Capital Gains Taxes and Stock Return Volatility
Zhonglan Dai
University of Texas at Dallas
Douglas A. Shackelford
University of North Carolina and NBER
Harold H. Zhang
University of Texas at Dallas
First version: August, 2006
This version: January 12, 2007
We thank Yexiao Xu for helpful discussions; Qin Lei, Dave Mauer, Kam-Ming Wan, and
seminar participants at Baruch College, the Southern Methodist University, and the University of
Texas at Dallas 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,
[email protected], 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
Abstract
We demonstrate that capital gains tax changes inversely affect stock return volatility. A
capital gains tax cut reduces the risk sharing between investors and the government and
increases stock return volatility. The tax effect on return volatility also differs depending
upon the characteristics of stocks such as dividend distribution and embedded capital
gains and losses. Using the Tax Relief Act of 1997, we empirically show that the return
volatility of the market index, industry portfolios, and individual stocks increases after
the capital gains tax cut. Furthermore, higher dividend-paying stocks experience smaller
increase in return volatility than lower dividend-paying stocks and stocks with large
embedded capital gains and losses see larger increase in return volatility than stocks with
small embedded capital gains and losses.
1
1. Introduction
This paper examines the effect of capital gains taxes on asset return volatility.
Existing studies on the effects of capital gains taxes on asset prices have primarily
focused on the level of asset returns and on trading volume. The goal of this study is to
investigate the relation between asset return volatility and capital gains taxes. We
demonstrate that imposing capital gains taxes reduces asset return volatility because the
government shares the gains and losses in assets held by investors subject to taxation
upon realization. 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. A
capital gains tax cut reduces risk sharing between investors and the government and has
an adverse effect on individual investors’ consumption smoothing. This leads to a more
volatile individual consumption growth rate and stochastic discount factor, resulting in a
higher asset return volatility. Using the Tax Relief Act of 1997, we uncover strong
evidence that a capital gains tax cut significantly increases the volatility of asset returns
and the magnitude of increases in return volatility differs depending upon the
characteristics of assets such as dividend distribution, embedded capital losses and gains,
and the percentage of shares owned by tax sensitive investors. To our knowledge, this is
the first study of the relation between asset return volatility and the capital gains taxes.
There is an increasing literature about how capital gains taxes affect asset prices.
Existing theoretical studies suggest that the effect of capital gains taxes on asset price is
likely to be ambiguous because introducing capital gains taxes decreases both the demand
and the supply of assets. Empirical investigations on 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 reduced 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).
Further, Dhaliwal and Li (2006) investigate the relation between investor tax
heterogeneity and ex-dividend day trading volume and document a concave relation
between ex-dividend day trading volume and investor tax heterogeneity measured by
2
institutional ownership. In a recent study, Dai, Maydew, Shackelford, and Zhang (2006)
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.
However, none of the existing studies has examined the relation between asset return
volatility and capital gains taxes. Asset return volatility is one of the key determinants of
investors’ demand and supply of risky assets. If the presence of capital gains taxes affects
asset return volatility, it will certainly impact investors’ demand and supply of risky
assets and ultimately influence asset returns. In this paper, we first discuss the relation
between the capital gains taxes and asset return 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 the relation between the capital gains taxes and asset return
volatility. We then empirically test the predictions using the Taxpayer Relief Act of 1997
as our event.
Overall, our analysis suggests the following testable implications when the capital
gains tax rate is reduced.
•
Return volatility is increased for the market index, industrial portfolios, and
individual stocks.
•
Higher dividend-paying stocks with high tax sensitive investor ownership will
experience lower volatility increase than lower dividend-paying stocks.
•
Stocks with large embedded capital gains (losses) and high tax sensitive investor
ownership will have higher volatility increase than stocks with small embedded
capital gains (losses).
The first prediction focuses on the effect of a capital gains tax cut on the return
volatility of portfolios and the market index. Thus, it represents the effect of a capital
gains tax cut on the volatility of the broad financial market. The next two predictions
focus on the effect of a capital gains tax cut on individual stock return volatility and
3
constitute the cross-sectional implications of a capital gains tax cut on individual stock
return volatility.
Our predictions are closely related to the roles played by the financial markets. From
investors’ perspective, financial markets have two important functions: risk sharing and
consumption smoothing. In addition to actively sharing risk with other market
participants, in the presence of the capital gains taxes, investors also share the risk of
holding risky stocks with the government (passively). This is clearly exemplified when
the investors’ asset holdings have depreciated in value. In this case, the investors’ net
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. When the capital gains tax rate is cut, risk sharing between
investors and the government is reduced. Investors thus experience more volatile
consumption growth rates resulting in increased volatility for the stochastic discount
factor. This then leads to an increase in stock return volatility. Because the risk sharing
role associated with the capital gains taxes varies with stocks with different
characteristics, the impact of a capital gains tax change on stock return volatility also
differs correspondingly. Ceteris paribus, lower- and non-dividend paying stocks are
riskier and will thus experience larger increases in return volatility than higher dividendpaying stocks after the capital gains tax rate is reduced. Stocks with larger embedded
capital gains and losses become riskier when the capital gains tax rate is lower because
there is less risk sharing with the government. These stocks will experience higher
volatility increases.
Our empirical analysis on stock return volatility surrounding the 1997 capital
gains tax rate cut provides strong support for our predictions on the effect of the capital
gains tax change on stock return volatility. For the market portfolio, we find the volatility
of monthly excess return of the value-weighted CRSP stocks is more than 3 percent
higher when the capital gains tax rate is reduced from 28 percent to 20 percent, after
controlling for several variables which are widely documented to be important
determinants of stock return volatility and the state of the economy. Further, for five
industry portfolios formed based on 4-digit SIC code including consumer industry,
manufacturing industry, high tech industry, healthcare industry, and other industries, the
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monthly return volatility is higher for all five portfolios when the capital gains tax rate is
reduced, controlling for variables often identified to be important factors affecting return
volatility. The increase in monthly return volatility ranges from 2.3 percent for the
healthcare industry to 5 percent for the high tech industry. In addition, the increase in
return volatility for all five industries is statistically significant (with four industries
having p-value less than 1 percent and one industry p-value of 0.03).
For individual firms, we find that stock return volatility is higher on average after
the capital gains tax rate cut, lending support to the results on the market index and
industry portfolios. Higher dividend-paying stocks with large tax sensitive investor
ownership experience lower volatility increase than lower dividend-paying stocks,
consistent with the prediction of our analysis. The finding is primarily concentrated on
dividend-paying stocks that experienced stock price decline in the past 18 to 36 months.
Stocks with large embedded capital losses and high tax sensitive investor ownership
show much larger volatility increase than average stocks after the capital gains tax rate
cut. For instance, every thing else the same, for a 50 percent additional loss, the monthly
individual stock return volatility is higher by 1.1 to 1.8 percent when the tax sensitive
ownership is measured by the percentage of shares owned by individual investors and
individual investors and mutual funds, respectively. We also find that stocks with large
embedded capital gains experience higher volatility increase. Further, this finding is
stronger for non-dividend paying stocks than for dividend-paying stocks. For instance,
for non-dividend paying stocks with a 50 percent additional gain, the monthly individual
stock return volatility is higher by 0.44 to 0.69 percent for the two measures of tax
sensitive ownership, respectively. Our findings are robust to alternative measures of
embedded capital gains and losses, the inclusion of diverse growth options for different
individual firms, and the subperiod excluding observations in year 2000 and year 2001
during which the stock market experienced significant decline.
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 improved return and
risk trade-off and thus face the same or better investment opportunities.
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The paper is organized as follows. In section 2, we discuss the mechanism that the
capital gains taxes affect stock return volatility and develop hypotheses on the effects of a
capital gains tax cut on return volatility both for market index and industry portfolios and
the cross-section of individual stocks. Section 3 presents empirical methodology to test
the predictions of our analysis. Section 4 discusses the results of the empirical analysis.
Conclusion remarks are provided in Section 5. In the appendix, we present a dynamic
model with capital gains taxes to derive testable implications on stock return volatility
when the capital gains tax rate is changed.
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, while others spend more than they currently earn.
Financial assets allow these individuals to shift their purchasing power from highearnings periods to low-earnings periods of life 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, consumption smoothing and risk sharing are
achieved among market participants through trading of financial assets on financial
markets.
In the presence of taxation, the government, however, plays an important role in
influencing the consumption smoothing and risk sharing among market participants.
Capital gains taxes in particular have a large impact on consumption smoothing and risk
sharing of investors participating in the financial markets and financial asset trading. 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. On the other hand, if the stock has depreciated in value upon selling, the
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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. The tax treatment of the gains and losses on stocks thus offers a risk
sharing mechanism between investors and the government. Consequently, the capital
gains taxes will affect the consumption smoothing of stock market participants.
The risk sharing between investors and the government associated with the capital
gains taxes will ultimately affect the stock return volatility. Under no arbitrage condition,
Harrison and Kreps (1979) demonstrate that there exist stochastic discount factors that
can be used to price the stochastic payoffs associated with any assets. Subsequently
studies have suggested that the stochastic discount factors (or pricing kernels) can take
different specifications depending upon investors’ preferences, consumption profiles, and
various forms of market frictions, among others. In particular, recent studies suggest that
the consumption growth rate of stock market participants is an important determinant of
stochastic discount factors (Mankiw and Zeldes, 1991, Jacobs, 1999, and Brav,
Constantinides, and Geczy, 2002, among others). In general, these studies document that
the stochastic discount factor using the more volatile consumption growth rates for
stockholders explains the volatile stock returns better than the aggregate consumption
growth rate. This suggests a positive relation between the volatility of the consumption
growth rate and the stock return volatility. Because the capital gains taxes affect the risk
sharing between investors and the government and the consumption smoothing of stock
market participants, the change in the capital gains taxes will impact the volatility of the
consumption growth rates of these investors and consequently the stock return volatility.
To facilitate the development of our hypotheses on 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 the
broad financial market and then discuss the cross-sectional implications of a change in
the capital gains taxes on individual stock return volatility. Our discussions above suggest
that the government serves as a partner in sharing the return of stock investments with the
taxable investor partner in the presence of the capital gains taxes. Suppose the capital
gains tax rate is close to 100 percent. The government “partner” thus gets almost all the
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returns of investments made by taxable investors. Consequently, it bears almost all the
risk while the risk borne by taxable investors is negligible. On the other hand, suppose
that the capital gains tax rate is 0. Then the taxable investor “partner” receives all the
returns and bears all the risk. In reality, the capital gains tax rate is typically positive but
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. When the capital gains tax rate
is reduced, however, 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, in the case of a
capital gains tax cut, taxable investors will receive a larger fraction of returns on all
stocks and bears more risk on all the stocks, leading to a more volatile consumption
growth rates for these 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 capital gains tax cut will lead to a higher return volatility for the market index,
industry portfolios, and individual stocks.
Because different stocks have different tax liabilities and investor bases, a capital
gains tax change will have different impact on risk sharing between investors and the
government. First, firms with different dividend payouts will likely have different impact
on the risk sharing between taxable investors and the government in the case of a capital
gains tax cut. Imagine that taxable investors receive all returns from a firm as dividends.
In this case, no income received is subject to capital gains taxes. Consequently, the
government bears no risk related to capital gains or losses and the capital gains taxes will
have little direct effect on the volatility of the stock return. On the other hand, if the
taxable investors receive no dividends and the entire return is in the form of capital gains,
all income will be subject to capital gains taxes and the government bears the maximum
risk associated with the capital gains. In this case, a capital gains tax change will have a
large effect on the risk sharing between the taxable investors and the government and the
consumption growth rate of the taxable investors. Consequently, it will have a large
impact on the stock return volatility. In general, the more the capital gains tax (or the less
8
the dividend tax) is levied on the firm’s profits, the more the government shares in the
risk. A capital gains tax change will have a larger effect on the risk sharing and the
consumption growth rates of taxable investors. This leads to the following hypothesis on
the relation between the individual stock return volatility and the dividend payouts of
these firms.
