Capital Gains Taxes and Stock Return Volatility:
Evidence from Taxpayer Relief Act of 1997
Zhonglan Dai
University of Texas at Dallas
Douglas A. Shackelford
University of North Carolina and NBER
Harold H. Zhang
University of Texas at Dallas
This version: January 15, 2008
We thank Kerry Back, Alex Butler, Michael Gallmeyer, Rick Green, Linda Krull, Harry Huizinga,
Qin Lei, Jing Liu, Gregory Mankiw, Dave Mauer, Lillian Mills, Casey Schwab, Stephanie Sikes,
Kam-Ming Wan, Steve Wei, Yexiao Xu, and seminar participants at Baruch College, Cheung
Kong Graduate School of Business, the Southern Methodist University, Texas A&M University,
the University of Texas at Dallas, the 2007 China International Conference in Finance, the 2007
NBER Summer Institute, the 2007 Oxford University Centre for Business Taxation Summer
Symposium, and the 2007 Western Finance Association meetings for comments; and Scott
Dyreng and Sudarshan Jayaraman for research assistance. Zhonglan Dai is at the School of
Management, University of Texas at Dallas, Richardson, TX 75083, [email protected], Douglas
A. Shackelford is at the Kenan-Flagler Business School, University of North Carolina, Chapel
Hill, NC 27599, doug_shack@unc,edu, and Harold H. Zhang is at the School of Management,
University of Texas at Dallas, Richardson, TX 75083, [email protected]. All errors are
our own.
Capital Gains Taxes and Stock Return Volatility:
Evidence from Taxpayer Relief Act of 1997
Abstract
This paper presents evidence consistent with capital gains tax changes inversely affecting
stock return volatility. We show that, since the government shares in the realized gains
and losses of assets held by taxable investors, a capital gains tax rate cut reduces risk
sharing between investors and the government. This reduction in risk sharing adversely
affects investors’ consumption smoothing, increasing consumption risk and leading to
higher asset return risk and volatility. Examining volatility before and after the 1997
reduction in the capital gains tax rate, we document a dramatic increase in the return
volatility of the market index and industry portfolios, even after controlling for all known
determinants of volatility. Furthermore, as predicted, non- or lower dividend-paying
stocks experience larger increases in return volatility than higher dividend-paying stocks
and stocks with large embedded capital losses have larger increases in return volatility
than stocks with small embedded capital losses. These empirical findings show that a
capital gains tax rate cut affects a firm’s return volatility differently depending on its
capital gains tax sensitivity.
1
1. Introduction
This paper examines the effect of capital gains taxes on asset return volatility.
Previous studies of the effects of capital gains taxes on asset prices have focused on the
level of asset returns and on trading volume. This study extends that literature to consider
whether a 1997 reduction in the capital gains tax rate increased the volatility of stock
returns.
Our analysis relies on the role of financial markets in facilitating risk sharing
between investors and the government in the presence of capital gains taxes. Since the
government shares in the realized gains and losses of assets held by taxable investors, a
capital gains tax rate cut reduces risk sharing between investors and the government.
This reduction in risk sharing adversely affects investors’ consumption smoothing,
increasing consumption risk and leading to higher asset return risk and volatility.
Empirically it is difficult to design a test that directly links a reduction in the
capital gains tax rate to an increase in asset return volatility. Thus, we pursue an indirect
approach using equity returns from 1993 to 2002. First, we control for all of the factors
known to affect the volatility of stock returns. Second, we test whether the remaining
stock return volatility increased following a 1997 reduction in the capital gains tax rate.
Third, we test whether the volatility increased more for the stocks whose returns were
most affected by the tax cut.
We find that stock return volatility doubled after 1997. Known determinants of
stock return volatility only account for less than half of the increase. This leads us to
conjecture that the 1997 capital gains tax cut may have contributed to the increase in
volatility. Further tests show that the magnitudes of the increases in return volatility vary
in a predictable manner with characteristics of the stocks, such as dividend distribution
and embedded capital losses. These cross-firm results provide more compelling evidence
that the reduction in the capital gains tax rate boosted stock return volatility.
To our knowledge, this is the first study of the relation between asset return
volatility and the capital gains taxes. It builds on an increasing literature about how
capital gains taxes affect asset prices and trading volume. With regards to asset prices,
existing theoretical studies suggest that the effect of capital gains taxes on asset price is
2
ambiguous because introducing capital gains taxes decreases both the demand and the
supply of assets. Consistent with this ambiguity, empirical investigations of the effect of
capital gains taxes have produced conflicting results. Several studies (Lang and
Shackelford (2000), Ayers, Lefanowicz, and Robinson (2003), among others) report that
the presence of capital gains taxes reduces stock price and current stock return, while
other studies document that imposing capital gains taxes increases stock price and current
stock return (Feldstein, Slemrod, and Yitzhaki (1980), Reese (1998), Klein (2001), Jin
(2005), among others).
With regards to capital gains taxes and trading volume, Dhaliwal and Li (2006)
report that tax-motivated trading activity creates excess trading volume around exdividend days.
Specifically, they find a concave relation between ex-dividend day
trading volume and institutional ownership, their measure of investor tax heterogeneity.
In other words, the more shareholders who face different tax rates (e.g., an even mix of
individuals and institutions), the more trading around ex-dividend dates, as differentially
taxed investors swap securities to minimize their tax liabilities.
In a recent study, Dai, Maydew, Shackelford, and Zhang (2008) investigate the
effect of capital gains taxes on asset price and trading volume by jointly considering the
impact on demand and supply of assets. Using the Taxpayer Relief Act of 1997 as the
event, they find that stock returns are higher in anticipation of a tax cut and stocks with
large embedded capital gains and high tax sensitive investor ownership experience a
lower return after the lower tax rate became effective. They also document that a capital
gains tax cut increases the trading volume the week before and immediately after the tax
cut announcement.
None of the existing studies, however, has examined the impact of capital gains
taxes on asset return volatility. Asset return volatility is one of the key determinants of
investors’ demand and supply of risky assets. Thus, if capital gains taxes affect asset
return volatility, then they affect investors’ demand and supply of risky assets and
ultimately asset returns.
In this paper, we first discuss the relation between the capital gains taxes and asset
return risk and volatility focusing on the risk sharing role of the capital gains taxes
between investors and the government. Based on our analysis, we develop hypotheses on
3
the relation between capital gains taxes and asset return volatility. Then, we empirically
test the predictions using the Taxpayer Relief Act of 1997 as our event.
We hypothesize that after the reduction in the capital gains tax rate:
•
Return volatility increased for the market index and industrial portfolios.
•
Non- or lower dividend-paying stocks experienced a higher volatility increase
than higher dividend-paying stocks.
•
Stocks with large embedded capital losses (gains) experienced a larger
increase in volatility than did stocks with small embedded capital losses
(gains).
The first prediction focuses on the effect of a capital gains tax rate cut on the
return volatility of portfolios and the market index. Thus, it represents the effect of a
capital gains tax rate cut on the volatility of the broad financial market. The next two
predictions focus on the effects of a capital gains tax rate cut on the return volatility of
stocks with different tax liabilities.
Our predictions reflect the roles played by the financial markets. From investors’
perspective, financial markets have two important functions: risk sharing and
consumption smoothing. Besides actively sharing risk with other market participants,
investors also share the risk of holding risky stocks with the government (passively)
through capital gains taxes. To demonstrate, if the investors’ asset holdings have
depreciated in value, then the investors’ after-tax losses are less than the decrease in the
market value of the asset because a fraction of the loss is borne by the government in the
form of reduced capital gains taxes or even tax rebate from the government. Therefore, a
cut in the capital gains tax rate reduces the risk sharing between investors and the
government.
This reduction in risk sharing causes investors to experience more volatile
consumption growth rates resulting in increased consumption risk. According to the
consumption capital asset pricing model (CCAPM), the risk of a portfolio of stocks is
determined by its equilibrium risk to consumption (Rubinstein (1976) and Breeden
(1979)). Thus, an increased consumption risk will lead to higher return risk and volatility
for a portfolio of stocks. While earlier empirical studies failed to provide supporting
4
evidence using contemporaneous consumption growth, 1 more recent studies show a
strong positive relation between stock return risk and the ultimate consumption risk, as
measured by the consumption growth over the quarter of return and subsequent quarters
(Parker and Julliard (2005) and Tedongap (2007)).
The impact of a capital gains tax change on risk sharing, and thus its impact on
stock return volatility, should vary depending on the characteristics of particular stocks.
For example, suppose investors receive all returns as dividends, then capital gains taxes
are irrelevant and changes in the capital gains tax should have no impact on consumption
risk and return volatility. Conversely, if all future returns are expected to be taxed at the
new capital gains tax rate, then we would expect the rate change to substantially increase
consumption risk and return volatility. More generally, the capital gains tax change
should matter to the extent that investors anticipate the capital gains tax rate change
affecting future returns.
In our tests, we assume that firms will maintain their current dividend policy, and
thus, predict that, ceteris paribus, non- and lower dividend-paying stocks are subject to
greater risk than other firms, when capital gains tax rates are lower. Consequently, a
capital gains tax reduction will result in larger increases in return volatility for non- or
low-dividend stocks than for higher dividend-paying stocks.
Similarly, when investors sell, stocks with large embedded capital losses (gains)
trigger larger capital losses (gains) than stocks with little or no depreciation
(appreciation). Thus, a capital gains tax reduction causes stocks with larger, embedded
capital losses (gains) to become riskier because there is less risk sharing with the
government. Therefore, we predict that these stocks will experience higher volatility
increases when capital gains tax rates are cut. Furthermore, the effect is likely to be
stronger on portfolios of stocks with large embedded capital losses than stocks with
embedded capital gains because the losses are likely to have a larger impact on
consumption risk than gains. This can be attributed to a number of reasons. For example,
investors’ preferences may exhibit habit formation so that reduced consumption
associated with investment losses increases the investors’ risk aversion while increased
1
See Mankiw and Shapiro (1986), Breeden, Gibbons, and Litzenberger (1989), Campbell (1996), Cochrane
(1996), Lettau and Ludvigson (2001), among others.
5
consumption associated with investment gains reduces the investors’ risk aversion (see
Campbell and Cochrane (1999)).
We test these predictions by comparing stock return volatility before and after the
1997 reduction in the individual capital gains tax rate from 28 percent to 20 percent.
Using data from January 1993 to December 2002, we construct a market portfolio before
and after the legislation. After controlling for numerous factors which are widely
documented to be important determinants of stock return volatility and the state of the
economy, we find the volatility of monthly excess return of the value-weighted CRSP
stocks is more than 1.9 percentage points higher after the 1997 rate cut. This compares
with an average monthly volatility of 2.7 percent before 1997. Similarly, we find that the
monthly implied volatility for the Standard & Poors index options (VIX) increased by 2.1
percentage points after the capital gains tax cut, controlling for the non-tax determinants.
This compares with an average of 4.1 percent before 1997.
We repeat the analysis for five industry portfolios based on 4-digit SIC code:
consumer industry, manufacturing industry, high tech industry, healthcare industry, and
other industries. We find that the monthly return volatility is higher for all five portfolios
after the capital gains tax rate is reduced, once again controlling for variables often
identified to be important factors affecting return volatility. The increase in monthly
return volatility ranges from 1.6 percentage points for the manufacturing industry to 2.5
percentage points for the high tech industry.
Together, these results provide evidence that stock return volatility increased after
1997 for reasons other than those previously documented in the literature. We conjecture
that the 1997 cut in the capital gains tax rate partly explains the increases. However, it is
impossible to fully rule out other, non-tax factors (previously overlooked in the literature)
that arose around the time of the 1997 tax cut. This leads us to cross-sectional tests in an
attempt to address any problems potentially arising from omitted correlated variables.
