huang 2003), or because they need
to hedge non-traded risk exposure (Lo, Mamaysky and Wang 2004), then the resulting
liquidity premium can be quite large.
Even though it is investors trading decisions that provide the link between
transaction costs and the liquidity premium on securities, lack of data on actual trades has
made it difficult to empirically examine how investors behave in the presence of
transaction costs. Using a unique dataset, this paper investigates the liquidity decisions
of 66,000 households that made over two million trades using a large discount brokerage
over a six-year time period. The focus of this paper is threefold. First, I examine
empirically the relationship between investors holding periods and the transaction costs
of securities they trade and hold in their portfolios. Second, I investigate the impact of
these liquidity decisions on investment performance. Finally, I examine the systematic
decisions of households as a group over time. This paper differs from other empirical
papers in this literature in that the focus is on investor (as opposed to stock) behavior.
I find that transaction costs play an important role in households trading and
investment decisions. Transaction costs are an important determinant of holding periods
1
of investors after controlling for various household and stock characteristics. However,
the effect of transaction costs on holding periods is much less than the effect predicted by
the models of Vayanos (1998) and Constantinides (1988). The results in this paper offer
an explanation for the discrepancy between the empirically-observed liquidity premium
and the one predicted by these models in which the holding period is endogenously
determined.1 I find that households differ in how much attention they pay to the liquidity
of the securities they trade and hold. More sophisticated investors tend to pay more
attention to liquidity than less sophisticated investors. In addition, more sophisticated
investors have holding periods that are strongly correlated with measures of transaction
costs, while less sophisticated investors have negative correlations.
Household liquidity decisions have important implications for investment
performance. I find that households with longer holding periods earn returns net of
amortized transaction costs that are greater than the net returns of households with shorter
holding periods. These results are consistent with Amihud and Mendelson (1986), who
postulate that investors with longer holding periods earn rents that exceed amortized
transaction costs for holding illiquid securities. This result drives the liquidity premium in
their model. Consistent with the notion that sophisticated investors pay closer attention
to liquidity, I find that households whose holding periods are negatively correlated with
transaction costs earn lower gross and net returns. That is, households that do not pay
attention to liquidity earn lower returns on both a gross and net basis.
I also find that there is systematic variation in the demand for liquid assets across
households. Consistent with the notion of flight to liquidity, the demand for liquid assets
goes up during times of low aggregate market liquidity, with households tending to buy
liquid securities and sell illiquid securities. However, a subset of investors with deep
pockets, i.e., those with higher incomes and higher levels of wealth, buys illiquid
securities when there is a negative liquidity shock and, consequently, earns a premium in
the process.
While investor decision making in the presence of transaction costs is important to
better understand how liquidity is priced in the financial markets, it also has implications
1
For empirical studies, see, for instance, Pastor and Stambaugh (2003), Acharya and Pedersen (2005),
Amihud (2002), and Amihud and Mendelson (1986).
2
for investor welfare and public policy. This paper shows that expected holding periods
and amortized transaction costs strongly impact the performance of household portfolios.
One implication is that investment advisors should consider the expected holding period
of investors when recommending illiquid stocks to their clients. The results in this paper
also have implications for the efficacy of a securities transaction tax. Such a tax has been
proposed to reduce excess speculation in order to reduce volatility and the influence of
short-term investors on management (Stiglitz 1989, Tobin 1984, Summers and Summers
1990). This paper provides an empirical link between the magnitude of such a tax and its
impact on trading frequency of retail traders.
This paper is also related to investor rationality and, in particular, to the increasingly
popular notion that individual investors overtrade, losing substantial amounts to trading
costs without any gain in performance.2 Usually a behavioral bias, such as
overconfidence, is proposed as an explanation for excessive trading by individual
investors who tend to ignore transaction costs. Barber, Odean and Zheng (2005), for
instance, show that investors pay attention only to the salient costs of mutual funds, but
ignore hidden operating costs. The findings in this paper suggest that most investors are,
to a large extent, cognizant of transaction costs when making trading decisions. The
findings suggest that, as investors trade more frequently, they pay greater attention to the
liquidity of the underlying stocks traded. A number of papers also document that a subset
of retail investors displays greater financial sophistication and market understanding than
the average retain investor, enabling them to earn positive abnormal returns.3 In this
paper, I show that sophisticated households are more likely to hold illiquid stocks over a
longer time period and earn greater net returns as a result.
In a related paper, Atkins and Dyl (1997) study the relationship between turnover and
bid-ask spreads for Nasdaq and NYSE stocks. They find a positive relationship between
bid-ask spreads and holding periods, which they proxy with turnover. There are,
however, two problems with using aggregate turnover to proxy for holding periods. First,
aggregate turnover is an average across many investors and can be highly skewed in a
2
Barber and Odean (2000) show that investors similarly ranked in terms of portfolio turnover have similar
gross returns, but substantially different net returns after accounting for transaction costs. Barber et al.
(2008), using a complete transaction history of all investors in Taiwan, find that individual investor losses
equal 2.2 % of GDP, and that such loses are mainly due to transaction costs.
3
See the discussion in Section 2.
3
market where a handful of investors trade to provide liquidity. Second, and more
importantly, holding periods are based on trading decisions of investors who, ex-ante,
consider the transaction costs of the underlying securities they trade. In a concurrent
paper, Naes and Odegaard (2008) use transaction-level Norwegian data to show that
turnover is indeed a poor proxy for actual holding periods of investors. Their focus is on
asset pricing, and they show that turnover is priced in size-sorted portfolios while average
holding period is not.
The remainder of the paper is organized as follows. The next section describes the
empirical questions pursued in this paper. Section 3 describes the liquidity measures and
the individual trade data used herein. Sections 4 to 6 present and discuss the main
findings, and Section 7 concludes.
2. Hypotheses and Related Literature
Although empirical studies document that the effects of transaction costs on asset prices
are both statistically and economically significant, there is a debate in the theoretical
literature as to the direction and the magnitude of this relationship.4 The debate centers
on how investors make optimal trading decisions in the presence of transaction costs.
The basic premise that the rate of return on a security should incorporate transaction costs
is straightforward and uncontroversial. An investor who buys a security and expects to
pay transaction costs when selling it will take this into account in valuing that security.
An investors required return on a stock will equal her required return in the absence of
transaction costs plus these costs amortized over the investors expected holding period.
The liquidity premium required by investors to hold illiquid securities thus depends
strongly on investors holding periods. The theoretical debate over the effect of
transaction costs on asset prices arises primarily from differences in how investors
holding periods are modeled.
One of the earlier papers to incorporate investors holding periods into asset pricing
with market frictions is Amihud and Mendelson (1986). They develop a model where
4
For empirical studies, see, for instance, Pastor and Stambaugh (2003), Acharya and Pedersen (2005),
Amihud (2002), Chordia et al. (2000, 2001), Hasbrouck and Seppi (2001), and Huberman and Halka
(1999).
4
risk neutral investors with different exogenous holding periods and limited capital trade
securities subject to fixed transaction costs. Amihud and Mendelson show that
transaction costs result in a clientele effect, with investors who have longer holding
periods selecting to hold illiquid stocks in equilibrium. Amortized transaction costs of
investors in each liquidity clientele group determine the liquidity premia for illiquid
securities.
The static model with exogenous holding periods has been extended to incorporate
dynamic decisions of investors. In models where the holding period decision is
determined endogenously (Constantinides 1986, Vayanos 1998, Vayanos and Vila 1999,
Heaton and Lucas 1996), the resulting liquidity premium is much lower. In these models,
the marginal utility from trading is low and investors respond to transaction costs by
turning over their portfolio less frequently. These models predict a liquidity premium on
asset prices that is a magnitude smaller than transaction costs, but they also predict
unrealistically low levels of trading activity and volume. In models where investors are
forced to trade frequently (Huang 2003, Lynch and Tan 2007, Lo, Mamaysky and Wang
2006) the resulting liquidity premium can be large.
In all these models, the magnitude of the relationship between holding periods and
transaction costs determines the liquidity premium in the market.5 Using individual trade
data, I test for the relationship between holding periods and transaction costs after
controlling for a number of investor and stock characteristics. I also analyze the
magnitude of the impact of transaction costs on holding periods, and compare the results
to calibrated values in the models of Vayanos (1998), Constantinides (1986) and Lo,
Mamaysky and Wang (2005). The first hypothesis is thus:
H1a: Holding periods are positively related to measures of fixed transaction costs after
controlling for investor and stock characteristics.
Previous studies have shown that, on average, households stock investments perform
poorly. Odean (1999), for instance, reports that individual investors purchases under-
5
Although in this study I only focus on a subset of investors in the market, namely retail investors, a
number of papers have shown that correlated trading by retail investors impact returns (Kumar and Lee
2006, Barber, Odean and Zhu 2006, and Hvidkjaer 2008).
5
perform their sales by a significant margin.6 However, other studies have concluded that
there exists a subset of retail investors who display greater financial sophistication and
market understanding than the average retail investor. For instance, Coval, Hirshleifer,
and Shumway (2005) document strong persistence in the performance of individual
investors trades, suggesting that some skillful individual investors might be able to earn
positive abnormal profits. Using the same dataset as this paper, Goetzmann and Kumar
(2008) find that the level of portfolio diversification is related to investor sophistication.
Feng and Seasholes (2005) find that investor sophistication reduces a well known
behavioral bias, the disposition effect. Given that previous studies have documented
heterogeneity in the performance and investment decisions of individual investors, we
should expect similar cross-sectional differences in the correlation between holding
periods and transaction costs across investors in the dataset. Furthermore, we should
expect this correlation to increase with investor sophistication and experience:
H1b: The correlation between holding periods and transactions costs is higher for
sophisticated investors.
The second empirical question I address in this paper is how holding periods and
transaction costs impact investment performance. In the Amihud and Mendelson (1986)
model, it is the rents earned by investors with longer holding periods that drive the
liquidity premium. Security prices reflect the marginal investors holding period, and
have to fall by the present value of transaction costs to induce the marginal investor to
buy the security.7 The price for the security with the lowest transaction cost, for instance,
is set such that the investor with the shortest holding period is indifferent between
investing in that security and the one with no transaction costs. Investors with longer
holding periods earn a premium (rent) when investing in that security because their
amortized transaction costs are lower, which implies:
6
Barber and Odean (2000, 2001), using the same dataset as this paper, further show that investors lose
substantial amounts to trading costs without any additional gain in performance, consistent with the
hypothesis that individual investors are overconfident and tend to trade excessively.
