ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
TRADING VOLUME
THEORY
and
with
EVIDENCE
PRIVATE VALUATIONS:
from the EX-DIVIDEND
Roni Michaely*
and
Jean-Luc Vila**
WP#3634-93
November 1993
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
DAY
TRADING VOLUME
THEORY
and
with
EVIDENCE
PRIVATE VALUATIONS:
from the EX-DIVIDEND
Roni Michaely*
and
Jean-Luc Vila**
WP#3634-93
November 1993
Johnson School of Management, Cornell University
Sloan School of Management Massachusetts Institute of Technology
,
First
Version
DAY
Abstract
We
develop and
costs
test a
theory of the interaction between investors' heterogeneity,
and trading volume. To
test
our model
we
risk,
transactions
take advantage of the specific nature of trading
motives around the distribution of cash dividends namely the costly trading of tax shields. Consistent
with the theory,
we show
that
when
trades occur because of differential valuation of cash flows an
increase in risk or transactions costs reduces volume.
plays a significant role in determining the
volume
to
is
engage
volume of
It is
trading.
shown
trade. Finally,
positively related to the degree of heterogeneity
is
also
that the non-systematic risk
we demonstrate
that trading
and the incentives of the various groups
I.
INTRODUCTION
Price and trading
Financial
volume are the two most important
statistics
describing financial markets activity.
economists have developed models to understand
information are aggregated into a single market price.
as a theory of aggregation.
By
contrast, a theory of
Hence
how
different
preferences and
asset pricing theory can
market volume must
be thought of
explicitly take agents'
heterogeneity into account. While differential liquidity needs or information have been proposed as
a source of trading
volume, there
is
no consensus
as to their relative importance.
Moreover,
a theory
of volume based on these motives must explain not only the level of volume, but also the timing of
the trades.
Constructing a model of trading volume
multiple agents,
no trade takes place
is
a non-trivial task. Indeed, in complete markets with
after the initial trading
Hence heterogenous preferences alone cannot
volume based on
differential preferences
Dumas
for instance
day (see for instance Arrow (1953)).
explain trading volume.
As
a
have assumed some degree of market incompleteness (see
(1989) and Campbell
et. al.
(1991)). Similarly, heterogenous information alone
does not explain market volume as shown by the rational expectations
assumed, agents have
common
priors,
consequence, models of
i.e.
literature.
If,
as usually
they agree on the prior distribution of uncertainty and
disagree only after observing different signals, then unobservable liquidity shocks are needed to
generate trading (see for instance Grossman (1981), Tirole (1982),
(1993)).
By
contrast
if
Wang
(1993) and
Blume
et al.
agents have different priors, they will trade even in the absence of liquidity
shocks (see Harris and Raviv (1992) or Biais and Bossaert (1993)).
In this work,
we develop and
test a
theory of the interaction betweeen investors' heterogeneity,
transactions costs and trading volume. For tractability,
risk,
we consider the case of heterogenous valuation
4
as
opposed
to heterogenous information.'
To
test
our theory,
we
take advantage of the specific
nature of trading motives around the distribution of cash dividends. Trading around
this
event results
neither from differences in information sets nor from differences in opinions but from tax induced
While the present work focuses on dividend
differential valuations of dividends.
distributions,
we
believe that the insights and the methodology can be applied in other contexts as well.^
We
analyze trading in the stock market around the ex-dividend day.' Because of the differential tax
treatment of dividends and capital gains investors do not value $1 of dividends as equal to $1 of
capital gains (see Elton
capital gain
income.'*'
income
By
and Gruber (1970)). For example,
if
dividend income
is
taxed at
50%
while
taxed at 20%, the investor values $1 of dividend income at $.625 of capital gain
is
contrast, corporate investors
who have
a higher tax rate
on
capital gain
income (46%)
than on dividend income (6.9%) value dividend income more than capital gain income: with these
rates,
tax
they are indifferent between $1 of dividend income and $1.72 of capital gain income.* Finally
exempt investors value $1 of dividend income
at $1
of capital gain income.
Since the tax code create differences in asset valuation as opposed to differences in opinion or
information,
teix
related trading will occur around the ex-day in a fairly predictable manner. For now,
Models of trading volume based on market incompleteness or heterogenous information generate important insights into the time
between price and volume. However they become untractable in the presence of transactions costs.
series relationship
^See the discussion
in the
^The ex-dividend date
is
concluding section.
defmed as a the
first
trading date in which the stock trades without the dividend.
^Prior to the 1986 Tax Reform Act (TRA), individual investors who held a stock for at least six months paid lower lax on capital gain
(20%) than on ordinary dividends (50%). The TRA eliminated all distinction between capital gains and ordinary income. However, it is
still
possible to defer taxes
'(l--5)/(l-.2)
=
on
capital gains by not realizing the gains.
.625.
*Before the 1986
TRA a corporation who holds
the stock of another corporation paid taxes on only
the effective tax rate for dividend income was .15x.46
the fraction of the dividend exempted from taxes
=
.069. After the
was also reduced
to
TRA
70%. The
the corporation
income
85%
of the dividend. Therefore
tax rate
effective tax rate for dividend
was reduced
income
is
now
to
34% and
= .102.
.3x.34
5
consider the following stylized example
$100' and
(iii)
$1 dollar in dividends
is
paid;
(ii)
the cum-day price
is
known and equal
to
the price drop subsequent to the payment of the dividend was
$.8. In this case, investors
dividend and
(i)
sell
it
who
value the dividend for
later at a $.8 loss.
By
$.8 follows the opposite trading strategy.
more than
contrast an investor
With the
who
$.8 will
buy the stock, cash the
values the dividend for less than
tax rates as described in the previous paragraph
(and ignoring transactions costs and risk for the time being), the after-tax per share proGts of the
individual investors, tax
From our
exempt investors and corporate investors are
discussion above,
to a higher
it is
$.14, $.2
First,
$.5, respectively.
clear that a greater degree of tax heterogeneity in the
volume around the
ex-day.
By
contrast, risk
economy
leads
and transactions costs reduce volume by
making the transfer of dividend paying stocks from investors who do not
do more
and
like dividends to those
who
costly.
a tax 'arbitrage' strategy entails a (temporary) deviation
from optimal
risk sharing since
around
the ex-day, investors do not hold the market portfolio.* For example, a corporate investor buying a
stock going ex for tax purposes will be overly exposed to
will
be large
even
if
if
the
minimum
movements of the
stock's price. This risk
holding period necessary to claim the dividend exclusion
the stock must only be held overnight, the risk
about $1 on a $100 stock, which
is
is
not
trivial.
is
large.
Assuming an overnight
But
risk of
not unreasonable, one can see that tax related trading should be
treated not as a pure arbitrage, but as a risky investment.
Second, transaction costs must be taken into consideration, given that the potential gains are only a
fraction of the dividend
The cum-day
In this
is
the
last
and are therefore
relatively small
compared
to the stock price. Indeed, the
date thai the stock trades with the dividend.
paper we refer to a lax-induced trading strategy as a tax 'arbitrage'. Academics usually defme as an arbitrage strategy a trading
no initial funds and yet provide positive profits. However, a more recent literature recognizes that, in the presence
strategy which requires
of frictions, 'arbitrage' strategies are often risky investment strategies (see
Tuckman and
Vila (1992, 1993)).
6
typical (retail)
brokerage costs for
common
stocks averages
2%
on the
dollar
amount of the
trade
while the bid-ask spread for actively traded stocks averages around .5% (see Ayiagari and Gertler
(1991)). This implies that dividend capture
and that only
large transactions costs
amount of
Finally,
tax related trading
is
probably not profitable for small investors
liquid stocks with a high dividend yield will
our model indicates that
as
the other hand,
its
if
market
risk
and transactions costs interact
To summarize
i)
risk
volume but the
the discussion so
reduces volume. At
volume since market
effect of the later will
this stage,
only point
(see for instance Gallant, Rossi and
risk
can be hedged.
is
as important
market
risk
and the
be smaller.
the main theoretical and empirical points of the paper are that
far,
iii)
Tauchen
ii)
transactions costs reduce
deserves comment.
empirical evidence shows that on regular trading days,
On
a significant
very interesting way. If
too costly to hedge, then the stock's market risk
is
investor's heterogeneity in valuation creates volume,
risk
in a
idiosyncratic risk in restricting volume. In the intermediate case, both the
idiosyncratic risk will affect
face
around the ex-day.
transactions costs are negligible, market risk does not affect
On
show
who
(1991)).
volume and
There
is
volume and
To our knowledge,
iii)
the existing
volatility are positively correlated
no theoretical contradiction however.
regular trading days, investors trade for risk sharing purposes, but because of transactions costs
they do not achieve a Pareto optimal risk sharing (see Heaton and Lucas (1992) for instance).
risk increases, the cost
increases.
By
When
of deviating from the Pareto optimal holdings also increases. Therefore volume
on the
contrast,
ex-day, investors trade
away from
their optimal holdings
and hence
risk
reduces volume.
In our empirical study
we
excess of regular volume.
and across stocks. In
consider the abnormal volume around the ex day, that
We
find that the
particular, the
abnormal volume
abnormal volume
is
is
much
significant
is,
the volume in
and varies both over time
larger for high yield stocks.
This
is
7
consistent with our theory since tax induced trading in high yield stocks
low
yield stock for the
same
and transactions
level of risk
costs. It
is
is
more
profitable than in a
also consistent with previous
evidence by Lakonishok and Vermaelen (1986).
Next,
we document
volume but
hedge
that both the
market
that the impact of the
risk
market
their transactions but only partially
and the idiosyncratic
risk
is
lower.
risk negatively affect the level of
These findings indicate that investors do
because of transactions
costs.
We then turn to the direct relationship between transactions costs and trading volume. Using the bidask spread as a measure of transactions costs and dividing stocks in three groups according to their
bid-ask spread,
we
find that
abnormal volume
is
about
five times higher for
low transactions costs
stocks than for high transactions costs stocks. This simple unconditional result extends to a
multivariate cross-sectional regression analysis. Using the abnormal
volume
as the left
variable with dividend yield, beta, idiosyncratic risk, and bid ask spread as right
the latter
To
is
found to have
interpret these results,
relationship
proportionally
So
far
remember
Stoll
that
costs
we
are talking about abnormal volume. While the negative
(1989)), our results indicate
that
transactions costs inhibit trading
in 'arbitrage' transactions
than on normal trading days.
that tax 'arbitrage' strategies subject investors to both risk
Derivative securities, such as options and futures, allow investors to hedge,
relatively small cost.
We
side variables,
and volume has been documented elsewhere (see for instance
more when agents engage
we have seen
side
a significant negative coefficient.'
between transactions
Demsetz (1968) and
hand
hand
and transactions
i.e.
reduce
costs.
risk, at a
provide both time series and cross-sectional evidence that the presence of
9
This negative relationship between transactions costs and abnormal volume can also be detected from time series evidence. In may
1975 brokerage commission schedules were changed from fixed to negotiated, thereby substantially reducing the cost of transacting,
especially for large traders. Consistent with
after that date.
Lakonishok and Vermaelen (1986), we find that abnormal volume around the ex day goes up
8
We
options increases abnormal volume.
abnormal ex-day volume on
exhibit
this particular stock
more abnormal volume than
Another implication of our model
stock going ex
is
lower
find that after
when many
an option on a particular stock
goes up.
is
listed,
the
We also find that stocks with listed options
similar stocks without listed options.
is
that,
because of transactions
stocks are going ex. This
is
costs,
the abnormal volume on a
because each transaction subjects the
investor to additional risk while the risk bearing capacity of investors
is finite.
