Full text of DOI:10.1111/1475-679X.00044

Journal of Accounting Research
Vol. 40 No. 1 March 2002
Printed in U.S.A
Intertemporal Tax Discontinuities
D O U G L A S A . S H A C K E L F O R D∗
A N D R O B E R T E . V E R R E C C H I A†
Received 13 August 1999; accepted 2 August 2001
ABSTRACT
We define an intertemporal tax discontinuity (ITD) as a circumstance in
which different tax rates are applied to gains realized at one point in time
versus some other point in time. We study the effects of ITDs on market
behaviors at the time of disclosures of firm performance, assuming that
all investors who trade firm equities are subject to tax. The results of our
paper suggest that relative to an economy in which ITDs are absent, ITDs
may dampen trading volume and amplify price changes at the time of
disclosure.
1
. Introduction
This paper discusses the economic tensions that affect firm equity prices
and trading volume around “good news” disclosures of firm performance in
a setting in which all investors who trade equities are subject to tax. We high-
light the different market behaviors that may arise in economies in which
tax considerations play a role, versus ones in which they do not. Specifically,
we define an intertemporal tax discontinuity (ITD) as a circumstance in
which different tax rates are applied to gains realized at one point in time
versus some other point in time (e.g., distinctions between long-term and
short-term capital gains tax rates). We then study the effects of ITDs on mar-
ket behaviors at the time of disclosures of firm performance. The results
of our paper suggest that relative to an economy in which ITDs are absent,
∗
University of North Carolina; †University of Pennsylvania. The paper has benefited from
discussions with Jana Raedy, and comments from Merle Erickson, Ed Maydew, and seminar
participants at the University of Chicago.
2
05
Copyright ꢀC , University of Chicago on behalf of the Institute of Professional Accounting, 2002

206
D. A. SHACKELFORD AND R. E.VERRECCHIA
ITDs may dampen trading volume and amplify price changes at the time of
1
disclosure.
We employ a stylized model of trade to analyze ITDs. Stylized trading
models are a common device in the accounting literature to study the effects
of disclosures on price changes and trading volume (e.g., Lundholm [1988],
Kim and Verrecchia [1991a], and Bushman, Gigler, and Indjejikian [1996]).
None of the extant models, however, consider the role of taxes. Among a host
of justifications for eschewing taxes, one could include: a preponderance
of traders, such as pension funds and tax-exempt organizations, who are
not subject to taxes; tax planning that mitigates the effect of taxes among
traders subject to tax; and perfect substitutability among financial assets
2
that allows potential tax gains to be offset against tax losses. While all of
these phenomena mitigate the effects of taxes, as a practical matter another
reason why taxes are eschewed in models of trade is that they create complex
modeling problems that are difficult to address. The novel feature of our
analysis is its attempt to integrate tax considerations into a standard model
of trade and grapple with these difficulties.3
The operative word here is “grapple.” Tax considerations are very diffi-
cult to address in general settings; consequently, for pedagogical reasons we
predicate our analysis on the polar case of an economy in which all investors
are subject to the tax implications of ITDs. The benefit of this setting is trans-
parency: in this polar case, the equilibrium is unique and well defined, which
makes transparent the effects of ITDs on the behaviors of price changes
and trading volume. In the concluding section of this paper, section 4,
we explore the general situation in which some investors are subject to
ITDs, while others are not. We refer to this setting as a “mixed economy.”
We discuss a mixed economy to acknowledge that, in general, anything can
happen. For example, in a mixed economy there may exist equilibria that
comport with economic regimes in which either no investor is subject to
ITDs or all investors are subject to ITDs. We postpone a discussion of the
general case until the end for pedagogical reasons: before pointing out that
in general “anything can happen,” we believe that it is useful for the reader
to understand first how this may arise by characterizing the general case as
1
Although this paper focuses specifically on price and volume responses to public dis-
closures about firm performance, its implications apply more generally. For example, Cutler
[1988], Erickson and Maydew [1998], Guether [2000], Blouin, Raedy, and Shackelford [2002],
and Lang and Shackelford [2000], among others, document equity price and volume responses
to public disclosures about tax legislation.
2
For a discussion of these issues, see Miller and Scholes [1982], Stiglitz [1983],
Constantinides [1983, 1984], Poterba [1987], Scholes and Wolfson [1992], and Shackelford
[
2000], among many others.
3
Tax studies have been similarly remiss by ignoring any trading implications for disclosures.
Although long recognizing the potential significance of taxes on asset pricing (e.g., Miller
1977], Poterba and Summers [1984], Balcer and Judd [1987], Fama and French [1998],
[
Reese [1998], Guenther and Willenborg [1999], Harris and Kemsley [1999], Poterba [2001],
among many others), to our knowledge no tax study incorporates the impact of disclosure on
trading.