7
Vayanos and Vila (1997) show a similar result when securities are identical except for transaction costs.
6
H2a: Investors with longer holding periods earn returns net of amortized transaction
costs that exceed net returns of investors with shorter holding periods.
The correlation between holding periods and transaction costs is likely to impact
portfolio performance on both a gross and a net basis. Households that do not pay
attention to transaction costs when they trade are likely to have lower net returns due to
transaction costs. As mentioned earlier, previous studies have shown investor
sophistication to be correlated with higher portfolio performance and lower levels of
behavioral biases. A negative correlation between holding periods and transaction costs
could, therefore, also indicate lack of financial sophistication and market knowledge,
which is associated with lower gross returns. Consequently:
H2b: Investors whose holding periods are negatively related to transaction costs earn
lower gross and net returns.
In other words, we would expect investors who do not pay attention to liquidity to make
other trading mistakes, which result in lower gross returns.
Previous studies have shown that there is a common time varying component to
liquidity across stocks (Chordia et al 2000, Hasbrouck and Seppi 2001, and Huberman
and Halka 2001). Other studies have shown that this common component is priced in
stock returns (Pastor and Stambaugh 2003, Acharya and Pedersen 2005, Korajczyk and
Sadka 2008). It is not clear, however, what causes this common variation. Commonality
in liquidity can arise from the supply side, if there is systematic variation in the costs of
providing liquidity.8 Commonality can also arise from the demand side, if a common
factor such as volatility or uncertainty causes a systematic variation in the demand for
liquidity.9 Even with constant exogenous transaction costs, a time-varying liquidity
premia can arise as investors willingness to bear these costs changes over time. Vayanos
(2004), for instance, develops a model with fixed transaction costs in which changes in
8
Chordia, Roll and Subrahmanyam (2000) find some evidence of asymmetric information and inventory
risk affecting the common component of liquidity. Comerton-Forde et al (2008) and Coughenour and Saad
(2004), examining liquidity of stocks at NYSE overseen by the same specialist, provide some support for
the supply side view. Huberman and Halka (2001), on the other hand, after failing to find inventory cost or
asymmetric information based explanations for the systemic component of liquidity, conjecture that
commonality emerges due to noise traders.
9
Chordia et al. 2001 shows that trading activity covaries with liquidity.
7
market volatility affect systematic liquidity by creating correlated trading patterns among
investors. By examining the actual trades of investors, I can test whether there is
systematic variation in the demand for liquid assets and whether liquidity shocks apply
(or transmitted) systematically across investors that can potentially cause market-wide
effects:
H3a: There is systematic variation in households' trades of illiquid stocks.
If there is systematic variation in demand for liquid assets across investors, it is
important to examine how this systematic demand varies over time with changes in
aggregate level of market liquidity. If investors demand liquid securities at the same time
when aggregate liquidity is low, the liquidity premium required to hold illiquid securities
would be high. The literature, to a large extent, treats individual investors as noise traders
who provide constant liquidity to the market. Kaniel, Saar, and Titman (2006),
Campbell, Ramadorai, and Schwartz (2007), Stoffman (2008), and Griffin et al. (2003),
investigating institutional and retail trades, provide evidence consistent with the notion
that retail traders provide liquidity to meet institutional demand for immediacy. These
studies, however, investigate short-term returns to institutional and individual buy/sell
imbalances, and do not consider the liquidity level of the market or the liquidity level of
the individual securities that are traded.10 With individual trade data, I can examine the
liquidity level of the securities bought and sold by individual investors, and examine
whether there is a flight to liquidity among households. With individual trade data, I can
also test if households are net demanders or suppliers of liquid securities when aggregate
market liquidity is low:
H3b: Households are net buyers of illiquid stocks when the market level of liquidity is
low.
There are likely to be cross-sectional differences in trading patterns in response to
aggregate liquidity shocks. Investors with deep pockets can take advantage of investment
opportunities during turbulent markets. The recent Goldman Sachs agreement to sell $5
10
In most of these studies, investors cannot be identified and their transactions cannot be tracked over time.
8
billion of perpetual preferred stock to Berkshire Hathaway illustrates both the adverse
effects that market participants can create when seeking liquidity at the same time and
the important role that external investors with deep pockets can play in providing
liquidity. We can expect households with higher wealth/income levels to buy illiquid
assets that have dropped in price:
H3c: Households with higher income and wealth levels are net buyers of illiquid stocks
when aggregate market liquidity is low.
3. Individual Trade Data and Liquidity Measures
The main dataset for this paper comes from a major U.S. discount brokerage house and
includes the daily trading records of 78,000 households from January 1991 to December
1996. These households hold a total of 158,034 accounts of various types including cash,
margin, IRA and Keogh. In this study, I focus on the common stock investments of the
households, which constitute nearly two-thirds of the total value of their investments in
the dataset. About 66,000 of the 78,000 households trade common stock, making close to
two million trades over the sample period. The transaction record includes number of
shares traded, price and any commissions paid. The dataset also includes each
households month-end positions including the value of security holdings at market close
on the statement date. For a sub-sample of households, the dataset includes demographic
information, such as income, age, gender, occupation and marital status. A more detailed
explanation of the dataset can be found in Barber and Odean (2000, 2001). A
comparison of this dataset with Survey of Consumer Finances, IRS and TAQ data has
shown it to be representative of U.S. individual investors (Ivkovic, Sialm, and
Weisbenner 2006, Ivkovic, Poterba, and Weisbenner 2005, and Barber, Odean, and Zhu
2006).
Liquidity is a multi-faceted concept, and is usually defined in terms of the costs and
risks associated with transacting financial securities. These costs relate to exogenous
costs of transacting including price impact, asymmetric information and inventory risk.
Given the multi- faceted and unobservable nature of liquidity, I use a number of different
9
measures that have been previously utilized in the literature. The first is a Bayesian
version of the Roll (1984) transaction cost measure:
cov(ri,t , ri,t 1 ) if cov(ri,t , ri,t 1 ) 0;
ci,t (1)
0 otherwise.
It is based on the model ri,t ci,t qi,t i ,t
where qi,t is a trade direction indicator, ci,t is
the transaction cost measure and i ,t
is an error term for stock i at time t. Equation (1)
can be derived under the assumption that buyer- and seller-initiated trades are equally
likely. The Bayesian estimation of this cost measure using the Gibbs sampler is
described in detail in Hasbrouck (2006).11
The second measure is the Amihud illiquidity ratio, calculated as:
1
Di ,t
ri,d
Illiqi,t (2)
Di,t d 1 dvoli,d
where Di,t is the number of days in month t for stock i, dvoli,t is the dollar volume in day
d, and ri,d is the daily return. While the bid-ask spread captures the cost of executing a
small trade, the Illiq variable is akin to Kyles lambda and is meant to capture the price
impact of a trade. I adjust this measure as in Acharya and Pedersen (2005) to make it
stationary and to remove outliers:
AdjIlliqi,t min 0.25 0.30 Illiqi,t Mt 1, 30 (3)
where M t 1
is the ratio of the value-weighted market portfolio at the end of the month t-1
to that of the market portfolio in July of 1962.
The third measure used in this paper is the Pastor and Stambaugh (2003) reversal
gamma:
11
The Gibbs estimate is obtained from Joel Hasbroucks website:
http://pages.stern.nyu.edu/~jhasbrou/Research/GibbsEstimates2006/Liquidityestimates2006.htm.
10
ried
, 1,t i ,t
r
i ,t i ,d 1,t i ,t
sign(ried ,t )vi,d ,t
, i ,d ,t
(4)
Above, ried
, 1,t
is the return in excess of the market return and vi,d ,t is the volume on day d
in month t for stock i. This measure is motivated by the Campbell, Grossman, and Wang
(1993) model and is meant to capture temporary price fluctuations arising from order
flow.
I also include in the analyses quoted and effective spread and quoted depth calculated
from intra-day data. I use a 5-second delay to match trades with quotes and apply the
same filters discussed in Hvidkjaer (2006). The quoted percentage spread is calculated
for each trade as the ratio of the quoted bid-ask spread to the prevailing transaction price.
The effective percentage half-spread is calculated for each transaction as the absolute
value of the difference between the transaction price and the quote midpoint, divided by
the bid-ask midpoint. The quoted depth is the average of quoted bid-ask lots multiplied
by bid-ask quotes. In addition, I compute a realized spread, which is the ex-post realized
bid-ask spread paid by the investors for each transaction in the dataset. The calculation is
the same as in Barber and Odean (2000):
Pcrsp
SprBuy = 1
Pbuy
(5)
Pcrsp
SprSell = 1
Psell
where Pcrsp is the closing price from CRSP, and Psell and Pbuy are the purchase and sale
prices from the dataset. This measure includes the bid-ask spread, market impact of the
trade as well as the intra-day return on the day of the trade. The total spread is the sum of
the realized buy and sell spreads. Previous studies (Korajczyk and Sadka 2008, and
Eckbo and Norli 2002) have shown that there is high correlation among these liquidity
measures and that there is a common component that accounts for most of the variation
across individual liquidity measures.
11
There is likely to be endogeneity in the relationship between holding periods and
liquidity measures used in this paper. As trading interest in a stock increases so does its
liquidity. But we can also think of a stock as having a baseline exogenous cost
component along the lines of Amihud and Mendelson (1986). Although the liquidity
level of a penny stock, for instance, will increase with increased trading interest, it will
not achieve the same level of liquidity of a large cap stock purely based on that
increase.12 Figure 1 illustrates this notion graphically. I plot the adjusted Amihud
illiquidity ratio for IBM and Crown Petroleum Corp. over the 1991 to 1996 period.
Although there is variation over time in the liquidity levels for both stocks, the average
AdjIlliq ratio is significantly lower for IBM over the sample period. To capture this
baseline component, I use annual averages of the liquidity measures in analyzing
household holding periods. I later extend the analyses to incorporate time series variation
in Section 6. Table 1 reports the summary statistics and correlations for the liquidity
measures for stocks traded by households in the dataset.