Our
empirical findings
are consistent with this implication.
we
Finally,
provide time series evidence that a greater degree of heterogeneity creates abnormal
volume. Our results indicate that heterogeneity has a significant effect on trading volume, especially
in stocks
of trade
where
is
corf>orate
and
significantly higher
institutional traders are
when
more dominant.
We also show that the volume
corporations have capital gains to offset the tax arbitrage capital
losses.
The paper
and
its
section
is
organized as follows. Section
II is
devoted to the presentation of the theoretical model
empirical implications. Section III presents the data
IV while
section
set.
V contains some concluding remarks.
The
empirical results are detailed in
9
n.
A THEORY OF THE EX-DIVIDEND DAY TRADING VOLUME
We
describe the determination of trading volume around the ex-dividend date in an equilibrium
model along the
trading in
on two
K+1
lines
of Michaely and Vila (1991).'" Agents
bond and
assets, a risk free
dates: the
cum-day which
is
the
last
K risky dividend
in this
economy
are assumed to be
paying stocks. These assets are traded
date where stocks are traded before the dividends are
paid and the ex-day which occurs after the dividends are paid. After the ex-day
all
assets are
liquidated."
The
stock prices at liquidation are represented by an exogenous
random vector </. This random vector
can be written as
V'
where
and
u,
assume that
u,
u,
=
V
-I-
Uj
-I-
U|
denote the information realized
and
Q,
are
mean
ex-day and liquidation respectively.
at the
zero, independent normally distributed
variance -covariance matrices o^ and
o),,
respectively.
The
random
We
variables with
variables p^ and p^ denote the stock price
vector at the cum-day and at the ex-day, respectively. In addition, the stocks pay a
known
dividend
d at the ex-day. Finally, the risk-free bond pays a constant interest rate which for the sake of the
exposition
is
There are
N
set equal to zero.
agents in the economy, n=l..N. Each agent n
stocks and b" bonds.
The
shares would take place
initial
where
it
share allocation (x\..3c'^)
is
is
initially
endowed with
?
shares of
Pareto optimal so that no trading of
not for the payment of dividends and the differential tax treatment
of dividends and capital gains described below. All agents are subject to proportional taxes on both
T4owever, unlike Michaely and Vila (1993), agents may trade
"As we
shall sec,
our simple model could be embedded
in
more than one
in a infinite
risky asset
horizon model.
and face transactions
costs.
10
dividends and capital gains at rate at rates tS and
when agent n
In addition,
cost of Ck per share.
The
trades at the cum-day in asset k, he
not as restrictive as
transaction, for
income,
i.e.
it
sounds. Indeed
We
subject to a proportional transactions
is
denoted by
c".
We make the
not subject to transactions costs. This assumption
to assuming that,
cum-day and
selling
when doing
taxes capital gains net of transactions costs. Finally,
agent k maximize his expected
utility
of after-tax
constant absolute risk aversion with coefficient
2.1.
Equilibrium prices and volume
We
first
final
a
b"
-I-
where
x^
Agent
n's taxes are
and
1"
where p "
x^
denote agent
= tH
is
wealth and that his
we assume
utility
- c"'
n's
Ix^-x"!
-I-
function exhibits
p°.
+
d'x^
p.'Cx^-xJ)
-I-
+
is
given by
^K
(1)
holding at the ex-day and the cum-day respectively.
(P'-P^yx"
+
(Pc-PcVx^
+
(v-p7x:
investor n's tax basis for asset k
{b"
that each
given by
Combining equations
W^T =
p/Cx-'-x^)
trip
capital gain
describe agent n's intertemporal budget constraint. Agent n's before-tax wealth
W"^ =
round
at the ex-day, transactions costs
it
assume that transactions costs can be deducted from taxable
IRS
that the
is
amounts
it
at the
example buying a share
are paid upfront.
is
vector of transactions costs faced by agent n
simplifying assumption that trading at the ex-day
is
respectively. All taxes are paid at liquidation.
t],
(1)
and (2
),
[p,-T,(p,-p")]'?}
Equation (3) says that after-tax
we
+
final
(i.e.
-
c"'
Ix^-^l
the price
+
tS d'x:
initially
(2)
paid for the xj shares).
write agent n's final wealth after taxes, W^-r as:
(l-T^{(p.-p,yX^
+
(v-p.yx^
wealth equals after tax
net of transactions costs plus after tax dividend income.
and by o" the tax induced preference
]
-
initial
C"'
|X.-?|}
+
(1-T,)d'x^.
(3)
wealth plus after tax capital gains
We denote by W^ the
for dividends vs. capital gains, that
is,
after tax initial wealth
11
1
-t"d
1
-t"
(4)
i
With these notations, agent
W^T = WS +
The
next step
is
(1-t",)
wealth after taxes can be written as
{(p.-p,+a"d)'x^
-
c"'
|x^-?|
+
(v-pjx:}
to describe the equilibrium prices and quantities
risk aversion assumptions,
and constant absolute
=V+U
(5)
.
on the
ex-day.
Given the normality
standard derivations yield that
-
1
-
p
n's final
-_<i),X
and
x^ =
_x
= x
with the following notations:
1
0" =
is
the tax-adjusted risk tolerance of agent
n,
N
=
is
0"
53
the aggregate risk tolerance and
N
X =
is
£ X"
the aggregate supply of stocks.
optimal risk sharing.
framework where
Finally,
we
denote by
p, the
p =
^'
-
Hence our ex-day
risk sharing
derive the
As expected, on
demand
is
trading equilibrium can be
reverts to the initial Pareto
embedded
in
an
infinite
horizon
for stocks
on the cum-day and the equilibrium
prices
and volume.
We
i.e.
-
1
_
economy
always optimal except around taxable distributions.
expected ex-day price
V -
the ex-day the
G),X
.
'
Given the assumptions of normality and constant absolute
risk aversion,
and equation
(5),
agent
n's
12
problem consists of maximizing
(p^-pjv
The
first
*
«"dv
order condition
- (c-y
€°
is
'
defined as
Kt>T^t
€l
=
-1
if
Kt<^t
-1
s
if
Kt =
the
first
6"
is
=
1
?k
as
order condition, the equilibrium price
[P.
(6)
=
if
^
2^«y<oX-
^
\
Pe
where
/»n
=
and the vector c°*€"
From
_ o)X
el
€",
-
is
- p + a"d - c"®€" p
re
re
where the vector
|<-?|
satisfies
-Sd -lojx] -Y^b^C^e"
(7)
the share of agent n in the economy, as measured by his risk tolerance, that
«" =
is
!"
e
and a
is
the average preference for dividends
vs. capital
gains
i.e.
N
S = 5^
6" o"
.
Equation (7) decomposes the cum-day price into two components. The
brackets)
is
the cum-day price in the absence of transactions costs.
It is
first
component
equal to the expected (risk
adjusted) ex-day price plus the after-tax market value of the dividend vector, od.
component measures the impact of
transactions costs
buyers face larger (lower) transactions costs than
(higher) than in the absence of transactions costs.
on the ex-day
sellers,
(within
price. Its sign
is
then the cum-day price
The second
ambiguous:
will
If
be lower
13
Plugging (7) into the
first
order condition yields the equilibrium holdings
D>1
The
term
first
equation (8) represents the investor's optimal trading strategy
in
transactions costs.
The
interpretation
and capital gain income of agent n
is
very simple.
If
in
the absence of
the tax differential between dividend income
greater than the market average, he will hold
is
more of the
dividend paying assets than he usually would have held during non-dividend paying periods.
second term represents the adjustment of his strategy due to the
be different because other traders face transactions costs and
The
difficulty
upon the
with equations (7) and (8)
sign of individual trades.
In what follows
we
will
The zero transactions
We
first
volume vectors on the cum
+
he himself faces transactions
that the variables el are
in
general
it is
the equilibrium price will
costs.
endogenous since they depend
impossible to solve for
el.
costs case
consider the case where
p
ii)
i)
analyze the properties of the equilibrium in a simple one factor model.
2.2.
p' =
Hence
is
fact that
The
all
day, p^
transactions costs are zero,
i.e.
c^sO. In this case, the price
and
and V^ are given by
od -_ o)X
(9)
and
V-
=
^[E
|8"(«"-S)i] |o;>d|
(10)
.
Given the normality assumption, the tax-adjusted
market
risks
and not upon idiosyncratic
not affected by the stock's market
a symmetric
one
risk.
factor case where:
risks.
To
CAPM holds so that stock prices depend only upon
By
contrast, the trading
volume on any given stock
see this point in the simplest possible manner,
we
is
consider
14
(i)
on the ex day u^ can be written
the information shock
u.k
=
6
+
nt
with 8 independent of the
with variance o^
(ii)
with variance a^, and the
fjk's
the supply of
portfolio comprises the
same
pays the same dividend
d,
In this case the matrices
dollar
all
the
to one), so that the
same (normalized
and
o),
o).'
(iii)
a fraction
s=S/K of all
market
the stocks
T
1+T
T
T
1+T
T
T
1+T
T
.
T
1+T
can be written
T
.
and independently distributed
while the other stocks do not pay any dividend.
T
T
is
identically
amount of each stock and,
1+T
b)
stocks
fj^'s
and
"'
-4)
1-4)
-4)
-4)
1-4)
-4)
-4)
1-4)
-4)
-4)
1-4)
.
-4)
=P
-4)
.
-4)
i-4>j
with
T =
-^
and
=
(|)
From equation
(8) with c^^O,
— e"(a" - a) (1
-
—L1+Kt
a"
_ 6"( a" - a)
and
-s)d
s
d
K large
(i.e.
K4>
=
1),
investor n's net trade
on each stock which pays
a dividend
on the cum day equals
and
(H-a)
on stocks which do not pay dividend.
(ll.b)
Investor n's trading strategy can be easily described. If investor n likes dividends
average investor,
i.e. if
o">o, then the investor
will
more than the
buy dividend paying stocks and hedge by
non- dividend paying stock. As can be seen from equation
(11), the
selling
volume does not depend upon
the market risk a^-
In addition,
if s is
small
compared
to one,
i.e.
when
the f)ortfolio of stocks going ex
of the market, the volume on each individual stock going ex does not depend upon
are going ex.
is
a small fraction
how many stocks
15
To summarize, when
Implication
1:
transactions costs are zero our
The trading volume
model
yields the following testable implications:
an increasing function of the degree of tax heterogeneity
is
in
the economy.
The
intuition
behind
this
proposition
is
tax heterogeneity increases, the gains
The trading volume
quite clear.
As
the differences in valuations widens,
i.e.
as the
from trade increase. Hence trading volume goes up.
an increasing function of the dividend
Implication
2:
Keeping
other variable constant, as the dividend yield increases the gains from transfering the
all
is
yield.
dividend from high tax investors to low tax investors also increases.
Implication
3:
The trading volume
is
a decreasing function of the idiosyncratic risk o^
Investors buying (selling) dividend paying stocks find themselves over- (under-) invested in these
stocks.
As
a result they are exposed to the idiosyncratic risk of these stocks.
Implication
4:
The trading volume does not depend on the market
risk
component of the stock
risk
oi..
In the absence of transactions costs, the market risk can be costlessly
inhibit trading. Implications 3
volume
differently.
trading
volume and not
Implication
5: If
Market
and 4 combined with equation
risk affects prices
(9)
show
hedged and hence does not
that risk affects prices and
and not trading volume while idiosyncratic
risk affects
prices.
only a small fraction of stocks are going ex, the trading volume on any stock going
ex does not depend
upon the number of stocks going
ex.
16
Since hedging the market risk
across stocks.