H2: A capital gains tax cut will increase the return volatility of lower dividendpaying stocks more than that of higher dividend-paying stocks.
Second, firms with different embedded capital gains or losses will also have different
effect on the risk sharing between taxable investors and the government in the case of a
capital gains tax cut. Suppose that the sale proceeds of a taxable investor in a stock are
equal to the taxable investor’s tax basis (the cost of purchasing the stock). The investor
would have no income subject to capital gains taxes upon realization because the
embedded gain or loss is zero. The government also bears no risk. However, if the
investor’s sale proceeds are equal to the gains (the cost of purchasing the stock is almost
zero relative to the sale proceeds) or the investor’s sale proceeds are almost zero (the loss
is equal to the cost of purchasing the stock), all income are subject to the capital gains
taxes or all losses can be used to reduce tax liabilities (first realized capital gains and then
ordinary income). In this case, the government bears the maximum risk. A capital gains
tax change will have a large impact on the risk sharing and consumption smoothing of the
taxable investors on these stocks. The effect of a capital gains tax change will also be
large on the return volatility of these stocks. We therefore have the following hypothesis
on the relation between stock return volatility and embedded capital gains or losses in the
case of a capital gains tax cut.
H3: A capital gains tax cut will increase stock return volatility of firms with large
embedded capital gains (losses) more than that of firms with small embedded capital
gains (losses).
In the appendix, we present a dynamic economic model with capital gains taxes to
derive the implications for stock return volatility in the case of a capital gains tax cut. For
tractability, we assume there are two stocks. One pays higher dividend than the other.
Capital gains and losses are realized every period. Under certain conditions, we show that
the return volatility of all stocks, consequently the market index, increase when the
9
capital gains tax rate is reduced. Further, the volatility increase is smaller for the higher
dividend-paying stock than for the lower dividend-paying stock. The predictions are
consistent with our hypotheses H1 and H2 discussed above. In the next section, we
discuss empirical methodology to test three hypotheses discussed above.
3. Empirical Methodology
To empirically test the effect on stock return volatility of a change in the capital
gains tax rate, we use the Taxpayer Relief Act of 1997 (TRA97) as our event. The
TRA97 lowered the top tax rate on capital gains from 28 percent to 20 percent for assets
held more than 18 months. TRA97 is particularly attractive for an event study because
the tax cut was both large and relatively unexpected. Often tax legislation follows a
protracted process with gradual changes in the probability of a particular bill becoming a
law. In TRA97, however, Congress provided researchers with an attractive setting by
coming to rapid agreement on a large, relatively unexpected reduction in capital gains tax
rates. For the Taxpayer Relief Act of 1997 (TRA97), little information was released 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.
The empirical implications we derived above apply not only to the broad
financial market, they also apply to individual stocks. In our empirical analysis, we first
examine return volatility at market level using the value-weighted market index, we then
move down to industry level using five industry portfolios including consumer,
manufacturing, high tech, health, and others, classified based on 4-digit SIC code, and
finally we examine return volatility of individual stocks. At each level, we use daily
returns to construct monthly volatility measure. For the test on the return volatility of the
market and industry portfolios, the sampling period is from January 1993 to December
10
2002. For the test on individual stock return volatility, the time period we use in our
baseline case is from 1/1/1994 to 12/31/2001. We also perform a robustness check on
individual stock return volatility using a shorter subsample that ends at 12/31/1999 to
exclude the period of significant market decline in year 2000 and 2001. To avoid the
transient effect caused by the capital gains tax cut announcement, we exclude April and
May of 1997 from our analysis.1
The capital gains rate reduction in the TRA97 is only applied to income that is
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).
Corporations pay capital gains taxes;
however, the rate reduction in TRA97 did not apply to corporations. Thus, our empirical
tests, especially at the individual stock level, will be based on the amount of holdings by
tax sensitive investor ownership, such as individual investors and/or mutual funds.
To capture the group of investors who are the most sensitive to the capital gains
taxes, we construct proxies for the percentage of tax sensitive investor ownership of a
stock (individual investors and/or mutual funds) using data on shares outstanding and
shares owned by institutional investors. The data on the institutional investors’ ownership
are obtained from their quarterly filings with the U.S. Securities and Exchange
Commission (known as Form 13F).
Let ritj be the return on stock (or industry) i on day j in month t and σ it be stock (or
industry) i’s return volatility in month t. We construct the monthly stock (or industry)
return volatility for each firm-month (or industry-month) as follows
σ it =
Jt
∑ (r
itj
− rit ) 2 ,
(1)
j =1
1
We have also performed our analysis by excluding June, July, and August in addition to April and May to
account for the actual signing of the tax cut bill. The results are qualitatively similar.
11
1
where rit =
Jt
Jt
∑r
j =1
itj
is the sample mean return for stock (or industry) i in month 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
thus defined (including the extra cross-product terms in the expression) adjusts for the
first-order autocorrelation in daily returns associated with nonsynchronous trading among
stocks included in the index.2
The research design we use to test our hypotheses on the change in stock return
volatility in response to the capital gains tax cut is to define a dummy variable Post t
which takes value 0 before 3/31/1997 and value 1 after 6/1/1997. Note that this is
different from standard event study on stock returns which focuses on announcement
effect. We actually take out those event months from our examination because we are
interested in the change of volatility level before and after the event. Another important
difference between stock return and the volatility of stock return is that the latter has
significant persistence which may cause problems in the statistical inference if not
appropriately accounted for. To allow for the serial correlation in stock return volatility,
we use lagged demeaned volatility as explanatory variable in our analysis.
Specifically, the specification we use for market index is:
p
q
j =1
j =1
σ t = α + β Post t + ∑ ρ j ∆σ (t − j ) + ∑ δ j rt − j + γ ' X t + ε t ,
where ∆σ t = σ t −
1
T
(3)
T
∑σ
k
is the demeaned volatility measure for the market index and
k =1
subscript j refers to its lags. Existing empirical asset pricing studies suggest that large
2
Similar measures are used in French, Schwert and Stambaugh (1987) and Guo and Whitelaw (2006),
among others.
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negative stock price changes tend to be followed by periods of high stock return
volatility. In other words, stock return volatility is asymmetric in stock return
performance. This is sometimes referred to as the leverage effect. To account for this
effect, we allow stock return volatility to depend on lagged stock returns ( rt − j ). Finally,
X t refers to a vector of aggregate control variables and they include the consumptionwealth ratio (CAY), the stochastically detrended risk free rate (RREL), and the industrial
production growth rate (GIP). Based on the capital asset pricing theory, Lettau and
Ludvigson (2001) propose that the consumption-wealth ratio be used as a determinant for
stock returns. They further demonstrate that the CAY variable is a better predictor than
the dividend yield, the term premium, the default premium, and other previously widely
used predictors combined. Campbell and Shiller (1988) document that the stochastically
detrended risk free rate 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.
For each industry portfolios i, we use the following specification:
p
q
m
n
j =1
j =1
j =1
j =1
σ it = α + β Post t + ∑ ρ j ∆σ (t − j ) + ∑ δ j r(t − j ) + ∑ θ j ∆σ i (t − j ) + ∑η j ri (t − j ) + γ ' X t + ε it .
(4)
Note that, in addition to the explanatory variables included in the specification for the
market index, we have also included lagged demeaned industry portfolio volatility
( ∆σ i ( t − j ) ) and lagged industry portfolio returns ( ri ( t − j ) ) to account for volatility
persistence and leverage effect at industry level.
For individual stocks, we first test the across board effect on individual stock
return volatility associated with a capital gains tax cut. This is achieved by applying
specification (4) to the return volatility of individual stocks. We then extend the
specification to jointly test the across board effect and the cross-sectional effect on
individual stock return volatility associated with a capital gains tax cut. We consider two
specifications for the joint test for the across board effect and the cross-sectional effect on
the return volatility of individual stocks. First, we consider the following model (we refer
to it as the basic joint specification):
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σ it = α + β Post t + λ1 Post t × Yield i (t −1) × TSOi (t −1)
+ λ 2 Post t × Losses i ( t −1) × TSOi ( t −1) + λ3 Post t × Gains i ( t −1) × TSOi ( t −1)
p
q
m
n
j =1
j =1
j =1
j =1
(5)
+ ∑ ρ j ∆σ ( t − j ) + ∑ δ j r( t − j ) + ∑ θ j ∆σ i ( t − j ) + ∑η j ri ( t − j ) + γ ' X t + ϕ ' Z it + ε it .
The specification is more complex relative to the above two and allows us to test
not only the across board effect of a capital gains tax cut on stock return volatility, but
also the differential tax effect across different stocks. In addition to the dummy variable
for the periods after enactment of TRA97 (Postt) this specification also includes
interactions to test the cross-sectional effect of a capital gains tax cut on individual stock
return volatility. Specifically, we include the interaction of the dummy variable (Post)
with the dividend yield ( Yield i ( t −1) ) and the tax-sensitive ownership ( TSOi ( t −1) ) to test if
higher dividend-paying stocks with large tax-sensitive ownership experience lower return
volatility increase than lower dividend-paying stocks after the capital gains tax cut. We
also include the interaction of the Post dummy with the embedded capital loss
( Losses i ( t −1) ) and tax-sensitive ownership, and the interaction with the embedded capital
gains ( Gains i ( t −1) ) and tax-sensitive ownership to test if firms with larger embedded
capital losses (gains) and high tax-sensitive ownership experience higher return volatility
increase after the capital gains tax cut. The Gains and the Losses are measured based
upon the stock price change (appreciation or depreciation) in the past 18 months up to the
most recent past month prior to t in our baseline case.3 Specifically, Gains i ( t −1) is stock i’s
embedded capital gains if the stock price change is positive and takes value of 0
otherwise, Losses i ( t −1) is stock i’s embedded capital losses if the stock price change is
negative and takes value of 0 otherwise. The tax-sensitive investor ownership TSOi ( t −1) is
measured as the percentage of shares owned by individual investors and/or mutual funds
(the two groups affected by the TRA97). In addition to all the control variables we use in
the equations for the return volatility of the market index and industry portfolios, we have
also included a vector of Z it which consists of firm-specific characteristics and
additional firm level interaction terms as of time t.
3
We also perform our empirical test using gains and losses measured at 12 months, 24 months, and 36
months in robustness check.
14
In our second specification for the joint test of the across board effect and the
cross-sectional effect, we extend the basic joint specification by allowing the relation
between the return volatility and the dividend yield to differ across stocks with embedded
gains and stocks with embedded losses. We also allow the relation between the return
volatility and the size of embedded gains and losses to differ across dividend-paying
stocks and non-dividend paying stocks. We provide the extended model for the joint test
of the across board effect and the cross-sectional effect below (we refer to it as the
extended joint specification):
σ it = α + β Post t + φ1 Post t × Yield i (t −1) × TSOi (t −1) × DGi (t −1)
+ φ 2 Post t × Yield i (t −1) × TSOi (t −1) × DLi ( t −1) + φ3 Post t × Losses i ( t −1) × TSOi ( t −1)
+ φ 4 Post t × Gains i ( t −1) × TSOi ( t −1) × NDivi ( t −1)
+ φ5 Post t × Gains i ( t −1) × TSOi ( t −1) × Divi ( t −1)
p
q
m
n
j =1
j =1
j =1
j =1
+ ∑ ρ j ∆σ ( t − j ) + ∑ δ j r( t − j ) + ∑ θ j ∆σ i ( t − j ) + ∑η j ri ( t − j ) + γ ' X t + ϕ ' Z it + ε it ,
(6)
where the embedded capital gain (loss) dummy DG i ( t −1) ( DLi ( t −1) ) takes value of 1 if the
stock has an embedded gain or Gains i ( t −1) > 0 (loss or Losses i ( t −1) < 0 ) and takes value of
0 otherwise, and the dividend distribution dummy ( Div i ( t −1) ) takes value of 1 if stock i
distributes dividends in prior year and 0 otherwise, and the non-dividend distribution
dummy ( NDiv i ( t −1) ) is defined as [ 1 − Div i ( t −1) ].