The cross-sectional tests exploit differences across stocks in dividend yields and
embedded capital losses and gains. In our first set of tests, as predicted, we find that the
portfolio of non-dividend paying stocks experiences higher volatility increase than
dividend-paying stocks, consistent with the prediction of our analysis. Specifically, after
the rate cut, non-dividend paying stocks experience 1.2 percentage points higher monthly
6
return volatility than dividend-paying stocks, on average, after controlling for
documented determinants of stock return volatility, the state of the economy, both
domestic and foreign stock market performances, the debt-asset ratio, turnover, the
percentage bid-ask spread, size, earnings volatility, and growth option, among others.
This is above and beyond the 1.8 percentage points higher monthly return volatility of
non-dividend paying stocks relative to that of dividend paying stocks before the capital
gains tax cut.
In our second set of tests, as predicted, we find that stocks with large embedded
capital losses (i.e., losses in the upper 25 percentile) experience 1.1 percentage points
higher monthly return volatility increase than stocks with small embedded capital losses
(i.e., losses in the lower 25 percentile). This is in addition to the 1.8 percentage points
higher monthly return volatility of the large loss stock portfolio relative to that of the
small loss stock portfolio, and after controlling for all other determinants of return
volatility. However, contrary to expectations, we find no evidence that volatility varied
with the amount of embedded capital gains.
Finally, we repeat our cross-sectional tests (dividend yield and embedded losses
and gains), assuming capital gains taxes had been cut one, two and three years earlier, i.e.,
in 1996, 1995, and 1995, respectively.
Using these hypothetical dates, we find no
evidence of higher volatility for non-dividend-paying stocks or those with large
embedded losses or gains. This provides some comfort that the changes in volatility
occurred in 1997.
It is worth noting that the stock return volatility increase associated with a capital
gains tax cut does not necessarily imply that investors are worse off when the capital
gains tax rate is lower. This is because a capital gains tax cut may increase the after-tax
stock return. Consequently, investors may experience the same or an improved returnand-risk trade-off and thus face the same or better investment opportunities. However,
the findings in this paper does suggest that, when capital gains taxes are cut, taxable
individual investors incur costs, which, to our knowledge, have heretofore gone
unnoticed.
The paper is organized as follows. In section 2, we discuss the relation between
the capital gains taxes and stock return volatility and develop hypotheses about the
7
effects of a capital gains tax cut on return volatility both for the broad market and the
cross-section of portfolios of individual stocks with different capital gains liabilities.
Section 3 presents empirical methodology to test the predictions of our analysis. Section
4 discusses the results of the empirical analysis. Section 5 provides closing remarks.
2. Capital Gains Taxes and Stock Return Volatility
Financial markets and the financial assets traded in those markets serve two
important roles for investors: consumption smoothing and risk sharing. Some individuals
earn more than they currently wish to spend; others spend more than they currently earn.
Trading in financial assets allows these individuals to shift their purchasing power from
high-earnings periods to low-earnings periods by buying financial assets in high-earning
periods and selling these assets to fund their consumption needs in low-earning periods.
Financial markets and the financial assets also allow investors to allocate risks among
themselves so that risk in their portfolio is commensurate with the return to the portfolio,
i.e., investors with high risk tolerance hold riskier assets, such as stocks, and those with
low risk tolerance hold more less risky assets, such as money market instruments. In an
economy without government taxation, market participants achieve consumption
smoothing and risk sharing through the trading of financial assets on financial markets.
However, through taxation and, in our case, capital gains taxation, the
government influences the consumption smoothing and risk sharing of market
participants. In the United States, capital gains taxes are levied upon selling an asset
based on the appreciation or depreciation on the asset. Specifically, in the case of
common stocks, if a stock has appreciated in value, the investor pays capital gains taxes
on the appreciation upon selling. Conversely, if the stock has depreciated in value upon
selling, the investor can use the realized losses to offset realized gains on other assets. If
the realized losses exceed the realized gains, the losses can be used to reduce the taxable
ordinary income up to a limit with the remaining losses carried forward to offset future
gains and ordinary income. (Because there are almost always capital gains available to
offset capital losses, we assume throughout the paper that all realized capital losses can
8
be fully and immediately utilized to offset other realized capital gains.2) Thus, the tax
treatment of gains and losses on stocks offers a risk sharing mechanism between
investors and the government that affects the consumption smoothing of stock market
participants.
The fundamental insight of the Consumption Capital Asset Pricing Model
(CCAPM) is that the risk of an asset is determined by its equilibrium risk to consumption.
A higher consumption risk of an asset is associated with a higher risk of its return. For
portfolios with a large number of stocks, the return risk is often measured by its volatility,
implying a positive relation between the consumption growth risk and the stock return
volatility. Until recently, most empirical tests on the CCAPM found the relation between
the consumption risk and the stock return to be weak, when the consumption risk was
measured by the contemporaneous consumption growth rate on the stock returns. Recent
studies have found strong evidence for a positive relation between consumption risk and
stock returns, when the consumption risk is measured over a longer horizon. For example,
Parker and Julliard (2005) document that the ultimate risk to consumption, defined as the
covariance of asset returns and consumption growth over a horizon of three years can
explain from 44 to 73 percent of the variation in expected returns across portfolios of
stocks. Because a reduction in the capital gains tax rate adversely affects the risk sharing
between investors and the government and the consumption smoothing of stock market
participants, it will increase the consumption risk over the long horizon and consequently
lead to higher stock return volatility.
To facilitate the development of our hypotheses about the relation between the
capital gains taxes and stock return volatility, we focus on some extreme cases and then
offer insights on general situations. We start with the effect of the capital gains taxes on
2
Individuals, the only investors affected by the reduction in the capital gains tax rate studied in this paper,
face no limit on the amount of capital losses that they can use to offset capital gains. If capital losses
remain after offsetting all capital gains, then individuals can apply up to $3,000 of capital losses against
ordinary income. In practice, this constraint is rarely binding (Poterba [1987] and Auerbach, Burman and
Siegel [2000]). The Internal Revenue Service [1999a, 1999b] reports that in the year of the capital gains
rate reduction (1997), individuals in the maximum tax bracket (39.6 percent), who accounted for 61 percent
of all net capital gains, reported $169 billion of long-term capital gains and only $5 billion of long-term
capital losses and $16 billion of short-term capital gains and only $8 billion of short-term capital losses. In
short, individual investors had far more capital gains than they had capital losses to offset them. Thus, for
our purposes, it is reasonable to assume that realized capital losses can be used to offset realized capital
gains.
9
the broad financial market and then discuss the implications of a change in the capital
gains taxes on return volatility across stocks. In all cases, we view capital gains taxes as
the mechanism through which the government “partner” shares the return of stock
investments with its taxable investor “partner.”
To begin, suppose the capital gains tax rate approaches 100 percent. The
government “partner” gets almost all the returns of investments made by taxable
investors. Consequently, the government bears almost all the risk, while the taxable
investors bear almost none. Conversely, suppose that the capital gains tax rate is zero.
Now, the taxable investor “partner” receives all the returns and bears all the risk. The
government collects no revenue and bears no risk.3
In reality, the capital gains tax rate is typically positive but well below 100
percent. When the capital gains tax rate increases, the government “partner” receives a
larger fraction of the return and bears more risk. The taxable investor “partner” receives a
lower fraction of the return and bears less risk. However, when the capital gains tax rate
is reduced, the government “partner” gets a smaller fraction of the return and bears less
risk, while the taxable investor “partner” receives a larger fraction of the return and bears
more risk. Because capital gains taxes apply to all stocks, a capital gains tax rate
reduction causes taxable investors to receive a larger fraction of returns on all stocks and
to bear more risk on all the stocks. This leads to more volatile consumption growth rates
for taxable investors. As a result, we have the following hypothesis on the relation
between the capital gains taxes and the return volatility for the broad stock market.
H1: A reduction in the capital gains tax rate will lead to higher return volatility
for the market index and industry portfolios.
Based on a firm’s characteristics, the impact of a capital gains tax rate change on
the risk sharing between taxable investors and the government may vary across stocks,
and, consequently, return volatility may vary across stocks. For instance, the impact of a
3
As a simple example, suppose an investor purchases a stock for $1 and intends to sell it three years later.
There is 50 percent chance that the stock will be traded at $2 in three years and a 50 percent chance that the
share will be worthless in three years. If the capital gains tax is zero, the investor will experience either a
$1 after-tax gain or a $1 after-tax loss in three years. If the capital gains tax rate is 100 percent, the investor
will have no after-tax gain or loss in three years, i.e., the investor will continue to have $1 of wealth. The
reason is that in the case of a pre-tax gain of $1, the entire profit will be taxed. In the case of a pre-tax loss
of $1, the loss will fully offset a $1 gain from another sale (which would otherwise have been fully taxed).
As a result, the $1 loss reduces the investor’s total tax bill by $1.
10
capital gains tax rate change on the risk sharing between taxable investors and the
government may vary across firms with different dividend yields.
For example, if taxable investors receive all returns from a firm as dividends, then
no income received is subject to capital gains taxes. Consequently, the government bears
no risk related to capital losses or gains and the capital gains taxes will have little direct
effect on stock return volatility. On the other hand, if the taxable investors receive no
dividends, then the entire return comes as capital gains. In that case, all income will be
subject to capital gains taxes and the government bears the maximum risk associated with
the capital gains. As a result, a capital gains tax change for these all-capital-gains firms
will have a large impact on the risk sharing between the taxable investors and the
government. This will affect the consumption risk of the taxable investors and the stock
return volatility. In general, the greater the percentage of profits taxed as capital gains,
the greater a cut in the capital gains tax rate reduces the amount that the government
shares in the risk and, thus, increases the return volatility of the stock. This leads to the
following hypothesis on the relation between stock return volatility and firms’ dividend
payouts.
H2: A reduction in the capital gains tax rate will increase the return volatility of
non- or lower dividend-paying stocks more than that of higher dividend-paying stocks.
Similarly, the impact of a capital gains tax rate change on the risk sharing
between taxable investors and the government and the consumption risk will likely vary
across firms with different embedded capital losses or gains. For example, if the sale
proceeds of a taxable investor in a stock are equal to his tax basis (i.e., the cost of
purchasing the stock), then the investor has no income subject to capital gains taxes upon
sale of the stock because he has neither gain nor loss. Furthermore, since there is no
income subject to capital gains taxes, the government bears no risk.
On the other hand, if the investor’s sale proceeds are equal to the gains (because
the cost of the stock was zero), then all proceeds are subject to the capital gains taxes.
Therefore, the government bears the maximum risk. Similarly, if the investor’s sale
proceeds are zero, then the loss is equal to the cost of purchasing the stock. In that case,
the full loss (which equals the tax basis) can be used to reduce the investor’s taxes, and,
again, the government bears the maximum risk.
11
In short, when a stock has large embedded gains and losses, a capital gains tax
change will have a major impact on the risk sharing and consumption risk of the taxable
investors in those stocks. Thus, the effect of a capital gains tax change will have a greater
impact on the return volatility of these stocks than on other stocks. This leads to the
following hypothesis about the relation between stock return volatility and embedded
capital losses or gains in the case of a capital gains tax rate cut.
H3: A reduction in the capital gains tax rate will increase the stock return
volatility of firms with large embedded capital losses (gains) more than that of firms with
small embedded capital losses (gains).
In the next section, we discuss the empirical methodology used to test the three
hypotheses discussed above.