Hence
costless, the additional risk in the ex-day 'arbitrage'
is
the trading activity
on one stock
is
is
indep)endent
not affected by the trading activity on
another stock.
23. The role of transactions costs
To
Transactions costs limit investors' tax related trading.
likely to
be
significant, consider a
see that the effect of transactions costs
is
$100 stock which pays a $1 quarterly dividend and assume that
o=.8." With these numbers, a corporate investor («"=1.72) makes $.92 per share. Hence the return
on
this strategy
is
about .92% which
makes .2% which
remarks above,
is
we
With transactions
is
comparable to transactions
costs.
A tax exempt investor (o"= 1)
well below the range of transactions costs for most investoi-s.
Given the casual
expect transactions costs to be a significant factor in the ex-day trading
costs,
the equilibrium prices and quantities are
Transactions costs limit the
trading activity of those
number of
who do
investors
participate.
The
who
much harder
to
activity.
calculate.
participate in the ex-day trading as well as the
effect
on volume
is
clear:
volume
is
reduced.
On
the
other hand, since transactions costs limit the trading of both buyers (o">o) and sellers (o"<a) the
resulting effect
To
see that,
we
on
prices
is
somewhat ambiguous."
construct a symmetric example along the lines of the one presented in section 2.2.
In addition to the assumptions in section
2.2.,
preference parameter a" (with probability 8")
This value
is
consistent with Elton and
"See Vayanos and Vila (1993)
is
we assume
that the distribution of investors' tax
symmetric around a and that
Gruber (1970), Michaely (1991) and our
for a discussion of the relationship
all
results in section (3).
between transactions costs and
prices.
investors face the
17
same
on every
transactions costs c^^c
The symmetry assumption makes
asset.
the model tractable which
is
unusual for multi-assets models with
transactions costs." In particular, prices are not affected by transactions costs and the tax-adjusted
CAPM holds. This allows for a simple description of trading strategies and therefore market volume
(the details of the derivation can be found in apjsendix A). Agents can be divided in five endogenous
groups characterized by two constants
0<t<h which depend among
other things on the level of
transactions costs and in the dividend amount:
(i)
\a"-a\ ^
The
t:
investor's valuation of a dollar of dividend
price of a dollar of dividend. Trading
(iia)
t
<
o"-o ^ h:
hedging
risk
this case,
(iiia)
h
<
«"-«:
-t:
The
too costly compared to the benefits,
dividend arbitrage subjects the investor to the total
of the portfolio of stocks going
-h i a"-o
close to the market
investor buys dividend paying stocks but does not hedge because
too costly. In
is
(iib)
<
The
is
is
ex.^'
Similarly, the investor sells dividend paying stocks
investor's private valuation of dividends
is
and does not hedge,
quite different from the
market's. Therefore he takes a large position in dividend paying stocks and hedges a portion
of the market
risk that
he undertakes. The optimal hedging strategy (derived
equates the marginal cost of hedging,
marginal cost of the market
risk.
i.e.
in
appendix A)
the transactions cost, to the marginal benefit
i.e.
the
In addition, the optimal arbitrage decision equates the
marginal profit net of transactions costs to the marginal cost of the additional
risk.
Since the
marginal cost of the additional risk equals the marginal cost of the idiosyncratic risk plus the
14
See also Fremault (1992) for another example.
Since transaction costs are proportional diversification
is
not costly:
The
investor prefers to buy all dividend paying assets than just
a subset. In the presence of fixed transactions costs, the investor will trade only a subset of the dividend paying stocks (see Fremault (1992)
for a similar result).
18
marginal cost of the market
we
risk,
obtain the
order condition: marginal profit of
first
arbitrage equals marginal cost of the idiosyncratic risk plus marginal cost of hedging.
that the investor's trade
independent of the
is
function of the idiosyncratic
o°-o
(iiib)
Given
this
<
-h:
investor sells dividend paying stocks
risk
and a decreasing
of investors,
we can
and hedges the market
risk.
derive the following testable
A for details):
The trading volume
6:
market
follows
risk,
relatively simple classification
implications (see appendix
Implication
The
level of the
It
is
lowered by the presence of transactions costs.
In the presence of transactions costs such as brokerage commissions and bid-ask spreads, investors
trade less and hedge
also
more
As
a result, transactions costs
make
tax 'arbitrage' not only
more
costly but
risky.
Implication
4':
The trading volume
and the idiosyncratic
the stock risk
The
less.
is
risk.
intuition for implication 4' follows
different groups.
The
trading of
all
a decreasing function of both the market risk
The
5':
effect of idiosyncratic risk is stronger.
from our previous discussion of the trading strategies of the
active agents
risk affects only the trading described in (iia)
Implication
component of
is
and
affected by the idiosyncratic risk while the market
(iib).
The trading volume on each individual stock
is
a decreasing function of the
number
of stocks going ex.
when
a large
portfolio contains less idiosyncratic risk.
Hence
This
may look
counterintuitive since
number of stocks are going
there will be
more
ex, the
dividend paying
aggregate dividend arbitrage
19
trading.
But the trading volume per stock
optimal amount of market risk
limited.'*
presence of transactions costs agents take smaller positions. This
Finally, in the
for agents
is
be lower since agents' willingness to assume a non-
will
who do
not hedge. As a result, the idiosyncratic risk
is
is
less a factor in
true in particular
the determination
of the trading volume.
Implication
7:
In the presence of transactions costs, the trading volume
is less
sensitive to the
idiosyncratic risk.
The model presented
in this section relies
necessary for analytical tractability.
First,
is
we have assumed
Two
all
assumptions
that the initial allocation
We
the only source of abnormal volume.
that
on several
also
specific assumptions that
in particular
if
not
deserve comment.
was Pareto optimal. As a
assumed
were useful
result, tax
heterogeneity
that transactions costs are paid
up front so
investors revert to their initial position at the ex-day. For example, long term investors sell
dividend paying stocks at the cum-day and buy them back at the ex-day. In the traditional literature
on the ex-day (Elton and Gruber
(1970)), long term investors trade around the dividend
precisely liquidity reasons. Sellers trade at the
priori reason to believe that there are
term investors behave as
in
cum
while buyers trade at the ex. Since there
more long term
our model.
sellers
we have
An
asseu
If
analogous situation occurs
in
a
a-
'^
portfolio theory:
each of them than he would
in the
presence of transactions
if
A constant absolute risk aversion investor having access to two positively correlated
he had access to only one of them. However the
total
amount
invested will be higher.
non Pareto-optimal initial allocations (which allows for long term traders as
minor modification (see Michaely and Vila (1991)).
transactions costs are zero, assuming
is
no
considered a simple symmetric model. While a more general model with a non-
will invest less in
Gruber (1970))
is
for
than long term buyers, as a group, long
Second, in order to obtain a closed form solution for trading volume
costs
payment
in
Elton and
20
symmetrical distribution of tax rates, cross sectional variation of factor loading and transactions cost
might yield
new
In appendix B,
insights,
we
we show
transactions costs.
believe that our empirical implications are robust to these specifications.
that our results hold in a
model with non
unit beta
and
differential
21
in.
DATA
Data on dividend
CRSP
distributions, ex-dividend dates,
and
volume are compiled from the
daily trading
1991 daily master tapes. Stocks are included in the sample
they are listed on the
if
NYSE
or
AMEX between January 1%3 and December 1991 and pay a taxable cash dividend (distribution types
1212 through 1292 on the
6,
and days
-1-6
Ex-dividend day events are included in the sample
to -1-45), to estimate the expected daily trading
the trading volume
(2)
final
tapes).
if:
there are at least 40 daily volume observations in the estimation period (days -45 to
(1)
The
CRSP
is
positive in at least
one of the
sample consists of 155,302 taxable cash dividend
calculated as the dividend
amount over the cum-dividend day
1 1
volume and,
days around the ex-day.
distributions.^*
price.
-
We
Dividend yields are
use the average of market
value of equity in the 80 day estimation period as a proxy for the firm's market capitalization around
the event.
1990
Our
ISSM
we
invsetigation also requires estimates of bid-ask spreads.
transaction
files
We use data from the
1988-
to calculate the average bid-ask spread.
have repealed the entire experiment for only ordinary quarterly dividends. The results are practically the same as reported
the paper. This
is
not surprising given that over
91%
in
of the dividends in our sample are quarterly dividends (2.30% are monthly, 2.38%
are categorized as unspecified, 1.2% are semi-annual, 1.68% are special, and no other category has more than 0.3% of the observations.)
Also the inclusion of events with zero trading volume on the ex-day, does not affect any of our conclusions. Finally, to ensure that our
results are not due to 'spillover' of abnormal volume from the announcement date, we included only events in which the announcement
dale was at least four days prior to the ex-drvidend day. The sample contains 138,142 ex-day observations (about 89% of the onginal
The cumulative abnormal volume for this sample is 94.7% (t = 23.46) compared with a CAV of 100.6% for the entire sample
and the ex-dividend day abnormal volume is 14.00% (t = 16.71) compared with an AV of 14.7% for the entire sample. We repealed
several of the experiments described below with this subsample. None of our conclusions changed.
sample).
22
IV.
4.1.
EMPIRICAL RESULTS
Summary
Table
I
(CAV),
statistics
contains
in the
and variable
summary
definitions.
on the abnormal volume (AV), the cumulative abnormal volume
statistics
eleven days centered around the ex-dividend day, and the cumulative abnormal volume
weighted by the market capitalization of the firms going
we
first
event
i
calculated the
is
mean volume
defined as the
mean
daily turnover for days -45 to -6
JQ
and
T
is
number of days with
the
in the
valid
event period
AV.
=
"
daily
N
is
the
Alternatively,
capitalization
to -1-45:
-
1
t
,
e
=
one may argue
that
Hence we
also
-5,...,
is
in
day
volume
as
+5.
calculated as
AV,
i-i
1:1
,
N
t
e -5
valid observations in
+5
day
t
more weight should be given
much
i
in the estimation period.
calculated the abnormal
TO
'L
ATO
E
number of events with
turnover in those stocks implies
smaller stocks.
volume observations
we
for
J
abnormal turnover for the entire sample
AV
where
-1-6
The mean volume
the daily turnover (shares traded relative to shares outstanding) for security
is
Then, for each day
The mean
and
these variables,
Ce|-45.-61U|^6.>45|
^
i
t
period for each event.
in the estimation
A
where TO;,
(WCAV). To compute
ex,
to larger stocks since a higher
higher abnormal dollar volume than the same turnover for
computed the average
daily turnover,
weighted by the stock's market
23
N
WAV
'\
=
'_
e
t
,
-5,...,
+5
EC,
i-l
where
C,
is
the stock's market capitalization calculated as
Z.^
It
It
te(-«.-«)U|*«,-45]
T
and
P|,
and
S|,
are the stock price and
The cumulative abnormal volume
the event that
is
number of shares outstanding
the
sum of the
daily
for event
i
in
day
respectively.
t,
abnormal volume for the eleven days around
is
-5
CAV
=
I
V
^
^
AV
.
It
t.-5
The average cumulative abnormal volume (CAV), and
volume (WCAV), are defined
for the
in the
same way
as
AV
the weighted average cumulative abnormal
and
WAV for abnormal volume.
volume behavior around the ex-dividend day are calculated using the
T-statistics
cross-sectional estimates
of the variance of abnormal volume."
For the entire sample, the ex-dividend day volume
day period, the cumulative abnormal volume
both are significant with a
the sample
is
1.001%.
t-statistics
is
is
14.7% higher than average, and
more than 100% higher than
of 24.62 and 33.07 respectively.