INTERTEMPORAL TAX DISCONTINUITIES
207
a variant of the polar case in which all investors are subject to an identical
tax structure.
The intuition underlying our analysis of a setting in which all investors are
subject to an ITD can be described briefly as follows. To the extent to which
disclosure leads to homogeneous expectations about the (uncertain) value
of a risky asset (e.g., a firm), all investors gravitate toward an equilibrium in
which the risk associated with holding the risky asset is optimally shared (in-
dependent of expectations). Optimal risk sharing in the disclosure period,
however, requires that those investors who are overweighted in the risky
asset relative to the optimal risk-sharing amount unwind their positions by
selling shares of the asset. From the perspective of overweighted investors,
selling ensures a certain profit and eliminates the risk of maintaining an
overweighted position in an asset whose future value is uncertain. But the
extent to which investors sell off an overweighted position, or whether they
4
sell at all, is unclear if the sale triggers an income tax. The greater the ap-
preciation on the asset sold, the greater the realization tax, and hence the
greater the incentive to defer selling. Consequently, at the time of the disclo-
sure, investors must choose between sharing risks optimally and reducing
taxes optimally by postponing asset sales in the event that the disclosure is
“good news.” This coordination of risk and tax suggests that investors who
are overweighted will unwind some, but not all, of their position at the time
of the disclosure. In addition, the amount sold should decrease as the dif-
ference between the expected long-term and short-term capital gains tax
rates increases.
In the absence of tax mitigating phenomena, these risk-tax trade-offs
should affect both share price and trading volume at the time of the dis-
closure. For example, if taxes preclude investors from fully unwinding their
overweighted positions, the supply of equity will be restricted. To compen-
sate for the tax-motivated restriction in supply, the share price will be bid
up. Consequently, price changes at the time of a “good news” disclosure will
be greater because of the unwillingness of potential sellers to unwind their
5
positions arising from the realization tax. In addition, the unwillingness of
sellers to unwind their positions should result in a reduction in the equity’s
trading volume.6
The specific ITD that motivates our study is the differential rate that exists
between long-term capital gains tax rates and short-term capital gains tax
4
Tax scholars have long recognized that a tax at realization provides incentives for investors
to defer the disposition of appreciated property. In the tax literature, this is commonly called
the “lock-in” effect (Holt and Shelton [1962]).
5
Independent of tax considerations, a “good news” disclosure may lead to price increases
for other reasons, e.g., a permanent increase in demand for the asset. See, for example,
Shleifer’s [1986] examination of the price response of firms who join the S&P 500.
6
See Blouin, Raedy, and Shackelford [2001] for empirical evidence consistent with these
claims. They investigate price and volume movements around quarterly earnings announce-
ments and find that price is increasing and volume is declining in the amount of taxes saved
by deferring the recognition of a capital gain from short-term to long-term.

208
D. A. SHACKELFORD AND R. E.VERRECCHIA
7
rates for individual investors under U.S. tax law. Long-term capital gains
tax rates in the U.S. have been less than short-term capital gains tax rates
since 1922, except for the period 1988–1990 when rates were equal. Under
current law, equity held for more than one year is characterized as long-term
and taxed at no greater than a 20% statutory tax rate, while other capital
gains face a 39.6% maximum statutory federal tax rate. We ignore capital
losses in this analysis because currently these losses provide the same tax
deduction regardless of whether they are long or short.8
2
. Description of the Economy
2.1 GENERAL ASSUMPTIONS
In this section we introduce all the assumptions that underlie our analysis.
We begin by assuming a model of trade in which two types of investors ex-
changeariskyassetanda risk-and-tax-free asset(as anumeraire commodity).
In period 1 both investor types hold shares of the risky and risk-and-tax-free
asset in anticipation of a public disclosure about the value of risky asset in
period 2. In period 2 the disclosure occurs and investors (potentially) trade
asset shares to rebalance their portfolio of investments. In period 3 all assets
liquidate and all investors consume their portfolio holdings.
In our analysis we characterize an ITD as follows. We assume that for
tax purposes periods 1 and 2 are sufficiently close in time that any profit
that arises from investors divesting part or all of their period 1 risky asset
investment in period 2 is taxed at the ordinary tax rate of t. Alternatively,
we assume that period 3 is sufficiently distant in time that divesting any of
their risky asset investment at that time is subject only to a long-term capital
gains tax rate that is lower than the ordinary tax rate. To capture the tension
arising from an ordinary tax rate on income that is higher than the long-
term capital gains tax rate, it is sufficient in our analysis to assume that the
ordinary income tax rate is positive (i.e., t > 0) and the capital gains tax rate
is 0. Consequently, for convenience we employ this convention. Henceforth
we refer to the tax differential between the ordinary income tax rate and
the capital gains rate as the ITD.
7
Our definition of an ITD is designed to embrace tax discontinuities that arise from situa-
tions other than a differential between long- and short-term capital gains. For example, an ITD
can arise when profits realized early are taxed at a higher rate than profits deferred until some
future period because the future period represents: a time at which the deferred profits are
realized and offset against other losses; a time at which deferred profits are passed to the next
generation or another organizational form at some reduced tax rate (e.g., step-up in tax basis
at death); or a time at which an anticipated rate reduction in the existing tax structure finally
occurs. All of these alternative interpretations are compatible with the results of our analysis.
8
This has not always been the case: from 1970 to 1986, long-term capital losses provided
one-half the deduction of short-term capital losses. Currently, individual investors are limited
to an annual deduction of $ 3,000 for capital losses in excess of capital gains. Corporations
cannot deduct any capital losses in excess of capital gains. Complex rules for netting capital
gains and losses, however, can create effectively a preference for short-term capital losses.