3. Empirical Methodology
We use the Taxpayer Relief Act of 1997 (TRA97) as our event to empirically test
the impact of a change in the capital gains tax rate on stock return volatility. TRA97
lowered the maximum tax rate on capital gains for individual investors from 28 percent to
20 percent for assets held more than 18 months. TRA97 is particularly attractive for an
event study because the capital gains tax cut was large and relatively unexpected, and the
bill included few other changes that might confound our analysis. Little information was
released about the Taxpayer Relief Act of 1997 (TRA97), until Wednesday, April 30,
1997, when the Congressional Budget Office (CBO) surprisingly announced that the
estimate of the 1997 deficit had been reduced by $45 billion. Two days later, on May 2,
the President and Congressional leaders announced an agreement to balance the budget
by 2002 and, among other things, reduce the capital gains tax rate. These announcements
greatly increased the probability of a capital gains tax cut. On Wednesday, May 7, 1997,
Senate Finance Chairman William Roth and House Ways and Means Chairman William
Archer jointly announced that the effective date on any reduction in the capital gains tax
rate would be May 7, 1997. As promised, the lower tax rate on long-term capital gains
(eventually set at 20 percent) became retroactively effective to May 7, 1997, when the
President signed the legislation on August 5, 1997.
12
Using TRA97 as the event that changed capital gains tax rates, we examine the
time series of return volatilities for various stock portfolios including:
•
the value-weighted market index,
•
the implied volatility of Standard & Poors index options (VIX),
•
five industry portfolios classified based on 4-digit SIC code (consumer,
manufacturing, high tech, health, and others),
•
constructed portfolios based on firms’ dividend distributions, and
•
constructed portfolios based on the past 18 months price changes.4
The primary focus of our empirical analysis is on the constructed portfolios based
on firms’ dividend distributions and past price changes, which exploit cross-sectional
differences in dividends and past price movements to test H2 and H3, respectively. As
discussed above, the reason for the focus on the cross-sectional tests is that unaccounted
for, non-tax factors potentially boosted the return volatility of the market and industry
stock portfolios, which are used to test H1. That said, we are unaware of any crosstemporal changes that would have coincided with passage of TRA97. Nonetheless, we
expect tests of H2 and H3 to provide more compelling evidence about the impact of the
capital gains taxes on stock return volatility than tests of H1.
To test H2 (that a capital gains tax rate cut leads to a larger increase in the return
volatility of non- or lower dividend-paying stocks than that of higher dividend-paying
stocks), we use the firm’s dividend distribution in the prior year to construct a nondividend paying portfolio and a dividend-paying portfolio. For the dividend-paying
stocks, we further form a low dividend yield portfolio and a high dividend yield portfolio
using the median dividend yield as a threshold. To mitigate any confounding effects on
return volatility from reducing the capital gains tax rate on stocks with large price
changes, we restrict our attention to stocks with share price changes (either positive or
negative) of less than 5 percent over the last 18 months.
To test H3 (that a capital gains tax cut increases the return volatility of stocks with
large embedded capital losses or gains more than stocks with small embedded losses or
gains), we dichotomize the non-dividend paying stocks into those whose share prices
4
We use 18-month price changes to form our portfolios because TRA97 established 18 months as the
minimum holding period for investors to apply the lower long-term capital gains tax rate.
13
have declined over the last 18 months and those whose share prices have increased over
the same period. Then, we divide the stocks whose share prices have declined into
quartiles based on the amount of their price depreciation. We call these quartiles, loss
portfolios. Similarly, we divide the stocks whose share prices have risen into quartiles
based on the amount of their appreciation. These quartiles are termed gain portfolios. We
limit our analysis to non-dividend paying stocks to mitigate any confounding effects on
stock return volatility arising from a firm’s dividend distribution.
For all of our tests, we use daily returns to construct monthly volatility measure.
The sampling period used in our empirical analysis spans from January 1993 to
December 2002. To avoid the transient effect caused by the capital gains tax cut
announcement, we exclude observations from April to September of 1997 from our
analysis.
Let ritj be the return on stock (or industry) portfolio i on day j in month t and σ it be
stock (or industry) portfolio i’s return volatility in month t. We construct the monthly
stock (or industry) portfolio return volatility for each portfolio-month as follows
Jt
σ it =
∑ (r
itj
− rit ) 2 ,
(1)
j =1
where rit =
1
Jt
Jt
∑r
itj
is the sample mean return for stock (or industry) portfolio i in month
j =1
t, J t is the number of observations in month t. For the market index, we construct the
monthly market return volatility for each month t, σ t , as follows
σt =
Jt
J t −1
j =1
j =1
∑ (rtj − rt ) 2 + 2∑ (rtj − rt )(rt ( j +1) − rt ) ,
where rtj is the market excess return on day j of month t and rt =
(2)
1
Jt
Jt
∑r
tj
is the sample
j =1
mean excess return for the market index in month t. Note that the market return volatility
(including the extra cross-product terms in the expression) adjusts for the first-order
autocorrelation in daily returns associated with nonsynchronous trading among stocks
14
included in the index.5 We also use the implied volatility for the Standard & Poors index
options (VIX) at month t as an alternative measure for the volatility of the market
portfolio.
To test our hypotheses on the effect of the capital gains tax rate cut on stock
return volatility, we introduce two dummy variables: Post and HVP. Dummy variable
Post t takes value 0 on and before 3/31/1997 and value 1 on and after 10/1/1997. Note
that this is different from a standard event study on stock returns which focuses on the
announcement effect. We exclude the “announcement” months from our examination
because we are interested in the change of the volatility level around the event. Dummy
variable HVPi takes the value of 0 if portfolio i is a pre-selected benchmark portfolio and
the value of 1 for an alternative portfolio believed to have a higher volatility than the preselected benchmark portfolio. Another important difference between stock returns and
the volatility of stock returns is that the latter has significant persistence. To allow for the
serial correlation in stock return volatility, we use lagged demeaned volatility as
explanatory variable in our analysis.
Specifically, to test the change in return volatility for different stock portfolios
under hypothesis 1, we use the following specifications:
For market index and the implied volatility index
p
q
p
q
σ t = α + β Post t + ∑ ρ j ∆σ (t − j ) + ∑ δ j rt − j + ∑ ξ j ∆σ t f− j + ∑ ζ j rt −f j + γ ' X t + ε t ,
j =1
j =1
j =1
j =1
(3)
For industry portfolios i
p
q
p
q
σ it = α + β Post t + ∑ ρ j ∆σ (t − j ) + ∑ δ j r(t − j ) + ∑ ξ j ∆σ t f− j + ∑ ζ j rt −f j
j =1
m
j =1
n
j =1
j =1
(4)
+ ∑ θ j ∆σ i (t − j ) + ∑η j ri (t − j ) + γ ' X t + ε it ,
j =1
j =1
For constructed portfolio i
5
Similar measures are used in French, Schwert and Stambaugh (1987) and Guo and Whitelaw (2006),
among others.
15
p
q
p
σ it = α + β Post t + ∑ ρ j ∆σ (t − j ) + ∑ δ j r(t − j ) + ∑ ξ j ∆σ
j =1
m
j =1
j =1
n
q
f
t− j
+ ∑ ζ j rt −f j
j =1
(5)
+ ∑ θ j ∆σ i (t − j ) + ∑η j ri (t − j ) + γ ' X t + ϕ ' Z it + ε it ,
j =1
where ∆σ t = σ t −
1
T
j =1
T
∑σ
k
is the demeaned volatility measure for the market index,
k =1
subscript j refers to its lags, and subscript k refers to the months, ∆σ t f− j and rt −f j represent
lagged demeaned return volatility and monthly average of daily return for foreign stock
markets, respectively, ∆σ i (t − j ) and ri (t − j ) are lagged demeaned industry (or constructed)
portfolio volatility and monthly average of daily return for industry (or constructed)
portfolio, respectively, X t refers to a vector of aggregate control variables, and
Z it represents a vector of characteristics specific to constructed portfolio i as of time t.
Existing empirical asset pricing studies suggest that stock return volatility exhibits
persistence and that large negative stock price changes tend to be followed by periods of
high stock return volatility. The latter is sometimes referred to as the leverage effect. To
control for these effects, we allow stock return volatility to depend on lagged return
volatility and stock returns. As the capital markets become more integrated, we also
consider the impact of foreign stock market return and volatility on domestic stock return
volatility by including ∆σ t f− j and rt −f j as control variables. For the industry and
constructed portfolios, our specifications also account for volatility persistence and
leverage effect at the portfolio level.
For both the market index and industry portfolios, we expect the return volatility
to be higher after the capital gains tax rate is cut. This implies that the estimated
coefficient for Post is positive, i.e., β > 0. On the return volatility of stock portfolios
constructed above, we predict that portfolios of non- or lower dividend-paying stocks and
portfolios with large embedded capital gains or losses will experience more return
volatility after the capital gains tax cut, compared with other firms. For these portfolios,
we expect the estimated coefficient for the dummy variable Post to be positive, i.e.,
β > 0. However, for portfolios of high dividend-paying stocks or portfolios of stocks with
small embedded gains or losses, a capital gains tax cut may have a negligible effect on
16
the return volatility of these portfolios. The estimated coefficient for the dummy variable
Post on these portfolios may be insignificant.
To test the cross-sectional implications stated in H2 and H3, we need to compare
the return volatility increases for different portfolios. This is achieved by estimating the
following panel regression model utilizing observations for both the benchmark portfolio
and the alternative portfolio:
p
q
σ it = α + β1 Post t + β 2 HVPi + β 3 Post t × HVPi + ∑ ρ j ∆σ ( t − j ) + ∑ δ j r(t − j )
j =1
p
+ ∑ ξ j ∆σ
j =1
q
f
t− j
m
+ ∑ζ r
f
j t− j
j =1
j =1
n
(6)
+ ∑ θ j ∆σ i (t − j ) + ∑η j ri (t − j ) + γ X it + ϕ Z it + ε it .
j =1
j =1
This specification allows us to test H2 and H3 by examining the coefficient
estimate for the interaction term, Post × HVP . For H2, we choose the dividend-paying
portfolio as the benchmark portfolio and the non-dividend paying portfolio as the
alternative portfolio. We expect the non-dividend paying portfolio to experience a larger
increase in return volatility than the dividend-paying portfolio does. This implies that the
interaction term Post × HVP will have a positive coefficient because HVP takes a value
of one for the non-dividend paying portfolio and a positive coefficient indicates a higher
volatility for the HVP portfolio. Consequently, testing H2 is equivalent to testing if
β 3 > 0.
Similarly, for H3, we choose the portfolio with the smaller embedded losses
(gains) as the benchmark portfolio and the portfolio with the larger embedded losses
(gains) as the alternative portfolio. We predict that the portfolio of stocks with larger
embedded losses (gains) will experience a greater increase in return volatility than the
portfolio of stocks with smaller embedded losses (gains). Thus, we expect the coefficient
estimate for Post × HVP to be positive, i.e., β 3 > 0.
This specification also allows us to test whether the benchmark portfolio
experiences a volatility increase after the capital gains tax rate cut ( β 1 ) and whether the
alternative portfolio indeed has a higher volatility over the benchmark portfolio prior to
the capital gains tax cut ( β 2 ). A positive coefficient estimate for β 1 indicates a higher
return volatility for the benchmark portfolio after the capital gains tax rate cut, and a
17
positive coefficient estimate for β 2 shows that the alternative portfolio has a higher
return volatility than the benchmark portfolio before the capital gains tax rate cut.
It is important to control for variables which may affect stock return volatility.
Based on the capital asset pricing theory, Lettau and Ludvigson (2001) propose using the
consumption-wealth ratio (CAY) as a determinant for stock returns. They show that the
CAY variable is a better predictor than are the dividend yield, the term premium, the
default premium, and other previously widely used predictors combined. Campbell and
Shiller (1988) document that stochastically detrended risk free rate (RREL) is an
important predictor for stock returns. We also include the growth rate of the industrial
production to account for the state of the economic activities. In summary, our regression
analysis includes the following aggregate control variables:
CAY --- the consumption-wealth ratio,
RREL --- the stochastically detrended risk free rate,
GIP --- the industrial production growth rate (GIP).