In a recent paper on stock return volatility, Campbell, Lettau, Malkiel, and Xu
(2001) document that over the period from 1962 to 1997 there has been a noticeable
increase in firm-level volatility relative to market volatility.4 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 statistically significant effect on the risks of their firms’ activities.
But the effect is small in magnitude. Gompers and Metrick (2001) and Xu and Malkiel
4
Similar results are also documented in Pastor and Veronesi (2006) for the more recent periods until 2002.
15
(2003) document that institutional ownership increases individual stock return volatility.
Dai, Maydew, Shackelford, and Zhang (2006) 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. Further,
between June 1997 to August 1997, both the New York Stock Exchange and the Nasdaq
reduced the tick size for stock trading. To capture these effects, we include debt-asset
ratio (D/A), institutional ownership in the most recent past quarter (InsOwn), turnover in
the most recent past month (Turnover), and the average monthly bid-ask spread in the
most recent past month (BidAskSpread) for each firm in our firm level return volatility
specification. As a robustness check we also perform the regression analysis on firm level
stock return volatility including the forecasted operating income growth rate
(GrowthOption) as a control variable in our robustness analysis in subsection 4.D.5
In addition, we include firm size measured in the logarithm of firm’s market
capitalization for the most recent month (Size), NDiv, dividend yield, embedded gains
and
losses,
interactions
Yield*Gains,
Yield*Losses,
NDiv*TSO,
NDiv*Gains,
NDiv*Losses, Post*Yield, Post*Gains, Post*Losses, Post*TSO, Post*Yield*Gains, and
Post*Yield*Losses as other firm level controls. Finally for all specifications, year
dummies are used for possible trend and monthly dummies are used to account for
calendar effect.
Our specifications above consider the effect of capital gains tax rate change on
three different levels of stock return volatility: the market volatility, the industry
volatility, and the firm volatility. Our discussion in section 2 predicts that in the case of a
capital gains tax cut stock return volatility generally will be higher after the lower capital
gains tax rate becomes effective. This implies that the coefficient β will be positive for
all specifications represented by equations (3) to (6). On the cross-sectional effect of a
capital gains tax cut on individual stock return volatility, our analysis predicts that the
coefficient for the interaction Post × Yield × TSO in specification (5) will be negative
( λ1 < 0 ). Our analysis also suggests that stocks with larger embedded capital losses and
high tax sensitive ownership will experience higher return volatility increase. This
5
Since the forecasted operating income growth is only available on a small subset of firms, we do not
include the growth option variable in the baseline specification but incorporate the growth option variable
in our robustness check.
16
implies that the coefficient for Post × Losses × TSO will be negative (λ2 < 0) because
Losses < 0. For stocks with large embedded capital gains and high tax-sensitive
ownership, our analysis predicts that they are likely to experience higher return volatility
increase. This suggests that the coefficient for Post × Gains × TSO will likely be positive
(λ3 < 0) . In the extended specification on the joint test of the across board effect and the
cross-sectional effect of a capital gains tax cut on individual stock return volatility
(equation 6), the interaction terms Post × Yield × TSO × DG and Post × Yield × TSO × DL
test if higher dividend-paying firms with large tax sensitive investor ownership will
experience lower volatility increase than lower dividend-paying stocks after the capital
gains tax cut. The return volatility response is allowed to differ across stocks with
embedded gains and losses. Our analysis predicts the coefficient for the interaction terms
to be negative ( φ1 < 0 and φ 2 < 0 ). The coefficient for the interaction term
Post × Losses × TSO will be negative (φ3 < 0) because Losses < 0. For stocks with
embedded capital gains, our extended specification allows the relation between the return
volatility and the embedded gains to differ across dividend paying firms and nondividend paying firms to respond differently to a capital gains tax cut. Our analysis in
section
2
suggests
that
the
coefficients
for
both
interaction
terms
Post × Gains × TSO × NDiv and Post × Gains × TSO × Div will likely be positive ( φ 4 > 0
and φ5 > 0 ).
4. Empirical Analysis
A. 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 five industry portfolios are
formed using the 4-digit SIC code and consist of (1) consumer industry (consumer
durables, non-durables, wholesale, retail, and some services such as laundries, repair
shops), (2) manufacturing industry (manufacturing, energy, and utilities), (3) high tech
industry (business equipment, telephone and television transmission), (4) health care
17
industry (healthcare, medical equipment, and drugs), and (5) other industries (mines,
construction, building materials, transportation, hotels, business services, entertainment,
finance).6 For the volatility of market index and industry portfolios, we use the sample
from January 1993 to December 2002 for our regression analysis. For individual stock
return volatility, the sample used in our regression analysis spans the period from January
1994 to December 2001. We choose the sample period based on two considerations.
First, we want to avoid the effects from the tax policy changes both before and after the
TRA97. Second, we want to choose the sample period so that we have about the same
observations before and after the announcement. In other words, the event months fall in
the middle of our sample period. We perform robustness check on individual stock return
volatility analysis using the subsample data from January 1994 to December 1999 to
exclude year 2000 and 2001 when the stock market experienced a large price decline.
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. The dividend
dummy variable Div is constructed based on dividend distribution in the prior year and
takes the value of 1 if the firm distributed dividend and 0 otherwise. We construct the
embedded capital gains and losses using a firm’s most recent 18 month stock price
change prior to month t. We then perform robustness check using 12 month, 24 month,
and 36 month price changes to calculate the measure of the embedded capital gains and
losses. To obtain measures of tax sensitive investor ownership, we use institutional
investors’ ownership information from Form 13F submitted to the Security Exchanges
6
The excess return on the value-weighted market index and returns on industry portfolios are obtained
from Kenneth French’s website.
18
Commission by investment management companies.7 We construct two measures of the
tax sensitive ownership on stock i at time t (TSOit) as follows:
the percentage of individual investor ownership (INDit)
INDit = 1 – Percentage of shares owned by institutional investors at time t
the percentage of individual investor and mutual fund ownership (IND&MFit)
IND&MFit = INDit + Percentage of shares owned by mutual funds at time t.
We construct 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. Firm size is
constructed by multiplying the shares outstanding by per share stock price at monthly
frequency. In our regression analysis, we use a fourth-order polynomial of logarithmic
firm size to control the effect associated with firm size. Monthly individual stock
turnover is constructed by dividing the monthly trading volume by the shares outstanding
at the end of the month. The average monthly percentage bid-ask spread for individual
stocks is constructed using the transaction level Trade And Quote (TAQ) data base.8 For
the measure on firms’ growth potentials, we use the forecasted operating income growth
rate on individual firms obtained from the IBES database as a proxy (GrowthOption).
Table 1 presents the summary statistics for variables used in our regression
analysis and variable definitions are at the bottom of the table. Panel A reports statistics
for the aggregate variables (market index, industry portfolios, and economy-wide
controls) and panel B reports statistics for individual firm variables. The aggregate
variables consist of 120 monthly observations (time series only) 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 0.224 percent. The monthly volatility of the
market excess return has a mean of 4.28 percent with a standard deviation of 2.31
percent. The industry portfolios have average daily return ranging from 0.032 percent for
the manufacturing to 0.053 percent for the healthcare. The manufacturing industry has the
lowest standard deviation of 0.188 percent and the high tech industry has the highest
standard deviation of 0.396 percent. Consistent with the daily statistics and our intuition,
7
8
We thank Rabih Mousssawei for providing us the institutional stock ownership data.
We thank Kam-Ming Wan for providing us the monthly bid-ask spread data on individual stocks.
19
the monthly return volatility is the lowest for the manufacturing industry with an average
of 3.48 percent and a standard deviation of 1.71 percent, and is the highest for the high
tech industry with an average of 6.88 percent and a standard deviation of 3.8 percent.
The CAY variable has an average of 0.033 percent and a standard deviation of 2.08
percent. The stochastically detrended risk free rate has a monthly average of -0.008
percent and a standard deviation of 0.07 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.
For individual firms, the average daily return is 0.098 percent with a standard
deviation of 0.772 percent. Both the average return and the standard deviation are higher
than the corresponding statistics for the industry portfolios. The monthly return volatility
for individual stocks is 14.43 percent with a standard deviation of 11.56 percent. The
average monthly return volatility for individual stocks is twice the average monthly
return volatility of the most volatile high tech industry portfolio. 53.34 percent of the
firms paid dividends. The average dividend yield is 2.09 percent. The 18 month stock
price change has an average of 29.2 percent with a standard deviation of 114.5 percent.
Individual investors own 62.1 percent of the shares, on average. Including mutual fund
ownership, individual investors and mutual funds together own an average of 73.8
percent of stocks. The debt-asset ratio for individual firms has an average of 0.56 with a
standard deviation of 0.31. The average firm size is 12.46 on the logarithmic scale with a
standard deviation of 2.26. The average turnover for individual stocks is 8.45 percent
with a standard deviation of 14 percent. The average monthly percentage bid-ask spread
is 2.62 percent with a standard deviation of 3.47 percent. For the subset of firms with the
forecasted operating income growth rate, the average forecasted operating income growth
rate for individual firms is 14.98 percent with a standard deviation of 7.46 percent.
For firm level analysis, we face a common problem associated with a panel data
base: correlated residuals among observations. To take this issue into account, we use
generalized least squares to estimate our regression model. Specifically, we use clustered
20
standard error estimates which are shown to be unbiased in regression analysis using
panel data by Peterson (2005).9
B. Tax effect on return volatility of market index and industry portfolios
We begin our discussion on the effect of a capital gains tax cut on stock return
volatility by first examining the market excess return and the return on five industry
portfolios including the consumer industry, the manufacturing industry, the high tech
industry, the healthcare industry, and other industries. Table 2 reports the regression
results of equation (3) on the volatility of the market excess return (column 3) and
equation (4) on the return volatility of five industry portfolios (column 4 to column 8).
Consistent with the prediction of our analysis, the volatility of the market excess return is
higher after the capital gains tax rate is reduced. Specifically, everything else the same,
the monthly volatility of the market excess return is 3.5 percent higher after the capital
gains tax cut than before the capital gains tax cut. This finding is statistically significant
at the 1 percent level. For our control variables, the lagged consumption-wealth ratio
(CAY) has a significant positive effect on the market volatility. The lagged market excess
return has a negative and significant effect on the return volatility. This is consistent with
the leverage effect which states that return volatility is related to the level of returns. This
negative relation also suggests that return volatility is higher when stock market performs
poorly (asymmetric return volatility).
For the five industry portfolios, the estimated coefficient for the dummy variable
is consistently positive indicating that the return volatility is higher after the capital gains
tax cut. Specifically, the monthly return volatility is higher by 2.79 percent for the
consumer industry, 2.57 percent for the manufacturing industry, 5.03 percent for the high
tech industry, 2.25 percent for the healthcare industry, and 3.55 percent for all other
industries after the capital gains tax cut than before the capital gains tax cut. The
volatility increase is highly statistically significant for four (consumer, manufacturing,
high tech, and other industries) out of five industries with a p-value less than 1 percent.