INTERTEMPORAL TAX DISCONTINUITIES
209
One caveat to our analysis is that we assume that tax rates in all periods
are known and fixed. As we discuss in the introduction, we predicate our
analysis on the coordination conflict that arises between risk sharing and
tax planning. To the extent to which uncertainty exists about tax rates in
the future, this is likely to make tax planning more difficult, and hence less
compelling in any risk-sharing-versus-tax-planning trade-off. Consequently,
uncertainty about future tax rates likely attenuates our results.
Continuing with a discussion of our model, the risk-and-tax-free invest-
ment pays out a return of 1 for each unit of investment (and has no tax
implications). Alternatively, when the risky asset liquidates in period 3, it
pays out an uncertain liquidating dividend to shareholders that is taxable at
the capital gains rate (which is 0). Let u˜ represent the (uncertain) liquidat-
ing value of the risky asset; the realized value of u˜ , u˜ = u, does not become
common knowledge until period 3. Let y˜ represent the public disclosure in
period 2. To ensure that the analysis is as facile as possible, we assume that
investors’ conditional expectations about u˜ in period 2 (i.e., conditional on
the disclosure) are that u˜ has a normal distribution with mean E[ u˜ | y˜ = y]
9
and variance V ar[ u˜ | y˜ = y].
We label the two investor types “A” and “B,” and assume that investors of
each type are identical to all other investors of that type. Let j ∈ (A, B)
represent a generic investor type. Each investor type is assumed to be risk-
averse with a utility for income of w given by U j (w), where U j (w) is the
negative exponential utility function with positive risk tolerance parameter
w
r j
ofr j > 0:U j (w) = −exp[− ]. While the assumption of risk aversion on the
part of investors plays a critical role in our analysis, it should be emphasized
that it is a standard assumption in models of trade. In addition, note that
investors can be very, very tolerant of risk (i.e., r j can be very large), provided
no one is explicitly risk neutral. Finally, let πA and πB represent the relative
proportions of type-A and type-B investors in the economy, respectively,
where πA +πB = 1. We assume that the proportion of investors of each type
remains fixed over the first two periods that we model.
Let P1 represent the price of the risky asset in period 1 and let D 1A and
D 1B represent the amounts of the risky asset held by investor-types A and B,
respectively, in that period. Similarly, let P2 represent the price of the risky
A
B
asset in period 2, and D and D the amounts of the risky asset held by types
2
2
A and B, respectively, in that period. Let x represent the per-capita supply
of the risky asset. Note that we do not require that x be of any particular
sign, although a conventional assumption is that the supply of a risky asset
is positive. One assumption we do require, however, is that the per-capita
supply also does not change over the first two periods. This implies that
investors’ per-capita demand for the risky asset in both periods 1 and 2
A
1
B
1
A
B
must equal the per-capita supply: πA D +πB D = πA D +πB D = x. One
2
2
9
A conventional, institutional interpretation of the assumption that y˜ subsumes all prior
information about u˜ is that any prior information is a forecast of y˜ , which the actual disclosure
of y˜ in period 2 subsumes: see, for example, Abarbanell, et al. [1995].

210
D. A. SHACKELFORD AND R. E.VERRECCHIA
A
1
A
B
1
B
straightforward implication of this relation is that if D > D , then D < D ,
2
2
and vice versa. Intuitively, this means that if one investor-type divests some
A
1
A
of its period 1 holdings of the risky asset in period 2 (e.g., D > D ), the
2
other investor-type must be simultaneously accumulating, or adding to, its
B
1
B
holdings of the risky asset in period 2 (e.g., D < D ), and vice versa.
2
2.2 THE ABSENCE OF AN ITD
Note that in the stylized economy we describe above, there are at least
two reasons why ITDs may be absent. As alluded to in the introduction, the
first reason is that taxes in general play no role. This could result from: a
preponderance of traders who are not subject to taxes; tax planning strate-
gies that mitigate the effect of taxes among investors subject to tax; and
financial assets that are perfect substitutes, thereby allowing any potential
tax gains to be offset against tax losses. In the context of our analysis, this is
tantamount to suggesting that t = 0. The second reason is that the ordinary
income tax rate and the capital gains tax rate are identical. In the context
of our analysis, this is tantamount to suggesting that the long-term capital
gains tax rate is t: that is, the same as the ordinary income tax rate. Because
both these cases yield equivalent results, for convenience we characterize
the absence of an ITD as a situation in which t = 0.
In the absence of an ITD, it is a straightforward exercise to show that the
unique, Pareto efficient equilibrium in period 2 is:
rA
D2A
D2B
=
=
x;
x;
πArA + πBrB
rB
πArA + πBrB
1
P2 = E[ u˜ | y˜ = y] −
V ar [ u˜ | y˜ = y]x.
πArA + πBrB
See, for example, Wilson [1968]. This equilibrium can be explained by the
fact that in period 2 all investors (regardless of type) have homogeneous
expectations about the value of the risky asset conditional on the disclosure;
hence, they hold per-capita amounts of the risky asset in relation to their risk
tolerance profiles (i.e., the r j s) and their proportional representation (i.e.,
the πj s). For example, if both investor types have the same tolerance for
risk (i.e., rA = rB), the Pareto efficient equilibrium is for each investor type
to hold the per-capita amount as its share of the risky asset (independent of
type): that is, D 2A = D2 = x.
B
For convenience, we refer to an investor type as being “overweighted”
in the risky asset if, in period 1, the type holds more than the Pareto effi-
cient amount described above, and “underweighted” if the type holds less.
A
rA
For example, type-A investors are overweighted if D >
x, and
1
π r + π r
A
A
B B
A
rA
underweighted if D <
x. Note that if one investor-type is over-
1
π r + π r
A
A
B B
weighted, then the other type must be underweighted. In addition, note
that “underweighted” does not imply necessarily a short-sale position: when