4. Holding Periods and Transaction Costs
4.1. Transaction Level Analyses
To examine the relationship between holding periods and transaction costs, I first
calculate a holding period for each transaction in the dataset. The holding period is
defined as the number of trading days from the first purchase of a stock to the first sale.13
This method provides 806,404 holding period observations. The average and the median
holding period are 185 and 86 trading days respectively. Figure 2 shows the median
holding periods for transactions grouped by investors age, account type, the amount of
capital they have invested in the stock market, as well as transactions grouped by the
12
In the analyses that follow, I also explicitly control for other potential determinants of holding periods
such as stock and investor characteristics.
13
This approach follows Seru, Shumway and Stoffman (2008). I obtain similar results by defining the
holding period as the time period until all positive positions are closed, as in Feng and Seasholes (2005).
12
underlying stocks liquidity.14 The median holding period is shorter for stocks held in
retirement accounts. Investors who are older and who have less wealth invested in the
market have shorter holding periods. There is also a strong relationship between holding
periods and liquidity of stocks traded by the investors in the dataset.
To explore this relationship further, I rank and assign the 806,404 holding period
observations to ten groups based on the length of the holding period. For the stocks in
each group, I then calculate averages for the liquidity measures, price, and market
capitalization. The liquidity measures are calculated as of the purchase day, by averaging
monthly or daily measures over the previous 12 months. The results are reported in
Table 2, which show a strong relationship between holding periods and liquidity
measures. The relationship is monotonic for most of the measures and is not a simple
function of price or market capitalization. The adjusted Amihud illiquidity measure, for
instance, increases monotonically from 0.91 to 1.75. There is a 54 basis points (bps)
difference in the quoted spread and a 64 bps difference in the realized spread between the
highest and the lowest holding period groups.
Figure 3 shows this relationship graphically. I plot Kaplan-Meier survival
probabilities for stocks that are in the highest illiquidity decile using the adjusted Amihud
illiquidity measure, and for all other stocks in the dataset. The x-axis shows the number
of days that have passed since the purchase of a stock, and the two lines plot the
probability of an investor holding a stock conditional upon no sale up to that point for the
two groups of stocks. Stocks ranked in the highest illiquidity decile have a significantly
higher survival probability. The initial univariate results suggest that holding periods are
strongly related to measures of baseline transaction costs as predicted in hypothesis H1a.
To incorporate stock and investor characteristics, I utilize a hazard model in the
analysis of household holding periods.15 With hazard models, an investors trade
decision can be explicitly modeled by considering the investors sell-hold decision each
14
In the figure, a stock is defined as Illiquid if it belongs to the lowest liquidity decile of stocks ranked
according to the adjusted Amihud illiquidity ratio. Other category includes all other stocks not in the
lowest liquidity decile.
15
The hazard framework has been previously used by Seru, Shumway and Stoffman (2008) and Feng and
Seasholes (2005) in a similar context to model the disposition effect.
13
day. In this paper, I use a Cox proportional hazard model with potentially time varying
explanatory variables.16 The hazard model takes the form:
'
t 0
t exp x t z' (6)
This is essentially a statistical model that describes how long an investor in the dataset
will hold a stock before selling it. The left hand side variable, t , is the hazard rate,
the probability of selling a stock at day t conditional upon holding that stock until that
point in time. The explanatory variables are called covariates and can either be static
time varying. In equation (6), x represents time-varying covariates and z represents
covariates that are fixed over time. 0
t is called the baseline hazard rate and describes
the average hazard rate when the independent covariates are equal to zero. Using the Cox
(1972) estimator one can estimate coefficients on x and z ( and ) without specifying a
baseline 0
t hazard rate.
The static covariates used in this paper are investor and stock characteristics, which
are explained in detail in the tables that follow. The only time-varying covariate is a
dummy variable that takes on a value of one for each day the stock price trades above its
purchase price. This dummy variable measures the disposition effect - a behavioral
tendency of investors to sell shares whose price has increased while keeping shares that
have dropped in value. Positions that are not closed by the end of the sample period are
treated as censored observations. As there is likely to be seasonality in purchases and
sales, calendar month dummies are also included as static variables in the hazard
regressions.17 I follow standard reporting conventions and report hazard ratios instead of
coefficients from the holding period regressions. The hazard ratio is similar to the odds
ratio in binary choice models. It is defined as the ratio of two hazard functions when one
of the explanatory variables is changed by one unit holding everything else constant.
Since the interpretation of a hazard ratio is more intuitive for dummy variables, I
transform the explanatory variables into dummy intervals.
16
Details about estimating the proportional hazard model can be found in Cox and Oakes (1984).
17
Open stock positions, for instance, may be closed out in December for tax reasons.
14
Table 3 shows the results of the hazard regressions. I report results using the adjusted
Amihud illiquidity ratio as the transaction costs measure to save space. Similar results
are obtained using Pastor and Stambaughs reversal gamma and the Gibbs estimate of
Rolls transaction costs measure. As explained before, the transaction costs measure is
calculated by averaging the monthly Amihud illiquidity ratio over the 12 months prior to
the purchase date. I rank all stocks by the Amihud illiquidity ratio and create dummy
variable (AdjIlliq Dum) that takes on a value of one if stock belongs to the highest
illiquidity quintile. The hazard ratios corresponding to the dummy variables have an
intuitive interpretation. They indicate the probability of a sale (conditional upon no sale
up to that point) given that the underlying stock belongs to the highest illiquidity group
divided by the probability of a sale given that the stock does not belong to that group. A
stock in the highest illiquidity group is 0.6 times as likely to be sold as a stock not
belonging to that group.18 In Model III, I control for investors characteristics and obtain
a similar result. As in the univariate analysis, I find that transaction costs are a significant
determinant of holding periods of individual investors. The average investor is cognizant
of liquidity and pays attention to the transaction costs of the stocks she trades.
The results I report are robust to fixed household effects. One way to capture
heterogeneity across households within a hazard framework is to assume a different
baseline hazard rate for each household, but compute common coefficients on the
explanatory variables. The model is estimated by partial likelihood using the method of
stratification. Model II in Table 3 shows that the effect of transaction costs variable
increases once I control for fixed household effects. The results suggest that there is
variation in holding periods for different stocks for a given household, and that these
holding periods are positively related to transaction costs.
I find support for the hypothesis (H1b) that the correlation between holding periods
and transactions costs increases with investor sophistication and experience.
Characteristics we associate with investor sophistication are correlated with shorter
holding periods. However, as evidenced by the hazard ratios on the interaction terms
(Model IV in Table 3), those who are sophisticated tend to pay attention to the transaction
18
A stock in the lowest illiquidity group, on the other hand is 1.2 times more likely to be sold than a stock
not belonging to that group.
15
costs of the stocks they trade. Individuals, who are professionals, who have traded
options or foreign securities or who have held short positions, have holding periods that
are positively correlated with transaction costs. Those who hold mutual funds, on the
other hand, have holding periods that are negatively correlated with transaction costs.
Individuals who are retired and individuals who trade stocks in their retirement account
are more sensitive to transaction costs. In addition, households who have more
concentrated portfolios pay more attention to the liquidity of the underlying stocks they
trade.
To explore the role of investor sophistication further, I create a numeric variable to
proxy for the level of investor sophistication. The Sophistication variable starts at a value
of zero and is increased by one for each characteristic that one would associate with
investor sophistication. I follow Goetzmann and Kumar (2008) and assume that financial
sophistication is correlated with education and resources available to an investor. I also
use information contained in investors trades. Table 4 describes the criteria used to
construct the Sophistication variable. I run the same hazard regression as before (Model I
in Table 3), but instead of pooling across all investors, I run a separate regression for each
group of investors who have the same Sophistication value. For instance, all investors
with a Sophistication value equal to six would be one group. Figure 4 plots the hazard
ratios on the AdjIlliq Dum variable for the different groups of investors ranked by
Sophistication. The relationship between holding periods and transaction costs is
stronger for more sophisticated households. The relationship is negative for households
that are least sophisticated, and there is a monotonic increase in the strength of this
relationship as we go from the lowest sophistication group to the highest. In Table 4, I
report similar result pooling all investors together. I create a dummy variable
(Sophistication > 3 Dum) that takes on a value of one if the Sophistication value for a
given household in the dataset is greater than three. An investor who is sophisticated is
0.4 times as likely to sell an illiquid security at a given point in time, compared to an
unsophisticated investor who is 0.6 times as likely to sell an illiquid security.
Although the differences in holding periods for stocks with different liquidity levels
are significant, they are substantially lower than the calibrated values in Vayanos (1998)
and Constantinides (1986). Vayanos, for instance, predicts an increase in holding period
16
of 6 years when transaction costs increase from 0.5% to 2%. In comparison, a similar
increase in transaction costs would increase the holding period of investors by about 190
trading days in the dataset used in this paper. The empirical results are closer to the
calibrated values in Lo, Mamaysky and Wang (2006) who predict a similar change in
holding periods as in this paper. The results in this section suggest that models that
incorporate potentially exogenous liquidity or trading needs are more likely to be
representative of actual investor behavior. The results also offer a potential explanation
for the discrepancy between the empirically observed liquidity premium and the one
predicted by the models in which the holding periods are endogenously determined as in
Vayanos (1998) and Constantinides (1986).
4.2. Robustness Checks
To make sure the results are robust to underlying stock characteristics, I include book-to-
market, size and momentum characteristics in the hazard regressions. As before, to get a
more intuitive interpretation of the results, each year I segment stocks into quintiles based
on these stock characteristics. Dummy variables are created and take on a value of one if
a stock in the dataset falls into one of the five groups. These characteristics are
calculated based on the information available at the beginning of the month in which a
sale is made. Table 5 summarizes the results from hazard regressions using these
characteristics. The transaction costs measure remains significant after I control for stock
characteristics, while the economic and statistical significance of stock characteristics is
reduced once I control for liquidity. On average, households tend to hold value and small
stocks longer. Relationship between momentum and holding period appears to be U-
shaped, but it is more significant at the high return end. A stock belonging to the highest
momentum quintile is 1.4 times more likely to be sold conditional on no sale up to that
point in time.