Also reported
in the table are the
volume
in the
eleven
regular trading volume,
The average dividend
statistics
when
yield in
the sample
is
partitioned by dividend yield. Observations are sorted into three groups according to their yield, and
means are calculated within each
yield groups are 1.70%,
yield group.
0.89% and 0.41%
Vorajcayk, Lucas and McDonald (1991) use
(see also Collins and
Dent (1984).)
this
The
dividend yields for the high, medium, and low
respectively.
Both the ex-day abnormal volume and the
procedure to examine price behavior around seasoned equity issue announcements
24
cumulative abnormal volume increase monotonically with
yield.
A significant difference
observed only between the medium and high yield groups: 6.17%
fact, for
the high yield group, the
medium
yield group.
CAV. For
unweighted
CAV
The
is
almost 200%, and
size -weighted cumulative
is
between
size
and transaction
finding of positive association
33.14% abnormal volume. In
abnormal trading volume
example, for the high yield group,
is
about three times higher than for the
WCAV
is
discussed later, the higher size-weighted volume
As
(196.3%).
association
The
CAV
vs.
however
higher than the
is
449%, more than double the
may be
related to the negative
costs.
between dividend
yield
and abnormal volume
is
consistent with
the model's implication (implication 2), as well as with several prior findings. Using a sample of 1200
Grundy (1985)
ex-dividend days,
greater than 1.2%,
test is reported).
is
finds that the trading
volume
for the
group with dividend yield
higher than for the group with dividend yield less than 1.2% (no significance
Similarly,
Lakonishok and Vermaelen (1986) report a higher increase
in
abnormal
trading in the three days preceding the ex-day of high yield stocks.
From Table I we can
see that trading due to the upcoming dividend does not occur only
day and on the ex-day, but
we
starts several
on the cum-
days before the ex-day. Therefore in subsequent analyses,
report the results using the cumulative abnormal trading volume in the eleven days around the
ex-day.
The second
sample.
part of Table
The
I
contains information about the bid-ask spreads of the stocks in our
bid-ask spread
transactions costs.
(1983) and
is
used as one of our proxies for cross sectional differences in
There are several reasons why
of the traders that are involved
bid-ask spread
is
in
it
is
considered as a good proxy.
First, for
many
ex-day trading, such as corporations and institutional investors, the
the major component of their transactions costs.
Amihud and Mendelson
Second, as Stoll and Whaley
(1986) show, the correlation between total transactions costs and
25
the bid-ask spread
show
(1990)
very high.
is
that the ex-day excess return
is
NASDAQ
sample of
Finally, using a
firms,
Karpoff and Wallding
positively correlated with the bid-ask spread, consistent
with the effect of transactions costs on ex-day returns in the presence of 'arbitrageurs'.
The ISSM data
includes intra-day bid-ask spreads, which were used to estimate the average bid-ask
spread for each event
in
our 1988-1990 sample. For each day
in the estimation period,
opening, mid-day, and closing bid-ask spread to calculate a daily spread.
i
is
Ask
3
AC
_
^
V^
^
V^
for event
1,
,..,5
3
,.,
- Bid
'ji
where
j
=
open, mid-day, or close transaction,
number of days
Table
I
contains
in the estimation
some
statistics
the period 1988 to 1990.
is
likely to
are 1.53% and 1.32% respectively, and the
be lower than what
is
described in Table
many of
It
should be noted however that the actual bid-ask
I.
First, since
the ex-dividend
is
a
non
the trades are not motivated by private information but rather by
private valuation, the adverse selection
component of the bid-ask spread
Indeed Koski (1991) show that the average
62%
is
on the bid-ask spread, using a sample of 15,900 ex-dividend day events
0.%%.
estimates that over
'
period with valid observations.
The mean and median spread
around 0.65%, compared with
.
iji
the day relative to the ex-dividend day and T,
is
information event and
days.
is
iji
mean spread
standard deviation of the
spread
t
'ji
l.^j^ ^gjj
*
'\
in
The mean spread
use the
defined as the average daily spread over the estimation period:
TJ
the
we
a regular
relative bid ask spread
day bid-ask spread of 1.53%
of the transactions on the
NYSE
in
is
lower than
in 'regular'
on the cum and ex-day
our sample.^
is
Lee (1993)
are executed between the bid and ask
quotes, and therefore argues that the quoted bid-ask spread overstates the actual spread. In addition.
Supporting evidence to
Madhavan and Smidt (1991)
this
claim can also be found in
Madhavan and Smidt (1991) and
Castanias,
Chung and Johnson (1988).
Chung and Johnson
find that the informativeness of the trade significantly affect specialist behavior. Caslanias,
(1988) report that the bid-ask spread for informationless trades
in
options are
much
smaller than for normal trades.
26
Koski (1991) brings direct evidence from the ex-day
activity, that
some
large traders are able to
However,
substantially reduce the actual bid-ask spread through bilateral bargaining.
cross-sectional
differences in the observed bid-ask spreads
reflects
the
actual
as long as the
cross-sectional
differences in transactions costs, our conclusions are not altered.
4.2. Risk,
As
Transactions Costs
and Trading Volume Around The Ex-Dividend Day
has been theoretically established in the previous section, the volume of trade depends,
other things on the risk and the amount of transactions costs involved
these two variables
on the trading volume, however, are
ex-dividend days associated with
more
however,depending on whether the
is
The
the trading.
interrelated. First, the
effect of
model predicts
that
experience lower trading volume. This relation varies,
risk will
risk
in
among
and
idiosyncratic or systematic (Implications 3
4).
These
predictions are tested empirically in section 4.2.1. Second, a change in transactions costs has a direct
effect
on the volume of trade when
investors have differential valuations of cash flows. Implication
6 states that as the level of transactions costs increases, the abnormal trading volume
The
direct relation
between transactions
and trading volume
and transactions costs and
their effect
have no effect on trading volume
in the
examined
presence of transactions
if
costs.
on trading volume. The model implies
there are
On
in section 4.2.2.
no
risk
that systematic risk will
transactions costs, but will have a negative impact
have a negative effect on trading volume with or without transactions
and transactions costs
between those
their effect
on trading volume: the higher the
risk factors
The
the other hand, the model implies that the idiosyncratic risk
interaction
results in
will
costs. In addition, the
an opposite prediction about
level of transactions costs, the
of the idiosyncratic risk on trading volume and the higher
The
is
and perhaps the most interesting conclusion of the model concerns the interplay between
third,
will
costs
will decrease.
lower
will
be the impact
be the impact of the systematic
intuition behind the result that idiosyncratic risk has a lesser role
when
risk.
transactions costs are
27
high
is
that agents will tend to
These implications are tested
The
4.2.1
3,
positive effect
less,
and consequently assume
in section 4.2.3.
4 and
on the
4' state that
level of
both the idiosyncratic
of the idiosyncratic risk
is
stronger.
eleven days around the ex-day.
idiosyncratic risk, normalized by the
latter
risk
have a non
abnormal trading volume. In the presence of transactions
regression analysis, reported in Table
The
and the systematic
risk
Implication 4 states that both risk factors have a negative effect
in the
significantly smaller positions.
of risk on trading volume.
direct effect
Implications
hedge
We
II.
examine the
The dependent
The independent
market
risk at
on trading volume and
effect of these
variable
is
that the effect
two types of
risk using a
the cumulative abnormal volume
variables are the stock's dividend yield, the
the same time period, and the systematic
two variables are calculated during the estimation period from
As predicted by the model, both the
costs,
idiosyncratic risk coefficient
risk, beta.
daily return observations.
and the beta coefficient are negative
with values of -0.49 and -0.33 respectively. Both coefficients are significantly different from zero with
a t-statistics of 18.65
and 7.82
respectively.
The
absolute value) than the beta risk coefficient.
idiosyncratic risk coefficient
The
difference
Finally, consistent with prior analysis, the yield coefficient
t-statistics
4.2.2.
As
The
who
about
50%
higher (in
significant with a t-statistics of 3.17.
positive
and highly
significant with a
of 8.51.
role
of transactions
costs.
the cost of trading increases, fewer investors will find
those
is
is
is
find
it
it
profitable to trade
around the ex -day, and
profitable to trade will trade for lesser amounts, (Implication 6).
implication of this proposition
is
The
cross-sectional
that stocks with lower transactions costs will exhibit higher
abnormal
28
trading
volume around the ex-dividend day." To
we
end,
this
first
divide the sample into three
subgroups according to the cost of trading, estimated by the security's bid-ask spread, [see equation
Indeed as reported
(12)].
in
the
last
row of Table
Panel A, as transactions costs increase, the
III,
abnormal volume decreases. For the low transactions costs group, the cumulative trading volume
519.68% higher than the average trading volume, and
highest transactions costs. For
However,
as has
all
is
groups, however, the
is
only 108.2% higher for the group with the
CAV
is
significantly greater
been established before (implication 2 and Table
than zero.
1) the incentive to trade increases
with dividend yield as well. In order to distinguish between the yield effect and the cost of trading
effect,
we
average bid-ask spread. The
2.08%
Each event
divided the sample into 9 categories.
for the high-
mean
its
dividend yield and
dividend yield for the three categories are 0.387%, 0.805% and
medium- and low-dividend
contains 5300 observations.
categorized by
is
yield groups respectively.
We sub-divided each of the
Each dividend
yield
group
three subsamples by the cost of transacting,
estimated by the bid-ask spread around the ex-day, and measure the abnormal volume for each of
those 9 groups.^
Our model
predicts that the
group as transactions costs decrease. Moreover,
volume of trade should increase within each
if
there
the high yield stocks, then the increase in the abnormal
is
more
'arbitrage'
yield
and dividend capture
volume should be more pronounced
in
in
those
stocks than in the lower yield stocks.
The
results indicate that the
group with the highest
yield
and the lowest cost of transactions
experience the highest volume of trade around the ex-day: more than 15.5 times the normal trading
volume. For the high yield group (third column), an increase
21
Lakonishok and Vennaelen (1986) show
in transactions cost
that reduction in transaction costs increases the overall trading
day.
^Because of data
limitation
on bib-ask spread, our sample contains events from 1988-1990
only.
has the biggest
volume on the ex-dividend
29
(negative) effect
group
is
on abnormal volume. The trading volume
only 2.3 times the regular trading volume. Consistent with the concentration of short term
we
traders and corporations in the high yield stocks,
medium
for the high yield/high transactions cost
yield stock are not affected
by increases
see that while the trading volume
in transactions costs to the
in the
same extent
low and
as the high
yield stocks.
In order to use a longer period in our analysis,
costs,
we
construct an additional measure of transactions
namely the market capitalization of the firms that are going ex. The use of market capitalization
as a proxy for the cost of transacting
correlation
largely motivated by the empirical findings of negative
between the bid-ask spread and market
through 1990
B shows
is
we
capitalization.
find that the correlation coefficient
a similar pattern to
what has been described
increases as the cost of transacting
group than for the low
is
is
-.298.""
in
As with
Indeed the
in the
results in
period 1988
Table
III,
Panel
Panel A: The abnormal volume of trade
reduced, and this increase
yield group.
For the events
is
more pronounced
for the high yield
the case of the bid-ask spread, the group that
is
associated with the lowest transactions costs and highest dividend yield exhibit the largest abnormal
trading volume: almost 5 times
more
trading than in regular days. Also, for the largest firms
lowest cost of trading), abnormal volume increases monotonically with yield. For the
size group,
however, there
is
no much difference between the trading volume
(i.e.,
medium and low
for the
medium and
low yield stocks.