Campbell, Lettau, Malkiel, and Xu (2001) document an increase in firm
idiosyncratic volatility relative to market volatility from 1962 to 1997. 6 They suggest
several factors as possible explanations. These factors include changing discount rates, a
shift towards reliance on external as opposed to internal capital markets, firms’ growth
potentials, changes in executive compensation, firms’ leverage position, and the
increased share of institutional ownership. Cohen, Hall, and Viceira (2000) find the
changes in executive compensation have a statistically significant effect on the risks of
their firms’ activities. But the effect is small in magnitude. Dai, Maydew, Shackelford,
and Zhang (2007) find that turnover has a significant effect on stock returns. Xu and
Malkiel (2003) and Cao, Simins, and Zhao (2006) document that firms’ growth options
have significant effect on idiosyncratic risk of equity. In addition, both the New York
Stock Exchange and the Nasdaq reduced the tick size for stock trading between June
1997 and August 1997, the same time that TRA97 was being finalized. To capture
possible effects on the return volatility of our constructed portfolios associated with these
variables, we include the value-weighted firm’s debt-asset ratio (D/A), turnover in the
most recent past month (Turnover), the average monthly bid-ask spread in the most
6
Similar results are also documented in Pastor and Veronesi (2006) for the more recent periods until 2002.
18
recent past month (BidAskSpread), price-earnings ratio as a proxy for growth option (P/E
ratio), and the average individual ownership in the most recent past quarter (IND) in the
regression analysis for each constructed portfolio. In addition, since the capital gains tax
change will not likely to affect earnings and stock return volatility are related to earnings
volatility, we also control for the earnings volatility (CV earnings) measured by the
coefficient of variation in quarterly earnings. The logarithm of market capitalization of
the portfolio (Size) is also included as a control. In summary, the list of control variables
specific to each constructed portfolios are as follows:
D/A --- the value weighted averages of firms’ debt-asset ratios,
Turnover --- the value weighted averages of individual stock turnover,
BidAskSpread --- the value weighted average of individual stocks’ percentage bid-
ask spread,
P/E ratio --- the value weighted average of individual stocks’ price-earnings
ratios,
IND --- the value weighted average of individual ownership of stocks in the
portfolio,
CV earnings --- the value weighted average of firm’s quarterly earnings’
coefficient of variation,
Size --- the logarithm of the market value of the portfolio.
For all specifications (equations (3) to (6)), we also include monthly dummies to
account for calendar effect.
Finally, recall that the 1997 capital gains tax rate reduction only applies to
individual investors. It follows that companies owned solely by individuals should have
experienced an increase in stock return volatility while companies owned solely by other
stockholders (e.g., pensions) should not have been affected by the legislation. More
generally, the capital gains tax rate change should only affect stock return volatility if the
marginal investor is an individual. Since the marginal investor is unobservable, we test
whether return volatility is increasing in individual stock ownership. Specifically, we
divide the non-dividend paying and dividend paying portfolios, according to the median
detrended individual ownership in each month, to form four portfolios:
•
non-dividend paying, low individual ownership portfolio,
19
•
non-dividend paying, high individual ownership portfolio,
•
dividend-paying, low individual ownership portfolio, and
•
dividend-paying, high individual ownership portfolio.
We then apply regression analysis to the four portfolios as we do for all other constructed
portfolios.
Unfortunately, our measure of tax-sensitive investors using individual stock
ownership is flawed. First, the returns on many institutional holdings are subject to the
individual income tax (e.g., street name holdings by brokerage houses on behalf of
individual investors). Thus, we measure tax-sensitive investors with measurement errors.
Second, Gompers and Metrick (2001) and Xu and Malkiel (2003) document that
institutional ownership increases idiosyncratic volatility.
Since they find a positive
correlation between institutional ownership and volatility and we predict a negative
relation, our tests are biased against rejecting the null. (Note that the null is that there is
no relation between institutional ownership and volatility, while we predict that volatility
will rise with the number of investors in the firm affected by the legislation).
In
summary, rejecting the null hypothesis will provide strong evidence that the 1997 rate
reduction increased volativity. Unfortunately, we may fail to reject the null because our
tests lack sufficient power to discriminate between the extant finding and our prediction.
4. Empirical Analysis
4.1. Sample and Summary Statistics
To empirically test the effect of TRA97 on stock return volatility, we use all
stocks included in the CRSP data base. The excess return on the market index is
constructed as the market return of the value-weighted portfolio of stocks included in the
CRSP data base after the risk free rate is subtracted. The monthly implied volatility index
for the Standard & Poors index options (VIX) is the average implied annualized volatility
for different call and put options on the index with expiration date in a month. The
returns for the foreign equity markets are based on the Morgan Stanley Capital Markets
International (MSCI) ACWIsm ex USA Index. This is a free float-adjusted market
capitalization index designed to measure equity market performance in all global
developed and emerging markets outside of the United States. The five industry
20
portfolios are formed using the 4-digit SIC code and consist of the (1) consumer industry
(consumer durables, non-durables, wholesale, retail, and some services, such as laundries
and repair shops), (2) manufacturing industry (manufacturing, energy, and utilities), (3)
high tech industry (business equipment, telephone and television transmission), (4) health
care industry (healthcare, medical equipment, and drugs), and (5) other industries (mines,
construction, building materials, transportation, hotels, business services, entertainment,
finance). 7 We construct monthly excess returns and volatility for non-dividend paying
and dividend-paying portfolios, low dividend yield and high dividend yield portfolios,
quartile gain portfolios, and quartile loss portfolios as discussed in the previous section.
These are value-weighted portfolios using daily individual stock return data.8 As noted
above, the investigation period is from January 1993 to December 2002, excluding April
through September of 1997. This sample period enables to have about the same number
of observations before and after the announcement, while avoiding any potentially
confounding effects arising during the legislative deliberations.
For the aggregate control variables, we obtain the consumption-wealth ratio
(CAY) from Martin Lettau’s website. Since the consumption-wealth ratio is at quarterly
frequency, we use linear interpolation to obtain monthly observations. The stochastically
detrended risk free rate is constructed by removing the average risk free rate in the prior
twelve months from the risk free rate in month t as in Campbell and Shiller (1988). The
growth rate of the industrial production is calculated using the monthly industrial
production index obtained from the Federal Reserve Bank of St. Louis.
We obtain daily individual stock return data from the daily CRSP data base.
Dividend and stock price are extracted from the monthly CRSP data base. We compute a
firm’s dividend yield based on dividend distribution in the prior year and the stock price
in the most recent month. We construct the embedded capital gains and losses using a
firm’s most recent 18 month stock price change prior to month t.9 To obtain measures of
investor ownership, we use institutional investors’ ownership information submitted by
7
The excess return on the value-weighted market index and returns on industry portfolios are obtained
from Kenneth French’s website.
8
To remove the influence from extreme values, we winsorize observations at the bottom and the top 5
percent for each portfolio.
9
We also performed the analysis for the loss and gain portfolios using price changes in the past 12 months.
The results are very similar to that for the 18 month price changes.
21
investment management companies to the Security Exchanges Commission on Form 13F.10 We compute the individual investor ownership on stock i at time t (INDit) as follows:
INDit = 1 – the percentage of shares owned by institutional investors at time t.
We compute a firm’s debt-asset ratio using data from the COMPUSTAT data
base. Because the COMPUSTAT data base is only available at quarterly frequency, we
assume that a firm’s debt-asset ratio remains the same within the quarter. Monthly
individual stock turnover is constructed by dividing the monthly trading volume by the
shares outstanding at the end of the month.11 The average monthly percentage bid-ask
spread for individual stocks is constructed using the transaction level Trade And Quote
(TAQ) data base.12 For the measure on firms’ growth options, we use the ratio of the endof-month price to the lagged earnings per share.13 The earnings volatility measure, we
use the coefficient of variation calculated using 24 quarterly earnings in the previous six
years.14 Firm size is measured by the end-of-month price multiplied by the total shares
outstanding for each firm. For each portfolio, we compute the monthly value weighted
averages of firms’ debt-asset ratios, turnover, percentage bid-ask spreads, price-earnings
ratios, the detrended individual ownership, the coefficient of variation for quarterly
earnings, and the logarithmic market value of the portfolio.
Table 1 presents the summary statistics for the market and industry portfolios and
economy-wide control variables used in our regression analysis in Panel A and the
univariate tests of mean return volatility changes for the market and industry portfolios in
Panel B. The dataset consists of 120 monthly time series observations from January 1993
to December 2002. The average daily excess return for the value-weighted market
portfolio is 0.019 percent with a standard deviation of 0.22 percent. The monthly
volatility of the market excess return has a mean of 4.3 percent with a standard deviation
of 2.3 percent. For the same time period, average daily return for the foreign equity
10
We thank Rabih Mousssawei for providing us the institutional stock ownership data.
Ideally, we would use the monthly trading volume for individual investors only. However, this
information is unobservable. Thus, we assume that the differences, in any, between individuals’ turnover
and other investors’ turnover do not affect the study’s inferences.
12
We thank Kam-Ming Wan for providing us the monthly bid-ask spread data on individual stocks.
13
We also used alternative measures such as the market value to book value ratio and the forecasted
operating income growth rate on individual firms obtained from the IBES database as a proxy. The results
are qualitatively similar.
14
The coefficient of variation is defined as the standard deviation scaled by the sample average.
11
22
markets is 0.012 percent with a standard deviation of 0.21 percent. The average monthly
volatility for the foreign equity markets is less than the U.S. equity market at 3.7 percent
with a standard deviation of 1.6 percent. The monthly implied volatility has a mean of 5.9
percent with a standard deviation of 2.0 percent.15
The industry portfolios have average daily returns ranging from 0.032 percent for
the manufacturing to 0.053 percent for the healthcare. The manufacturing industry has the
lowest standard deviation of 0.19 percent and the high tech industry has the highest
standard deviation of 0.40 percent. Consistent with the daily statistics and our intuition,
the monthly return volatility is the lowest for the manufacturing industry with an average
of 3.5 percent and a standard deviation of 1.7 percent, and is the highest for the high tech
industry with an average of 6.9 percent and a standard deviation of 3.8 percent. The CAY
variable has an average of 0.033 percent and a standard deviation of 2.1 percent. The
stochastically detrended risk free rate has a monthly average of -0.008 percent and a
standard deviation of 0.071 percent. Over the sample period, the industrial production
grew at 0.28 percent per month on average with a standard deviation of 0.53 percent.
The univariate test results in Table 1, Panel B suggest that both the market and
industry portfolios experienced dramatic increases in return volatility during the
investigation period. Specifically, the monthly average of return volatility for the market
portfolio increased from 2.7 percent before the capital gains tax rate cut to 5.6 percent
after the capital gains tax rate cut. Similarly, the implied volatility also increased from 4.2
percent to 7.3 percent. For industry portfolios, the monthly average of return volatility
increased the least for manufacturing industry from 2.2 percent to 4.5 percent and the
most for the high technology industry from 3.9 percent to 9.4 percent. All increases are
statistically greater than zero. The question facing this study is the extent to which these
dramatic increases in stock return volatility are attributable to the 1997 reduction in the
capital gains tax rate
Table 2 reports the summary statistics for the constructed portfolios based on a
firm’s dividend distribution in Panel A and the embedded capital losses (gains) in the past
18 months in Panel B (C), and the univariate tests for the mean volatility changes for the
15
Because the raw VIX data are for annual return volatility of the Standard & Poors index, we scale the
VIX by the square root of 12 to obtain monthly return volatility measure.