INTERTEMPORAL TAX DISCONTINUITIES
211
x is positive, an investor-type can be underweighted and still hold a positive
amount of the risky asset. To facilitate the discussion, in this paper we ignore
tax issues that arise from investors executing short-sales, and price change
and trading volume effects that arise from restrictions and/or prohibitions
on short-sales.
Let a circumstance in which P2 − P1 > 0 be defined as one in which the
disclosure in period 2 is “good news.” In the subsequent analysis we focus
A
on the “good news” case and determine endogenously values for P2, D and
2
B
D2 in the presence of an ITD (i.e., t > 0); then we contrast these values to
those that arise in the absence of an ITD (i.e., t = 0). Alternatively, all of P1,
A
B
D
and D are treated as exogenous. The reason for this is twofold. First,
1
1
A
B
determining P1, D and D endogenously complicates the analysis without
1
1
further enhancing the paper’s contribution, which is to understand the
behavior of price and volume in period 2 at the time of a disclosure. Second,
and perhaps more salient, there is no need to determine endogenously
A
1
B
1
values for P1, D and D because the results ofour analysis donot depend on
these values. Specifically, as discussed in more detail below, the equilibria we
describe depends exclusively on the economic characteristics of the investor
type that is overweighted in the risky asset in period 1. The actual values of
A
B
D and D , however, play no role.
1
1
While the actual values of D1 and D B play no role, for convenience we
A
1
assume that in period 1 investors are not in the period 2 Pareto efficient
equilibrium: That is, D1A
ꢁ
rA
x and D1B
ꢁ
rB
x. While there
π r + π r
A
A
B
B
π r + π r
A
A
B
B
are many rationales for why this may not be the case, the one most
commonly cited in the extant literature is that in period 1 different investor
types have heterogeneous expectations of heterogeneous quality about ei-
ther the value of the risky asset or the forthcoming disclosure in period 2 (or
both).10 These heterogeneous expectations likely arise from different priors
and/or different private information. While in principle there is no harm
A
rA
B
x and D =
1
rB
in assuming the alternative that D =
x, it
1
π r + π r
π r + π r
A
A
B
1
B
A
A
B B
1
precludes the possibility of trade in period 2. No trade is an uninteresting
case from the perspective of this paper because it results in no difference
in market behaviors in ITD-free versus ITD economies, and it characterizes
a situation that does not appear to be descriptive of real market settings
around disclosure events. Consequently, we ignore this case.
3
. An ITD Economy
3.1 EQUILIBRIA IN THE PRESENCE OF ITDS
In this section we assume that both investor types (in effect, everyone in
the economy) face an identical tax structure characterized by the existence
1
0
See, for example, the discussions in Kim and Verrecchia [1991a,1991b] and Abarbanell,
et al. [1995].
1
1
See Milgrom and Stokey [1982] and Verrecchia [2001] for more discussion of why no
trade occurs for this circumstance in an economy of the type we employ.

212
D. A. SHACKELFORD AND R. E.VERRECCHIA
of an ITD. That is, we assume that the reduction of any investor type’s risky
asset position from period 1 to period 2 in the presence of “good news”
implies paying tax on the profit at the ordinary income tax rate of t. For
A
A
example, if D > D , then type-A investors reduce their holdings in the
1
2
A
A
risky asset by an amount D1 − D > 0, and register a profit net of tax on
2
A
A
that transaction of (P2 − P1)(D1 − D )(1 − t). Alternatively, we assume
2
that the increase in any investor type’s risky asset position from period 1 to
period 2 implies no taxable profit at the ordinary income tax rate of t. For
example, if D 1A ≤ D , there are no tax implications to the behavior of type-A
A
2
investors in period 2. In effect, we treat profits realized in period 2 as tax
disadvantaged because insufficient time elapses between periods 1 and 2 to
allow investors to avail themselves of the favorable long-term capital gains
tax rate.
To briefly sketch the results of this section, first we introduce and discuss
the two potential equilibria in period 2 that result from investors’ actions in
the presence of ITDs. Then we establish that despite two candidates, there
is in fact a unique equilibrium with the following feature. The investors
among the type that is overweighted in the risky asset in period 1 always
reduce their risky asset position in period 2. Similarly, investors among the
type that is underweighted in the risky asset in period 1 always increase
their risky asset position in period 2. This implies that investors who are
overweighted in period 1 have their profits taxed at a rate t. Consequently,
tax effects on prices and trading volume in our model arise exclusively
through the behavior of investors who are overweighted in the risky asset in
period 1.
To start, note that when a “good news” disclosure occurs in period 2,
type-A investors face one of two optimization problems. If D 1A − D2 > 0,
type-A investors divest themselves of part of the risky asset position they
established in period 1. Consequently, here a type-A investor solves:
A
ꢀ
ꢀ
ꢆ
1
ꢁ
ꢂ
ꢃ
ꢄ ꢅ
ꢅ
A
2
A
1
A
2
max E −exp −
( u˜ − P1)D + (P2 − P1) D − D (1 − t) y˜ = y .
A
D
rA
2
For example, in this characterization, a type-A investor’s risky asset position
A
A
in period 1 is D . Type-A investors pay capital gains tax on that part of D
1
1
A
that they retain through to period 3, which is D . Note, however, that in our
2
characterization the capital gains tax is zero, and hence their profit for this
A
A
part is ( u˜ − P1)D . They pay ordinary income tax of t on that part of D that
2
1
A
1
A
they sell in period 2, which is D −D . Here, their profit (or loss) on this part
2
A
1
A
net of the ordinary income tax is (P2 − P1)(D − D )(1−t). If, alternatively,
2
A
1
A
D − D ≤ 0, here type-A investors (weakly) increase their holdings of the
2
risky asset in period 2. Hence, here they pay capital gains tax (which is 0)
A
A
A
1
A
1
on their profit in period 3 of u˜ D − P2(D − D ) − P1 D , which, one can
2
2
A
A
1
A
show, equals ( u˜ − P1)D + (P2 − P1)(D − D ). Consequently, here they
2
2