For the healthcare industry, the volatility increase is significant at conventional 5 percent
test level (p-value of 3.3 percent for a two-sided test). The lagged consumption-wealth
9
We use SAS PROC MIXED procedure to estimate our models treating firm as our subject so that each
firm is one cluster. The goodness of fit for this procedure is given by the -2 residual log likelihood.
21
ratio has a significant effect on the monthly return volatility for the consumer, high tech,
and the other industries at the conventional 5 percent test level. The coefficient estimates
for lagged industry returns ri ( t −1) and/or ri ( t −2 ) are significantly negative for the consumer,
healthcare, and other industries at conventional 5 percent test level, and for the
manufacturing industry at 10 percent test level. The results suggest that a negative stock
price change for an industry will likely be followed by a high return volatility in that
industry, providing empirical support for the asymmetric return volatility with respect to
lagged industry return. There is also some evidence of asymmetric volatility of industry
returns with respect to the market price change for the manufacturing, the healthcare, and
other industries as indicated by significant negative coefficient estimates for r( t −1) and/or
r( t − 2 ) .
The return volatility of industry portfolios also exhibit persistence as indicated by
the coefficient estimates for demeaned lagged return volatility. For all five industries the
coefficient estimates for ∆σ i ( t −1) are positive and significant at the conventional 5 percent
level. Month dummies are not significant at conventional levels indicating insignificant
calendar effect for the volatility of the market excess return and the volatility of industry
portfolio returns. The year dummies are mostly insignificant lending support to the
finding of no long-run evident trend for the volatility of the market index documented by
Schwert (1989).
Our results on the effect of the capital gains tax cut on the volatility of market
excess return and the volatility of industry portfolio returns provide empirical support for
the prediction that stock return volatility increases after the capital gains tax rate is
reduced. Our findings are consistent with the explanation that a capital gains tax cut
reduces the risk-sharing function of financial markets and increases stock return
volatility.
C. Tax effect on the return volatility of individual firms
We first examine the across board effect on individual stock return volatility of
the capital gains tax cut under the TRA 97. This is achieved by fitting equation (4) using
firm level data. The results are reported in the last column of Table 2. Consistent with the
findings on the market index and industry portfolios, the capital gains tax cut under the
TRA 97 increases the return volatility of individual stocks. The estimated coefficient
22
suggests that the individual stock return volatility is higher by 0.47 percent on average
post the capital gains tax cut than prior to the capital gains tax cut. The effect is highly
statistically significant. The leverage effect is stronger at firm level than at industry
portfolio level. This is evidenced by highly statistically significant negative coefficient
estimates for both ri ( t −1) and ri ( t −2 ) . Stock return volatility is also more persistent than both
the market index and industry portfolios as indicated by highly statistically significant
positive coefficient estimates for both ∆σ i ( t −1) and ∆σ i ( t − 2 ) . Further, most of the
macroeconomic variables have statistically significant effect on the return volatility at
firm level. These include the consumption-wealth ratio, the stochastically detrended risk
free rate, the growth rate of industrial production, and lagged market returns.
However, different firms have different tax liabilities (both current and possible
future liabilities) and offer different risk-sharing opportunities. When the capital gains tax
rate changes, investors respond differently depending upon firms’ characteristics. This
leads to different tax effects on the return volatility of individual stocks. As our analysis
above shows, while all stocks will experience increases in their return volatility due to the
reduced risk-sharing associated with the capital gains tax cut, the increase in volatility
will be smaller if the firm pays dividends and higher if the firm has large embedded
capital gains or losses. To jointly test the across board effect and the cross-sectional
effect of a capital gains tax change on individual stock return volatility, we perform
regression analysis using equations (5) and (6). Since the extended specification offers a
richer setup, our discussions on the joint test of the across board effect and the crosssectional effect of the capital gains tax cut will be focused on the results of equation (6).
Table 3 reports the results of the regression analysis on joint test of the across
board effect and the cross-sectional effect of the capital gains tax cut under the TRA 97
for the baseline 18 month embedded capital gains or losses using the basic joint
specification (equation 5). The tax-sensitive investor ownership is measured either by the
percentage of shares owned by individual investors (the group directly affected by the
TRA 97) or the percentage of shares owned by individual investors and mutual funds.
Consistent with the predictions of our analysis, the coefficient for the dummy variable
Post is positive and statistically significant at 1 percent level when the tax sensitive
ownership is measured by either the percentage of shares owned by individual investors
23
(IND) or the percentage of shares owned by individual investors and mutual funds
combined (IND&MF). The coefficient estimate suggests that everything else the same the
monthly return volatility of individual stocks is 1.05 percent higher, on average, after
enactment of TRA97 for the IND group and 1.71 percent higher for the IND&MF group.
The estimated coefficient for the interaction Post × Yield × TSO is negative
indicating stocks with higher dividend yield and large tax-sensitive ownership experience
lower return volatility increase. This is consistent with our prediction discussed above.
But the coefficient estimate is only marginally significant at 10 percent level when the
TSO is measured by individual investor ownership (IND) and is insignificant for
IND&MF. Consistent with the prediction of our analysis, stocks with large embedded
losses and gains experience and high tax-sensitive ownership experience higher return
volatility increase. Specifically, the estimated coefficient for Post × Losses × TSO is
negative indicating stocks with larger losses experiencing higher return volatility increase
after the capital gains tax cut under the TRA 97. In the meantime, the estimated
coefficient for Post × Gains × TSO is positive suggesting stocks with larger embedded
gains experiencing higher return volatility increase after the capital gains tax cut. The
findings are highly statistically significant for both measures of tax-sensitive ownership.
Further, the coefficient estimate for the interaction Post × TSO is negative and highly
statistically significant. This indicates that firms with high tax sensitive investor
ownership experience a smaller return volatility increases after the tax rate cut and is
consistent with the risk sharing role of the capital gains tax.
Table 4 reports the results of the regression analysis on individual stock return
volatility for the baseline case using the extended joint specification (equation 6).
Consistent with the findings reported for the basic joint specification (equation 5), the
coefficient for the dummy variable Post is positive and statistically significant at 1
percent level when the tax sensitive ownership is measured by either the percentage of
shares owned by individual investors (IND) or the percentage of shares owned by
individual investors and mutual funds combined (IND&MF). The coefficient estimates
also are very similar to estimated coefficients reported in Table 3.
The interaction Post × Yield × TSO × DL is negative indicating that higher
dividend-paying stocks with large tax sensitive investor ownership will experience
24
smaller increases in return volatility than lower dividend-paying stocks after the capital
gains tax cut. The estimated coefficient is − 5.28 and significant at conventional 5
percent level with a p-value of 0.036 when the TSO is measured by the IND. When the
TSO is measured by the percentage of shares owned by individual investors and mutual
funds combined (IND&MF), the estimate is − 3.92 and statistically significant at 10
percent level with a p-value of 0.07. The coefficient estimate for the interaction
Post × Yield × TSO × DG is also negative but not statistically significant for either
measure of tax sensitive investor ownership. The result suggests that the effect of lower
volatility increase for dividend-paying stocks is concentrated primarily on dividendpaying stocks experienced price decline in the past 18 months.
The interaction term Post × Losses × TSO has a negative coefficient indicating
that stocks with larger embedded capital losses (Losses<0) and high tax sensitive
ownership experience higher volatility increase after the capital gains tax cut. The
coefficient estimate is highly statistically significant for both measures of tax sensitive
investor ownership (IND and IND&MF) with a p-value less than 1 percent. The estimated
coefficient implies that for stocks with average percentage of individual investor
ownership (IND), for every 50 percent higher losses, the monthly return volatility
increase is higher by 1.14 percent ( −3.68 × ( −50%) × 62.06%) after the capital gains tax
cut than before the capital gains tax cut. When the tax sensitive ownership is measured by
the IND&MF, the estimated coefficient suggests that for a 50 percent higher loss, the
monthly return volatility increase of individual stocks is higher by 1.84 percent
( −5.0 × (−50%) × 73.77%) after the capital gains tax cut. In both cases, our estimates
suggest that the return volatility of stocks with large embedded capital losses and high tax
sensitive ownership experiences large increase after the capital gains tax cut because of
reduced risk sharing with the government on stocks with loss positions.
For stocks with embedded capital gains, we further decompose them into nondividend paying versus dividend paying stocks. The coefficients for both interaction
terms Post × Gains × TSO × NDiv and Post × Gains × TSO × Div are positive implying
stocks with large embedded capital gains will see higher return volatility increase after
the capital gains tax cut. The interaction Post × Gains × TSO × NDiv is highly significant
with a p-value less than 1 percent when the tax sensitive investor ownership is measured
25
by both the IND and the IND&MF. The estimated coefficient suggests that for nondividend paying stocks with average percentage of individual investor ownership, for
every 50 percent higher embedded gains, the average monthly return volatility will be
higher by 0.44 percent (1.43 × 50% × 62.06%) after the capital gains tax cut than before
the capital gains tax cut. When the tax sensitive investor ownership is measured by
IND&MF, the estimated coefficient suggests that for a 50 percent higher embedded gain
the
average
monthly
return
volatility
is
higher
by
0.69
percent
(1.87 × 50% × 73.77%) after the capital gains tax cut. Similarly, the interaction
Post × Gains × TSO × Div is also highly significant with a p-value less than 1 percent
when the tax sensitive investor ownership is measured by both the IND and the
IND&MF. The increases in return volatility for dividend-paying firms are however
slightly smaller than for the non-dividend paying firms.
The coefficient for NDiv is positive and highly statistically significant for both
regressions, indicating that non-dividend paying stocks have higher return volatility
throughout the sample period. Stocks with large embedded gains and losses also
experience higher volatility as indicated by a significant positive coefficient for the gains
variable (Gains) and a significant negative coefficient for the loss variable (Losses). The
coefficient estimate for the interaction Post × TSO is negative and highly statistically
significant as reported in Table 3. Stock turnover also has a strong positive effect on
return volatility. This suggests that higher turnover is associated with higher return
volatility. The coefficient for BidAskSpread is positive and highly statistically significant.
One possible explanation is that a wider bid-ask spread allows for larger price movement
and leads to higher return volatility. Finally, firm size has a highly significant and
nonlinear effect on the return volatility of individual stocks.
Some of the control variables also have significant effect on the monthly
individual stock return volatility. Specifically, the consumption-wealth ratio CAY has a
positive effect on stock return volatility. The growth rate of the industrial production has
a negative coefficient implying that stock return volatility is likely to be higher when the
overall economy performs poorly. We also see the asymmetry in stock return volatility as
shown by the negative coefficients for both ri ( t −1) and ri ( t −2 ) . Individual stock return
26
volatility exhibits some persistence indicated by a positive and significant coefficient
for ∆σ i ( t −1) .
Overall, our cross-sectional regression analysis provides supporting evidence for
our prediction on the effect of a capital gains tax cut on the return volatility of individual
stocks with different characteristics. The findings indicate that in the case of a capital
gains tax cut the reduced risk sharing between investors and the government tends to
increase the return volatility of individual stocks in general. In particular, higher
dividend-paying stocks with declined stock price experience smaller return volatility
increases. Stocks with large embedded capital gains and losses experience higher return
volatility increases than other stocks because of larger reduction in risk sharing between
investors and the government in the case of a capital gains tax cut.
D. Robustness check
We now perform robustness check on our findings reported above using the
extended joint specification (equation 6). First, we use alternative measures of embedded
capital gains and losses calculated using different holding periods. Three alternative
measures of the embedded capital gains and losses are examined. The first is calculated
based on the stock price change in the past 12 months (one year), the second is based on
the stock price change in the past 24 months (two years), and the third is based on the
stock price change in the past 36 months (three years). Second, we introduce individual
firm’s growth option measured by the forecasted operating income growth rate for these
firms. Third, we exclude observations in year 2000 and 2001 and use the subsample from
January 1994 to December 1999 to perform our regression analysis. The analysis on the
subsample allows us to address whether the increased volatility is caused by the possibly
higher volatility caused by the aftermath of the internet bubble burst.