23
constructed portfolios in Panel D. Specifically, Panel A presents the summary statistics
for the non-dividend paying, dividend-paying, low dividend yield, and high dividend
yield portfolios. To focus on dividend-paying dimension, we restrict to those stocks with
price changes less than 5 percent in the past 18 months. The non-dividend paying
portfolio has an average daily return of 0.010 percent with a standard deviation of 0.30
percent. The dividend-paying portfolio has a mean daily return of 0.031 percent with
standard deviation of 0.17 percent. Consistent with results on the non-dividend and
dividend paying portfolios, the low dividend yield portfolio has a lower mean return of
0.024 percent with standard deviation of 0.20 percent while the high dividend yield
portfolio has a higher mean return of 0.037 percent with standard deviation of 0.18
percent. The monthly return volatility for the non-dividend paying portfolio has a mean
of 5.9 percent with a standard deviation of 2.5 percent. Both statistics are much higher
than those for the dividend-paying portfolio which has a mean of 3.5 percent with a
standard deviation of 1.4 percent. The low dividend yield portfolio has a mean return
volatility of 4.1 with a standard deviation of 1.5 percent while the corresponding statistics
are lower at 3.5 percent and 1.3 percent for the high dividend yield portfolio,
respectively.
Panels B and C present summary statistics for the losses and gain portfolios,
respectively. To focus on the embedded price change dimension, we restrict the analysis
to stocks that have not paid dividends. Recall that we dichotomize the non-dividend
paying stocks into depreciated and appreciated stocks and further divide the two groups
into quartiles. For the loss portfolios, the average daily return is the highest at 0.044
percent for the quartile portfolio with the largest embedded capital losses (the upper 25
percentile). For the quartile portfolio with the smallest embedded capital losses (the lower
25 percentile) the average daily return is lower at 0.014 percent. The average monthly
return volatility increases from 5.8 percent for the smallest loss portfolio to 7.6 percent
for the largest loss portfolio.
For the gain portfolios, the average daily returns range from 0.0008 percent for
the quartile portfolio with the smallest embedded capital gains (lowest 25th percentile) to
0.078 percent for the quartile portfolio with the largest embedded capital gains (upper
25th percentile). The quartile portfolio with the largest embedded capital gains also has
24
the highest monthly return volatility of 7.9 percent while the quartile portfolio with the
smallest embedded capital gains has a lower monthly return volatility at 5.4 percent.
Overall, the results on the gains and loss portfolios provide empirical evidence that higher
return is associated with higher risk.
Consistent with the return volatility increases for the market index and industry
portfolios (in Table 1, Panel B), the univariate test results in Panel D indicate that all
constructed portfolios have experienced significant return volatility increases. Moreover,
there are also differences in the increases in return volatility across different portfolios.
Non-dividend paying stocks see a larger return volatility increase than dividend paying
stocks (3.1 percent for non-dividend paying stock portfolio versus 1.8 percent of dividend
paying stock portfolio). However, among dividend paying stocks, the amount by which
return volatility increased did not vary with the dividend yield (the low dividend yield
portfolio increased by 1.84, while the high dividend yield portfolio increased by 1.85).
The quartile portfolio of stocks with the largest embedded capital losses
experienced a 5.3 percent return volatility increase compared to 3.1 percent volatility
increase for the quartile portfolio of stocks with the smallest embedded capital losses.
However, the return volatility increases are similar for portfolios of stocks with different
embedded capital gains (2.9 percent for the portfolio of stocks with the smallest gains
versus 2.4 percent for portfolios of stocks with the largest gains).
Table 3 presents the summary statistics for the portfolio control variables
including the value-weighted averages of firms’ debt-to-asset ratio (D/A), turnover
(Turnover), percentage bid and ask spread (BidAskSpread), price-earnings ratio (P/E
ratio), individual ownership (IND), coefficient of variation for quarterly earnings (CV
earnings), and the logarithm of market value of the portfolio (Size). Panel A reports the
summary statistics for the non-dividend and dividend paying portfolios. The nondividend paying portfolio has a lower average debt/asset ratio (D/A=0.49) and a higher
standard deviation (0.12) than dividend-paying portfolios (0.64 and 0.05, respectively for
the portfolio of all dividend-paying stocks, 0.60 and 0.06 for low yield portfolio and 0.69
and 0.06 for high yield portfolio) with a higher standard deviation. This is consistent with
dividend-paying firms utilizing more debt financing to gain the tax benefit associated
with issuing debt, although formal analysis of that relation, if any, is beyond the scope of
25
this paper. The non-dividend paying portfolio also has a much higher average turnover
(16.1 percent) than dividend-paying portfolios (6.3 percent for all dividend-paying
stocks, 7.1 percent for low yield portfolio and 5.7 percent for high yield portfolio). The
average bid-ask spread is higher for the non-dividend paying stocks at 0.68 percent than
for the dividend paying stocks at 0.30 percent. The average price-earnings ratio is 20 for
non-dividend paying stocks and 31 for dividend paying stocks. The lower P/E ratio for
the non-dividend paying stocks may be the result of restricting the stocks to be included
in the portfolios with price changes less than 5 percent. The average individual investor
ownership is 44 percent for the non-dividend paying stocks and slightly higher at 47
percent for dividend paying stocks. The earnings volatility measured by the coefficient of
variation in the past 24 quarters is substantially higher at 3.1 for non-dividend paying
stocks than 0.7 for dividend paying stocks. Finally, the average size is larger for dividend
paying stocks than for non-dividend paying stocks.
Panel B shows the summary statistics for the portfolio control variables for the
loss portfolios. The debt/asset ratio (D/A) stays in a narrow range between 0.46 and 0.47.
The turnover rate is 16 percent for the smallest loss portfolio and 20 percent for the
largest loss portfolio. The average percentage bid-ask spread increases steadily from 65
basis points for the smallest loss portfolio to 133 basis points for the largest loss portfolio.
The price-earnings ratio declines from 21 for the portfolio of stocks with smallest losses
to around 6 for stocks with largest losses. The average individual investor ownership
increases from 46 percent for the smallest loss portfolio to 59 percent for the largest loss
portfolio. Except for the smallest loss portfolio, the earnings volatility measured by the
coefficient of variation is negative and the magnitude increases as the embedded losses
increase. Finally, the logarithm of market value declines from 15 for the smallest loss
portfolio to 13 for the largest loss portfolio.
Panel C shows the same summary statistics for the gain portfolios. The debt/asset
ratio steadily decreases from 0.49 to 0.40 as the embedded capital gains increase. The
turnover rate is 17 percent for the smallest gain portfolio and 25 percent for the largest
gain portfolio. The average percentage bid-ask spread is hump-shaped. The smallest gain
portfolio has a spread of 0.68. The interquartile portfolios have values of 0.96 and 0.82.
The largest gain portfolio is only 0.49. The P/E ratio increases steadily from 29 for the
26
portfolio with the smallest gains to 38 for the portfolio with the largest gains. The
individual investor ownership remains in a narrow range between 42 to 45 percent.
Contrary to the loss portfolios, the earnings volatility becomes more positive as the
embedded gains increase, ranging from -5.7 for the portfolio with the smallest gains to
1.1 for the portfolio with the largest gains. Finally, there is little difference in market
value across gain portfolios.
4.2. Time series analysis of the capital gains tax effect on stock return volatility
This section discusses our time series analysis of the effect of a capital gains tax
cut on stock return volatility. Table 4 reports the coefficient estimate for the dummy
variable Post for the market index, implied volatility of Standard & Poors index options,
industry and constructed portfolios using equations (3) to (5).
As predicted, the volatility of the market excess return is higher after the capital
gains tax rate is reduced. We find that the monthly volatility of the market excess return
is 1.9 percentage points higher after the capital gains tax cut than before the capital gains
tax cut, after controlling for domestic and foreign equity market performances and the
aggregate economic variables. This estimated regression coefficient is statistically
significant at the 5 percent level. The 1.9 percentage point increase also is economically
significant. It accounts for 66 percent of the difference between the pre-TRA97 average
volatility of 2.7 and the post-TRA97 average of 5.6 (see Table 1, Panel B). Restated, this
implies that the non-tax factors from previous studies account for only 34 percent of the
overall increase in volatility after 1997. In other words, a substantial portion of the
increase in stock return volatility from the period, 1993 to 1997, to the period, 1997 to
2002, cannot be accounted for with documented factors. This leaves us to ponder the
change around 1997 that led to dramatic increases in volatility. Because the capital gains
taxes were cut in 1997, we conjecture that at least a portion of the increase in volatility
was attributable to TRA97.
We find similar results using the implied volatility for the S&P index options. The
implied volatility is higher by 2.1 percentage points, after the capital gains tax rate
reduction. The coefficient is highly statistically significant. Using the same computation
as above, we conclude that the non-tax factors in our analysis only account for 32 percent
27
of the difference between the pre-TRA97 average volatility of 4.2 and the post-TRA97
average of 7.3 (see Table 1, Panel B).16
For the five industry portfolios, the estimated coefficients for the categorical
variable, Post, is always significantly greater than zero. This indicates that, for every
industry, the return volatility is higher after the capital gains tax cut, controlling for
domestic and foreign equity market performances and the aggregate economic variables.
Specifically, the monthly return volatility is higher by 2.1 percentage points for the
consumer industry, 1.6 percentage points for the manufacturing industry, 2.5 percentage
points for the high tech industry, 2.1 percentage points for the healthcare industry, and
2.4 percentage points for all other industries after the capital gains tax cut than before the
capital gains tax cut. When we compare the regression coefficient with the increase in
overall return volatility in Table 1, Panel B, we find that the non-tax factors in our
regression analysis only accounts for 22 percent of the volatility increase for the
consumer industry, 30 percent for the manufacturing industry, 55 percent for the high
tech industry, 16 percent for the healthcare industry, and 25 percent for all other
industries. In short, as with the market excess return and the S&P index options, we find
that much of the increase in volatility from 1993 to 2002 cannot be explained by
previously documented reasons.
For the constructed portfolios, the estimated regression coefficient for the dummy
variable, Post, is always positive. After controlling for domestic and foreign equity
market performances, the aggregate economic variable, and portfolio specific
characteristics, we find that the coefficient is statistically significant for the non-dividend
paying and dividend paying portfolios and three of the loss portfolios, but never
significantly greater than zero for any of the gain portfolios.
As predicted, following TRA97, the non-dividend paying portfolio experienced a
greater increase in volatility than the dividend paying portfolio. The coefficient for the
non-dividend paying portfolio is 2.5 percentage points, compared with 1.9 percentage
points for all dividend-paying stocks. Also consistent with our prediction, the low
dividend yield portfolio experienced a higher volatility increase (2.4) than the high
dividend yield portfolio does (1.5).
16
We compute the 32 percent from 1-[2.1%/(7.3%-4.2%)].
28
The estimated coefficients for the Post dummy are positive in all four quartile loss
portfolios, consistent with a higher return volatility after the capital gains tax cut than
before the tax cut. As expected, the increase in return volatility is largest for the portfolio
with the largest losses (6.4 percentage points). With the exception of the second lowest
quartile, the return volatility increase is higher as the embedded losses increase. For the
gain portfolios, while the estimated coefficient is positive for the dummy variable Post, it
is insignificant at the 5 percent test level. Nonetheless, both the magnitude of the
estimates and the significance increase as the embedded gains increase.
For our time series regressions, the lagged consumption-wealth ratio (CAY) in
general has a significant positive effect on the return volatility. Lagged returns for each
portfolio have a negative effect on the return volatility of the portfolio, lending support to
the leverage effect. Past return volatility of the portfolio also has a positive effect on
current return volatility, implying some return persistence. We also find that turnover has
a positive effect on dividend paying portfolios and gain portfolios.
To summarize, we find that returns were about twice as volatile from 1997 to
2002 as they were from 1993 to 1997. After analyzing the volatility of the market excess
return, the implied volatility of S&P index options, and the return volatility across
industries, we estimate that less than half of the increase can be attributed to non-tax
influences on stock return volatility identified in prior studies. This leaves us to infer that
something around 1997 caused a substantial increase in stock return volatility. The factor
we identify and study in this paper that may have contributed to the increase in volatility
is the 1997 capital gains tax rate reduction.
In an attempt to better link the increase in volatility to the reduction in capital
gains taxes, we turn to cross-firm tests based on dividend yields and embedded losses and
gains. We expect the capital gains tax reduction to affect firms differently depending on
their dividend yields and embedded depreciation or appreciation.