The disposition effect (Shefrin and Statman 1985), the tendency of individual
investors to hold on to losing stocks too long and to sell winners too quickly, has been
shown to be a significant driver of trading behavior in a variety of contexts for both
individual and institutional investors. If the disposition effect is the main driver of a
decision to buy/sell (Grinblatt and Kellaharjou 2001), then the holding period and the
17
liquidity of a stock would be determined to some extent by how much the stocks current
price is above the investors weighted average purchase price for that stock. Given the
robust and significant relationship that has been established in the literature between
trading decisions and the disposition effect, and given its close relation to liquidity, I use
the disposition effect as a control in the hazard regressions. To do this, as mentioned
earlier, I create a time-varying covariate to capture the disposition effect. A dummy
variable (Disp Dum) is set to one for each day a stock in an investors portfolio trades
above its purchase price. I run the same hazard model as before, but now I include the
disp variable as a time-varying covariate. The results are provided in Table 5. Using
household level controls, I find that an individual is 1.8 times more likely to sell a stock
when it is trading above its purchase price than when it is not. The transaction costs
variable is significant after controlling for the disposition effect, but is not able to explain
away this effect. It is also worth noting that the interaction term is positive, indicating
that the disposition effect is stronger among less liquid stocks. Households are more
likely to sell an illiquid stock that is trading above the purchase price than one that is not
illiquid.
Existence of asymmetric information complicates the analysis. It is not entirely clear
how aggregate asymmetric information for a given security would affect its average
holding period. On the one hand, one can think of asymmetric information as a
component of transaction costs, which investors take into account in selecting which
securities to hold. On the other hand, if investors trade for both liquidity and information
reasons, allocational inefficiencies could reduce the correlation between holding periods
and liquidity (Garleanu and Pedersen 2007). I control for aggregate asymmetric
information in a given security by including the probability of information based trading
(PIN) measure (Easley et al. 1997) calculated from intra-day data.19 As before, I
compute an annual PIN dummy variable for each stock in the dataset. PIN Dum takes on
a value of one if the stock is in the highest PIN group. The results appear in Table 5
under Model V. The PIN measure significantly reduces the holding period of investors.
19
A detailed description is contained in Easley, Hvidkjaer and OHara (2004). The data is provided by
Soeren Hvidkjaer at http://www.smith.umd.edu/faculty/hvidkjaer/pin1983-2001.zip.
18
The transaction costs measure, however, does not lose its economic or statistical
significance.
As an additional control, I also remove potentially informative trades from the
sample. To control for information at the investor level, I run the same model as in the
previous section, but remove from the sample trades that may have been conducted for
informational reasons. To identify trades that are not motivated by liquidity needs, I
follow the same approach in Stoffman (2007). If an individual investor sells his holdings
of one security and then immediately uses the proceeds to buy another security, it is
unlikely that the particular trade is motivated by liquidity needs. I thus exclude trades
that are one trading day apart and for which differences in the values of the trades are less
than 5%. Model I in Table 5 shows the results from the hazard regression with these
trades removed from the sample. The prior results become stronger when I exclude these
potentially informative trades from the dataset.
4.3. Portfolio Level Analyses
I have thus far examined trading decisions of households at the transaction level. I now
consider liquidity decisions at the portfolio level. As Amihud and Mendelson (1986)
argue, it makes sense for investors with longer holding periods to hold more illiquid
stocks in their portfolio since those investors would face lower amortized transaction
costs. In this section, I analyze the determinants of overall liquidity of household
portfolios and examine how portfolio liquidity is related to households average holding
periods.
Portfolio liquidity is calculated on a monthly basis using position data reported at
month end:
N AdjIlliq k,t
i
Eqik,t
k 1 MktIlliqt
PIlliqi,t N
(7)
k
Eq i ,t
k 1
19
Above, Eqik,t is the value of stock k in household is portfolio at time t, and AdjIlliq k,t is
i
the adjusted Amihud illiquidity measure of stock k in month t. MktIlliq t is the market
illiquidity, calculated as the equal weighted average AdjIlliq of all stocks in month t.
Since average liquidity varies over time, MktIlliq t is used as an adjustment factor as in
Amihud (2002). I average the PIlliqi,t over the sample period to compute an average
portfolio illiquidity for each household. Households hold mostly liquid stocks in their
portfolio. If we were to rank all stocks by the AdjIlliq measure, assign them to percentile
ranks, and then calculate a weighted average illiquidity rank for the stocks in an
investors portfolio, 50% of the households would have an average portfolio illiquidity
rank that is in the bottom 8th percentile and 75% of the households would have an
average portfolio illiquidity rank that is in the bottom 20th percentile.
I calculate a holding period for each household by averaging the holding period for
the transactions made by that household. In calculating the average holding periods, I
treat positions that are not closed by the end of the sample period as censored. The cross-
sectional average and median holding period across households are 437 and 348 trading
days respectively.20 Figure 5 shows the distribution of the average holding periods of
households calculated based on transactions that are closed by the end of the sample
period, as well as the distribution of holding periods calculated taking into account
transactions that are not closed and treated as censored.
Table 6 shows the results from regressing average portfolio liquidity on household
holding periods and household characteristics:
K
PIlliqi 0 HP
HPi k
InvChi,k i (8)
k 1
In equation (8), PIlliqi is the average portfolio illiquidity of household i. HPi is the
average holding period of household i, and InvChi,k is the kth demographic characteristic
of household i described in detail in Table 6. Holding period is a statistically significant
20
The average and median holding period considering only positions that are closed (e.g. ignoring
censored observations) are 217 and 168 trading days respectively.
20
determinant of portfolio liquidity. Given that the median and the 75th percentile adjusted
portfolio illiquidity, PIlliqi , across households is 0.037 and 0.105 respectively, what I
report is also an economically significant relationship. In Model II, I show that
households with higher amounts of wealth invested in the stock market hold more liquid
stocks in their portfolio. The same is true for individuals who are older and retired.
Investors who hold less diversified portfolios hold more liquid stocks in their portfolios.
Overall, the portfolio level results are consistent with the earlier results and hypothesis
H1a.
5. Holding Periods and Returns
5.1. Amortized Transaction Costs and Returns
In this section, I study the implications of liquidity decisions of individual investors on
investment performance. More specifically, I test hypothesis H2a outlined in Section 2.
The liquidity premium in Amihud and Mendelson (1986) is driven by rents earned by
investors who have longer investment horizons. These investors can amortize transaction
costs over a longer expected time period and therefore require a lower compensation for
holding assets with higher transaction costs. Illiquid assets are shunned by investors who
have a shorter time horizon and heavily discounted by them. As a result, long-term
investors who bear these costs less frequently earn rents above and beyond the amortized
costs of transacting these assets.
I calculate a holding period for each transaction in the dataset that is closed-out by the
end of the sample period. I then calculate cumulative raw returns and returns in excess of
size, book-to-market and momentum matched portfolios, as in Daniel et al. (1999), over
the holding period for each transaction. Characteristics-adjusted excess returns are
calculated to make sure that the differences in returns are not driven by differences in
stock characteristics.21 To be able to make comparisons across different holding periods,
I calculate average daily returns from cumulative raw and excess returns as:
21
In the Amihud and Mendelson (1986) model, investors are risk-neutral and in the absence of transaction
costs all securities would earn the risk free rate in equilibrium.
21
HP
avgri 1/ HP
1 ri,d 1 (9)
d 1
HP is the holding period measured in days, and ri,d is the daily raw or characteristics-
adjusted excess return for transaction i in day d. I also compute 1, 6, and 12 month raw
and excess returns starting from the day of purchase. Transaction costs consist of round
trip commissions divided by the value of purchases and sales, as well as the realized bid-
ask spread for purchases and sales, as described in Section 3. Transaction costs are
divided by the holding period to arrive at amortized transaction costs. Consistent with
Barber and Odean (2000), I find that on average, each transaction costs one percent in
bid-ask spread and 1.4 percent in commissions. In the analyses that follow, I exclude
transactions with a holding period of less than two days and stocks priced below two
dollars.
I rank all transactions by the holding period and place them into five groups. I then
average returns for the transactions in each group. The results are reported in Table 7.22
In the lowest holding period group, stocks are held on average for 10 days and earn 34.21
basis points (bps) per day before transaction costs. In contrast, stocks in the highest
holding period group are held on average for 543 days and earn 2.31 bps per day before
transaction costs. Average characteristics-adjusted excess returns are 20.65 bps and -3.59
bps per day before transaction costs, respectively, for the two groups. Thus, short-term
traders earn greater daily returns before transaction costs than long-term traders. Short
term traders also earn greater 1, 6 and 12 month returns before transaction costs. Once I
control for transaction costs, however, the picture changes. For the lowest holding period
group, the average return minus amortized commissions and bid-ask spreads is 0.39 bps
per day, compared with a net return of 1.14 bps per day for the highest holding period
group. Moreover, characteristics-adjusted excess returns are negative for all groups after
controlling for transaction costs, but significantly more so for the low holding period
group. The difference in returns between the lowest and highest holding period groups is
significant. These results are consistent with hypothesis H2a outlined in Section 2, in the
22
Results are reported at the transaction level. I obtain similar results if I aggregate to the household level.
22
sense that the returns, net of transaction costs, for households with longer holding periods
are higher than for households who have shorter holding periods. The relationship for
raw returns, however, is not monotonic.
Since I am examining transaction returns as opposed to returns for the whole
portfolio, the results could be biased if only profitable trades are closed out producing a
disposition effect. In other words, there might be an upward bias for short-term trades,
since they may consist mostly of positions that are closed out because the prevailing price
is above the purchase price. I consider returns for fixed holding periods from the day of
purchase (1, 6, 12 month returns are also reported in Table 7). However, this gets us
away from the notion of holding period returns. As a result, I also remove from the
sample those households with a strong tendency to close out positions that trade above
the purchase price. To identify these households, I split the dataset into two equal time
periods and use the first period (from 1991 to 1993) to calculate coefficients on the disp
variable explained in Section 4. I eliminate households with a positive disp coefficient
calculated with a 10% confidence level or higher. To make sure that I do not introduce a
new bias I also eliminate households with a significant negative disp coefficient. I use
the second time period (from 1994 to 1996) to calculate holding period returns and
amortized transaction costs as described earlier. The results are in Panel B of Table 6.
Holding period raw and characteristics-adjusted excess returns are now more uniform.
Differences in raw returns between the high and low holding period groups are not
significant. There is now a monotonic relationship in returns net of amortized transaction
costs across holding period groups, consistent with hypothesis H2a.