Table 5 reports the results of the regression analysis on equation (6) using the
alternative embedded capital gains and losses measures based on the past 12, 24, and 36
month stock price change, respectively. In all three cases, the tax sensitive ownership is
measured by the percentage of shares owned by individual investors (the group directly
affected by TRA97). The coefficient estimates are qualitatively similar to the baseline
case. Specifically, the coefficient for the dummy variable Post is positive and highly
statistically significant in all three cases with a p-value of 0.0001. The coefficient
27
estimate implies that everything else the same the monthly individual stock return
volatility is higher by 0.9 percent for the 12 month stock price change, by 1.0 percent for
the 24 month stock price change, and by 1.16 percent for the 36 month stock price
change, respectively. The coefficient estimate for the interaction Post × Yield × TSO × DL
remains negative for all three cases and is statistically significant at conventional 5
percent level for 24 and 36 month stock price changes. The interaction
Post × Yield × TSO × DG also has a negative coefficient and is significant at 10 percent
for 24 month stock price change and at 5 percent for 36 month stock price change. The
estimated coefficient for the interaction Post × Losses × TSO is negative at -1.75 and
statistically significant at 5 percent level for the 12 month stock price change, at -2.81
with a p-value of 0.002 for the 24 month stock price change, and at -2.6 with a p-value of
0.01 for the 36 month stock price change. All three estimates are consistent with the
coefficient estimate for the baseline 18 month stock price change. The results offer
additional empirical support for the prediction that stocks with large embedded capital
losses experience larger increase in return volatility after the capital gains tax cut. For
interaction terms Post × Gains × TSO × NDiv and Post × Gains × TSO × Div , our results
using the alternative measures of stock price change are also consistent with the findings
in the baseline case. In all three cases, the coefficient estimates for both
Post × Gains × TSO × NDiv and Post × Gains × TSO × Div remain positive as in the
baseline case. Further, the interaction Post × Gains × TSO × Div is statistically significant
at 5 percent for all three holding periods. The interaction Post × Gains × TSO × NDiv is
highly significant at 12 month holding period and also significant 10 percent level for 24
and 36 month holding period. The coefficient estimates for NDiv, Gains, Losses, and the
interaction Post × TSO all have the same sign and similar magnitude as their counterpart
in the baseline case and remain highly statistically significant. Finally, the aggregate
control variables also have similar effect on the stock return volatility as in the baseline
case.
Xu and Malkiel (2003) and Cao, Simins, and Zhao (2006) document that firm’s
growth potentials have a significant impact on a firm’s idiosyncratic volatility. In Table
6, we include the forecasted operating income growth rate as a control variable to
proximate for a firm’s growth potential. Because only a subset of firms have forecasted
28
operating income growth rate, the number of observations used in our regression analysis
is much smaller than that in the baseline case. However, the estimated coefficient for the
dummy variable Post remains highly statistically significant with a p-value less than 1
percent. The coefficient estimates for Post × Yield × TSO × DL remain negative but
insignificant at conventional test level. The interaction Post × Losses × TSO has a
negative coefficient as in the baseline case. The estimated coefficients are -4.91 and -5.61
for the two measures of tax sensitive ownership IND and IND&MF, respectively, and are
slightly larger in magnitude than in the baseline case. The estimated coefficients for the
interactions Post × Gains × TSO × NDiv and Post × Gains × TSO × Div are very close to
their counterparts in the baseline case. The estimates are also statistically significant at 1
percent level. Further, the coefficient estimates for NDiv, Gains, Losses, and the
interaction Post × TSO all have the same sign and similar magnitude as their counterpart
in the baseline case. Consistent with the finding in Xu and Malkiel (2003), the forecasted
operating income growth rate (GrowthOption) has a positive effect on the monthly
individual stock return volatility. The effect is highly statistically significant with a pvalue of 0.0001. This indicates that firms with higher forecasted operating income growth
rate will also have more uncertainty and thus higher risk. The estimated coefficient for
GrowthOption is very similar at 0.091 and 0.092 for the two measures of tax sensitive
ownership IND and IND&MF, respectively.
In Table 7, we report the regression analysis results for the subsample from
January 1994 to December 1999. The sign and statistical significance of the coefficient
estimates for key tax-related variables using the subsample remain similar to the baseline
case. The estimated coefficient for the dummy variable Post is positive and highly
statistically significant as in the baseline case. The magnitude of the coefficient estimate
is higher than in the baseline case. For this subperiod, the monthly return volatility is
about 1.96 to 2.61 percent higher after the capital gains tax cut than before the capital
gains tax cut when the tax sensitive ownership is measured by the percentage of shares
owned by individual investors (IND) and the percentage of shares owned by individual
investors and mutual funds combined (IND&MF), respectively. The coefficient estimates
for both
Post × Yield × TSO × DG and Post × Yield × TSO × DL are negative and
consistent with our prediction. As in the baseline case, the coefficient estimate is only
29
significant for Post × Yield × TSO × DL . The p-value is less than 1 percent for both
measures of tax sensitive ownership (IND and IND&MF). The magnitude of the
coefficient estimates is much higher than in the baseline case. The coefficient estimate for
the interaction Post × Losses × TSO is negative as in the baseline case and is statistically
significant at 1 percent level. The estimate ranges from -2.79 to -3.48 for both measures
of the tax sensitive ownership and smaller in magnitude than the estimate for the baseline
case. Finally, the coefficient estimates for interactions Post × Gains × TSO × NDiv and
Post × Gains × TSO × Div are also similar to the baseline case. The effects are highly
statistically significant with p-values consistently lower than 0.0001 for both measures of
tax sensitive ownership. Once again, the coefficient estimates for NDiv, Gains, Losses,
and the interaction Post × TSO have the same sign and similar magnitude as their
counterpart in the baseline case and remain highly statistically significant.
Overall, our robustness analysis results suggest that our findings on the crosssectional effect on stock return volatility associated with a capital gains tax cut are robust
and broadly consistent with our predictions discussed in Section 2.
5. Conclusion
We analyze the effect 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. The effect of a capital gains tax change on stock return
volatility varies depending upon dividend distribution and the size of the embedded
capital gains and losses. Using the Tax Relief Act of 1997, we empirically test the
predictions on the stock return volatility of a capital gains tax cut. Our empirical analysis
provides strong support for the predictions of our analysis for both the return volatility of
the market index and industry portfolios and the cross-sectional implications for
individual stock return volatility. Higher dividend-paying stocks with declined stock
price experience a smaller increase in return volatility and stocks with large embedded
capital gains and losses show a larger increase in return volatility after a capital gains tax
rate reduction.
30
While a capital gains tax cut increases stock return volatility, investors are not
necessarily worse off. From investors’ 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 may also increase investors’ after-tax 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.
31
Appendix: A Model on Capital Gains Taxes and Stock Return Volatility
The economy is populated with a large number of tax sensitive representative
investors. Each investor derives utility from consuming a numeraire good. Besides
consumption, the investor also invests his savings in a one-period riskless bond and N
risky stocks. Holding one unit of the riskless bond pays off one unit of consumption in
next period. The payoff to holding one share of a risky stock consists of dividend and
capital gains. We assume that earned interests are taxed at the effective income tax
rate τ i , dividend is taxed at the effective rate of τ d , and the capital gains are taxed at the
effective tax rate of τ c . Considering the possible exemptions, tax credits, and complex
netting rules allowed by the tax code, we allow the effective tax rates to be different from
the statutory rate denoted as τ is , τ ds , and τ cs , respectively. However, we assume that the
effective tax rates are increasing functions of their respective statutory rates, i.e.,
∂τ d
∂τ ds
> 0,
and
∂τ c
∂τ cs
∂τ i
∂τ is
> 0,
> 0.
Let C t be the investor’s time t consumption expenditure, Bt be the investor’s time t
bond investment, X it be the investor’s time t holding of stock i, rt f be the risk free rate at
time t, Pit be the time t price of stock i, and d it be the dividend distribution of stock i. We
assume that the investor’s objective is to maximize the expected discounted life time
utility subject to the intertemporal budget constraint, i.e.,
∞
MaxE0 ∑ β t u (C t )
t =0
s.t.
N
N
i =1
i =1
C t + Bt + ∑ Pit X it = [1 + (1 − τ i )rt f ]Bt −1 + ∑ [ Pit + (1 − τ d )d it ] X i ( t −1) − ∑τ c Git
(A1)
where β is the investor’s subjective discount factor and the last term in the budget
constraint represents the investor’s capital gains taxes at time t. We assume that the
investor’s capital gains taxes are given by the following specification
N
∑τ
i =1
N
c Git = ∑ τ c [ Pit − Pi ( t −1) ]X i ( t −1) .
i =1
32
(A2)
While the tax liability is calculated using the previous period price as the basis,
the specification allows the investor to use efficient trading strategies to lower his tax
liability. This is reflected in the effective capital gains tax rate being lower than the
statutory rate.
The first-order condition of maximizing the investor’s objective function yields
the pricing equation for risky stock i as follows
⎧ u ' (Ct +1 )
Pit = Et ⎨β
(1 − τ c ) Pi (t +1) + τ c Pit + (1 − τ d )d i (t +1)
⎩ u ' (Ct )
[
]⎫⎬.
⎭
(A3)
We further assume that the investor’s preference is represented by the logarithmic utility
N
function, i.e., u (C t ) = ln C t . Let d t = ∑ d it be the aggregate dividends at time t. Using
i =1
the market clearing condition on the consumption goods, we have
⎧ d
⎫
Pit = Et ⎨β t (1 − τ c ) Pi (t +1) + τ c Pit + (1 − τ d )d i (t +1) ⎬.
⎩ d t +1
⎭
[
]
(A4)
Rearranging the above equation yields
⎧
(d t / d t +1 )
Pit = Et ⎨β
(1 − τ c ) Pi (t +1) + (1 − τ d )d i (t +1)
−
1
βτ
E
(
d
/
d
)
c
t
t
t
+
1
⎩
[
]⎫⎬.
⎭
(A5)
For analytical tractability, we assume that Et (d t / d t +1 ) = δ < 1 for all t. The solution to
the above equation is then given by
⎧⎪ ∞ ~ (1 − τ d ) d i ( t + j ) ⎫⎪
Pit = ⎨∑ β j
Et
⎬d t ,
(1 − τ c )
d t + j ⎪⎭
⎪⎩ j =1
(A6)
~ β (1 − τ c )
< 1.
where β =
(1 − βδτ c )
To derive testable empirical implications, we set the number of risky stocks to
two ( N = 2 ). Specifically, we let stock 1 be the low dividend paying stock and stock 2 be
the high dividend paying stock. Let ε t be a random variable distributed in [0,1] and
follow a markov process for which Et ε t + k = ρ k ε t , | ρ | < 1. We can specify the dividend
distribution of the two firms as follows
d 1t =
1
1
(1 − ε t )d t , d 2t = (1 + ε t )d t .
2
2
33
(A7)
For the above specification, it is straightforward to show that
⎛ d1( t + j )
Et ⎜
⎜ d
⎝ t+ j
⎛d
⎞ 1
⎟ = (1 − ρ j ε t ), E t ⎜ 2 ( t + j )
⎜ d
⎟ 2
⎝ t+ j
⎠
⎞ 1
⎟ = (1 + ρ j ε t ).
⎟ 2
⎠
(A8)
Using the above results, we arrive at the following expressions for the prices of
the two stocks
P1t =
~
~
~
~
β ρε t ⎞⎟
β ρε t ⎞⎟
(1 − τ d ) ⎛ β
(1 − τ d ) ⎛ β
⎜
⎜
d
P
,
+
=
−
~
~ dt .