INTERTEMPORAL TAX DISCONTINUITIES
213
solve:
ꢀ
ꢀ
ꢆ
1
ꢁ
ꢂ
ꢃꢄ ꢅ
ꢅ
A
2
A
1
A
2
max E −exp −
( u˜ − P1)D + (P2 − P1) D − D
y˜ = y .
A
D
rA
2
Well known properties of the moment generating function for the normally
distributed uncertain liquidating value of the risky asset (i.e., u˜ ) imply that
A
a type-A investor’s optimization problem with regard to choosing D can be
2
summarized as follows (ignoring irrelevant proportionality factors). Type-A
A
A
A
investors choose D to maximize f (D ), where f (D ) is defined by:
2
2
2
ꢀ
ꢂ
ꢃ
1
1
2r2
ꢂ
ꢃ
ꢃ
2
A
A
A
f D = −exp − (E[ u˜ | y˜ = y] − P1)D +
Var[ u˜ | y˜ = y] D2
2
2
rA
ꢆ
1
ꢂ
ꢃ
A
1
A
2
− r (P2 − P1) D − D (1 − t)
when D 2A < D , and
A
1
ꢀ
ꢂ
ꢃ
1
1
2r2
ꢂ
2
A
2
A
2
A
f D = −exp − (E[ u˜ | y˜ = y] − P1)D +
Var[ u˜ | y˜ = y] D2
rA
ꢆ
1
ꢂ
ꢃ
A
1
A
2
− r (P2 − P1) D − D
when D 2A ≥ D . Note that f (·) is continuous and has, potentially, two local
A
1
optima (i.e., points at which the first derivative of f (·) equals 0). One local
optimum occurs at
E[ u˜ | y˜ = y] − (1 − t) P2 − t P1
D 2A = rA ·
;
Var[ u˜ | y˜ = y]
the other occurs at
E[ u˜ | y˜ = y] − P2
Var[ u˜ | y˜ = y]
D 2A = rA ·
.
Furthermore, both these optima are local maxima because at these points
the second derivative of f (·) is negative. The existence of two local maxima
implies the existence of two potential equilibria. These equilibria can be
characterized as follows.
1
) An equilibrium in which type-A investors in period 2 divest themselves
of some of their holdings of the risky asset acquired in period 1 (i.e.,
A
A
D2 < D ), which, in turn, implies that type-B investors accumulate
1
B
B
1
more of the risky asset (i.e., D2 ≥ D ) because the total supply of the
risky asset is fixed at x; and
2
) An equilibrium in which type-A investors in period 2 accumulate more
A
A
of their holdings of the risky asset from period 1 (i.e., D ≥ D ),
2
1
which, in turn, implies that type-B investors divest themselves of some
B
B
1
of their holdings of the risky asset (i.e., D2 < D ).

214
D. A. SHACKELFORD AND R. E.VERRECCHIA
While in principle there exist multiple equilibria, the first result of the paper
12
demonstrates that the period 2 equilibrium is actually unique. (The proof
to this result is in the appendix.)
PROPOSITION 1. In an economy in which all investors face an identical tax
structure characterized by an ITD, the (unique) equilibrium that occurs in period 2
in conjunction with a “good news” disclosure (i.e., P2 − P1 > 0) is the one in which
the investor-type that is overweighted in the risky asset in period 1 always divests in
period 2, and the investor-type that is underweighted in the risky asset in period 1
always accumulates in period 2. For example, if investors of type j are overweighted
in the risky asset in period 1, where j ∈ (A, B) and k is its complement, the equilibrium
in period 2 is characterized by:
ꢇ
ꢇ
ꢈ
ꢈ
πkrkt
E[ u˜ | y] − P1
Var[ u˜ | y]
r j (1 − t)
j
2
D = r j ·
+
x
πj r j (1 − t) + πkrk
πj r j (1 − t) + πkrk
−
πj r j t
E[ u˜ | y] − P1
rk
k
D = rk ·
+
x; (1)
2
πj r j (1 − t) + πkrk
Var[ u˜ | y]
πj r j (1 − t) + πkrk
(
πj r j + πkrk)E[ u˜ | y] − πj r j t P1 − Var[ u˜ | y]x
P2 =
.
πj r j (1 − t) + πkrk
To understand better proposition 1, it is useful to compare its results to those
in the absence of an ITD (i.e., t = 0). Henceforth we use the expression
“fully unwind” to describe a situation in which investors among the type
that is overweighted in the risky asset in period 1 reduce their position
down to the amount that is implied by the Pareto efficient equilibrium
described in section 2.2: that is, D2A
=
rA
x and D2B
=
rB
x.
π r + π r
A
A
B
B
π r + π r
A
A
B
B
In the absence of an ITD, investors always fully unwind their positions in
period 2 because disclosure results in homogeneous expectations for both
investor-types about the value of the risky asset. Consequently, absent an
ITD, Pareto efficiency dictates that investors of either type hold amounts of
the per-capita supply of the risky asset in relation to their tolerance for risk
and proportional representation. The Pareto efficient equilibrium may not
result in the presence of an ITD, however, because the incentive to share
risk optimally through trade may militate against the incentive to avoid tax.
To elaborate on this, suppose that type-A investors are overweighted in
the risky asset in period 1 and type-B investors are underweighted, and the
disclosure in period 2 is “good news.” There are always two potential equi-
libria. Type-A investors could divest themselves of shares of the risky asset
in period 2 and type-B investors could accumulate. This equilibrium has
negative tax consequences for type-A investors in that they net only 1 − t
1
2
Recallthatweignorecapitallossesinthisanalysisbecausecurrentlytheselossesprovidethe
same tax deduction regardless of whether they are long or short. Consequently, in the context
of our analysis a (weakly) “bad news” disclosure, i.e., P2 − P1 ≤ 0, has no tax implications, and
results in a unique equilibrium that is identical to the ITD-free equilibrium characterized in
section 2.2.