5.2. Liquidity Decisions and Returns
There are cross-sectional differences in the correlation between holding periods and
transaction costs across households. As described in Section 2, this correlation may
impact portfolio performance of households on a gross and a net basis. First, households
that do not pay attention to transaction costs would be expected to pay higher transaction
costs, generating lower net returns. Second, a negative correlation between holding
periods and transactions costs could also indicate low levels of sophistication and market
knowledge, resulting in lower gross returns. To identify the two types of households, I
23
use the same hazard model as before, but now instead of pooling across all households, I
estimate the coefficient on the transaction costs variable for each household separately. I
then use the correlation between holding periods and transaction costs as a proxy for how
much each investor pays attention to transaction costs. In order to obtain robust
estimates, I require that households make at least 50 round-trip trades over the sample
period, and I only keep estimates that are calculated with a 10% confidence level or
higher.23 The summary statistics for the transaction costs coefficient calculated from
household level hazard regressions are reported in Table 8. For the majority of
households in the dataset (over 60%), the correlation between holding periods and
transaction costs is positive. Most investors pay attention to the liquidity level of stocks
they trade.
The relationship between holding periods and transaction costs has strong
implications for investment performance. I form two groups based on the sign of the
coefficient on the transaction costs variable, and calculate 1, 6 and 12 month and holding
period returns for each transaction as described in the previous section. I then calculate
averages for the two groups. The results are in Table 9. There is a stark difference in the
investment performance between the two groups. Households that pay attention to
transaction costs earn about 20.5 bps in gross returns and 10.7 bps in characteristics-
adjusted excess returns each day, compared to 0.1 bps in gross returns and -6.6 bps in
excess returns each day for households that do not. Households that pay attention to
transaction costs pay less in amortized spreads and have higher net returns and net
characteristics-adjusted excess returns. They earn 7.1 bps per day in net returns,
compared to a loss of -10.9 bps per day for households whose holding periods are
negatively related to transaction costs. The differences in returns are all statistically
significant except for the one month returns. Since the differences are significant for
both gross and net returns, the positive relationship between holding periods and
transaction costs is consistent with the hypothesis (H2b) that investors who pay attention
to liquidity earn greater gross and net returns.
23
I obtain similar results using 20 or 30 trades instead of 50 trades.
24
6. Individual Investors and Demand for Liquid Securities
6.1 Common Demand for Liquid Securities
In this section, I extend the analysis to consider how households as a group make
liquidity decisions over time. As described in Section 2, commonality in liquidity can
arise from investors demanding liquidity at the same time. Increase in uncertainty about
changes in future income or wealth, for instance, can cause investors to tilt their
portfolios towards more liquid assets at the same time. To test whether there is
systematic variation in the trades of liquid assets, I employ a similar methodology used in
Kumar and Lee (2006) and Barber, Odean and Zhu (2003), who investigate correlation in
the trades of individual investors. Since I make comparisons over time under different
regimes of aggregate liquidity, I consider stock liquidity rankings instead of stock
liquidity levels. Each month, I rank stocks based on the adjusted Amihud illiquidity
measure and assign them to percentile ranks. A stock ranked in the 100th percentile
would be the most illiquid stock in a given month. Similarly, a stock ranked in the 1st
percentile would be the most liquid.
For groups of non-overlapping investors, G, I compute a time series of normalized
differences in the liquidity ranks of stocks purchased and sold:
BVti BAdjIlliqRankti 1
SVti SAdjIlliqRankti 1
i G i G
IlliqBSI tG (10)
BVti BAdjIlliqRankti 1
SVti SAdjIlliqRankti 1
i G i G
where BVti and SVti are the total value of purchases and sales, respectively, for investor i
in month t. BAdjIlliqRank ti 1 and SAdjIlliqRankti 1 are the weighted average adjusted
illiquidity rank of stock holdings of investor i belonging to group G in month using one
month lagged adjusted illiquidity ranks. IlliqBSI tG is similar to a buy-sell imbalance
index and indicates whether investors belonging to group G are net buyers or sellers of
liquid securities in a given month. 24 If the trades of liquid securities are independent
24
There are number of different ways to formulate this analysis. Another approach would be to examine
how investors over time tilt their portfolios towards stocks in the top/bottom illiquidity deciles. Kumar
25
across households, then purchases and sales of liquid stocks by one group of investors
will be uncorrelated with that of another group. To test for this independence, I form
5,000 pairs of non-overlapping investor groups containing 500, 1,000 and 5,000
investors. For each IlliqBSI tG , I then remove the effects of common dependence due to
the market factor and common variation in all household trades by running the following
regression:
IlliqBSI tG G
0
G
MKT
MKTt G
BSI
BSI t G
t (11)
In the equation above, MKTt is the month t market return in excess of the risk free rate,
and BSI t is the buy-sell imbalance for all households in a given month t, defined as:
Vti,Buy Vti,Sell
i N i N
BSI t (12)
Vti,Buy Vti,Sell
i N i N
Vti,Buy andVti,Sell are the total value of purchases and sales, respectively, of investor i in
month t. I aggregate over all N investors. The reason for this regression is to remove the
common component in the households net demand for liquid securities due to market
movements and changes in overall household demand unrelated to liquidity. I then
G
compute correlations of the residuals, t , for different pairs of investor groups.
The results are reported in Table 10. The correlation values range from 18% to 32%
depending on the number of investors used in the simulation. All correlations are
statistically different from zero. These results suggest the existence of a systematic
component in the demand for liquid securities across households. The results support
hypothesis H3a, that there is systematic variation in households trades of illiquid
securities.
6.2 Aggregate Market Liquidity and Household Demand for Liquid Securities
(2009) uses this methodology to investigate dynamic style preferences of individual investors. I obtain
similar results examining shifts in portfolio positions as in Kumar (2009).
26
As mentioned in Section 2, a number of papers treat retail investors as noise traders
providing constant liquidity to the market. However, if there is systematic variation in
the demand for liquid assets by individual investors, as I have shown in the previous
section, then their role as liquidity providers to the rest of the market is not clear. In fact,
changes in aggregate liquidity can arise endogenously from correlated trading by
individual investors. In this section I investigate how this systematic demand for liquid
securities varies with changes in aggregate market liquidity. I test whether there is a
flight to liquidity, and examine if a subset of individual investors provide liquidity to the
market by buying illiquid securities during times of low market liquidity.
I calculate monthly market liquidity as the equal-weighted average of the adjusted
Amihud illiquidity ratio for all stocks in a given month (as in Amihud 2002 and Acharya
and Pedersen 2005).25 As before, since I make comparisons over time under different
regimes of aggregate liquidity, I consider the liquidity rankings of stocks instead of their
liquidity levels. For all households, I compute difference in the liquidity ranks of stocks
purchased and sold in a given month as:
BVti BAdjIlliqRankti 1
SVti SAdjIlliqRankti 1
ALL i N i N
IlliqBSI t (13)
BVti BAdjIlliqRankti 1
SVti SAdjIlliqRankti 1
i N i N
The variables are defines as in equation (10), but now we compute the sum over all N s.
Figure 6 plots IlliqBSI ALL and the aggregate market level of illiquidity, MktIlliq, over the
sample period. In the figure, the period with low market liquidity corresponds with the
Mexican peso crises in 1994. The correlation between IlliqBSI ALL and MktIlliq is -35%.
Individual investors tend to buy liquid stocks and sell illiquid stocks when market
liquidity is low.
I split the data into five equal time periods ranked by the aggregate level of market
illiquidity. The first time period corresponds to the 34 months with the lowest level of
market illiquidity, and the last period to 34 months with the highest level. Table 11
25
I obtain qualitatively similar results if I use the Pastor and Stambaugh (2003) liquidity measure. The
correlation between the measure used in this paper and the Pastor and Stambaugh measure is 30%.
27
reports the differences in the illiquidity ranks of stocks bought and sold during these five
time periods, and also during the month corresponding to the highest level of market
illiquidity. When market illiquidity is at its highest point during the 1991 to 1994 period,
the difference in the illiquidity rank of the stocks purchased and sold by households is
1.1. When one considers the fact that 50% of the households have an average portfolio
illiquidity rank that is in the bottom 8th percentile, the differences I report are both
economically and statistically significant. The last column shows the differences in
illiquidity ranks of stock purchases and sales adjusted for household portfolio level of
liquidity. For this adjustment, I subtract the weighted average illiquidity rank of each
households portfolio from the illiquidity rank of stocks transacted by that household.
The magnitude of the differences is lower but still significant and consistent with the
earlier result that investors tend to purchase more liquid securities when aggregate
liquidity is low.
Table 12 shows the results from regressing illiquidity ranks of stocks purchased or
sold in a given month on market illiquidity and investor wealth and income. I estimate
the following regression:
TransAdjIlliqrankk ,t 0 1
Buyk ,t 2
Affluenti MktIlliqDumt
3
4
Buyk ,t Affluenti Buyk ,t
5
MktIlliqDumt 6
MktIlliqDumt Affluenti (14)
7
Buyk ,t MktIlliqDumt Affluenti
In equation (14), TransAdjIlliqrankk ,t is the lagged adjusted illiquidity rank of the
underlying stock for transaction k in month t. 26 To get a more intuitive interpretation of
the regression results, I transform the market illiquidity variable into a dummy variable (
MktIlliqDumt ) that takes on a value of one for the month in which market illiquidity is at
its highest during the sample period. Buyk ,t is a dummy variable that takes on a value of
one if the transaction k in month t is a purchase, and Affluenti is a dummy variable that
takes on a value of one if investor i is in the highest income bracket (>$100,000) and has
26
In the regressions, I use lagged (previous months) illiquidity ranks for stocks transacted in a given
month. I obtain similar results using contemporaneous illiquidity ranks.
28
invested more than $100,000 in the stock market during the sample period.27 Model I in
Table 11 shows that on average, when market illiquidity is high, households trade more
liquid stocks. The coefficient on the interaction term, MktIlliq Dum Buy , in Model II
is negative. Since I am using dummy variables, the coefficient on the interaction term
shows how much the illiquidity rank of the stocks purchased are higher or lower than
stocks sold during times of low market liquidity. The -1.6 coefficient on the interaction
term is economically and statistically significant. Controlling for fixed household effects
in Model III slightly reduces the effect to -1.0.
In hypothesis H3c, I predict that households with higher levels of wealth and income
buy illiquid assets that have dropped in price providing liquidity to the market. The
interaction term, MktIlliq Dum Buy Affluent , in Model IV in Table 12 is positive.
Households with higher incomes and higher amounts invested in the stock market tend to
buy more illiquid stocks during times of low market liquidity. The net effect of an
increase in illiquidity rank of purchases by Affluent households during times of high
market illiquidity is 0.93. As before, this result is both economically and statistically
significant. The results are consistent with the hypothesis that investors with deep
pockets provide liquidity to the market by purchasing illiquid stocks when market
liquidity is low.