~
~
t
2t
2(1 − τ c ) ⎜⎝ 1 − β 1 − β ρ ⎟⎠
2(1 − τ c ) ⎜⎝ 1 − β 1 − β ρ ⎟⎠
(A9)
The expressions in (A9) suggests that the high dividend paying stock two has a
higher price than the low dividend paying stock one, i.e., P2t is greater than P1t . Denote
the ex-dividend stock return as the percentage price appreciation from period t to period
t+1. We have
~
~
β ρε t ⎞ d t
1−τ d ⎛ β
⎜
− 1,
r1t =
~ ⎟
~−
2(1 + τ c ) ⎜⎝ 1 − β 1 − β ρ ⎟⎠ P1( t −1)
~
~
1−τ d ⎛ β
β
ρε t ⎞⎟ d t
⎜
r2t =
− 1.
~
~+
⎜
2(1 + τ c ) ⎝ 1 − β 1 − β ρ ⎟⎠ P2 (t −1)
(A10)
Denote the conditional variance of stock returns as Vart −1 (rit ). If we assume that
the split of dividends between two stocks is independent from the aggregate dividend, we
arrive at the following expression for the conditional variance of stock 1 and 2:
2
2
~
~
⎡⎛ β~
⎞
⎛ βρ ⎞
βρ
2
Vart −1 (r1t ) = ⎢⎜⎜
~−
~ ρε t −1 ⎟⎟ Vart −1 (d t ) + ⎜⎜
~ ⎟⎟ (Et −1 (d t ) ) Vart −1 (ε t )
⎢⎣⎝ 1 − β 1 − β ρ
⎠
⎝1 − βρ ⎠
2
~
⎤⎛ (1 − τ ) ⎞ 2 1
⎛ βρ ⎞
d
⎟⎟ 2 .
+ ⎜⎜
~ ⎟⎟ Vart −1 (ε t )Vart −1 (d t )⎥⎜⎜
2
(
1
)
τ
+
1
β
ρ
−
⎥
c ⎠ P1( t −1)
⎠
⎝
⎦⎝
(A11)
2
2
~
~
⎡⎛ β~
⎞
⎛ βρ ⎞
βρ
2
Vart −1 (r2t ) = ⎢⎜⎜
~+
~ ρε t −1 ⎟⎟ Vart −1 (d t ) + ⎜⎜
~ ⎟⎟ (Et −1 (d t ) ) Vart −1 (ε t )
⎢⎣⎝ 1 − β 1 − β ρ
⎠
⎝1 − βρ ⎠
2
~
⎤⎛ (1 − τ ) ⎞ 2 1
⎛ βρ ⎞
d
⎟⎟ 2 .
+ ⎜⎜
~ ⎟⎟ Vart −1 (ε t )Vart −1 (d t )⎥⎜⎜
2
(
1
)
τ
+
1
β
ρ
−
⎥
c ⎠ P2 ( t −1)
⎠
⎝
⎦⎝
(A12)
34
~
Substituting in β and rearranging, we have
2
⎡⎛
⎞
β
βρ
ρε t −1 ⎟⎟ Vart −1 (d t )
Vart −1 (r1t ) = ⎢⎜⎜
−
⎢⎣⎝ 1 − β + β (1 − δ )τ c 1 − βρ + β ( ρ − δ )τ c
⎠
2
⎛
βρ
+ ⎜⎜
⎝ 1 − βρ + β ( ρ − δ )τ c
⎞
⎟⎟ (Et −1 (d t ) )2 Vart −1 (ε t )
⎠
⎛
βρ
+ ⎜⎜
⎝ 1 − βρ + β ( ρ − δ )τ c
2
⎤⎛ (1 − τ ) ⎞
⎞
d ⎟
⎟⎟ Vart −1 (ε t )Vart −1 (d t )⎥⎜
,
2
⎜
⎥⎦⎝ 2 P1( t −1) ⎟⎠
⎠
(A13)
2
2
⎡⎛
⎞
β
βρ
Vart −1 (r2t ) = ⎢⎜⎜
ρε t −1 ⎟⎟ Vart −1 (d t )
+
⎢⎣⎝ 1 − β + β (1 − δ )τ c 1 − βρ + β ( ρ − δ )τ c
⎠
2
⎛
βρ
+ ⎜⎜
⎝ 1 − βρ + β ( ρ − δ )τ c
⎞
⎟⎟ (Et −1 (d t ) )2 Vart −1 (ε t )
⎠
⎛
βρ
+ ⎜⎜
⎝ 1 − βρ + β ( ρ − δ )τ c
⎤⎛ (1 − τ ) ⎞
⎞
d ⎟
⎟⎟ Vart −1 (ε t )Vart −1 (d t )⎥⎜
.
2
⎜
P
2
⎥⎦⎝ 2 (t −1) ⎟⎠
⎠
(A14)
2
2
Since | ρ | < 1 and ε t −1 ∈ [0,1], the conditional variance of both stock returns
increase (decrease) as the capital gains tax rate decreases (increases) under the
condition ρ > δ . Because a firm’s dividend process is often very persistent, this condition
will be satisfied in most situations. Since the market portfolio is a value weighted
average of individual stocks, our result also suggests that the volatility of the returns to
the market portfolio will increase (decrease) when the capital gains tax rate is reduced
(increased) under the same condition.
In addition, equations (A13) and (A14) also have cross-sectional implications.
Because the low dividend paying stock has a lower price, it will more likely have a larger
return volatility response to the change in the capital gains tax rate than the high dividend
paying stock. In the case of a capital gains tax rate cut, the return volatility of a low
dividend paying stock will increase more than that of a high dividend paying stock.
35
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37
Table 1 Summary Statistics
Variable
Mean
Median
Std
Min
Max
Panel A: market or industry level variables
rt
0.01887
0.05250
0.22370
-0.81762
0.40600
σt
4.28393
3.72106
2.31162
1.14089
13.47769
r1t
0.03760
0.05174
0.19744
-0.66238
0.52261
r2t
0.03235
0.04138
0.18795
-0.70867
0.58095
r3t
0.04220
0.07952
0.39592
-1.30000
0.83739
r4t
0.05329
0.08731
0.22793
-0.61524
0.56191
r5t
0.04477
0.07728
0.22639
-0.99524
0.61304
σ 1t
4.20179
3.95541
2.01454
1.36115
11.09683
σ 2t
3.47898
3.15529
1.71258
1.23093
11.20402
σ 3t
6.87807
5.86460
3.80486
2.01788
18.76379
σ 4t
5.24268
4.73629
2.32152
1.67003
14.57388
σ 5t
4.43622
3.93285
2.34291
1.22332
12.91087
CAY
0.00033
0.00116
0.02076
-0.04622
0.03312
RREL
-0.00757
-0.00887
0.07144
-0.20375
0.14783
GIP
0.00282
0.00314
0.00528
-0.00836
0.02163
Panel B: individual firm level variables
rit
0.09758
0.06115
0.77203
-13.10861
107.4074
σ it
14.42749
11.43772
11.55747
0.00000
1086.9300
Yield
0.02093
0.00448
0.16090
0.00000
13.0933
Div
0.53344
1.00000
0.49889
0.00000
1.0000
∆P / P
0.29199
0.10869
1.14513
-1.00000
77.4444
IND
0.62061
0.63436
0.25524
0.00000
0.9999
IND&MF
0.73767
0.74578
0.18108
0.00298
1.0000
D/A
0.55777
0.56565
0.31358
0.00000
22.7883
Size
12.45984
12.32870
2.25671
5.73402
20.2165
Turnover
0.08453
0.04849
0.14024
0.00000
18.8480
BidAskSpread
0.02619
0.01332
0.03468
0.00019
0.4000
GrowthOption
14.97832
13.50000
7.45920
-4.10000
162.0000
rt is the average daily excess return of value-weighted CRSP stock index at month t; σ t is the monthly
volatility of the excess return of the value-weighted CRSP stock index at month t; rkt , k = 1,...,5, is the
average daily return for month t for the five industry portfolios (defined by Fama and French);
σ kt , k = 1,...,5, is the monthly volatility of the five industry portfolios at month t; CAY is the demeaned
consumption-wealth ratio; RREL is the stochastically detrended risk free rate; GIP is the growth rate of
industrial production; rit is the average daily return of individual stocks at month t; σ it is the monthly
return volatility of individual stocks at month t; Div is a dummy variable which takes value of 1 if a firm
38
distributed dividend in prior year and 0 otherwise; Yield is dividend distributed in prior year divided by
share price in most recent month prior to t; ∆P / P is 18-month stock price change up to the most recent
month prior to t; IND is the percentage of shares of stocks owned by individual investors; IND&MF is the
percentage of shares of stocks owned by individual investors and mutual funds combined; D/A is firms’
debt-Asset ratio in the most recent quarter; Size is the logarithmic market value of a firm; Turnover is
monthly trading volume divided by outstanding shares in prior month; BidAskSpread is the average
monthly percentage bid-ask spread for individual stocks from prior month, and GrowthOption is the analyst
forecast for firm’s long-term operating income growth rate.
39
Table 2 Market and Industry Regression Analysis
This table reports the regression results on the effect of TRA97 on the monthly volatility of the excess return of the
value-weighted CRSP stock index (equation 3), the return volatility of five industry portfolios (equation 4) including
consumer (Ind. 1), manufacturing (Ind. 2), high tech (Ind. 3), healthcare (Ind. 4), and others (Ind. 5) constructed using 4
digit SIC code, and on the across board effect of TRA97 on monthly volatility of individual stock returns fitted to
equation (4). The numbers in parentheses are p-values. See table 1 for variable definitions. Post is a dummy variable
which takes value of 1 if the observation is after 6/1/1997 and 0 if it is before 3/31/1997. The last column is for
individual firms.
Variable
Post
∆σ t −1
∆σ t −2
Pred.
sign
+
Market
Ind. 1
Ind. 2
Ind. 3
Ind. 4
Ind. 5
Individual
3.4960
consumer
2.7891
manufact.
2.5729
high tech.