Our
long sample period enables us to observe a profound structural change
to test
its
effect
on the incentives
to trade
around the ex-day. The
May
in transactions costs
1975 change
in
and
commission
schedules, from fixed to negotiated, substantially reduced the cost of transacting, esp)ecially for large
^Ve are not the first to use market capitalization as
and Karpoff and Walkling(1988) use a similar measure.
a proxy for transactions costs in this context.
Lakonishok and Vermaelen (1986)
30
traders. Therefore,
one would expect an increase
Indeed, as reported in Table FV there
is
a
the abnormal volume of trade after 1975.
in
marked increase
in
the ex-dividend day in the period 1976-1991, compared to the
with the cross sectional analysis reported in Table
yield stocks than for the
Of more
risk
interest
is
medium or low
is
for the three dividend yield samples.
is
The
we examine
A
is
where the dependent
Table V. Because of the inclusion
restricted to the 1988-1990 time period.
The
t-statistics
of -5.72 and -8.76 respectively.
medium and low
The spread
yield groups.
The
coefficient
is
idiosyncratic risk
negative and significant for the entire sample and for each subgroup, and the beta
coefficient has the right sign,
is
for the high
these relationship for the entire sample and
results are reported in
negative but statistically insignificant for the
size
more pronounced
negative and highly significant for the entire sample as well as for the high
dividend yield group, with a
is
is
a multivariate regression analysis,
of the bid-ask spread variable, the sample in Panel
coefficient
the increase
11,
period of 1%2-1975. Consistent
the combined effect of transactions costs, the idiosyncratic risk and the systematic
the cumulative abnormal volume,
spread coefficient
first
dividend yield stocks.^
on the ex-day trading volume. Using
variable
the abnormal trading volume around
and
significant for the entire sample.
used as the transactions costs proxy (Panel B):
it
is
A similar
positive
and
pattern emerges
when
significant for the entire
sample and for the high yield group, negative and insignificant for the medium yield group, and
negative (and significant) for the high yield group.
Note
that
using size as a proxy for the
cross-sectional variation in transactions costs enables us to utilize the entire 1963-1991 period.
Overall, the results are consistent with the model's predictions: securities with higher transactions
costs experience lower
^Tiese
abnormal trading volume, even
results are consistent with
after controlling for the level of risk associated
what has been reported by Lakonishok and Vermaelen (1986).
31
with the trade.
It is
also
found that for high dividend yield stocks, where the incentives to trade are
on trading volume
higher, the effect of transactions costs
4.2.3
The
Thus
far
model
will
interaction between risk
we have examined
and
the direct effect of risk and transactions costs
market
risk
volume
is
on
trading
First,
on trading volume. As the
and beta on the ex-day volume of trade
implies, however, the effect of the idiosyncratic risk
volume (Implications 4 and
more pronounced.
transactions costs.
vary def)ending on the cost of transacting.
comparing the
effect of the
volume
increases.
The
effect of the idiosyncratic risk
become
higher, investors choose to
Even without
costs increase, investors
test
hedge
hedge
7).
less,
The
intuition behind these results
less,
trade less and hence the idiosyncratic risk
these predictions using a regression analysis.
dividend yield, the idiosyncratic
be zero
if
trading
risk,
The dependent
distribution.
variable
The independent
variable.
1"
is
transactions
1976 and December 31" 1991. Both
risk
According to the model, the idiosyncratic
component are
risk
trading
the cumulative
variables are the
we
define Q,
the ex-day occurred
multiplied by these
component's coefficient should be
lower prior to 1976 since the transactions costs level were higher during
were fewer hedging instruments around (such
As
less important.
the security's beta, and a size variable. In addition
if
that the
risk affects their
becomes
the ex-dividend day occurred before January 1976, and one
between January
dummy
and consequently, the systematic
As
is
trading costs, however, investors bear the idiosyncratic risk.
abnormal volume (CAV) around the dividend
to
on
predicted to be the opposite: as transactions cost increase the effect of the idiosyncratic
trading decision.
We
risk
component on
systematic risk can be hedged away at no cost in the absence of transactions costs,
costs
market
reveals that as transactions costs increase the effect (negative) of the
4'),
on trading volume decreases, (Implication
risk
is
this
time period and there
as futures or options contracts).
The beta
coefficient
32
is
predicted to be higher before 1976.
all
is
The
results are
ex-dividend day observations are included, the
presented in Table VI. In the
dummy
row, where
first
slope coefficient for the idiosyncratic risk
negative and significant indicating that the idiosyncratic risk had bigger (in absolute value) effect
on trading volume
coefficient has a
much
yield
more hedging
In the second
on trading volume.
group (top
to negotiated commission schedule.
vehicles
row of the
-r
became
table
the entire sample.
on both the beta and the
The beta
1976, consistent with the assertion that as
we
available, the beta risk
had a smaller
present the results for the high dividend
of both
1/3 yield). Consistent with prior analysis, the effect
negative on this yield group than
bigger effect
fix
larger coefficient prior to
transactions costs got lower, and
effect
from
after the transition
The change
risk
component
in transactions costs
idiosyncratic risk coefficients.
The beta
affect the trading
volume
transactions costs had
for the
no
row show
that while the risk
bottom 2/3 of the sample
significant effect
on these
(in
coefficient
As
the
model
cash flows, an increase
predicts,
when
is
term of their
yield),
volume
is
the change in
than the effect of the systematic
between transactions
and
supported by the data: The effect of the systematic
risk
when
when
trading costs are low.
risk.
trade around the ex-day,
do so
in stocks
is
risk
on
risk,
The
effect
Also, the data confirms
The model's
and their effects on trading
on volume
is
trading costs are high, and the idiosyncratic risk has a larger effect
The evidence
and
or nonsystematic), reduces trading volume.
costs
times
more
coefficients.
the assertion that trading volume and transactions costs are negatively correlated.
predictions about the interaction
is
less
trade occurs because of the differential valuations of
risk (either systematic
of the nonsystematic risk component
is
components negatively
Overall, the results of this section demonstrate the importance of transactions costs
trading volume.
more
ha also a
negative after the reduction in transactions costs, and the idiosyncratic risk coefficient
negative. Finally the results reported in the last
is
more pronounced
at
on abnormal volume
also consistent with the assertion that
most investors who
with large dividend yield. These stocks therefore will be
33
affected the most by change in transactions costs or by the availability of hedging instruments; both
through the direct effect of transactions
costs,
and the indirect effect through the idiosyncratic and
the systematic risk of the stock.
4.3
The
role
of derivative
The evidence presented
assets.
in the last section
investors' trading decisions
when
shows that
risk
and transactions costs
their private valuation differs
significantly affect
from the market's valuation.
It is likely
therefore, that the introduction of instruments that enables investors to reduce the ex-day trading
risk, will result in
a higher trading volume.
can be used to reduce the
is
already in place. In both cases, the predicted effect
expect more trading since the risk exposure
is
such as options,
is
is
clear:
We would
lower, and the effective cost of the entire transactions
lower.
A potential way to investigate
is
specifically, derivative securities,
exposure of the underlying transaction, or alternatively, reduce the cost
risk
of an hedging strategy that
More
to
examine the
effect of the introduction of a stock index future contract, such as the
Market Index (MMI)
events
the effect of the availability of hedging instruments on trading volume
However, such
1984.
in July
may have occurred around
the
same time
a test
period, for
may be problematic
example the 1984
Major
since several other
TRA which increased
the required holding period for corporations from 16 to 46 days.
This type of problem
is
much
less
severe around the introduction of stock options.
First,
stock
options were introduced gradually and do not concentrate in a particular time f>eriod. Second, since
a stock option
in the
To
is
most
likely to
same time period are
this
end,
we
be used
as a
less likely to
hedge against trades
in the
underlying stock, other stocks
be affected, and therefore can be used as a control sample.
collected a comprehensive sample of
all
stocks with a traded option.
Our
initial
34
sample consists of
all
options listed on the
CBOE, NYSE, AMEX,
Pacific Stock
Philadelphia Stock Exchange from 1973 through 1987, with an underlying asset that
NYSE or AMEX. A firm
is
included in the sample
around the option inception and
option
listing
and
if
Exchange and
is
traded on the
return data was available for ten years centered
has at least four ex-dividend dates in the three years prior to the
it
at least four ex-dividend dates in the three years after the
option
listing.
The
final
sample contains 448 stocks.
Table VII presents some summary
yield for the pre-
and
statistics for this
sample. First
For each firm
post-listing periods.
calculated the dividend yield as the average yield over
The sample average
yield
was then calculated
all
we
calculated the average dividend
in the pre-listing (post-listing)
sample we
the ex-dividend days in the five year period.
as the average firm's dividend yield."
The same
procedure was followed for the calculation of both the average dollar amount of dividend paid and
the average price.
The
sample's average standard deviation of returns was calculated using daily
returns in the year before (after) the option
listings.
$0,298 and $0,312 before and after the option
listing,
The average amount of
and the average dividend yield changed from
an average of 0.834% to an average of 0.9%. Both differences are
average post-listing price
is
$36.7,
which
standard deviation of daily returns
before, but the difference
is
is
is
3.72 dollar lower than
somewhat lower
distribution of the inception of options in our
We
compare the trading volume
manner.
activity
statistically insignificant.
the average prelisting price.
after the listing: 2.153
Lastly, as alluded to before.
insignificant.
dividend paid was
The
The
compared with 2.257
Panel
B
presents the
sample by year.
before and after the option
listing
day
in the following
We calculate the cumulative abnormal volume for each event using the procedure described
25
This procedure
sample average.
is
followed so that firms with larger
number of ex-day events
will
not receive a greater weight
in calculating the
35
in
Section 4.1.
Then,
order to give each stock
in
number of ex-dividend days
in the
it
had,
we compute
in
in
Table VIII,
is
the cross-sectional
cross-sectional variation of the cumulative
CAV for the entire sample
report the
listing.
abnormal volume.
The
for the pre-listing period
and the
1%
The same
level (t=5.88).
listing
abnormal trading volume
compared with the
It is
is
The
third
column of the
first
we
calculated using the
CAV of the
volume of trade
significantly
is
32.8% compared with 118.6%
emerges from the sample of the higher
The
level of
is
significant at the
yield stocks or only
abnormal volume
is
significantly
than before. Consistent with our prior findings, the absolute level of
higher both before and after the option listing for the high yield groups,
entire sample.
possible that the
upward trend
in
the ex-day abnormal trading volume through time
contributed to our findings of higher abnormal volume in the three years after the option
in the
three years prior to the option
listings.
To
an alternative procedure. For each firm with a
option, and
sample
first
we
compare
their
screen the
is
in the
CRSP
20%
may have
listing
control for this potential confounding effect
listed
option
we
find a
matched firm without
than
we
use
a listed
abnormal volume of trade around the ex-day. In order to find the matched
tapes for stocks without options traded in the
three years after the option
yield that
we
report the results for only
post-listing period, respectively. This difference
results
table
column contain the
results indicate that the
stocks with dividend yield greater than 12.5 cents:
higher after the option
In the
The cumulative abnormal volume
listing:
stock in our sample both
t-statistic is
of 448 firms, and in the second
top third stocks in term of their yield.
regardless of the
The mean cumulative abnormal volume,
mean of CAVj. The
those stocks that had a dividend greater than 12.5 cents.
increase after the option
same weight,
CAV for each
the average
period before and the period after the option
reported
the sample the
listings).
(in the
We then choose a subsample of stocks that have a dividend
range of the yield of the stock with option.
stocks with market value of equity in the
same time period
50%
From
this
group we select
range of the stock with option, and then
we
all
select the
36
stock that
Using
closest in price.
is
this criteria
The sample
we
This procedure
is
repeated for every stock with an underlying option.
are able to find 368 matched pairs of stocks with and without options.
characteristics are described in Table IX.