INTERTEMPORAL TAX DISCONTINUITIES
215
of any profits realized in period 2, but it has the advantage that it improves
risk sharing. As an alternative to absorbing the deadweight tax loss of t on
their realized profits, type-A investors could instead (weakly) accumulate
more shares in period 2 (i.e., accumulate more shares or “stand pat”). This,
however, would force type-B investors to (weakly) divest. The problem with
this second equilibrium is that divesting has negative tax consequences for
type-B investors and exacerbates risk sharing for both investor types. Conse-
quently, investors gravitate toward the equilibrium in which type-A investors
divest and type-B investors accumulate.
It is useful for the subsequent analysis to expand on this intuition more
formally. For example, we know from the proof of proposition 1 in the
appendix (see eqn. [A4]) that in the presence of “good news,” the demand
for the risky asset of the investor-type that divests in period 2, say type-A, can
be represented as follows:
ꢇ
ꢈ
πBrBt
P2 − P1
rA
D 2A = rA
+
x.
(2)
Var[ u˜ | y] (πArA + πBrB)
πArA + πBrB
Note, however, that “good news” is defined by P2 − P1 > 0, and hence the
first term on the right-hand-side of equation (2) is positive. This implies
that in the presence of an ITD, type-A investors do not fully unwind their
overweighted positions to hold the optimal risk-sharing amount: that is,
A
rA
D2
>
x. Type-A investors hold back from the market some of their
π r +π r
A
A
B
B
overweighted position established in period 1 because their realized profits
are net of a tax of t, whereas they face no tax for divesting in period 3. Note,
also, that the amount that they hold back increases as t, the size of the ITD
increases. In short, an ITD yields an equilibrium in which the investor-type
that is overweighted in the risky asset sells less aggressively in the presence of
a “good news” disclosure vis a` vis the case in which ITDs are absent because
realized profits are tax disadvantaged.13
3.2 TRADING VOLUME IN THE PRESENCE OF ITDS
Now we extend the intuition developed so far to address how ITDs affect
trading volume. Note that per-capita trading volume in period 2 is charac-
terized in our model by the expression:
1
2
ꢅ
ꢅ
1
2
ꢅ
ꢅ
A
A
1
B
B
1
ꢅ
ꢅ
ꢅ
ꢅ
πA D − D
+
πB D − D
.
2
2
1
3
Note that the amount D2A
r A
−
x can be interpreted as the tax deferred portion
πAr A+πBrB
of a type-A investor’s holdings of the risky asset after trade in period 2. In should be clear from
equation (2) that this deferral is zero if t = 0. The deferral is also zero, however, if there is a
tax on realized profits in period 3 and the period 3 tax equals the period 2 tax of t, because
if the tax is the same in both periods there is no reason to defer the realization of profits.
This result may seem at odds with Klein [1999], who suggests a model of intertemporal asset
pricing in which deferrals are positive despite the existence of a single tax rate. In Klein [1999],
however, deferrals are introduced exogenously. By demonstrating that positive deferrals arise
endogenously through ITDs, our results strengthen Klein’s claims about the role of deferrals
on asset pricing.

216
D. A. SHACKELFORD AND R. E.VERRECCHIA
rA
Recall that in the absence of an ITD, type-A investors would hold
x
πArA + πBrB
rB
and type-B investors would hold
per-capita trading volume is:
x. This implies that absent an ITD,
πArA + πBrB
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
1
2
rA
1
2
rB
A
B
πA
x − D
+
πB
x − D
.
1 ꢅ
1 ꢅ
πArA + πBrB
πArA + πBrB
As discussed above, however, if type-A investors are overweighted in the risky
asset and type-B investors underweighted, a “good news” disclosure results
A
A
rA
B
B
rB
in D1 > D2
>
x and D1 < D2
<
x. But this, in turn,
π r + πBrB
A
A
π r + πBrB
A
A
implies that
1
2
ꢅ
ꢅ
ꢅ
1
2
ꢅ
ꢅ
ꢅ
ꢅ
A
A
B
2
B
ꢅ
πA D − D
+
πB D − D
2
1
1
1
ꢂ
ꢃ
1
2
ꢂ
ꢃ
A
A
2
B
2
B
= 2
πA D − D
+
πB D − D
1
1
ꢇ
ꢈ
ꢇ
ꢈ
1
2
rA
1
2
rB
A
B
<
πA D −
x
+
πB
x − D1
1
πArA + πBrB
πArA + πBrB
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
ꢅ
1
rA
ꢅ
1
2
rB
A
B
ꢅ
= 2
πA
x − D
+
πB
x − D
.
1 ꢅ
1 ꢅ
πArA + πBrB
πArA + πBrB
In other words, a “good news” disclosure results in less trading volume in
the presence of an ITD because investors who are overweighted in the risky
asset do not fully unwind their positions.
COROLLARY 1. In the presence of a “good news” disclosure and relative to the
absence of an ITD, trading volume is lower in the disclosure period (i.e., period 2); the
extent to which it is lower increases as the size of the ITD increases (i.e., as t increases).
3.3 PRICE CHANGES IN THE PRESENCE OF ITDS
With regard to the price of the risky asset in period 2, recall from the
discussion in section 2.2 that absent an ITD (i.e., t = 0), the price of the risky
1
asset in period 2 is P2 = E[ u˜ | y] −
Var[ u˜ | y]x, and hence the
πArA + πBrB
change in price is
1
P2 − P1 = E[ u˜ | y] −
Var[ u˜ | y]x − P1.
πArA + πBrB
Now consider price change in period 2 in the presence of an ITD. If we
exclude from consideration the no trade case discussed in section 2.2, price
change in period 2 can be characterized as:
(
πj r j + πkrk)E[ u˜ | y] − πj r j t P1 − Var[ u˜ | y]x
P2 − P1 =
− P1
πj r j (1 − t) + πkrk
ꢇ
ꢈ
πj r j + πkrk
1
=
E[ u˜ | y] −
Var[ u˜ | y]x − P1
,
πj r j (1 − t) + πkrk
πj r j + πkrk
where the jth subscript, j ∈ (A, B), describes the investor type that is over-
weighted in the risky asset, and the kth subscript describes its complement.