5.0293
healthcare
2.2539
others
3.5468
Firms
0.4711
(0.0013)
(0.0017)
(0.0013)
(0.0006)
(0.0332)
(0.0005)
(0.0001)
0.0055
-0.2435
-0.2143
-0.1938
-0.3480
-0.2969
-0.0233
(0.9571)
(0.0765)
(0.0299)
(0.3344)
(0.0113)
(0.0346)
(0.5188)
0.0255
0.0231
-0.0271
-0.2665
-0.1925
0.1278
0.8815
(0.7944)
(0.8569)
(0.7801)
(0.1760)
(0.1200)
(0.3619)
(0.1176)
CAYt-1
107.2477
64.8377
44.4866
142.5800
59.8984
76.5369
-0.0248
(0.0084)
(0.0442)
(0.0921)
(0.0079)
(0.1242)
(0.0346)
(0.1800)
CAYt-2
-45.6376
-35.669
-16.246
-71.9759
-38.930
-31.457
22.8706
(0.2019)
(0.2162)
(0.4937)
(0.1368)
(0.2636)
(0.3336)
(0.0001)
0.2505
2.6119
-1.3462
0.5029
1.1606
2.0668
12.5745
(0.9517)
(0.4430)
(0.6275)
(0.9290)
(0.7767)
(0.5756)
(0.0110)
RRELt-1
RRELt-2
GIPt-1
GIPt-2
rt −1
rt − 2
-3.6763
-2.8537
-0.2961
-1.0188
-2.1673
-0.7973
38.4265
(0.3470)
(0.3663)
(0.9093)
(0.8471)
(0.5820)
(0.8192)
(0.0001)
32.0340
38.1473
40.2599
95.6081
34.1501
52.6497
-29.484
(0.4245)
(0.2359)
(0.1364)
(0.0793)
(0.3915)
(0.1465)
(0.0001)
47.8942
-0.0813
10.2284
27.5367
51.4181
-14.729
-1.2827
(0.2375)
(0.9980)
(0.7020)
(0.6169)
(0.2027)
(0.6869)
(0.0001)
-3.1920
-1.2131
-2.0385
1.0932
0.2705
-2.6736
3.3361
(0.0001)
(0.2738)
(0.0145)
(0.6518)
(0.7695)
(0.0303)
(0.0001)
-1.0390
1.4184
0.1814
-3.2446
-2.4434
2.1582
-1.1404
(0.2417)
(0.2836)
(0.8362)
(0.2028)
(0.0195)
(0.0907)
(0.0001)
ri ( t −1)
ri ( t −2 )
∆σ i ( t −1)
∆σ i ( t − 2 )
N
Adj. R
-1.8039
-0.1589
-2.1816
-3.4039
-0.8212
-0.7914
(0.1515)
(0.8633)
(0.1059)
(0.0005)
(0.4816)
(0.0115)
-2.8651
-1.6509
0.7500
0.0216
-3.8949
-0.4918
(0.0444)
(0.0802)
(0.5963)
(0.9828)
(0.0010)
(0.0001)
0.3463
0.4233
0.3548
0.3115
0.3415
0.2603
(0.0396)
(0.0054)
(0.0221)
(0.0209)
(0.0203)
(0.0001)
0.0657
0.0933
0.1759
0.3514
0.0076
0.0787
(0.6917)
(0.5549)
(0.2378)
(0.0037)
(0.9605)
(0.0001)
116
116
116
116
116
116
189,745
0.4943
0.5792
0.6081
0.6827
0.5215
0.6152
N/A
40
Table 3 Individual Stock Regression Analysis (Basic Joint Specification)
This table reports the regression results on the effect of TRA97 on the monthly return volatility of
individual stocks for the basic joint specification (equation 5). The embedded capital losses (Losses) and
gains (Gains) are calculated based on past 18-month stock price change up to the most recent month. Two
measures of tax-sensitive ownership (TSO) are used: individual ownership and individual and mutual fund
ownership. The equation is estimated using clustered standard error estimation method to account for
possible correlated residuals in our panel data. The goodness of fit measure is represented by -2 residual
loglikelihood. Sample period covers January of 1994 to December of 2001. See Table 1 for variable
definitions. Post is a dummy variable which takes value of 1 if the observation is after 6/1/1997 and 0 if it is before
3/31/1997.
Individual ownership
Variable
Prediction
Post
Individual and mutual fund
Ownership
Estimate
P-value
Estimate
P-value
+
1.0521
(0.0001)
1.7090
(0.0001)
Post*Yield*TSO
-
-2.5681
(0.1020)
-1.5621
(0.3633)
Post*Losses*TSO
-
-3.6132
(0.0001)
-4.9644
(0.0001)
Post*Gains*TSO
+
1.4078
(0.0001)
1.8287
(0.0001)
NDiv
2.3181
(0.0001)
2.9444
(0.0001)
Yield
-0.0097
(0.9889)
-0.0145
(0.9837)
Gains
1.1118
(0.0001)
1.1073
(0.0001)
Losses
-2.4892
(0.0001)
-2.4766
(0.0001)
Yield*Gains
1.0264
(0.1440)
1.0407
(0.1378)
Yield*Losses
0.2195
(0.8384)
0.1400
(0.8992)
NDiv*TSO
-0.6855
(0.1264)
-1.3964
(0.0080)
NDiv*Gains
-0.2426
(0.0224)
-0.2413
(0.0237)
NDiv*Losses
-0.2486
(0.5135)
-0.2563
(0.5044)
Post*Yield
1.5375
(0.2263)
1.2613
(0.4250)
Post*Gains
-0.6935
(0.0001)
-1.1890
(0.0001)
Post*Losses
2.2000
(0.0002)
3.6273
(0.0001)
Post*Yield*Gains
-1.0989
(0.1210)
-1.1008
(0.1177)
Post*Yield*Losses
-0.2508
(0.8855)
0.0380
(0.9831)
-1.3881
(0.0001)
-2.0542
(0.0001)
Size
-40.8669
(0.0042)
-41.9046
(0.0042)
Size2
3.5284
(0.0286)
3.5329
(0.0284)
3
-0.1337
(0.0916)
-0.1338
(0.0912)
4
Size
0.0018
(0.1929)
0.0019
(0.1927)
D/A
-0.0869
(0.1328)
-0.0884
(0.1230)
InsOwn
0.2912
(0.4182)
-0.0919
(0.8021)
Turnover
4.0051
(0.0001)
4.0167
(0.0001)
Post*TSO
Size
-
41
BidAskSpread
0.7916
(0.0001)
0.7913
(0.0001)
∆σ t −1
0.0244
(0.0733)
0.0222
(0.1032)
∆σ t −2
1.9500
(0.0001)
1.9633
(0.0001)
CAYt-1
0.0277
(0.0238)
0.0268
(0.0289)
CAYt-2
27.9701
(0.0001)
27.9249
(0.0001)
GIPt-1
-51.1420
(0.0001)
-51.1184
(0.0001)
GIPt-2
-1.4021
(0.0001)
-1.4072
(0.0001)
RRELt-1
9.2148
(0.0560)
8.8968
(0.0649)
RRELt-2
35.6400
(0.0001)
35.4457
(0.0001)
rt −1
2.5114
(0.0001)
2.4917
(0.0001)
rt − 2
-1.1846
(0.0001)
-1.1944
(0.0001)
∆σ i ( t −1)
0.1112
(0.0001)
0.1114
(0.0001)
∆σ i ( t − 2 )
0.0544
(0.0001)
0.0546
(0.0001)
ri ( t −1)
-0.6055
(0.0001)
-0.6067
(0.0001)
ri ( t −2 )
-0.1854
(0.0001)
-0.1869
(0.0001)
N
143,737
143,737
-2 res. Loglikelihood
929,387
929,384
42
Table 4 Individual Stock Regression Analysis (Extended Joint Specification)
This table reports the regression results on the effect of TRA97 on the monthly return volatility of
individual stocks for the extended joint specification (equation 6). The embedded capital losses (Losses)
and gains (Gains) are calculated based on past 18-month stock price change up to the most recent month.
Two measures of tax sensitive ownership (TSO) are used: individual ownership and individual and mutual
fund ownership. The equation is estimated using clustered standard error estimation method to account for
possible correlated residuals in our panel data. The goodness of fit measure is represented by -2 residual
log-likelihood. Sample period covers January of 1994 to December of 2001. See Table 1 for variable
definitions. Post is a dummy variable which takes value of 1 if the observation is after 6/1/1997 and 0 if it is before
3/31/1997.
Individual ownership
Variable
Prediction
Post
Individual and mutual fund
Ownership
Estimate
P-value
Estimate
P-value
+
1.0645
(0.0001)
1.7702
(0.0001)
Post*Yield*TSO*DL
-
-5.2781
(0.0364)
-3.9179
(0.0705)
Post*Yield*TSO*DG
-
-1.4229
(0.3023)
-0.9072
(0.5814)
Post*Losses*TSO
-
-3.6783
(0.0001)
-5.0009
(0.0001)
Post*Gains*TSO*NDiv
+
1.4253
(0.0001)
1.8704
(0.0001)
Post*Gains*TSO*Div
+
1.2883
(0.0001)
1.5991
(0.0003)
NDiv
2.3290
(0.0001)
3.0268
(0.0001)
Yield
-0.0142
(0.9842)
0.0218
(0.9760)
Gains
1.1410
(0.0001)
1.1988
(0.0001)
Losses
-2.5112
(0.0001)
-2.4993
(0.0001)
Yield*Gains
0.9846
(0.1948)
0.8732
(0.2428)
Yield*Losses
0.2299
(0.8333)
0.1900
(0.8656)
NDiv*TSO
-0.7236
(0.1054)
-1.5185
(0.0031)
NDiv*Gains
-0.2795
(0.0211)
-0.3584
(0.0034)
NDiv*Losses
-0.2311
(0.5436)
-0.2489
(0.5167)
Post*Yield
1.1746
(0.3401)
0.9984
(0.5256)
Post*Gains
-0.6916
(0.0001)
-1.1789
(0.0001)
Post*Losses
2.2502
(0.0002)
3.6694
(0.0001)
Post*Yield*Gains
-1.1500
(0.1416)
-1.0248
(0.1804)
Post*Yield*Losses
-3.5476
(0.2563)
-3.1466
(0.3225)
-1.3852
(0.0001)
-2.0943
(0.0001)
Size
-40.8311
(0.0043)
-41.0679
(0.0040)
2
Size
3.5241
(0.0289)
3.5509
(0.0275)
Size3
-0.1334
(0.0923)
-0.1346
(0.0890)
4
Size
0.0018
(0.1942)
0.0019
(0.1890)
D/A
-0.0861
(0.1373)
-0.0876
(0.1267)
Post*TSO
-
43
InsOwn
0.2635
(0.4611)
-0.0666
(0.8516)
Turnover
4.0057
(0.0001)
4.0178
(0.0001)
BidAskSpread
0.7915
(0.0001)
0.7912
(0.0001)
∆σ t −1
0.0242
(0.0759)
0.0220
(0.1073)
∆σ t −2
1.9532
(0.0001)
1.9622
(0.0001)
CAYt-1
0.0276
(0.0245)
0.0266
(0.0297)
CAYt-2
28.0549
(0.0001)
27.9505
(0.0001)
GIPt-1
-51.1028
(0.0001)
-51.0283
(0.0001)
GIPt-2
-1.4004
(0.0001)
-1.4056
(0.0001)
RRELt-1
9.1764
(0.0571)
8.8792
(0.0654)
RRELt-2
35.7271
(0.0001)
35.4723
(0.0001)
rt −1
2.5175
(0.0001)
2.4921
(0.0001)
rt − 2
-1.1844
(0.0001)
-1.1943
(0.0001)
∆σ i ( t −1)
0.1113
(0.0001)
0.1115
(0.0001)
∆σ i ( t − 2 )
0.0545
(0.0001)
0.0548
(0.0001)
ri ( t −1)
-0.6051
(0.0001)
-0.6070
(0.0001)
ri ( t −2 )
-0.1846
(0.0003)
-0.1867
(0.0001)
N
143,737
143,737
-2 res. Loglikelihood
929,376
929,375
44
Table 5 Individual Stock Regression Analysis for Different Holding Period
This table reports the robustness check results on the effect of the TRA97 on the return volatility of
individual stocks for the extended joint specification (equation 6) for three alternative measures of
embedded capital losses (Losses) and gains (Gains) using past 12-month, 24-month or 36-month price
change up to the most recent month. The tax sensitive ownership is measured by the percentage of shares
owned by individual investors. The equation is estimated using clustered standard error estimation method
to account for possible correlated residuals in our panel data. The goodness of fit measure is represented by
-2 residual log-likelihood. See Table 1 for variable definitions. Post is a dummy variable which takes value of 1
if the observation is after 6/1/1997 and 0 if it is before 3/31/1997.