7. Conclusion
This paper investigates both portfolio and stock level liquidity decisions of 66,000
households from a large discount brokerage. It provides an empirical link between
investor decisions and the liquidity premium observed in the market. Three main
conclusions follow from the analysis. First, transaction costs are an important
determinant of investment policies and trading decisions. Consistent with theoretical
models of investor behavior, households rationally reduce the frequency with which they
trade illiquid securities subject to high transaction costs. This finding is robust to various
controls, including household and stock characteristics as well as the disposition effect
and the level of asymmetric information. The results also hold at the portfolio level.
27
I obtain similar results if I use a $75,000 or $150,000 cut-off for income and wealth invested in the stock
market.
29
Consistent with the notion of liquidity clienteles, investors with longer investment
horizons tend to hold more illiquid securities. There is cross-sectional variation in the
relationship between holding periods and transaction costs across households, and I find
that this relationship is stronger among more sophisticated investors. Second, I show that
liquidity decisions have important implications for investment performance. As
postulated by Amihud and Mendelson (1986), households with longer holding periods
earn significantly higher returns after amortized transaction costs. In addition,
households that have holding periods that are negatively related to transaction costs earn,
on average, lower gross and net returns. Finally, this paper shows that there is systematic
variation in demand for liquid assets across investors. Consistent with the notion of flight
to liquidity, households are net demanders of liquid securities during times of low
aggregate market liquidity. Households with higher incomes and higher wealth invested
in the stock market supply liquidity when market liquidity is low.
30
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34
Table 1: Liquidity Measures Summary Statistics
This table reports summary statistics and correlations for the liquidity measures used in this paper. Only
stocks that are traded by households in the dataset are considered. Summary statistics and correlations are
calculated by pooling annual observations over the 1991-1996 time period. All liquidity measures are
annual averages and are defined in the text. Price is the average of the daily closing prices. Mkt Cap is the
average market capitalization. PS Gamma is Pastor and Stambaugh (2003) reversal gamma. AdjIlliq is the
adjusted Amihud illiquidity ratio. Rolls C is the Bayesian estimate of the Roll (1984) transaction cost
measure. The quoted spread is the ratio of the quoted bid-ask spread to the prevailing transaction price.
The effective spread is the absolute value of the difference between the transaction price and the quote
midpoint, divided by the bid-ask midpoint. The quoted depth is the average of quoted bid-ask lots
multiplied by bid-ask quotes. Realized spread is the realized bid-ask spread paid by the investors for each
transaction in the dataset. Spreads are reported in basis points.
PS Mkt Cap Amihud Quoted Effective Quoted
Roll's C Price $
Gamma 000s AdjIlliq Spread Spread Depth
Mean 26.81 1.73 18.61 1,045 7.23 324.32 205.53 685.72
Median 0.49 1.06 12.50 105 1.66 162.13 95.54 385.06
Std 316.79 2.05 124.04 4,549 9.70 532.61 385.57 898.28
P25 -0.34 0.45 5.00 30 0.38 100.54 54.56 161.69
P75 9.18 2.26 24.50 452 11.64 301.51 186.85 845.93
Pearson Correlations
PS Gamma 1.00
Rolls C 0.15 1.00
Price -0.01 -0.07 1.00
Mkt Cap -0.02 -0.15 0.09 1.00
AdjIlliq 0.16 0.76 -0.07 -0.16 1.00
Quoted Spread 0.17 0.58 -0.30 -0.13 0.54 1.00
Effective Spread 0.18 0.60 -0.29 -0.12 0.53 0.94 1.00
Quoted Depth -0.04 -0.24 0.40 0.61 -0.28 -0.27 -0.25 1.00
Spearman Correlations
PS Gamma 1.00
Rolls C 0.41 1.00
Price -0.34 -0.81 1.00
Mkt Cap -0.38 -0.83 0.85 1.00
AdjIlliq 0.39 0.85 -0.76 -0.91 1.00
Quoted Spread 0.15 0.71 -0.80 -0.76 0.75 1.00
Effective Spread 0.16 0.72 -0.81 -0.79 0.78 0.97 1.00
Quoted Depth -0.13 -0.53 0.61 0.78 -0.77 -0.78 -0.78 1.00
35
Table 2: Univariate Results
This table presents the univariate results. Transactions in the dataset are ranked by holding-periods and
placed into ten groups. Averages for the various liquidity measures for the underlying securities are then
calculated for each group. All liquidity measures are annual averages and are defined in the text. Price is
the average of the daily closing prices. Mkt Cap is the average market capitalization. PS Gamma is Pastor
and Stambaugh (2003) reversal gamma. AdjIlliq is the adjusted Amihud illiquidity ratio. Rolls C is the
Bayesian estimate of the Roll (1984) transaction cost measure. The quoted spread is the ratio of the quoted
bid-ask spread to the prevailing transaction price. The effective spread is the absolute value of the
difference between the transaction price and the quote midpoint, divided by the bid-ask midpoint. The
quoted depth is the average of quoted bid-ask lots multiplied by bid-ask quotes. Realized spread is the
realized bid-ask spread paid by the investors for each transaction in the dataset. Spreads are given basis
points. Statistical significance at the 10%, 5% and 1% levels is denoted by *, **, and ***, respectively.
Holding Price Mkt Cap PS Amihud Quoted Effective Quoted Realized
Roll's C
Period $ 000s Gamma AdjIlliq Spread Spread Depth Spread
Low 6 32.89 7,940 1.2743 0.9142 0.6608 118.84 83.61 3,140 62.99
2 20 32.04 7,602 1.7055 0.9943 0.6834 124.19 86.96 3,027 78.27
3 44 31.28 7,833 2.2359 1.0893 0.7054 123.82 86.83 3,058 104.96
4 79 31.52 9,029 2.3783 1.1265 0.7072 119.13 83.38 3,185 112.82
5 127 33.96 9,199 2.7837 1.2606 0.7337 119.24 84.20 3,266 132.60
6 194 31.21 10,513 3.1087 1.2421 0.7312 117.93 83.26 3,415 130.82
7 294 30.36 9,886 3.9784 1.3535 0.7382 115.72 81.57 3,341 139.63
8 470 29.47 10,266 3.6685 1.3819 0.7312 113.94 80.57 3,519 136.90
9 771 31.74 11,434 4.4004 1.4889 0.7425 115.51 81.71 3,748 129.28
High 1225 40.76 11,270 6.4303 1.7578 0.8182 172.55 121.30 2,977 127.18
High Low 1219*** 7.87*** 3330*** 5.156*** 0.8436*** 0.1575*** 53.71*** 37.69*** -162*** 64.19***
36
Table 3: Hazard Regressions
This table reports hazard ratios from the holding period regressions where the conditional probability of
sale is the dependent variable. Independent variables consist of a transactions costs measure and a set of
investor demographic and trade variables. AdjIlliq Dum is a dummy variable that takes on a value equal to
one if a stock in the dataset is in the highest quintile ranked by the adjusted Amihud illiquidity ratio
calculated over the previous 12 months prior to a transaction. Age [40-64] Dum is a dummy variable set
equal to one if the age of the head of the household is between 40 and 64. Age 65+ Dum is a dummy
variable set equal to one if the age of the head of the household is over 64. Income > 75K Dum is a dummy
that is set to one if the total annual household income exceeds $75K. Married Dum is a dummy variable set
to one if the head of the household is married. Male Dum is set to one if the head of the household is male.
Professional Dum and Retired Dum are dummy variables that reflect investors occupation. Professional
Dum is set to one for investors who hold technical and managerial positions and Retired Dum is set to one
for investors who are retired. Retirement Account Dum is set to one if the underlying account is a
retirement (IRA or Keogh) account. Trade variables are derived from the trades made by investors in the
dataset. Short User Dum is set to one if an investor executed at least one short-sell during the sample
period. Option User Dum is set to one if an investor has traded in options. Mutual Fund user Dum is set to
one if an investor has held mutual funds during the sample period. Foreign User Dum is set to one if an
investor made at least one trade in a foreign asset including ADRs, foreign stocks or foreign mutual funds
during the sample period. Total Equity > 45K is dummy variable set to one if households total value of
equity invested in the stock market exceeds $45K. Diversification is defined as in Goetzmann and Kumar
(2008), and is equal to the sum of the squared value weight of each stock in a households portfolio.
Diversification < 0.3 Dum is dummy variable if this diversification measure for a given household is less
than 0.3. Calendar month dummies (not reported) are twelve dummy variables that take on a value of one
if the month of the transaction is equal to the month dummy. Robust standard errors are calculated as in
Lin and Wei (1989). Ties are handled using the Efron procedure. Wald test is for each additional set of
regressors. Statistical significance at the 10%, 5% and 1% levels is denoted by *, **, and ***, respectively.