The dividend
yield,
market value of equity and
the daily standard deviation in returns are insignificantly different from each other between the two
samples.
The average
price of the stocks with options
is
about $2.5 higher than the stocks without
options.
When
comparing the cumulative abnormal return of the two samples
find that the difference in the
volume of trade
for the stocks without options,
comparing the mean
CAV
is
CAV
is
listings
Vni), the differences are much lower (though
cross sectional basis instead of
with and without options
on a time
when keeping
part of the increase in the trading
respectively.
we eliminate
we
worth noting however, that when
listing
we
(32.8% compared with 118.6%,
still
significant),
series basis:
We
when
find only a
find that the
mean
as reported in
Table
the comparison
30%
is
done on
a
difference between stocks
the time variable constant. This seems to imply that at least
volume
after the option listing
the market and not directly related to the option listing per
of Table X,
It is
period before and after the option
about four times higher after the
column of Table X), we
significantly higher for the stocks with options than
130.4% and 99.4%
in the
(first
find significant difference in trading
5^.
is
related to
As reported
in
some other
the
last
trends in
two columns
volume around the ex-dividend day even
after
stocks with dividends smaller than 12.5 cents, (second column), or included only the high
yield securities in the
sample (third column).
4.5. Portfolio effects
Without transactions costs the systematic
volume of trade
is
the idiosyncratic
risk.
risk
can be easily hedged, and the only constraint to the
Since the idiosyncratic risks are independent across stocks,
37
the mcxlel implies that the
When
stocks going ex.
amount invested
in
each stock going ex
is
independent of the number of
investors incur transactions costs, however, not
be hedged, and therefore the trading volume on each individual stock
of the number of stocks going ex, (Implication
will
5'),
though the
be higher the higher the number of stocks going
effect of the
number of
stocks that go ex in a given day
Table XI contains some summary
statistics
standard deviation of 20.56."
the
will
be a decreasing function
volume on the ex-day
test this implication
number of
stock that go ex in the
As can be seen from
of the systematic risk can
on the trading volume
regarding the
The mean (median) number of
dividend day.
We
ex.
total
all
last
in
by examining the
each stock.
stocks that have the
same day
is
is
no
clustering of ex-days by yield.
It is
one day
The
is
minimum
153 and the
effect of the
number of
is
evident, however, that the
stocks that have the
independent variables are the dividend
in
the
same day (ND).
second and third rows the
yield groups
combined.
significant for the entire
^t
is
number of ex-dividend days
same ex-dividend day
first
yield, the
two
is
an ex -dividend day
days
examined In Table XII.
and the number of stocks that go
risk variables
row we report the
results for the entire sample,
results are reported for the high yield
First, consistent
is
with implication
sample and for each sub-sample.
5',
It
and
in the
group and for the low and medium
the
ND
coefficient
is
negative and
seems, however, that the number of
is
not even. There are twice the
number of
ex-
any other day of the week. We have also calculated summary statistics regarding the number of stocks that have
the same month. An average of 431.8 stocks have an ex -dividend day in a given month, with a maximum and a
in
in
maximum ex-dividend
the cumulative abnormal volume and the
worth noting that the distribution of ex -dividend days across the day of the week
day on Monday than
minimum
In the
at a given day.
zero.
Using regression analysis where the dependent variable
ex
ex-
three columns of the table, the high-,
are not uniformly distributed across days. For the entire ex-day sample, the
in
same
20.63 (13) with a
medium-, and low-yield groups have the same average number of stocks that go ex
There
portfolio
of 805 and 16.
38
stocks that go ex, has a
ND coefficient
The
is
greater impact on the high yield group than
much
on the
about 10 times larger for that group of stocks.
Tax heterogeneity and trading volume
4.6.
One
of the major implication of the model
is
that the higher the dispersion in investors' private
volume of
valuation, the stronger the incentives to trade, and consequently, the larger the
to the ex-dividend day trading,
are
rest of the sample.
more
it
implies that as the tax heterogeneity
gains from trade, (Implication
1).
Given the changes the
among
US
identified,
tax code,
is
no
reliable data
risk aversion), across holders
It is feasible,
if
on the
it
is
and the changes
However,
be precisely
to the best of
cross sectional variation in tax rates (and in absolute
of different stocks.
however, to estimate the time series variations
Using the IRS
in tax heterogeneity.
Individuals Statistics of Income, Corporations Statistics of Income, and the Federal Reserve
Funds publications
for the years
as explained below.
The IRS
1%3
through 1989,
we
calculate the yearly
mean and
publications provide information regarding the
income received by individuals
corporations.
in
clear that the tax
clientele groups could
a firm sp)ecific tax heterogeneity variable."
one could construct
our knowledge, there
In principle,
As
investors increases there
the relative importance of the various trading groups in the economy,
heterogeneity variable varies through time.
trade.
in
each tax bracket
The Federal Reserve
as well as the
received by pension funds and insurance companies (institutional investors).
we
variance of a"
amount of dividend
amount of dividend received by
publications contain information about the
marginal tax bracket of each group,
Flow of
are able to construct the yearly
amount of dividends
From
this data,
mean and
and the
variance of the
Several studies, such as Auerbach(1985) and Maclcie-Mason (1988) have attempted to use firm specific tax clientele variable to analyze
corporate financial policy. This variable can be viewed as the
distribution.
Even though the former
policy using this variable.
is
mean
of the tax distribution, while our interest
easier to measure, these studies
do not seem
is in
the variance of this
to have great success in explaining corporate dividend
39
relative tax preference variable a".
The weights on each
o" are set to the relative
amount of dividend
received by this group of investors.^
Another factor
is
that
may
affect the level of
abnormal trading volume through the tax heterogeneity,
the incentives of the various groups to trade. In particular, corporate investors' incentives to trade,
and
their effects
the return
The
first
manifest
on the ex-day trading are measured using three additional
on the
overall market in the current year and the return
variables: the level of o,
on the market
in the prior year.
variable capture the increase weight of the corporate traders in the market place as
itself
it
through o. The second and third variables capture the corporate traders' incentives to
trade through a proxy of their capital gains. Since the capital losses from dividend capture activity can
be deducted only against capital
gains, prior
used as proxies for corporate capital gains.
to trade
around the ex-day increases
and current year changes
As
in
the level of the market are
their level of capital gains increases, the incentives
as well. In other words, the higher the level of corporate profits
from capital gains, the higher the incentives to trade around the ex-day.
Given the nature of out
test,
we
constructed a monthly abnormal volume variable.
cumulative abnormal volume for each month
volume
for
all
securities with
of the firm's equity.
We
is
The mean
calculated as the average of the cumulative abnormal
an ex-dividend day
in that
month, weighted by the market capitalization
then estimate the effect of differential valuation on the monthly abnormal
volume:
CAV
^t
= a„ + a,
(
_), + a^RM^ + ajRM^., *
a,a, + a^yar^ioT^) +
should be noted that our construction of the distribution of o°
is
a^VaT^(a°) *
a,<^^,
+ a^LogCt) + €,.
only a proxy. First, the weights are proportional to the dividend
received and not to the absolute risk tolerance. This can be justined by noting that the share of dividend received
for risk bearing capacity. Second, our
measure
discrete, year-end,
changes
measure of
tax heterogeneity
in tax heterogeneity.
mean of a by
available
on
a yearly basis only,
is
a reasonnable proxy
which implies that we actually
Since most lax changes occurs at year-end (though not changes
of the various trading groups), this empirical approximation
a very similar estimate of the
is
may be
appropriate.
using a slightly different data source.
It
is
in
the weights
comforting to note that Poterba (1987) arrives
al
40
The
(13)
1963-1985
reported
in
years
are
data
for
the
monthly
using
results of estimating equation (13)
Table XIII.^ In addition to the explanatory variables described above, the estimating equation
includes a monthly dividend yield variable, calculated as the average dividend yield of
an ex-dividend day on that month, weighted by
their
all
stocks with
market capitalization; the monthly market
variance o^„ calculated as the daily return variance of the equally weighted index in the 60 days prior
to
month
t;
and
a log time variable (in years) that captures the overall
volume through the
years, Log(t). Finally,
it is
possible,
and quite
upward trend
in trading
likely, that individual investors will
not engage in the ex-day trading to a large extent because of transactions costs. In that case, the
variability in the tax rates
volume, and
We
in fact
(and weights) of
this investor
group may not affect the ex-dividend day
may not even be the appropriate measure of
the cross sectional variance of o".
therefore calculate an alternative measure of the variance of a" [labeled as Var2(«")], which
include the weights and relative tax rates of corporations and institutions alone.
serial correlation
present in the data using a
maximum
We
account for the
likelihood procedure as in
Beach and
Mackinnan (1978).
In the
first
and second rows of Table XIII the regressions are estimated for
events in the sample period. In the second regression, however,
we
all
ex-dividend days
use the cross-sectional variance
of a" that accounts for the variation in the relative tax rates and weights of only corporate and
institutional investors (Var2(«")).
the yield coefficient
is
positive
day abnormal trading volume
month. Also,
29
For most
and
is
is
significant, indicating that the
positively related to the
as the risk level in the
A potential complication
parts, the results using either variables are quite similar:
time series variation in ex-dividend
amount of dividend paid
market increases (measure by the market's variance), the trading
(he activities of the Japanese insurance companies in the mid- and late 80s. Their dividend related trades
are regulatory rather than tax motivated. While this type of incentive can be easily incorporated into the model,
tax heterogeneity variable.
in a particular
As shown
it is
not capture
Koski(1992), these trades had a substantial effect on the volume of trade, especially
therefore limit out time series to the period 1%3 through 1985.
in
in
the
in 1988.
We
41
volume decreases.
abnormal volume
It
is
seems
that the effect of dividend yield
in the
same direction they affected the
and
risk
on time
cross-sectional behavior of ex-day
abnormal volume. The measures of the corporate traders to engage
in the ex-day trading are
the right direction, but significant only for the second regression. That
indicate greater presence of corpwrate traders, the abnormal
significant
when
series behavior of
is,
as a increases,
volume increases
as well,
all
in
which
and
is
the heterogeneity variable accounts for the activity of institutional and corporate
market
traders. Likewise, the level of the
is
positive,
and
significant at the
10%
level, indicating that
higher level of capital gains increases the incentive to trade and consequently increases volume.
Perhaps most importantly, as the degree of tax heterogeneity between
traders increases, the
In the third
volume of trade increases
row of the
table
we
in a significant
institutional
and corporate
way.
analyze the effect of these variables on a subsample where the
corporate and institutional trading
is
the most pronounced, namely on the high dividend yield stocks.
Indeed, the current level of the market as well as o and the tax heterogeneity variable are positive
and highly
significant,
and the market
risk
proxy
is
negative and significant. Comparing the level of
the coefficients between regressions (2) and (3) indicate that
role in determining the
volume of trade
all
these variable plays a
for the high yield stocks than for the entire sample.
picture emerges from the last regression in the table (fourth row).
of the sample (in term of yield)
results are not surprising
if
is
more important
included,
non of the
variables
When
is
A similar
only the bottom two third
statistically significant.
These
individual investors faces higher transactions costs than large institutional
and corporate trades, which prevents them from
actively participate in the ex-dividend
Overall, the results indicate that heterogeneity has a significant effect
30
It is still possible that delay and acceleration of trades by individual
document evidence around the 1986 TRA which is consistent with this
investors
on trading volume,
may occur (see Grundy
assertion.
day tradings.^
especially
1985). Michaely and Vila (1993)
42
in stocks
where corporate and
institutional traders are
more dominant.