INTERTEMPORAL TAX DISCONTINUITIES
217
This characterization suggests that holding the disclosure itself constant, the
change in price in the presence of an ITD is always greater than in the ab-
πj r j + πkrk
sence of an ITD by a factor of
; this expression is greater than 1
πj r j (1−t) + πkrk
because t > 0. In effect, in the presence of a “good news” disclosure and an
ITD, price changes are greater vis a` vis the no-ITD case. The economic in-
tuition underlying this result is that the realization tax makes investors who
are overweighted in the risky asset unwilling to fully unwind their (over-
weighted) positions.
COROLLARY 2. In the presence of a “good news” disclosure and relative to the
πj r j + πkrk
absence of an ITD, price changes are greater by a factor of
; the extent
πj r j (1−t) + πkrk
to which they are greater increases as either the ITD increases (i.e., as t increases), the
proportion of investors who are overweighted increases (i.e., as πj increases), or the
risk tolerance of the proportion of investors who are overweighted increases (i.e., as r j
increases).
4
. Caveats and Conclusion
As a caveat to our results, in this concluding section we discuss the role
of the assumption employed in section 3 that all investors in the economy
are subject to an ITD. Assuming identical tax treatments for all investors is
clearly an abstraction from real market settings in which both taxable and
14
tax-free investors participate. We refer to an economy in which both tax
and tax-free investors participate as “mixed.” The problem with analyzing
mixed economies is that trading volume and price change behaviors are
governed by the tax characteristics of those investors who are overweighted
in the risky asset. In the absence of specific knowledge about those char-
acteristics, definitive statements and results about how ITDs affect market
behaviors are elusive.
To elaborate further on this issue, recall from the discussion in section 3.1
that the disclosure period equilibrium is characterized by investors who
are overweighted in the risky asset divesting and investors who are under-
weighted in the risky asset accumulating. Suppose, however, that either
type-A investors are tax-free institutions while type-B investors are subject
to ITDs, or type-A investors are subject to ITDs while type-B are tax-free
institutions. Both scenarios comport with a mixed economy. In the case of
the former, the equilibrium that results is identical to an ITD-free equi-
librium described in section 2.2, because as tax-free institutions divesting
1
4
For example, in the case of the latter, distinctions between short-term and long-term
capital gains and losses matter only for sales that are reported on individuals’ tax returns (e.g.,
sales of investments held in personal accounts, street-name, trusts, mutual funds, partnerships,
S corporations, limited liability corporations, and other entities that pass-through taxable gains
and losses from investments). Short-term and long-term distinctions are irrelevant for sales of
investments held in C corporations, tax-exempt organizations, estates, foreign investors, and
individuals investing through individual retirement accounts, 401(k) retirement accounts, and
other defined contribution plans.

218
D. A. SHACKELFORD AND R. E.VERRECCHIA
investors (i.e., type-A investors) are not subject to tax. Hence, this equilib-
rium results in market behaviors at the time of disclosure that are indis-
tinguishable from the ITD-free regime. Alternatively, if type-A investors are
subject to ITDs and type-B investors are tax-free institutions, the equilib-
rium that results is identical to the ITD equilibrium outlined in proposi-
tion 1 because in this situation divesting investors (i.e., type-A investors)
are subject to tax on their short-term capital gains. In short, in a mixed
economy in which some investors are subject to tax considerations while
others are not, some equilibria may have features indistinguishable from
an ITD-free regime, while other equilibria are indistinguishable from an
ITD regime. In other words, all manner of behavior may result. This limits
any claims about how ITDs affect market behaviors in mixed economies in
the absence of specific knowledge of the tax characteristics of investors who
actively participate in the buying and selling of equities at the time of firm
disclosures.
While we acknowledge this limitation, our contribution is to make clear
the economic tension that arises from investors who are subject to an ITD
choosing between optimal risk sharing considerations associated with un-
winding an overweighted position and optimal tax planning considerations
associated with postponing the sale of firm equities. In the case of “good
news,” this coordination of risk and tax suggests that investors who are over-
weighted will unwind less of their position at the time of the disclosure
than is implied by optimal risk sharing. We point out that in the absence
of tax mitigating phenomena, these risk-tax trade-offs should affect both
share price and trading volume behaviors at the time of disclosures of firm
performance.
APPENDIX
PROOF OF PROPOSITION 1. Recall that type-A investors have two local max-
ima:
E[ u˜ | y˜ = y] − (1 − t) P2 − t P1
D 2A = rA ·
D 2A = rA ·
, and
Var[ u˜ | y˜ = y]
E[ u˜ | y˜ = y] − P2
.
Var[ u˜ | y˜ = y]
Similarly type-B investors have two local maxima that are equivalent to those
of type-A investors:
E[ u˜ | y˜ = y] − (1 − t) P2 − t P1
D 2B = rB ·
D 2B = rB ·
, and
Var[ u˜ | y˜ = y]
E[ u˜ | y˜ = y] − P2
.
Var[ u˜ | y˜ = y]
The existence of two local maxima implies the existence of two potential
equilibria. These equilibria can be characterized as follows.