If the cross-firm
increases in volatility correspond with the cross-firm differences in the impact of the
capital gains tax, then we will have more confidence that TRA97 actually was a factor in
the increase in stock return volatility after 1997. Consistent with TRA97 contributing to
the increase in volatility, the findings above show volatility moved indirectly with
dividend yield and more for firms with larger embedded losses. We find less evidence
29
that volatility was greater for firms with larger embedded gains. The next section extends
these cross-firm tests in an attempt to provide further evidence that the capital gains tax
cut in 1997 contributed to stock return volatility increase.
4.3. The cross-sectional test on the effect of a tax cut on return volatility
To test the cross-firm effect of a capital gains tax change on return volatility of
portfolios of stocks with different sensitivities to the capital gains tax rate cut, we
estimate the panel regression model specified in equation (6). The specification requires
that we identify a benchmark portfolio and an alternative portfolio with possibly a higher
return volatility.17 We start by comparing non-dividend paying portfolios and dividend
paying portfolios. Both our intuition and time series analysis results suggest that nondividend paying stocks have a higher return volatility than dividend paying stocks. We
thus choose the portfolio of non-dividend paying stocks as the alternative portfolio and
the dividend paying, the low yield, and the high yield portfolio as benchmark portfolios.
Table 5 presents the estimation results. As predicted, the coefficient estimate for
the interaction term, Post × HVP , is positive and statistically significant, when the
benchmark portfolio consists of all dividend paying stocks or high-yield stocks. The
estimated coefficient indicates that the portfolio of non-dividend paying stocks
experiences 1.2 percentage points (Column 1) higher monthly return volatility than the
portfolio of all dividend-paying stocks and 1.6 percentage points (Column 3) higher
monthly return volatility than the portfolio of high-yield stocks. The statistical
significance is less when the benchmark portfolio consists of only low-yield stocks (p=
0.06). This is not surprising because low-yield stocks are more similar to non-dividend
paying stocks than high-yield stocks. Still, the estimated coefficient shows that the
portfolio of non-dividend paying stocks has almost 0.8 percentage points (Column 2)
more monthly return volatility than the portfolio of low-yield stocks. The estimated
higher monthly return volatility for the non-dividend paying stocks than the dividend
paying stocks after the capital gains tax cut is above and beyond the 1.8 percentage points
higher monthly return volatility of non-dividend paying stocks relative to dividend
17
We use the PROC MIXED Procedure in SAS to estimate our panel regression model. Our estimation
method utilizes the clustered estimate for the standard errors.
30
paying stocks before the capital gains tax cut as indicated by the estimated coefficient for
β2.
Table 6 presents the results from the cross-sectional tests of the return volatility
increases on portfolios of stocks with different embedded capital losses (or gains). Our
discussions in Section 2 and the time series analysis on the return volatility of different
portfolios of stocks suggest that stocks with large embedded capital losses (or gains) have
larger return volatility increase relative to stocks with small embedded capital losses (or
gains). Therefore, we choose the portfolio of stocks with the lowest 25 percentile capital
losses (gains) as the benchmark portfolio and the portfolio of stocks with the highest 25
percentile of capital losses (gains) as the alternative portfolio.
For the loss portfolios, the coefficient estimate for the interaction term,
Post × HVP , is positive and statistically significant on the margin at the 5 percent test
level. The estimated coefficient implies that, after the reduction in the capital gains tax
rate, the monthly return volatility of the portfolio of stocks with the largest 25 percentile
embedded capital losses was 1.1 percentage points higher than that of stocks with the
lowest 25 percentile embedded capital losses. This is in addition to the 1.8 percentage
points higher monthly return volatility of large loss stock portfolio relative to the small
loss stock portfolio before the capital gains tax rate cut as indicated by the estimated
coefficient estimate for β 2 . The result is consistent with investors holding stocks with
large embedded capital losses suffering more reduction in risk sharing with the
government and incurring a larger consumption risk increase after the capital gains tax
rate cut.
For the gain portfolios, we choose the portfolio of stocks with the largest 25
percentile embedded capital gains as the alternative portfolio and the portfolio of stocks
with the lowest 25 percentile embedded capital gains as the benchmark portfolio. The
coefficient estimates for Post × HVP is positive, but insignificant. This is contrary to
expectations that firms with larger embedded gains would experience a greater reaction in
stock return volatility following TRA97. These findings imply that the adverse effect on
the risk sharing between investors and government is not nearly as severe when investors
have large embedded capital gains as when they have large embedded capital losses.
Restated, the results are consistent with a capital gains tax rate cut not increasing the
31
consumption risk as much when investors have large embedded capital gains as when
they have large embedded capital losses.
Overall, the empirical results on the cross-sectional tests discussed above suggest
that, after the capital gains tax rate reduction, the non-dividend paying portfolio
experienced a higher return volatility increase relative to the dividend-paying portfolios.
The results also are consistent with the capital gains tax rate cut increasing the return
volatility of stocks with large embedded capital losses more than that of stocks with small
embedded capital losses. However, we find no similar evidence for embedded capital
gains.
4.4. Comparisons with other years before TRA97
As a robustness check, we repeat the cross-firm tests for other years before
TRA97, when the capital gains tax rate was not reduced. Finding similar relations for the
interaction term, Post × HVP , in years without a capital gains tax rate cut will raise
concerns about the inferences drawn above.
Using the same sample and regression variables, we conduct the same panel
regression analysis, assuming hypothetically that the event window was the same months
from April to September but in 1994, 1995 and 1996. 18 In other words, in these
robustness tests, we redefine Post as months following September 1994, September 1995,
and September 1996, respectively.
Table 7 reports the results of the cross-sectional tests on portfolios of stocks with
different sensitivity to a capital gains tax cut assuming hypothetically that the capital
gains tax rate cut took place in either 1994, 1995, or 1996. None of the coefficients on the
interaction term, Post × HVP , are significantly greater than zero in any of the nine
regressions. For the non-dividend paying versus dividend paying portfolios (Panel A),
the coefficient estimate for Post × HVP remains positive for all three regressions, but
insignificant. For the losses portfolios (Panel B), the estimated coefficients for the
interaction term Post × HVP is positive in 1994 and 1996, but negative in 1995. For the
gain portfolios (Panel C), the coefficients on Post × HVP are always negative. In short,
18
We do not perform the robustness check for time periods after TRA97 because the tax effect on return
volatility has already taken place and return volatility in subsequent years are higher.
32
none of these robustness tests provide any evidence that the inferences drawn above are
spurious.
The findings in Table 7 provide comfort about the inferences that we drew from
Tables 5 and 6. Stock return volatility increased significantly more for non-dividend
paying stock (than for dividend paying stocks) and for stocks with large embedded losses
(than for stocks with small embedded losses) after 1997. We do not observe similar
increases after 1994, 1995 and 1996. This implies that whatever caused the stock return
volatility to increase had not occurred before 1997. These robustness tests cannot fully
rule out that some other non-tax event in 1997 was the driver of higher stock return
volatility after 1997, but it provides further support for the hypothesis that the capital
gains tax rate cuts in 1997 increased stock return volatility thereafter.
4.5. Investor ownership and the effect of a capital gains tax cut on return volatility
The capital gains rate reduction in the TRA97 only applies to income reported on
personal tax returns, i.e., capital gains from the selling of shares held directly by
individuals or held indirectly by individuals in flow-through entities, such as mutual
funds, partnerships, trusts, S corporations, or limited liability corporations that pass
income to investors’ personal tax returns. Capital gains taxes are not levied on taxdeferred accounts (e.g., qualified retirement plans, including pensions, IRAs and 401(k)),
tax-exempt organizations, and foreigners.
C corporations pay capital gains taxes;
however, the rate reduction in TRA97 did not apply to corporations. Thus, portfolios of
stocks with more tax sensitive investor ownership (i.e., stocks with returns that are
expected to trigger capital gains taxes that will be reported on personal tax returns) may
have experienced higher return volatility than portfolios of stocks with less tax sensitive
investor ownership.
We now examine if investor ownership has additional effect on the return
volatility increase associated with the capital gains tax cut. To achieve this objective, we
use a measure of individual investor ownership as a proxy for tax sensitive ownership and
then form portfolios based on the tax sensitive ownership measure. Specifically, we
compute the detrended individual investor ownership and then sort individual stocks
included in the non-dividend paying portfolio and the dividend-paying portfolio
33
constructed above into four portfolios based on the median detrended individual investor
ownership. They are (a) non-dividend paying, low individual ownership portfolio; (b)
non-dividend paying, high individual ownership portfolio; (c) dividend-paying, low
individual ownership portfolio; and (d) dividend-paying, high individual ownership
portfolio. We then perform both the time series regression using equation (5) and the
panel regression analysis using equation (6) to analyze the effect of the capital gains tax
cut on the return volatility of portfolios with different levels of individual investor
ownership.
There is a problem with this specification that deserves mentioning before we
discuss our findings. As discussed in Section 3, Gompers and Metrick (2001) and Xu and
Malkiel (2003) document that institutional ownership increases idiosyncratic volatility.
Based on their findings, we include a measure of institutional ownership as a control in
our earlier tests. Now, we are identifying individual ownership as a factor in determining
the extent to which capital gains taxes affect stock return volatility. Consequently, we
have one firm characteristic, the individual-institutional mix of the shareholders, serving
two roles in the determination of stock return volatility. This dual capacity potentially
undermines our ability to conduct this robustness test and may account for any inability
to reject the null hypothesis.
Turning to the results, Panel A in Table 8 shows summary statistics from the time
series regression of the relation between stock return volatility and individual ownership.
The first two columns show the results for the two non-dividend paying portfolios. The
last two columns show the results for the two dividend paying portfolios. All four Post
coefficient estimates are positive. Each is significant at the 5 percent test level, except
for the non-dividend paying, high individual ownership portfolio, which is significant at
the 10 percent level. However, contrary to expectations, in both cases, the portfolios with
the higher level of individual ownership have smaller estimated coefficients for the Post
dummy than the portfolios with the lower level of individual ownership. That said,
neither difference is statistically significant. Thus, these results provide no evidence that
the level of individual ownership affected the impact of the capital gains tax rate on stock
return volatility.
34
In Panel B, we report the results for the cross-sectional tests on the return
volatility increases for different portfolios. Column 1 shows the comparison between the
non-dividend versus dividend paying portfolios with low individual ownership while
Column 2 shows the comparison for the two portfolios with high individual ownership. In
both cases, we use the dividend paying portfolio as the benchmark portfolio and the nondividend paying portfolio as the alternative portfolio. In both columns, the coefficient
estimate for the variable of interest, Post × HVP , is positive. However, contrary to
expectations, the coefficient is only significant for the low individual ownership
portfolios. As in Panel A, these results provide no evidence that the level of individual
ownership affected the impact of the capital gains tax rate on stock return volatility.
Together, these tests provide no evidence that higher levels of individual investor
ownership contributed to higher stock return volatility following TRA97. There are
several possible explanations for this failure to reject the null hypothesis. First, as
discussed above, the fact that idiosyncratic volatility increases in institutional ownership
(Gompers and Metrick (2001) and Xu and Malkiel (2003)) may mean that our
institutional ownership measure is confounded by non-tax effects and thus a poor
measure of tax-sensitive stock ownership. Second, from a theoretical perspective, as long
as the marginal investor of a stock is tax sensitive, the stock return volatility will respond
to a capital gains tax change, regardless of the percentage of individual investor
ownership on the stock. Third, the individual investor ownership may not be a good
proxy for the tax sensitive ownership because of measurement error. As discussed in
other studies (e.g., Blouin, Raedy and Shackelford, 2007), 13-F filings crudely measure
the amount of capital gains that will be reported in individual tax returns. Finally,
individual investors are subject to the “disposition effect” and may not be tax-savvy.