Model I Model II Model III Model IV
Haz Ratio p-val Haz Ratio p-val Haz Ratio p-val Haz Ratio p-val
AdjIlliq Dum 0.617*** <.0001 0.602*** <.0001 0.632*** <.0001 0.804** 0.0470
Demographic Variables
Age [40 - 64] Dum 0.988 0.1698 0.986 0.1168
Age 65 + Dum 0.83*** <.0001 0.829*** <.0001
Income > 75K Dum 0.921*** <.0001 0.921*** <.0001
Married Dum 0.945*** <.0001 0.945*** <.0001
Male Dum 1.101*** <.0001 1.101*** <.0001
Professional Dum 1.009 0.3158 1.01 0.2319
Retirement Acct Dum 0.852*** <.0001 0.852*** <.0001
Retired Dum 1.091*** <.0001 1.093*** <.0001
Trade Variables
Foreign securities Dum 1.146*** <.0001 1.147*** <.0001
Mutual fund user Dum 0.988** 0.0701 0.985** 0.0232
Option user Dum 1.492*** <.0001 1.497*** <.0001
Short user Dum 1.968*** <.0001 1.976*** <.0001
Total Equity > 45K Dum 1.314*** <.0001 1.318*** <.0001
Diversification < 0.3 Dum 0.705*** <.0001
Interactions
AdjIlliq Dum * Age [40 - 64] Dum 1.151* 0.0832
AdjIlliq Dum * Age 65+ Dum 1.189 0.1286
AdjIlliq Dum * Income > 75K Dum 0.933*** <.0001
AdjIlliq Dum * Married Dum 1.019 0.7706
AdjIlliq Dum * Male Dum 0.975 0.8240
37
AdjIlliq Dum * Professional Dum 0.863** 0.0364
AdjIlliq Dum * Retirement Acct Dum 0.959* 0.0521
AdjIlliq Dum * Retired Dum 0.858** 0.0129
AdjIlliq Dum * Foreign Dum 0.919** 0.0179
AdjIlliq Dum * Mutual fund Dum 1.274*** <.0001
AdjIlliq Dum * Option user Dum 0.794*** 0.0013
AdjIlliq Dum * Short user Dum 0.781*** <.0001
AdjIlliq Dum * Total Equity 0.854** 0.5464
AdjIlliq Dum * Diversification < 0.3 Dum 1.197*** 0.0032
Household effects No Yes No No
Calendar month dummies Yes Yes Yes Yes
Wald test <.0001 <.0001 <.0001 <.0001
38
Table 4: Household Sophistication Measure
The top panel lists the criteria used to construct the Sophistication variable. This variable is increased by a
value of one if an investor in the dataset meets anyone of the criteria listed n the table. The bottom panel
reports hazard ratios from the holding period regression, where the conditional probability of sale is the
dependent variable. AdjIlliq Dum is a dummy variable that takes on a value equal to one if a stock in the
dataset is in the highest quintile ranked by the adjusted Amihud illiquidity ratio calculated over the
previous 12 months prior to a transaction. Sophistication > 3 Dum is dummy variable set to one if the
Sophistication variable for an investor in the dataset is greater than three. Calendar month dummies (not
reported) are twelve dummy variables that take on a value of one if the month of the transaction is equal to
the month dummy. Robust standard errors are calculated as in Lin and Wei (1989). Ties are handled using
the Efron procedure. Statistical significance at the 10%, 5% and 1% levels is denoted by *, **, and ***,
respectively.
Criteria Sophistication
Income > $75K +1
Equity Investments > $45K +1
Investor is a professional +1
Trades Options +1
Trades Foreign Securities +1
Does not invest in Mutual Funds +1
Has held a Short position +1
Portfolio Diversification < 0.3 +1
Haz Ratio p-val
AdjIlliq Dum 0.625*** <.0001
Sophistication > 3 Dum 1.110*** <.0001
Sophistication > 3 * AdjIlliq Dum 0.714*** <.0001
Calendar Month Dummies Yes
39
Table 5: Robustness Checks
This table reports the result of hazard regressions where the holding period is the dependent variable. The independent
variables are the transaction costs measure, stock characteristics, the disposition effect proxy, and the PIN measure. AdjIlliq
is the average adjusted Amihud illiquidity ratio over a year. Size is the market capitalization. Book-to-market is the book
value from the previous fiscal year divided by the current market capitalization. Momentum is the previous 12 month return.
PIN is the annual average of probability of informed trading (Easley et al. 1997) variable. Dummy variables (Dum) are
created for the transaction costs measure, stock characteristics, and the PIN measure and set to one if a stock is in the highest
quintile ranked according to one these variables. For the transaction costs and the PIN measures, stocks are ranked and
sorted into quintiles at the beginning of the month of a purchase. The same procedure is repeated for the stock
characteristics, but the ranking is done at the beginning of the month when there is a sale. Disp Dum is the disposition proxy.
It is a time-varying dummy variable that takes on a value of one if the stock at given day is trading above its purchase price.
The investor characteristics are the household demographic and trade variables defined in Table 3. Calendar month dummies
(not reported) are twelve dummy variables that take on a value of one if the month of the transaction is equal to the month
dummy. Robust standard errors are calculated as in Lin and Wei (1989). Ties are handled using the Efron procedure.
Statistical significance at the 10%, 5% and 1% levels is denoted by *, **, and ***, respectively.
Model I Model II Model III Model IV Model V Model VI Model VII Model VIII Model IX
AdjIlliq Dum 0.587*** 0.660*** 0.687*** 0.695***
<.0001 <.0001 <.0001 <.0001
Book-to-Market Dum 0.837*** 0.913**
<.0001 <.0001
Size Sum 1.174*** 1.146***
<.0001 <.0001
Momentum Dum 1.438*** 1.417***
<.0001 <.0001
PIN Dum 1.182*** 1.229***
<.0001 0.1015
Disp Dum 1.810*** 1.793***
<.0001 <.0001
AdjIlliq Dum * Disp Dum 1.141***
<.0001
Calendar month dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes
Investor Characteristics Yes Yes Yes Yes Yes Yes Yes Yes Yes
40
Table 6: Portfolio Liquidity and Holding Periods
This table reports the results of regressions using portfolio illiquidity as the dependent variable. The
independent variables are investor holding periods and investor characteristics. PIlliq is the average
household portfolio illiquidity as defined in Section 4.3. Holding period is the average household holding
period. It is calculated by averaging holding periods for all transactions of a given investor. Positions that
are not closed-out by the end of the sample period are treated as censored observations. A censored
average is calculated assuming a Weibull distribution for the holding period. Investor characteristics are
described in Table 3. Robust standard errors are reported below coefficient estimates. Statistical
significance at the 10%, 5% and 1% levels is denoted by *, **, and ***, respectively.
Model I Model II
Holding Period (years) 0.0515*** 0.0631***
0.0079 0.0152
Age -0.0012***
0.0002
Income 0.0002
0.0008
Married Dum -0.0219
0.0007
Professional Dum -0.0205***
0.0069
Retired Dum -0.0181**
0.0099
Male Dum 0.0591***
0.0097
Foreign securities Dum 0.0487***
0.0079
Mutual fund user Dum 0.001
0.0057
Option user Dum 0.0709***
0.0096
Short user Dum 0.0122***
0.0065
Log Total Equity -0.0981***
0.0024
Diversification -0.0334***
0.0113
N 63,024 19,746
Adj R2 0.01 0.09
41
Table 7: Holding Period Returns
This table reports transaction returns to holding period groups. Holding period is defined as the time period
from the first purchase to the first sale of a security. Transactions are ranked and put into holding period
quintiles. 1, 6, and 12 month returns are calculated starting from the date of purchase. Holding period
returns are average daily returns (reported in basis points) over the holding period. Excess returns are
returns net of characteristics matched portfolios, as in Daniel et al. (1997). Amortized spread is the realized
spread (as defined in Table 2) divided by the holding period. Amortized commission is the round-trip
commission divided by the holding period. Transactions with a purchase or sale price less than $2, and
holding periods less than 2 days, are excluded from the sample. Panel B reports returns for a sub-sample of
the households in the 1994-1996 time period. The 1991-1993 time period is used to calculate a coefficient
on the disp variable for each household in the dataset. Households with a positive disp coefficient
significant at the 10% level are removed from the sample. Statistical significance at the 10%, 5% and 1%
levels is denoted by *, **, and ***, respectively.
Panel A: Returns to Holding Period Groups
Low 2 3 4 High High - Low
1 Month Ret 0.045 0.036 0.011 0.004 0.001 -0.044***
1 Month Excess Ret 0.018 0.010 -0.006 -0.012 -0.013 -0.031***
6 Month Ret 0.079 0.112 0.132 0.054 0.008 -0.071***
6 Month Excess Ret -0.009 0.011 0.025 -0.031 -0.055 -0.045***
12 Month Ret 0.148 0.187 0.200 0.188 0.056 -0.092***
12 Month Excess Ret -0.014 0.007 0.012 -0.003 -0.081 -0.067***
Holding Period Ret (bps) 34.211 15.080 8.085 4.116 2.307 -31.904***
Holding Period Excess Ret (bps) 20.648 4.446 0.045 -2.778 -3.587 -24.235***
Holding Period Net Ret (bps) 0.386 3.280 2.603 1.358 1.137 0.751*
Holding Period Net Excess Ret (bps) -13.177 -7.354 -5.436 -5.537 -4.757 8.420***
Amortized Spread (bps) 5.257 3.063 1.501 0.721 0.264 -4.993***
Amortized Commission (bps) 28.568 8.737 3.981 2.037 0.906 -27.662***
Holding Period 10 36 87 192 543 533***
Panel B: Bias Adjusted Returns to Holding Period Groups
Low 2 3 4 High High - Low
1 Month Ret 0.016 0.027 0.020 0.010 0.002 -0.014***
1 Month Excess Ret -0.002 0.006 0.001 -0.006 -0.009 -0.007***
6 Month Ret 0.049 0.078 0.109 0.119 0.051 0.002
6 Month Excess Ret -0.034 -0.013 0.007 0.011 -0.032 0.002
12 Month Ret 0.112 0.153 0.201 0.232 0.187 0.075***
12 Month Excess Ret -0.038 -0.014 0.004 0.013 -0.024 0.014***
Holding Period Ret (bps) 1.383 2.626 4.739 5.031 4.371 2.988
Holding Period Excess Ret (bps) -2.402 -4.392 -2.846 -2.547 -3.517 -1.115
Holding Period Net Ret (bps) -38.105 -12.659 -2.171 1.514 2.676 40.781***
Holding Period Net Excess Ret (bps) -41.889 -19.677 -9.756 -6.065 -5.212 36.677***
Amortized Spread (bps) 5.588 3.844 1.819 0.886 0.377 -5.210***
Amortized Commission (bps) 33.900 11.441 5.091 2.631 1.318 -32.582***
Holding Period 7 24 59 125 309 302***
42
Table 8: Household Transaction Costs Coefficient Estimates
This table reports summary statistics of the transaction costs coefficient, which is calculated from
household level hazard regressions described in Section 5.2. AdjIlliq variable is used as the transaction
costs measure. To get robust estimates, households are required to have made at least 50 trades during the
sample period to be included in the analysis. The summary statistics for the coefficients calculated with at
least 10% statistical significance are reported in the second column.