It is
also
shown
that the
higher the incentives to engage in these trades (proxied by level of capital gains and dividend yield),
the volume of trade
is
significantly higher.
hand, reduces the trading volume.
The amount
of risk involved in those trades, on the other
43
V.
CONCLUSION
In this paper
We
volume.
we consider the
impact of investors' heterogeneity, risk and transactions costs on trading
on
focus our empirical analysis
volume around ex-dividend
trading
days.
These events
represent an almost ideal environment for our experiment since the dominant motive of trade around
these events
is
the differential valuation of cash flows (dividends relative to capital gains) across
investors. In a relatively simple
volume. This result
trading
volume
is
not surprising and
that are based
that higher risk will
framework, the model indicates that transactions costs reduce trading
on
is
risk.
on heterogeneous valuation,
As
the present model reveals,
risk
risk
investors' trading motives are based
and the idiosyncratic
risk
have different effects on the
always affected by the idiosyncratic risk involved
effect of the idiosyncratic risk
is
bigger the lower the transactions costs are.
be
fully
level of systematic risk.
hedged
in
empirical evidence that
we
the absence of transactions costs.
becomes more
costly, investors
At the same time they
results in a lesser role for the idiosyncratic risk in
The
when
non-Pareto
is
transactions costs increases and hedging
some
as the cost associated with
volume
contrast, the systematic risk can
to
Models of
reduces the incentives to trade, an consequently the trading volume.
trading volume. Unlike prices, the trading
The
trading volume.
portfolio rebalancing towards optimal holdings, however, predict
Perhaps more interestingly, the systematic
the trade.
many models of
to
be associated with higher trading volume
holdings increases with
in
common
find
is
As
By
the level of
choose to expose themselves
also reduce their level of trade,
which also
determining trading volume.
consistent with the model's implications: (1) Stocks with higher
bid-ask spreads experience lower abnormal trading volume; (2) Stocks with higher idiosyncratic risk
experience lower trading volume; (3) Stocks
reduction in transactions costs in
The non-systematic
May
with lower beta exhibit higher volume; (4)
The
1975 resulted in an overall higher ex-day trading volume; (5)
variance coefficient
is
found to be lower before 1976, and the beta coefficient
44
to be higher. Also, stocks with underlying options,
trading
volume than otherwise
It is
also
day
is
shown
cheaper, experience higher ex-day
abnormal trading volume around the ex-dividend
positively related to the degree of tax heterogeneity
in
is
identical securities.
that the time series variations in the
groups to engage
and
where hedging
those trades. Specifically,
their incentive to trade increase the
we
and the incentives of the various trading
find that as the influence of the corporate traders
volume of trade increases
significantly, especially in the high
yield stocks.
While our
analysis focuses
be extended beyond
to better
on the ex-dividend
this specific
for
we
believe that the implications of this
work can
event and that the methodology developed here can be generalized
our understanding of trading volume
framework allowing
day,
in
other contexts as well. For instance a more general
heterogenous information, as opposed to heterogenous valuation, could be
used to analyze the abnormal trading volume around information shocks such as dividends or earnings
announcements or takeover rumors.
Modelling the interaction between trading volume, private
information, risk and transactions costs will not be an easy task. However,
developed herein
Finally,
will
be useful and that our main
of trade and the price
movement on
amount of tax revenues
that are lost
due
of tax-related trading
substantial.
There are three
seller
government to the
deadweight
loss
is
its
loss
to those trades.
Our
of research. Using the volume
may come with an
empirical results
show
estimate of the
that the
amount
parties involved in those trades: the buyer, the
seller
expect a gain while the government (the
of tax revenues. In addition to a transfer of wealth from the
traders, tax related trading
due
this line
the ex-dividend day one
and the government. Both the buyer and the
third party) looses through
think that the insights
results will hold true.
an important policy implication may be drawn from
is
we
around the ex-day creates deadweight
to the cost of trading the tax shields (commission, time spent etc.)
loss.
and the
This
risk
45
involved in the transactions (deviation from pareto optimal risk sharing).
it
follows that an estimate of the tax revenue losses
distributional
be of
and efficiency impacts of
interest to fXDlicy makers.
due
tax 'arbitrage'.
Indeed even
if
From our above
to ex day trading will shed
As
some
discussion
light
on the
a result such an estimate will undoubtedly
the wealth transfer due to tax 'arbitrage'
is
desirable
the fact that risk and transactions costs create a deadweight loss suggest that there should be a
more
46
Appendix
To
solve for the equilibrium trading strategies,
p' = p^ +
ad
-
_(1+Kt)x
A
we show
that at the zero transactions costs prices
for dividend paying stocks
and
6
-
p' = p
-
o^
_
(1+Kt)x
for
non dividend paying stocks
6
supply equals demand.
We
then calculate trading volume
at
these prices.
Consider an investor n with «">«. Let
y"
=
x^- j?
From equation
(6)
(-ad
and
(7),
the investor's objective
-o)x)'(x"+y)
+
+ o"d'y - (c")' |y
o
with respect to
?
=
y.
is
to
maximize
-
|
—
[3c"' oj
x"
+23?
w
y +y'
o
26"
(al)
y
]
Since
l"x
6
investor n's objective
is
reduced to maximizing
(o"-S)d'y - (c")'|y
J-y'wy
-
(a2)
.
I
Given the symmetry, the
investor's
a of the dividend paying assets to
sell
problem can be described
as follows:
Choose how many shares
buy and how many shares b of the non dividend paying
for hedging motives. Indeed, since transactions costs are proportional diversification
Hence, the investor prefers to buy
all
is
From
dividend paying assets than just a subset.^'
assets to
not costly.
(a2), a
and
b are chosen so as to maximize
(a"-5)Sda
-
c[Sa+(K-S)b] -^J a^(S'T +S) +b'( (K-S)'t +K-S
)
-2abS(K-S)T
(a3)
with respect to a^O and b^O.
The
solution to (a3)
is
described below
In the presence of fixed transactions costs, the investor will trade only a subset of the dividend paying assets.
]
47
b=0
a=0,
3=6°
ifo"ia
1
2^
+
d
b=0
,
ifo +
o^(1+St)
_<a°$a
1+kt
o^
_[2+
d
[(tt°-5)d-2c](lf(K-S)T)-c
_ e°
+
d
^ 6°
^^
]
(a4)
[(a°-5)d-2c]ST-c
^
'
—
St
niG
if
a°
> 5
+
£[2
d^
+
J_]
St^
Therefore,
t
=
£andh=f[2
d^
d
Since the distribution of o"
o''-o
= o-a". From
is
and
a
assumption that
K
is
we
b,
A convenient way to write
Then
St^
it
o">o
can be seen that y°+y°'=0 and hence supply equals demand.
calculate the trading
volume on any dividend paying stock under the
g°
(«''-«)d-c
the volume on the
and
^
^
cum day
c
v = d
•
the volume can be written
V
ed
=^[E
V
cr
From equation
^
(a6),
there exists a a'°<o such that 6"=0" and
large:
V=^[ ^
—
ii" = o"-o
^
J-].
symmetrical, for every
equation (a4),
Having derived
+
6"max{ JLlI, ^"-2y;0}
1+St
we can
see that
]
is
5"((«"-5)d-2c)].
to define
(a5)
48
Combining (a7)-(a9)
av
next
show
costs. In the
V
follows that
av
r
^<
We
it
c
a(|)
that the effect of the idiosyncratic risk o^
no
transactions costs case
volume
is
is
smaller in the presence of transactions
given by
=
c
so that
(a8)
49
Appendix B
A
simple model with non unit betas
In order to solve for trading volume with
Two
i)
The
risky assets are traded.
other one
is
non
first
pS+e
a stock which pays
unit beta,
Trading
in
the stock
trading in the index
is
is
stock
and index that pays 8
The random
mean zero and
at the ex.
variables 6
variance
subject to proportional transactions costs
The
stock pays a dividend
iii)
The
distribution of the parameter o"
in
the simplifying assumptions:
The
and € are
o^ and o^
subject to proportional transactions costs Cs while
is
iii)
Following the analysis
is
at the ex.
independently normally distributed with
ii)
one
we make
c,.
d.
appendix A,
it
is
symmetrical.
easy to show that the zero transactions costs prices are
is
equilibrium prices.
We next calculate the investor's trading strategy.
If
o°>o, the investor buys
hedges by shorting b shares of the index. His objective
(a"-o)da-c,a-ch- _^L11
^
is
to
a shares of the stock
and
maximize
(bl)
.
26"
'
with respect to a^O and b^O.
It is
useful to rewrite the objective (bl) with respect to a and the unhedged market risk z
o?, z^
(a"-a)da-(c +pc,)a+c,z-
_^!
with respect to x^O and z^px.
The
solution to (b2)
is
described below
+ o^ a^
=
pa-b:
/.
OS
(^2)
50
C-
a=0, z=0
a = e°
ifa":sa
this
^'^J^^'^'J'
formulation
(i)
When
J
d
,
z =
[(a"-o)d-c -pc,]
'
'\
'
a=e"i^^
With
+
it is
Pa
if
S-1^ <
c,
^
if
z=e"'
a" ^
_
a"
o^
> a*^[c3.(^*P)c,].
Cs=c,=0, then implications 1-4 hold. In addition
When Cs>0
1
or/and C|>0, then implications
6, 4'
is
and 7
we
obtain
independent of
still
p.
hold. In addition
Implication bl': In the presence of transactions costs, the trading volume
is
be shorted.
Second high beta stocks are
costlier to
we
obtain
decreasing in p.
This result follows from two concurring effects: First high beta stocks are risky for traders
afford to hedge.
(b3)
easy to see that:
Implication bl: If transactions costs are zero, trading volume
(ii)
5*^[c, + (J^*P)c,]
who cannot
hedge since more shares of the index must
51
References
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and
P. Bossaert, 1993, "Asset Prices
and Trading Volume
in a
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mimeo.
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Statistics
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M. and A.
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Lakonishok,
J.
Michaely, R. and J.-L. Vila, 1993, "Investors' Heterogeneity, Prices and
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the Ex-
Dividend Day", Working Paper, Massachusetts Institute of Technology.
Miller
M. and
F. Modigliani,
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Policy,
Growth and the Valuation of
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503.
J.,
1987,
Tax
Policy and Corporate Savings", Brookings Papers
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2,
455-
52
Schaefer,
S.,
1982,
Taxes and
Security
Market Equilibrium," Financial Economics: Theory and
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StoU, H.R., 1989, "Inferring the
Components of the Bid-Ask Spread: Theory and Empirical
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Journal of Finance, 41, 115-134.
Tirole,
J.,
1982,
"On
the Possibility of Speculation under Rational Expectations," Econometrica 50,
1163-1181.
Tuckman,
B.
and
J.-L. Vila, 1992, "Arbitrage
Journal of Finance, vol. 47,
Tuckman, B. and
Wang,
J.,
1991,
4,
with Holding Cost:
A
Utility
Based Approach," The
1283-1302.
J.-L. Vila, 1993,
"Holding Costs and Equilibrium Arbitrage"
MIT
mimeo.
"A Model of Competitive Stock Trading Volume", Working Paper, Massachusetts
Institute of Technology.
53
Table
I
Descriptive statistics on ex-dividend day abnormal volume, cumulative abnormal volume for
the eleven days centered around the ex-dividend day, the dividend yield and the bid-ask
spread for a sample of ex-dividend events on NYSE/AMEX stocks in the years 1963-1991.