5. Conclusion
We analyze the impact of capital gains taxes on the volatility of stock returns. Our
analysis predicts that reducing capital gains taxes increases the stock return volatility
because a capital gains tax cut reduces the risk sharing role of financial markets between
investors and the government and increases the consumption risk. Using the Tax Relief
Act of 1997, we empirically test the predictions on the stock return volatility of a capital
35
gains tax cut. Our time series regression analysis uncovers that the return volatility
increases for the market index, the implied volatility of Standard & Poors index options,
and industry portfolios, after controlling for all known determinants of stock return
volatility. These findings are consistent with something happening in 1997 that increased
stock return volatility. We conjecture that the 1997 reduction in the capital gains tax rate
accounted for at least some of the increase in volatility.
To provide more compelling evidence that the 1997 tax cut affected volatility
(and mitigate concerns about omitted correlated variables), we turn to cross-sectional
tests. We hypothesize that the effect of a capital gains tax change on stock return
volatility should vary depending upon dividend distribution and the size of the embedded
capital losses (or gains). We find that non- and lower dividend-paying stocks experience
a larger increase in return volatility than high dividend-paying stocks. We also find that
stocks with large embedded capital losses exhibit a larger increase in return volatility
after a capital gains tax rate reduction than stocks with small embedded capital losses.
However, we do not find a similar relation with embedded capital gains. We also show
that the different return volatilities for portfolios of stocks did not exist before 1997.
It is difficult, if not impossible, to construct a test that provides strong direct
evidence that a reduction in the capital gains tax rate caused stock return volatility to
increase. Our approach has been to control for every other possible determinant of stock
return volatility and see if the remaining volatility shows the footprints of taxes. We infer
from the findings in this study that the volatility left after controlling for every known
determinant appears to reflect the influence of the 1997 capital gains tax rate cut. Stock
return volatility was substantially greater after 1997. Furthermore, firms most affected by
the rate reduction showed the greatest change in volatility. Specifically, non-dividend
paying firms had a greater increase in volatility than dividend paying firms and firms
with large embedded capital losses experienced a greater increase in volatility than firms
with small embedded losses. Since we are unable to provide direct evidence that the tax
cut increased stock return volatility, we are cautious in our conclusions. However, we are
left without an alternative explanation for the surge in volatility following the rate
reductions in 1997, in particular, why portfolios of stocks with different sensitivities to
the capital gains taxes experience different increases in return volatility. Thus, we infer
36
from these findings that the 1997 reduction in the capital gains tax rate contributed to an
increase in stock return volatility in subsequent years.
In closing, while a capital gains tax cut may increase stock return volatility,
investors are not necessarily worse off. From an investor’s perspective, the expected
investment opportunities or the risk and return trade-off are the key consideration for
long-term investment decisions. A capital gains tax cut also may increase investors’ aftertax stock return leading to better risk and return trade-off. In this case, investors may
benefit from a capital gains tax cut. It is interesting to see the effect of a capital gains tax
cut on the risk and return trade-off on stock investment. We leave this for future research.
37
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40
Table 1 Market and Industry Portfolios and Aggregate Control Variables
Panel A of this table provides summary statistics for the market, industry portfolio and aggregate control
variables. Panel B provides univariate tests on the mean volatility change before and after TRA97 for the
market and industry portfolios. rmarket is the monthly average daily excess return of value-weighted CRSP
stock index;
σ market
is the monthly volatility of the excess return of the value-weighted CRSP stock index;
r foreign is the monthly average daily excess return of value-weighted Morgan Stanley Capital International
(MSCI) world stock index excluding the United States;
σ foreign
is the monthly volatility of the excess
return of the value-weighted MSCI world stock index excluding the United States; VIXt is the monthly
implied volatility for the Standard & Poors index options at month t, rindustry , is the monthly average daily
gross return for the five industry portfolio as defined in Fama and French: consumer; manufacturing; high
technology; heathcare and all others; σ industry is the monthly volatility for each of the five industry
portfolios; CAY is the demeaned consumption-wealth ratio; RREL is the stochastically detrended risk free
rate; and GIP is the growth rate of industrial production. The sample period covers January of 1993 to
December of 2002. Note that observations between April and September of 1997 are excluded in the
calculation of volatility mean in the univariate tests.
Panel A: Summary Statistics
Variable
Mean
Median
Std
Min
Max
Market Portfolio and Implied Volatility
rmarket
0.01887
0.05250
0.22370
-0.81762
0.40600
σ market
4.28393
3.72106
2.31162
1.14089
13.47769
r foreign
0.01169
0.03063
0.21066
-0.71839
0.46165
σ foreign
3.65546
3.32699
1.57619
1.37693
9.22375
VIXt
5.92684
6.06362
1.99210
3.06862
12.78254
Industry Portfolios
rconsumer
rmanufacturing
rhightech
rhealthcare
rother
0.03760
0.05174
0.19744
-0.66238
0.52261
0.03235
0.04138
0.18795
-0.70867
0.58095
0.04220
0.07952
0.39592
-1.30000
0.83739
0.05329
0.08731
0.22793
-0.61524
0.56191
0.04477
0.07728
0.22639
-0.99524
0.61304
σ consumer
σ manufacturing
σ hightech
σ healthcare
σ other
4.20179
3.95541
2.01454
1.36115
11.09683
3.47898
3.15529
1.71258
1.23093
11.20402
6.87807
5.86460
3.80486
2.01788
18.76379
5.24268
4.73629
2.32152
1.67003
14.57388
4.43622
3.93285
2.34291
1.22332
12.91087
Aggregate Controls
CAY
0.00033
0.00116
0.02076
-0.04622
0.03312
RREL
-0.00757
-0.00887
0.07144
-0.20375
0.14783
0.00282
0.00314
0.00528
-0.00836
0.02163
GIP
41
Panel B: Univariate Tests for the mean volatility change for market and industry portfolios
Mean volatility
Pre-TRA97
Post-TRA97
Difference
p-value
σ market
2.7090
5.6008
2.8918
0.0001
VIXt
4.1519
7.3328
3.1809
0.0001
σ consumer
σ manufacturing
σ hightech
σ healthcare
σ other
2.7161
5.4143
2.6982
0.0001
2.2179
4.4929
2.2750
0.0001
3.9430
9.4113
5.4683
0.0001
3.8496
6.3451
2.4955
0.0001
2.6695
5.9034
3.2339
0.0001
42
Table 2 Summary Statistics for Constructed Portfolios
Panel A reports the monthly average of daily returns and monthly volatility for non-dividend paying,
dividend-paying, low dividend yield, and high dividend yield portfolios constructed based on whether a
firm pays dividends and the magnitude of dividend yield in the past year. We only include stocks with price
changes (gains or losses) in the prior 18 months being less than 5 percent. r is the monthly average of
daily return for month t. σ is the monthly volatility at month t. We use the subscript “ND” to represent the
non-dividend paying portfolio, “D” for the dividend paying portfolio, “LY” for the low dividend yield
portfolio (with dividend yield in the lower 50 percentile), and “HY” for the high dividend yield portfolio
(with dividend yield in the upper 50 percentile), respectively. Panel B reports the monthly average of daily
returns and monthly volatility for four quartile loss portfolios constructed based on a firm’s stock price
depreciation in the past 18 months up to month t in ascending order with portfolio 1 corresponding to the
smallest embedded capital losses and portfolio 4 the largest embedded capital losses. Panel C reports the
monthly average of daily returns and monthly volatility for four quartile gain portfolios constructed based
on a firm’s stock price appreciation in the past 18 months up to month t in ascending order with portfolio 1
corresponding to the smallest embedded capital gains and portfolio 4 the largest embedded capital gains.
r% t denotes the average daily return for month t for the quartile portfolios and σ % t denotes the monthly
volatility of the quartile portfolios at month t. For both the gains and loss portfolios, we exclude dividendpaying stocks to mitigate possible confounding effect on stock return volatility from a firm’s dividend
distribution. The sample period covers January of 1993 to December of 2002.
Variable
Mean
Median
Std
Min
Max
Panel A: Non-Dividend and Dividend Paying Portfolios
rND
rD
rLY
rHY
σ ND
σD
σ LY
σ HY
0.01020
0.00690
0.29672
-1.24217
1.01549
0.03126
0.04418
0.17322
-0.50811
0.43754
0.02438
0.03442
0.19979
-0.59497
0.54784
0.03713
0.04691
0.17608
-0.55451
0.47131
5.89013
5.11680
2.51470
2.33783
16.10004
3.49784
3.28363
1.36005
1.46585
8.02294
4.05311
3.87738
1.49104
1.63227
8.75432
3.51169
3.30966
1.34652
1.45658
8.37397
Panel B: Loss Portfolios (smallest to largest losses)
r25%t
r50% t
r75%t
r100% t
σ 25% t
σ 50%t
σ 75% t
σ 100% t
0.01382
0.04874
0.29515
-1.08488
0.73012
-0.01582
0.01873
0.37703
-1.40639
0.94808
0.02781
0.02734
0.40893
-1.26344
1.54829
0.04368
0.05614
0.55178
-1.93861
2.03547
5.75504
5.01138
2.34971
2.21929
14.06575
6.40039
5.29427
3.44350
1.65766
17.11815
7.14459
5.74115
3.67043
2.22324
17.40801
7.60548
5.95752
4.33132
2.85232
20.48670
43
Panel C: Gain portfolios ( smallest to largest gains)
r25%t
r50% t
r75%t
r100% t
σ 25% t
σ 50%t
σ 75% t
σ 100% t
0.00079
0.01519
0.29946
-0.99960
0.91874
0.02260
0.02076
0.28016
-0.93593
0.69403
0.04010
0.04708
0.29947
-0.97831
0.91414
0.07830
0.09727
0.41447
-1.80513
1.04318
5.44185
4.81950
2.25315
1.64414
11.62200
5.35551
4.57299
2.51103
1.62656
14.87364
6.00811
5.30272
2.48089
2.22233
14.54936
7.87081
7.03272
3.15716
3.52583
17.62147
Panel D: Univariate Tests for the mean volatility change for constructed portfolios
Mean volatility
Pre-TRA97
Post-TRA97
Difference
p-value
Non-dividend and dividend paying portfolios
σ ND
σD
σ LY
σ HY
4.2028
7.2952
3.0924
0.0001
2.5230
4.3327
1.8097
0.0001
3.0796
4.9237
1.8441
0.0001
2.5083
4.3583
1.8500
0.0001
Loss portfolios
σ 25% t
σ 50%t
σ 75% t
σ 100% t
4.0982
7.1851
3.0869
0.0001
4.0956
8.4404
4.3448
0.0001
4.9036
9.1382
4.2346
0.0001
4.7921
10.0737
5.2816
0.0001
Gain portfolios
σ 25% t
σ 50%t
σ 75% t
σ 100% t
3.8700
6.7648
2.8948
0.0001
3.7845
6.7189
2.9344
0.0001
4.7062
7.1358
2.4296
0.0001
6.6287
8.9819
2.3532
0.0001
44
Table 3 Summary Statistics for Portfolio Control Variables
This table reports the value-weighted monthly averages for the debt/asset ratio (D/A), turnover (Turnover),
percentage bid-ask spread (BidAskSpread), price-earnings ratio (P/E ratio), individual investor ownership
(IND), coefficient of variation for quarterly earnings (CV earnings), and logarithm of market value (Size)
for each portfolio constructed the same as in Table 2. The sample period covers January of 1993 to
December of 2002. For brevity, we report only mean and standard deviation.