Obs Significant at
All Obs
>10%
Mean -0.3002 -0.5834
Median -0.1089 -0.2752
Std Dev 4.8435 7.5727
Skew -29.745 -20.165
Kurtosis 1170.52 507.27
P5 -1.1015 -1.5748
P25 -0.3366 -0.5266
P75 0.1188 0.3018
P95 0.6860 1.2017
43
Table 9: Transaction Costs and Holding Period Returns
This table reports transaction returns to two groups formed based on the sign of the transaction costs
coefficient, which is calculated from household level hazard regressions described in Section 5.2. AdjIlliq
variable is used as the transaction costs measure. To get robust estimates, households are required to have
made at least 50 trades during the sample period to be included in the analysis. 1, 6, and 12 month returns
are calculated starting from the date of purchase. Holding period returns are average daily returns (reported
in basis points) calculated from the first purchase of a security to the first sale. Excess returns are returns
net of characteristics matched portfolios, as in Daniel et al. (1997). Amortized spread is the realized spread
(as defined in Table 2) divided by the holding period. Amortized commission is the round-trip commission
divided by the holding period. Transactions with a purchase or sale price less than $2, and holding periods
less than 2 days, are excluded from the sample. Panel B reports returns for the full sample, and Panel A
reports returns where the coefficient on the AdjIlliq variable is calculated with at least 10% significance.
Statistical significance at the 10%, 5% and 1% levels is denoted by *, **, and ***, respectively.
Panel A: Observations with AdjIlliq Coefficient at >10% Significance
Positive Negative Positive - Negative
1 Month Ret 0.018 0.018 0.001
1 Month Excess Ret -0.001 -0.001 0.001
6 Month Ret 0.079 0.066 0.013***
6 Month Excess Ret -0.010 -0.020 0.01***
12 Month Ret 0.161 0.132 0.029***
12 Month Excess Ret -0.010 -0.035 0.025***
Holding Period Ret (bps) 20.450 0.122 20.327***
Holding Period Excess Ret (bps) 10.756 -6.564 17.32***
Holding Period Net Ret (bps) 7.077 -10.950 18.027***
Holding Period Net Excess Ret (bps) -2.617 -17.636 15.019***
Amortized Spread (bps) 0.675 2.202 -1.527***
Amortized Commission (bps) 12.697 8.870 3.827***
Holding Period 100 157 -57***
Panel B: All Observations
Positive Negative Positive - Negative
1 Month Ret 0.018 0.017 0.001**
1 Month Excess Ret -0.001 -0.002 0.002**
6 Month Ret 0.079 0.070 0.009***
6 Month Excess Ret -0.010 -0.019 0.009***
12 Month Ret 0.162 0.146 0.016***
12 Month Excess Ret -0.009 -0.027 0.018***
Holding Period Ret (bps) 16.909 4.125 12.785***
Holding Period Excess Ret (bps) 7.621 -3.542 11.163***
Holding Period Net Ret (bps) 4.228 -7.570 11.798***
Holding Period Net Excess Ret (bps) -5.060 -15.236 10.176***
Amortized Spread (bps) 0.942 2.259 -1.317***
Amortized Commission (bps) 11.739 9.435 2.304***
Holding Period 116 147 -32***
44
Table 10: Common Demand for Liquidity
This table reports correlation statistics from three different simulations that test for a systematic component
in the demand for liquid assets across households. A pair of non-overlapping investor groups containing N
investors (where N = 500, 1,000 and 5,000) is selected from the dataset. The normalized difference in the
liquidity ranks of stocks the investors in each group purchase and sell each month are calculated (IlliqBSI
variable in Equation 10). IlliqBSI for each investor group is regressed on the market factor and the
aggregate buy-sell imbalance to remove the common variation in all household trades unrelated to liquidity.
A time series correlation of the residual from the regression is calculated between two groups of investors.
The same procedure is repeated 5,000 times. The summary statistics for the 5,000 simulated correlations
are reported below.
# of Investors Mean Median Std Dev t-value
500 0.1782 0.1559 0.3005 41.95
1000 0.2108 0.2409 0.2790 53.43
5000 0.3799 0.3826 0.1636 164.18
45
Table 11: Illiquidity Rank of Transactions
This table reports the differences in the adjusted illiquidity ranks of household purchases and sales of
securities under different levels of aggregate market illiquidity. Market illiquidity is calculated as the
equal-weighted average of the adjusted Amihud illiquidity ratio of all stocks in a given month. The sample
period is broken into five equal time periods determined by the level of market illiquidity, ranked from
,,Low to ,,High in the table. ,,MAX is the month corresponding to the highest level of market illiquidity.
Stocks are ranked each month based on the adjusted Amihud Illiquidity measure and assigned to percentile
ranks. The adjusted illiquidity rank of purchases and sales and the difference between purchases and sales
are reported for five different levels of aggregate liquidity and for the month in which the market illiquidity
is at its highest. Statistical significance at the 10%, 5% and 1% levels is denoted by *, **, and ***,
respectively.
HH demeaned Adj
Market Illiquidity Buy/Sell N Obs Adj Illiquidity Rank
Illiquidity Rank
Low Buy 188,601 16.71 0.94
Sell 155,111 16.05 0.24
Diff 0.66*** 0.7***
2 Buy 226,817 15.87 0.29
Sell 185,471 15.86 -0.03
Diff 0.01 0.32***
3 Buy 186,929 16.00 0.43
Sell 155,989 15.44 -0.18
Diff 0.56*** 0.61***
4 Buy 244,573 15.97 0.36
Sell 201,018 15.44 -0.31
Diff 0.53*** 0.67***
High Buy 215,823 16.35 0.58
Sell 174,064 17.21 0.99
Diff -0.86*** -0.41***
MAX Buy 11,436 14.94 -0.20
Sell 7,659 16.06 0.27
Diff -1.13*** -0.47*
46
Table 12: Market Liquidity and Liquidity of Transactions
This table reports the result of regressions using the illiquidity rank of the security that is purchased or sold
as the dependent variable. The independent variables are aggregate market illiquidity and investor income
and wealth. Market illiquidity is calculated as the equal-weighted average of the adjusted Amihud
illiquidity ratio of all stocks in a given month. MktIlliq is a dummy variable that takes on a value of one if
the aggregate market illiquidity is in the lowest month during the sample time period. Buy is a dummy
variable that takes on a value of one if the transaction is a purchase. Affluent is a dummy variable that
takes on a value of one if the investor is in the highest income bracket (>$100,000) and has invested more
than $100,000 in the stock market during the sample period. Statistical significance at the 10%, 5% and
1% levels is denoted by *, **, and ***, respectively.
Model I Model II Model III Model IV
MktIlliq -0.8688 *** 0.0715 0.039 0.5357
0.1509 0.2380 0.2108 0.3710
Buy 0.2892*** 0.2961*** 0.3174***
0.0301 0.0267 0.0433
Buy * MktIlliq -1.5957*** -1.009*** -2.6296***
0.3078 0.2710 0.4817
Buy * MktIlliq * Affluent 2.1666***
0.8313
Affluent -1.2371***
0.0210
Buy * Affluent -0.7172
0.6384
Affluent * MktIlliq -0.2302***
0.0782
Adj R2 0.01 0.01 0.01 0.08
Household Effects No No Yes No
47
Figure 1: Illiquidity Ratio
This figure shows the adjusted Amihud illiquidity ratio for IBM and Crown Petroleum Corp from Jan. 1991
to Dec. 1996.
3.500 0.251
3.000 0.251
Crow n Petroleum
IBM
2.500 0.251
2.000 0.250
Adj Illiq
Adj Illiq
1.500 0.250
1.000 0.250
0.500 0.250
0.000 0.250
Jan-91
May-91
Jan-92
May-92
Jan-93
May-93
Jan-94
May-94
Jan-95
May-95
Jan-96
May-96
Sep-91
Sep-92
Sep-93
Sep-94
Sep-95
Sep-96
Jan-91
May-91
Jan-92
May-92
Jan-93
May-93
Jan-94
May-94
Jan-95
May-95
Jan-96
May-96
Sep-91
Sep-92
Sep-93
Sep-94
Sep-95
Sep-96
48
Figure 2: Holding Periods of Households
This figure shows the median holding period for various investor and stock groups. Age is the age of the
investor. Account type denotes whether the account is a retirement account. Investment value is the
average amount invested by the household in the stock market. A stock is defined as illiquid if it belongs to
the lowest liquidity decile of stocks ranked according to the adjusted Amihud illiquidity ratio. The holding
period is calculated only for positions that are closed-out by the end of the sample period.
160
140
Median Holding Period (Trading Days)
120
100
80
60
40
20
0
< 45 45 - 65 >65 Other Retirement < 10K 10K-45K >45K Other Illiquid
Age Account Type Investment Value Liquidity
49
Figure 3: Survival Probabilities
This figure plots Kaplan-Meier survival probabilities for two groups of stocks held by households in the
dataset. Illiquid stocks in the figure are stocks that are in the highest illiquidity decile of stocks ranked
according to the adjusted Amihud illiquidity measure.
1.0
All Stocks
0.9 Illiquid Stocks
0.8
0.7
Survival Probability
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
Days
50
Figure 4: Hazard Ratios by Investor Sophistication
This figure plots the hazard ratios on the AdjIlliq Dum variable for different groups of investors ranked by
sophistication. Hazard ratios are calculated by running a separate regression for each group of investors
who have the same Sophistication value. The regression model used is the same as in Model I in Table 3.
1.8
1.6
1.4
1.2
Hazard Ratio
1.0
0.8
0.6
0.4
0.2
0.0
1 2 3 4 5 6 7
Sophistication
51
Figure 5: Distribution of Holding Periods
This figure plots the distribution of holding periods for the households in the dataset. Holding period is
calculated as the average holding period for all the transactions of a given household. Positions that are not
closed-out by the end of the sample period are treated as censored observations. A censored average is
calculated assuming a Weibull distribution for the holding period. The figure shows distribution of holding
periods calculated using positions that are closed out by the end of the sample period (,,Closed line), and
calculated using censored observations (,,Censored line).
4500
Closed
4000 Censored
3500
3000
2500
2000
1500
1000
500
0
0
180
360
540
720
900
1080
1260
1440
1620
1800
52
Figure 6: BSI and Illiquidity BSI
This figure plots the difference in the illiquidity ranks of buys and sells (IlliqBSI), and the aggregate level
of market illiquidity (Mktilliq). Market illiquidity is calculated as the equal-weighted average of the
adjusted Amihud illiquidity ratio of all stocks in a given month.
0.20
IliqBSI 14
0.15 MktIlliq
12
0.10
BSI / IllliqBSI
10
MktIlliq
0.05
8
0.00
1991-01
1991-04
1991-07
1991-10
1992-01
1992-04
1992-07
1992-10
1993-01
1993-04
1993-07
1993-10
1994-01
1994-04
1994-07
1994-10
1995-01
1995-04
1995-07
1995-10
1996-01
1996-04
1996-07
1996-10
-0.05 6
-0.10 4
Date
53