Statistics are provided for the entire sample and for each of the three dividend groups
separately. Abnormal volume is calculated as the daily turnover relative to normal turnover,
and the dividend yield is defined as the dividend amount over the cum-day price. The bidask spread for each stock is calculated as:
BAS, = -^
Tj
I
t=-45
^ i
3
j=i
|(Ask,j.
- Bidy,)/
Askyi
+
Bid.j,
[
where j = open, mid-day, and close transaction, t is the day relative to the ex-dividend day,
and Tj is the number of days in the estimation period with valid bid-ask observations (usually
40 days).
54
Table
The
Effect of Risk on
II
Trading Volume
The
effect of dividend yield, idiosyncratic lisk and beta on abnormal volume in the 1 1 days
around the ex-day is analyzed using a regression analysis. Abnormal volume is defined as
the daily turnover relative to average turnover and the cumulative abnormal volume (CAV) is
the sum of abnormal volume in the 1 1 days around the ex-day. Dividend yield is calculated
as the dividend paid over the cum-day price. The idiosyncratic variance, scaled by the
market variance in the same time period, and beta are estimated from the OLS market model
in the estimation period (using daily returns). 155,302 ex-dividend events on NYSE/AMEX
dividend-paying stocks in the period 1963-1991 are included in the sample. Standard errors
are adjusted for heteroscedasticity using White's (1980) procedure. T-statistics are reported
in parentheses.
CAVi =
Po +
Pi
-r^^
+ p.
—
+
P3 Beta,
D,
Dependent Variable
(Mean)
CAV(-5->+5)
(100.6)
Intercept
1.96
a^i
"^
^^
(16.43)
+ 0,
Betai
t-i
63.08
(8.51)
^m
-0.49
(-18.65)
-0.33
(-7.82)
55
Table
III
Transaction Costs and Ex-Day Trading Volume:
Cross-Section Analysis
Ex-dividend events are divided into nine categories by dividend yield and bid-ask spread
(Panel A) and by dividend yield and market value of equity (Panel B). The sample is first
sorted by yield into three groups and then by bid-ask spread, resulting in nine subgroups.
The bid-ask spread is calculated as the average bid-ask spread in the 40 days prior to the exday (see equation 9 in the text). Dividend yield is calculated as dividend amount over the
cum-dividend day price, and the market value of equity is calculated as its average value in
the estimation period. The average cumulative abnormal volume (in percentage) is then
calculated for each category. T-statistics appears in parentheses and number of observations
appears in brackets. In Panel A, the ex-dividend day events are constraint to the years 19881990, and in Panel B the sample contains the entire sample period of 1963-1991.
Panel A: Sorting by Dividend Yield and Bid-Ask Spread (BAS)
BAS
Category
56
Panel B: Sorting by Dividend Yield and Market Capitalization (Size)
SIZE Category
(in
dividend
yield
category
millions of $)
57
Table IV
Transaction Costs and Ex-Day Trading Volume:
Time Series Analysis
Mean cumulative abnormal volume. CAY,
for the first subperiod, 1963-1975, and for the
second subperiod of 1976-1991. CAV is calculated in the 1 1 days around the ex-dividend
day. In the first subperiod the mean dividend yield is 0.93% and the mean daily turnover is
0.12%. There are 21,287 observations in each subgroup with a dividend yield of 1.52%,
0.87%, and 0.41% for the high, medium, and low yield groups respectively. In the second
subperiod (1976-1991), the mean dividend yield is 1.05% and the mean daily turnover is
0.19%. Each subgroup contains 30,398 observations with a dividend yield of 1.82%, 0.91%,
and 0.41% for the high, medium, and low yield groups respectively. T-statistics appears in
parentheses.
Dividend Yield Group
Dependent Variable:
(1)
(2)
CAV
Entire
Sample
High
Medium
Low
1963-1975
(63862 obs.)
29.42%
26.22%
29.46%
32.57%
(10.14)
(4.18)
(5.75)
(7.70)
1976-1991
(91193 obs.)
150.10%
311.92%
73.49%
62.67%
(31.36)
(25.22)
(15.57)
(13.42)
58
Table
The
The
Effect of Transaction Costs
V
and Risk on Ex-Day Trading
on ex-day trading is analyzed using a regression
abnormal volume in the 1 1 days around
the ex-dividend day for the entire sample (first row), for the high yield group (second row),
for the medium yield group (third row), and for the low yield group sample (fourth row).
The independent variables are the stock's dividend yield, calculated as the dividend paid over
the cum-day price, the idiosyncratic variance, scaled by the market variance in the same time
period, and the systematic risk, estimated by beta. The latter two variables are estimated
using the OLS market model during the estimation period. In Panel A we use the average
bid-ask spread (BAS) calculated as the average BAS in the 40 days prior to the event (see
equation 9) as a proxy for the cross-sectional variation in transaction costs, and in the Panel B
market value of equity is used as the transaction costs proxy. Standard errors are adjusted for
effect of transaction costs
analysis.
The dependent
and
variable
risk
is
the cumulative
heteroscedasticity using White's (1980) procedure. T-statistics are reported in parentheses.
CAV, =
tto
-t-
tt]
— -1-02
P;
Panel A:
1988-1990
—^
+ a^
Beta,
-i-
a^ BASj
59
Table VI
The
Effect of the Systematic
and Idiosyncratic Risk Components
in the
Two
Different
Transaction Costs Regions
that the systematic risk will have a greater effect on trading volume when
transaction costs are high, and the idiosyncratic risk will have lower impact on trading
volume when transaction costs are high. The dependent variable is the cumulative abnormal
volume (CAV) in the 1 1 days around the ex-day for the entire ex-day sample (first row), for
the high yield group only (second row), and for the low and medium yield groups combined
The model implies
The independent variables are the stock's dividend yield, calculated as the
dividend paid over the cum-day price; the idiosyncratic variance, scaled by the market
(third row).
variance; the systematic risk, estimated by beta; and the average market value of equity. The
risk components are estimated using the OLS market model during the estimation period. Qi
is a dummy variable that takes the value of one if the ex-day occurred after 12/31/75 and zero
otherwise. Using these variables we create two slopes dummies, one for each risk
component. Standard errors are adjusted for heteroscedasticity using White's (1980)
procedure. T-statistics are reponed in parentheses.
Cav,
=
tto
+
ttil
—
+
I
a2—
+
a3— Qi
+ a4betai + ajbetaiQi + agsize
60
Table VII
AMEX
stocks from
table provides descriptive statistics for options listed on NYSE and
April 1973 through December 1987. A firm is included in the sample if it has at least four
ex-dates in the three years prior to the option listing and at least four ex-dates in the three
years after the option was listed. The dividend yield and dollar dividend is calculated as the
mean over the pre- and post-listing periods. Average prices are calculated using the cum day
prices, and the daily standard deviation is calculated using daily prices for the year before and
after the option listing. Average values are reported in the body of the table, and standard
deviation are in parentheses. 448 companies are included in the sample.
The
61
Table VIII
Trading Volume Before and After Option Listing
table reports the cumulative abnormal volume (CAV) in the 1 1 days centered around the
ex-dividend day for a sample of stocks with traded options, in the three years before and the
three years after the option start to trade. A firm is included in the sample if it has at least
four ex-dates in the three years prior to the option listing and at least four ex-dates in the
three years after the option is listed. CAVj is first calculated for each firm (either before or
after the option listing), and then the average CAV for each respective sample is calculated.
The sample contains 448 firms. In the second column we exclude all stocks that pay
dividends less than 12.5 cents and in the last column only the top third of the stocks in terms
of yield are included. T-statistics are in parentheses.
The
62
Table IX
The
table compares the average price, size, dividend yield and standard deviation of return
between a group of stoclcs with option traded and a matched group of stocks without traded
option. For each stock in the former group we select a matching stock using the following
criteria:
we
first
screen the
CRSP
tapes for stocks without options traded in the same time
±20% of the yield of the stock with option.
stock with market value of equity in the range of ±50% of the
period, with a dividend yield in the range of
From
this
group we select
all
equity value of the stock with option and then
Standard deviations are in parentheses.
Panel A: (368 pairs)
we choose
the stock that
is
closest in price.
63
Table
The
table reports the cumulative
X
abnormal volume (CAV)
in the
eleven days centered around
the ex-dividend day for a sample of stocks with traded options and a matched sample of
stocks without options. For each stock with option we match a dividend paying stock
without option that traded in the five year period after the option listing. Matching is based
on dividend yield, market capitalization, and size. T-statistics are reported in parentheses.
CAV
(%) Entire
Sample (N = 368)
Stocks with option
Stocks without option
130.4
(10.83)
99.4
(5.84)
Mean-difference
(without-with)
-30.95
(2.25)
CAV (%) Only Stocks
With Yield Greater Than
12.5 cents (N = 288)
156.4
High Yield
Stocks Only
322.6
(4.29)
117.6
(3.45)
-38.78
(2.44)
208.7
(2.80)
-113.9
(2.29)
64
Table XI
Descriptive statistic about the number of stocks that had an ex-dividend day in the same day
(ND). Statistics are calculated for the entire sample of NYSE/AMEX stocks with at least one
ex-dividend day in the period 1963-1991, as well as for the three yield subgroups.
65
Table XII
The
We
Portfolio Effect on
Ex-Day Trading
examine the effect of the number of stocks that go ex in the same day (ND), on the
volume activity of each stock. Standard errors are adjusted for heteroscedasticity
trading
using White's (1980) procedure.
Dependent Variable: Cumulative Abnormal Volume
Sample
All
Ex-Day
Intercept
(D/P)i
oe/c
^^^^'
^^^^'
^^
66
Table XIII
The
Effect of
We construct
a series of
volume of
NYSE/AMEX
Tax Heterogeneity on Trading Volume
monthly mean abnormal volume, using the cumulative abnormal trading
stocks with an ex-dividend day in that month. We test the effect of
tax heterogeneity and risk on abnormal volume using regression analysis. The dependent
variable is a monthly time series cumulative abnormal volume, (CAV) calculated as the average
of the cumulative abnormal volume for all securities with an ex-day on that month, weighted by
the market capitalization of the firm's equity. The independent variables are the monthly
dividend yield, D/P, the market return in prior year RMi.i, and current year, RMt, the weight
all
average of preference of dividends relative to capital gains, a a tax heterogeneity variable,
market return in the prior three months, 0^, and an indicator variable for
time, log(t). For each month, the weighted mean CAV of all securities paying dividends are
calculated, weighted by firm's market capitalization. The weighted average dividend yield is
calculated in a similar way. The market return on the NYSE/AMEX value weighted portfolio in
the current and prior year are used as a proxy for corporate capital gains, which affect their
incentive to engage in dividend capture, a is calculated using data on the marginal rate of
substitutions between dividends and capital gains for each trading group, as well as actual
statistics (for the SOI bulletin) on the relative weights of each group. The tax heterogeneity
variable measures the within year variability in those preferences. Lastly, the market variance
tries to capture the perceived risk involved in those transactions. We account for the serial
correlation present in the data using a maximum likelihood procedure as in Beach and
Mackinnan (1978). The regression is estimated in the period 1963-1985. We truncated the data
at the end of 1985 to avoid a time period in which heavy trading that is not related to taxes by
Japanese insurance companies affected the volume statistics in a significant way, see Koski
(1992). In the first row of the table the results are presented for the entire sample of securities; in
the second row we analyze the top 1/3 stocks, in term of their yield, alone and in the last row the
analysis is applied to the bottom 2/3 of securities, sorted by yield. T-statistics are in parenthesis.
,
var(ai), the variance of
Dep
Variable:
Monthly
CAV
(1)
Constant
D/P
RMt
RMt-i
a
Vari(ai)
Var2(ai)
log(l)
r2
DWa
5236
nu
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