Panel A: Non-Dividend and Dividend paying Portfolios
Non-Div. Paying
mean
std
Div. Paying
mean
std
Low-Yield
mean
High-Yield
std
mean
std
D/A
0.4943
0.1206
0.6370
0.0494
0.5996
0.0646
0.6914
0.0634
Turnover
0.1611
0.0678
0.0627
0.0190
0.0707
0.0246
0.0566
0.0180
BidAskSpread
0.6815
0.3484
0.3023
0.1283
0.3510
0.1751
0.2822
0.1093
P/E ratio
20.0411
35.9818
31.1732
64.5378
25.4008
46.2705
37.6375
145.3361
IND
0.4405
0.0952
0.4714
0.0540
0.4445
0.0652
0.4946
0.0575
CV earnings
3.0734
14.6450
0.6817
0.8714
0.8408
1.7461
0.5604
1.1522
Size
14.8446
1.2549
16.5291
0.9074
16.5517
1.1110
16.0920
0.7767
Panel B: Loss portfolios ( smallest to largest losses)
Port. 1 (25%)
mean
std
Port. 2 (50%)
mean
std
Port. 3 (75%)
mean
Port. 4 (100%)
std
mean
std
D/A
0.4763
0.0971
0.4607
0.1049
0.4635
0.1040
0.4604
0.0948
Turnover
0.1633
0.0554
0.1663
0.0635
0.1844
0.0644
0.1968
0.0654
BidAskSpread
0.6515
0.3483
0.8152
0.4884
0.9455
0.4933
1.3275
0.7072
P/E ratio
20.5068
24.5023
21.7288
36.9862
13.5860
27.6493
5.6140
35.4093
IND
0.4591
0.0768
0.4913
0.0973
0.5040
0.0999
0.5920
0.0999
CV earnings
5.2095
18.1340
-1.9583
19.1837
-3.0090
24.3061
-4.8815
67.5841
Size
15.1925
1.4664
14.8591
1.5998
14.4564
1.4629
13.4353
1.8123
Panel C: Gain portfolios ( smallest to largest gains)
Port. 1 (25%)
mean
std
Port. 2 (50%)
mean
std
Port. 3 (75%)
mean
Port. 4 (100%)
std
mean
std
D/A
0.4925
0.0811
0.4867
0.0748
0.4294
0.0812
0.4050
0.0770
Turnover
0.1667
0.0537
0.1539
0.0543
0.1822
0.0657
0.2459
0.0594
BidAskSpread
0.6842
0.6761
0.9672
0.9808
0.8209
0.8089
0.4874
0.3098
P/E ratio
28.6664
24.0376
31.6232
22.6895
34.1299
23.6667
37.7229
15.7612
IND
0.4232
0.0870
0.4470
0.1008
0.4284
0.1045
0.4204
0.0844
CV earnings
-5.6750
57.1063
-2.0627
27.6997
0.4420
4.3358
1.1467
4.2161
Size
15.1664
1.0915
15.5426
1.1167
15.8103
1.1679
15.9727
1.7030
45
Table 4 Time series regression analysis on stock return volatility increases
This table reports the test results of time series analysis on the effect of TRA 97 on stock return volatility.
The tests are conducted for the excess return of the value-weighted CRSP stock market index ( σ market ), the
implied volatility of the S&P index options (VIXt), five industry portfolios including the consumer,
manufacturing, high tech, healthcare, and others, and the constructed portfolios with different sensitivity to
the capital gains tax rate cut using equations (3), (4), and (5). The sample period covers January of 1993 to
December of 2002. Post is a dummy variable which takes value of 1 if the observation is after 10/1/1997 and 0 if it is
before 3/31/1997. The p-value for dummy variable post is based on one-sided test.
Variable
Estimate
Std. Error
t-statistic
Prob.
β >0
Adj. R2
Market and Industry Portfolios
σ market
1.8992
1.0070
1.89
0.0314
0.4715
VIXt
2.1048
0.6599
3.19
0.0010
0.7592
σ consumer
2.0813
0.7796
2.67
0.0046
0.5953
σ manufacturing
1.6252
0.6938
2.34
0.0108
0.6335
σ hightech
2.5370
1.3615
1.86
0.0330
0.6875
σ healthcare
2.1204
0.9871
2.15
0.0174
0.5503
σ other
2.3549
0.8769
2.69
0.0044
0.6232
Non-Dividend and Dividend Paying Portfolios
σ ND
2.4814
1.4388
1.72
0.0444
0.4675
σD
1.9205
0.8203
2.34
0.0110
0.5940
σ LY
2.4224
0.8547
2.83
0.0030
0.5654
σ HY
1.5206
0.6318
2.41
0.0093
0.6485
Loss portfolios (smallest to largest losses)
σ 25% t
2.7938
1.5760
1.77
0.0402
0.5630
σ 50%t
1.1549
1.4666
0.79
0.2168
0.6985
σ 75% t
3.7202
1.9391
1.92
0.0295
0.6801
σ 100% t
6.3805
1.7908
3.56
0.0003
0.7505
Gain portfolios (smallest to largest gains)
σ 25% t
0.5297
1.1435
0.46
0.3223
0.4795
σ 50%t
1.1499
1.1708
0.98
0.1646
0.5449
σ 75% t
1.3680
1.1771
1.16
0.1245
0.6076
σ 100% t
2.0770
1.5822
1.31
0.0967
0.5711
46
Table 5 Cross-Sectional Tests on Volatility Increases for Non-Dividend versus
Dividend Paying Portfolios
This table reports the cross-sectional test results on the effect of TRA97 on the monthly volatility of the excess return
of the value-weighted portfolios formed based on whether a stock pays dividends and the magnitude of dividend yield
in the prior year. To mitigate the effect of large embedded capital gains or losses on stock return volatility, we only
include stocks with price changes in the past 18 months prior to current month to be less than 5 percent. See tables 1, 2
and 3 for variable definitions. The sample period covers January of 1993 to December of 2002. Post is a dummy
variable which takes value of 1 if the observation is after 10/1/1997 and 0 if it is before 3/31/1997. The numbers in
parentheses are p-values. The p-value for variables post, HVP and PostxHVP are based on one-sided test.
Variable
Post
Predicted
HVP
PostxHVP
D/A
Turnover
BidAskSpread
P/E ratio
IND
CV earnings
Size
N
-2 log likelihood
+
ND vs. D
2.1128
(0.0003)
1.7657
(0.0030)
1.1591
(0.0177)
0.3834
(0.7765)
-3.1389
(0.3747)
0.2811
(0.8010)
0.0026
(0.0977)
0.0175
(0.7552)
-0.0024
(0.8564)
-0.1170
(0.5200)
224
743.3
47
ND vs. LY
1.5824
(0.0120)
1.1199
(0.0190)
0.7928
(0.0612)
-1.0165
(0.4388)
-2.7996
(0.4151)
-0.3501
(0.7482)
-0.0020
(0.3633)
0.0350
(0.5014)
0.0015
(0.9107)
-0.2777
(0.1282)
224
767.9
ND vs. HY
1.7799
(0.0005)
1.7699
(0.0075)
1.6196
(0.0021)
2.1152
(0.0772)
0.1785
(0.9591)
0.4603
(0.6519)
0.0001
(0.8995)
-0.0611
(0.1880)
-0.0041
(0.7540)
0.0767
(0.6449)
224
731.8
Table 6 Cross-Sectional Test of Volatility Increases for Losses and Gain portfolios
This table reports the cross-sectional test results on the effect of TRA97 on the monthly volatility of the excess return
of the value-weighted portfolios formed based on the price depreciation (appreciation) in the past 18 months prior to
current month. Only non-dividend paying stocks in the past year are included. See tables 1, 2 and 3 for variable
definitions. The sample period covers January of 1993 to December of 2002. Post is a dummy variable which takes
value of 1 if the observation is after 10/1/1997 and 0 if it is before 3/31/1997. The numbers in parentheses are p-values.
The p-value for variables post, HVP and PostxHVP are based on one-sided test.
Variable
Predicted
LgL. vs. SmL.
LgG. vs. SmG.
2.6979
0.5528
(0.0013)
(0.2551)
1.8396
1.1116
(0.0042)
(0.0319)
1.0952
0.0348
(0.0527)
(0.4760)
3.4841
-2.3868
(0.0647)
(0.3375)
Post
HVP
PostxHVP
+
D/A
4.0660
7.2320
(0.1957)
(0.0616)
0.1074
0.0201
(0.8851)
(0.9369)
-0.0017
0.0077
(0.7274)
(0.2645)
-0.0617
-0.0627
(0.3121)
(0.3479)
0.0036
-0.0027
(0.2304)
(0.3535)
0.2287
0.3043
(0.2630)
(0.1081)
N
224
224
-2 log likelihood
860.0
857.8
Turnover
BidAskSpread
P/E ratio
IND
CV earnings
Size
48
Table 7 Robustness Check on Cross-Sectional Volatility Increase Test
This table reports the robustness test results of volatility increase for different portfolios. Post is a dummy variable
which takes value of 1 if the observation is after 10/1/1997 and 0 if it is before 3/31/1997. HVP is a dummy variable
which takes value of 0 if the observation is in a benchmark portfolio and 1 if it is in an alternative portfolio. The last
column reports the probability of a one-sided test on a positive coefficient for Post × HVP. The sample period
covers January of 1993 to December of 2002.
Break point
Variable
Estimate
Std. Error
t-statistic
Prob
β =0
Panel A: Non-dividend paying Vs. dividend-paying portfolios
4/1994 – 9/1994
4/1995 – 9/1995
4/1996 – 9/1996
PostxHVP
PostxHVP
PostxHVP
1.0380
0.9496
0.8098
0.7424
0.5928
0.5260
1.40
1.60
1.54
0.1637
0.1109
0.1254
Panel B: Large losses (upper 25%) Vs. small losses (lower 25%) portfolios
4/1994 – 9/1994
4/1995 – 9/1995
4/1996 – 9/1996
PostxHVP
PostxHVP
PostxHVP
0.1372
-0.5003
0.0397
0.9827
0.8189
0.7701
0.14
-0.61
0.05
0.8891
0.5420
0.9590
Panel C: Large gains (upper 25%) Vs. small gain (lower 25%) portfolios
4/1994 – 9/1994
4/1995 – 9/1995
4/1996 – 9/1996
PostxHVP
PostxHVP
PostxHVP
-0.0974
-0.0395
-0.2536
49
0.8800
0.6626
0.5971
-0.11
-0.06
-0.42
0.9120
0.9526
0.6715
Table 8 Test for Volatility Changes for Non-Dividend and Dividend Paying
Portfolios with Low and High Individual Ownership
This table reports the test results of time series and cross-sectional analyses on the effect of TRA97 on the monthly
volatility of the excess return of the value-weighted portfolios formed based on a stock’s dividend distribution in the
prior year and the detrended individual ownership in the most recent past quarter. Stocks with detrended individual
ownership in the lower 50 percentile are included in the low individual ownership portfolios (Low IND) and stocks
with detrended individual ownership is the upper 50 percentile are included in the high individual ownership portfolios
(High IND). The price change in the past 18 months prior to current month is restricted to less than 5 percent. The
sample period covers January of 1993 to December of 2002. Post is a dummy variable which takes value of 1 if the
observation is after 10/1/1997 and 0 if it is before 3/31/1997. The numbers in parentheses are p-values based on onesided test.
Panel A: Time Series Analysis
Variable
Post
Pred.
Non-dividend
sign
Low IND Port.
+
N
Adj. R2
Non-dividend
High IND Port.
Dividend Paying
Dividend Paying
Low IND Port.
High IND Port.
3.4382
2.9993
1.6843
1.1574
(0.0109)
(0.0350)
(0.0273)
(0.0941)
112
112
112
112
0.2904
0.4245
0.4671
0.5852
Panel B: Cross-Sectional Analysis
Variable
Pred.
Non-dividend vs. dividend paying
Non-dividend vs. dividend paying
sign
With low individual ownership
With high individual ownership
Post
+
1.6873
1.5943
(0.0041)
(0.0040)
HVP
+
1.8652
2.9475
(0.0012)
(0.0001)
PostxHVP
+
1.3540
0.1345
(0.0083)
(0.3973)
N
224
224
-2 log likelihood
798.5
776.5
50