INTERTEMPORAL TAX DISCONTINUITIES
219
1
2
) An equilibrium in which type-A investors in period 2 divest themselves
of some of their holdings of the risky asset acquired in period 1 (i.e.,
A
A
D2 < D ), which, in turn, implies that type-B investors accumulate
1
B
B
1
more of the risky asset (i.e., D2 ≥ D ) because the total supply of the
risky asset is fixed at x; and
) An equilibrium in which type-A investors in period 2 accumulate more
A
A
of their holdings of the risky asset from period 1 (i.e., D ≥ D ),
2
1
which, in turn, implies that type-B investors divest themselves of some
B
B
1
of their holdings of the risky asset (i.e., D2 < D ).
First we analyze these two equilibria. Then we establish that there exists a
unique equilibrium that is characterized as follows. That investor-type that is
overweighted in the risky asset always sells in period 2, and that investor-type
that is underweighted in the risky asset always accumulates in period 2.
Recall that if D 2A < D then D > D , and vice versa. Consequently, the
A
B
B
1
2
1
A
B
requirement that πA D + πB D = x implies that the price of the risky asset
2
2
in period 2 can be characterized as either:
(
π r + π r ) E[ u˜ | y] − π r t P − Var[ u˜ | y]x
A
A
B
B
A
A
1
P2 =
(A1)
πArA (1 − t) + πBrB
if D 2A < D (and hence D > D ); or
A
1
B
B
1
2
(
π r + π r ) E[ u˜ | y] − π r t P − Var[ u˜ | y]x
A
A
B
B
B
B
1
P2 =
(A2)
πArA + πBrB (1 − t)
if D 2A > D (and hence D < D ). Equations (A1) and (A2), in turn, imply
A
1
B
B
1
2
the following refinements for the demand of the risky asset in period 2 on
the part of type-A and type-B investors. If D 2A < D (and hence D > D ),
A
B
B
1
2
1
then
ꢇ
ꢈ
πBrBt
E[ u˜ | y] − P1
Var[ u˜ | y]
rA (1 − t)
D 2A = rA ·
+
x
πArA (1 − t) + πBrB
πArA (1 − t) + πBrB
(
A3)
and
ꢇ
ꢈ
−
πArAt
E[ u˜ | y] − P1
Var[ u˜ | y]
B
rB
D 2B = rB ·
+
x;
πArA (1 − t) + πBrB
πArA(1 − t) + πBrB
while if D A > D (and hence D < D ), then
A
1
B
2
2
1
ꢇ
ꢈ
ꢈ
−
πBrBt
E[ u˜ | y] − P1
Var[ u˜ | y]
rA
D 2A = rA ·
+
+
x
πArA + πBrB (1 − t)
πArA + πBrB (1 − t)
and
ꢇ
πArAt
E[ u˜ | y] − P1
Var[ u˜ | y]
rB (1 − t)
D 2B = rB ·
x.
πArA + πBrB (1 − t)
πArA + πBrB (1 − t)
To establish the existence of a unique equilibrium, let a circumstance in
which P2 − P1 ≥ 0 be defined as one in which the disclosure in period 2 is

220
D. A. SHACKELFORD AND R. E.VERRECCHIA
“weakly good news,” henceforth WGN. We prove proposition 1 by showing
that WGN in combination with the assumptions that A-type investors are
underweighted in the risky asset and divest themselves of some of the risky
asset in period 2 leads to a contradiction. This implies that in the presence
of WGN, investors among the type that is underweighted must accumulate
more of the risky asset in period 2; correspondingly, investors among the
type that is overweighted must divest. To begin, assume type-A investors
are underweighted in the risky asset (i.e., D1A
<
rA
x), divest some of
π r + π r
A
A
B
B
the risky asset in period 2, and the disclosure in period 2 is WGN. First, note
that equation (A1) can be rearranged to yield:
(
π r (1 − t) + π r ) P + π r t P + Var[ u˜ | y]x
A
A
B
B
2
A
A
1
E[ u˜ | y] =
(
π r + π r )
A
A
B B
=
(πArA (1 − t) + πBrB)
πArAt
1
P2 + (
P1 +
Var[ u˜ | y]x
(πArA(1 − t) + πBrB )
.
πArA(1 − t) + πBrB )
×
(
π r + π r )
A
A
B B
Substituting this expression for E[ u˜ | y] into equation (A3) implies the
following demand:
πBrArBt
D2A
=
Var[ u˜ | y]
ꢉ
ꢊ
πArAt
πArA(1 − t) + πBrB )
1
(πArA+πBrB )
P2 + (
P1 +
Var[ u˜ | y]x −
B B
P1
(πArA(1−t)+πBrB )
(πArA(1−t)+πBrB )
×
(
π r + π r )
A
A
rA (1 − t)
+
x
πArA (1 − t) + πBrB
ꢉ
ꢊ
πArAt
πArA(1 − t) + πBrB )
(πArA + πBrB )
(πArA(1 − t) + πBrB )
(πArA + πBrB)
P2 + (
P1 −
P1
πBrArBt
Var[ u˜ | y]
=
=
rArB πB t
πArA + πBrB )
+
rA (1 − t)
(
+
x
πArA (1 − t) + πBrB
ꢇ
ꢈ
πBrArBt
P2 − P1
rA
+
x.
(A4)
Var[ u˜ | y] (πArA + πBrB)
πArA + πBrB
But equation (A4), in turn, implies that if the disclosure is WGN (i.e., P2 −
A
rA
P1 ≥ 0), D
≥
x. But this contradicts the assumption that type-A
B
2
π r + π r
A
A
B
investors are underweighted in the risky asset and divest because divesting
A
1
A
rA
shares in period 2 requires D > D2
≥
x, and by assumption
π r + πBrB
A
A
D1A
<
rA
x.
π r + πBrB
A
A
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