12 months
Variable
Prediction
Post
24 months
36 months
Parameter
P-value
Parameter
P-value
Parameter
P-value
+
0.9042
(0.0001)
0.9910
(0.0001)
1.1564
(0.0001)
Post*Yield*TSO*DL
-
-0.0199
(0.9886)
-5.3384
(0.0214)
-4.3131
(0.0278)
Post*Yield*TSO*DG
-
-0.1081
(0.9391)
-2.3937
(0.0963)
-3.3953
(0.0403)
Post*Losses*TSO
-
-1.7521
(0.0375)
-2.8147
(0.0022)
-2.5968
(0.0112)
Post*Gains*TSO*NDiv
+
1.8164
(0.0001)
0.5610
(0.0585)
0.4579
(0.0727)
Post*Gains*TSO*Div
+
1.8869
(0.0006)
0.8453
(0.0100)
0.5813
(0.0227)
NDiv
2.4018
(0.0001)
2.2791
(0.0001)
2.2471
(0.0001)
Yield
0.3609
(0.4840)
-0.4099
(0.6687)
-0.3199
(0.6984)
Gains
1.5044
(0.0001)
0.7754
(0.0001)
0.5261
(0.0001)
Losses
-2.2623
(0.0001)
-2.1033
(0.0001)
-1.9566
(0.0001)
Yield*Gains
0.7791
(0.2686)
1.6930
(0.1747)
1.5174
(0.0684)
Yield*Losses
0.8935
(0.2724)
-0.6850
(0.6288)
-0.9002
(0.6085)
NDiv*TSO
-0.8642
(0.0480)
-0.8589
(0.0633)
-0.7159
(0.1520)
NDiv*Gains
-0.1069
(0.5034)
-0.1128
(0.3232)
0.0726
(0.4541)
NDiv*Losses
-0.4957
(0.1614)
-0.4696
(0.2384)
-0.0571
(0.8989)
Post*Yield
-0.3960
(0.6467)
1.7423
(0.2199)
1.9034
(0.1635)
Post*Gains
-1.0524
(0.0001)
-0.2064
(0.2159)
-0.4224
(0.0025)
Post*Losses
-0.2270
(0.6881)
1.9258
(0.0018)
1.9795
(0.0051)
Post*Yield*Gains
-0.6768
(0.3419)
-1.3725
(0.1806)
-1.2108
(0.1510)
Post*Yield*Losses
-1.5378
(0.1161)
-5.0228
(0.2494)
-2.8574
(0.3764)
-1.2552
(0.0001)
-1.2413
(0.0001)
-1.2574
(0.0001)
Size
-47.7991
(0.0008)
-46.6857
(0.0019)
-48.3974
(0.0027)
2
4.2064
(0.0088)
4.2406
(0.0127)
4.3499
(0.0173)
3
-0.1625
(0.0395)
-0.1712
(0.0410)
-0.1723
(0.0562)
4
Size
0.0023
(0.1029)
0.0026
(0.0888)
0.0025
(0.1236)
D/A
-0.1201
(0.0441)
-0.0742
(0.1724)
-0.1068
(0.0577)
Post*TSO
Size
Size
-
45
InsOwm
0.3715
(0.2911)
0.2453
(0.4953)
0.4564
(0.2365)
Turnover
3.5575
(0.0001)
4.5581
(0.0001)
2.7408
(0.0350)
BidAskSpread
0.8114
(0.0001)
0.7828
(0.0001)
0.7614
(0.0001)
∆σ t −1
0.0187
(0.1664)
0.0226
(0.1027)
0.0146
(0.3042)
∆σ t −2
2.3101
(0.0001)
1.6982
(0.0004)
1.6754
(0.0008)
CAYt-1
0.0101
(0.4020)
0.0257
(0.0400)
0.0257
(0.0455)
CAYt-2
33.0251
(0.0001)
28.0274
(0.0001)
30.3265
(0.0001)
GIPt-1
-51.7563
(0.0001)
-52.6353
(0.0001)
-52.1486
(0.0001)
GIPt-2
-1.3510
(0.0001)
-1.3674
(0.0001)
-1.3934
(0.0001)
RRELt-1
11.1065
(0.0224)
9.7554
(0.0456)
7.3642
(0.1472)
RRELt-2
39.5485
(0.0001)
36.6099
(0.0001)
36.0585
(0.0001)
rt −1
2.6626
(0.0001)
2.2507
(0.0001)
2.4773
(0.0001)
rt − 2
-1.2062
(0.0001)
-1.2564
(0.0001)
-1.2339
(0.0001)
∆σ i ( t −1)
0.1121
(0.0001)
0.1101
(0.0001)
0.1163
(0.0001)
∆σ i ( t − 2 )
0.0528
(0.0001)
0.0509
(0.0001)
0.0487
(0.0001)
ri ( t −1)
-0.6090
(0.0001)
-0.5672
(0.0001)
-0.5592
(0.0001)
ri ( t −2 )
-0.1477
(0.0001)
-0.1498
(0.0003)
-0.1529
(0.0006)
N
151,264
137,892
128,851
-2 res. Loglikelihood
982,752
890,534
833,271
46
Table 6 Individual Stock Regression Analysis with Growth Options
This table reports the regression results on the effect of TRA97 on the monthly return volatility of
individual stocks for the extended joint specification (equation 6). The embedded capital losses (Losses)
and gains (Gains) are calculated based on past 18-month stock price change up to the most recent month.
Two measures of tax sensitive ownership (TSO) are used: individual ownership and individual and mutual
fund ownership. The equation is estimated using clustered standard error estimation method to account for
possible correlated residuals in our panel data. The goodness of fit measure is represented by -2 residual
loglikelihood. Sample period covers January of 1994 to December of 2001. See Table 1 for variable
definitions. Post is a dummy variable which takes value of 1 if the observation is after 6/1/1997 and 0 if it is before
3/31/1997.
Individual ownership
Variable
Prediction
Post
Individual and mutual fund
Ownership
Estimate
P=value
Estimate
P-value
+
1.2889
(0.0001)
2.0851
(0.0001)
Post*Yield*TSO*DL
-
-3.8051
(0.1161)
-2.4568
(0.2973)
Post*Yield*TSO*DG
-
-1.0578
(0.5184)
0.0511
(0.9765)
Post*Losses*TSO
-
-4.9066
(0.0003)
-5.6101
(0.0010)
Post*Gains*TSO*NDiv
+
1.8393
(0.0003)
1.8074
(0.0044)
Post*Gains*TSO*Div
+
1.1371
(0.0049)
1.4326
(0.0115)
NDiv
3.1113
(0.0001)
3.9322
(0.0001)
Yield
0.4253
(0.5237)
0.4376
(0.5257)
Gains
1.2685
(0.0001)
1.2594
(0.0001)
Losses
-1.5197
(0.0003)
-1.4666
(0.0005)
Yield*Gains
0.4409
(0.2478)
0.4660
(0.2138)
Yield*Losses
-0.1041
(0.9063)
-0.2140
(0.8149)
NDiv*TSO
-0.9577
(0.0917)
-1.9419
(0.0038)
NDiv*Gains
-0.2496
(0.0982)
-0.2288
(0.1302)
NDiv*Losses
0.3772
(0.4185)
0.3934
(0.4000)
Post*Yield
0.5013
(0.6193)
-0.0257
(0.9837)
Post*Gains
-1.0599
(0.0001)
-1.4364
(0.0001)
Post*Losses
1.2646
(0.1049)
2.4716
(0.0367)
Post*Yield*Gains
-0.5457
(0.1666)
-0.5834
(0.1321)
Post*Yield*Losses
-2.8190
(0.5241)
-3.0210
(0.5353)
-0.9497
(0.0078)
-1.9291
(0.0001)
Size
-92.4953
(0.0002)
-94.1081
(0.0001)
2
Size
9.1139
(0.0004)
9.2700
(0.0003)
Size3
-0.3966
(0.0009)
-0.4032
(0.0007)
4
Size
0.0064
(0.0016)
0.0065
(0.0013)
D/A
-1.1168
(0.0028)
-1.1465
(0.0022)
Post*TSO
-
47
InsOwn
1.5947
(0.0001)
0.9452
(0.0072)
Turnover
3.2210
(0.0001)
3.2414
(0.0001)
BidAskSpread
1.1290
(0.0001)
1.1239
(0.0001)
GrowthOption
0.0913
(0.0001)
0.0919
(0.0001)
∆σ t −1
0.0267
(0.0376)
0.0249
(0.0529)
∆σ t −2
3.7408
(0.0001)
3.7362
(0.0001)
CAYt-1
0.0903
(0.0001)
0.0892
(0.0001)
CAYt-2
30.1205
(0.0001)
29.9193
(0.0001)
GIPt-1
-54.4216
(0.0001)
-54.5588
(0.0001)
GIPt-2
-1.3729
(0.0001)
-1.3779
(0.0001)
RRELt-1
24.5832
(0.0001)
23.9875
(0.0001)
RRELt-2
24.4710
(0.0001)
23.9851
(0.0001)
rt −1
2.9926
(0.0001)
2.9530
(0.0001)
rt − 2
-1.3331
(0.0001)
-1.3426
(0.0001)
∆σ i ( t −1)
0.0098
(0.1014)
0.0126
(0.0361)
∆σ i ( t − 2 )
-0.0072
(0.1276)
-0.0052
(0.2736)
ri ( t −1)
-0.7191
(0.0001)
-0.7193
(0.0001)
ri ( t −2 )
-0.2796
(0.0003)
-0.2792
(0.0001)
N
88,774
88,774
-2 res. Loglikelihood
516,385
516,393
48
Table 7 Individual Stock Regression Analysis for Subsample
This table reports the regression results on the effect of TRA97 on the monthly return volatility of
individual stocks for extended joint specification (equation 6). The embedded capital losses (Losses) and
gains (Gains) are calculated based on past 18-month stock price change up to the most recent month. Two
measures of tax sensitive ownership (TSO) are used: individual ownership and individual and mutual fund
ownership. The equation is estimated using clustered standard error estimation method to account for
possible correlated residuals in our panel data. The goodness of fit measure is represented by -2 residual
loglikelihood. Sample period covers January of 1994 to December of 1999. See Table 1 for variable
definitions. Post is a dummy variable which takes value of 1 if the observation is after 6/1/1997 and 0 if it is before
3/31/1997.
Individual ownership
Variable
Prediction
Post
Individual and mutual fund
Ownership
Estimate
P=value
Estimate
P-value
+
1.9631
(0.0001)
2.6073
(0.0001)
Post*Yield*TSO*DL
-
-25.9038
(0.0013)
-24.2447
(0.0029)
Post*Yield*TSO*DG
-
-5.7529
(0.1816)
-8.6334
(0.1353)
Post*Losses*TSO
-
-2.7869
(0.0246)
-3.4755
(0.0396)
Post*Gains*TSO*NDiv
+
1.7005
(0.0001)
2.3214
(0.0001)
Post*Gains*TSO*Div
+
1.9577
(0.0001)
2.4607
(0.0001)
NDiv
2.4703
(0.0001)
2.7615
(0.0001)
Yield
0.1028
(0.8986)
0.1252
(0.8767)
Gains
1.0774
(0.0001)
1.1023
(0.0001)
Losses
-2.5729
(0.0001)
-2.5603
(0.0001)
Yield*Gains
0.9213
(0.2666)
0.8600
(0.2886)
Yield*Losses
0.1888
(0.8671)
0.1688
(0.8818)
NDiv*TSO
-0.5339
(0.2749)
-0.8228
(0.1384)
NDiv*Gains
-0.2030
(0.0958)
-0.2372
(0.0569)
NDiv*Losses
-0.5434
(0.2459)
-0.5617
(0.2391)
Post*Yield
4.8940
(0.1507)
7.7186
(0.1196)
Post*Gains
-1.2656
(0.0001)
-1.9275
(0.0001)
Post*Losses
0.8357
(0.2976)
1.6499
(0.1854)
Post*Yield*Gains
-1.7135
(0.0739)
-1.5507
(0.0831)
Post*Yield*Losses
-20.5453
(0.0172)
-17.9354
(0.0864)
-1.3828
(0.0001)
-2.0305
(0.0001)
Size
-32.2049
(0.1008)
-33.0233
(0.0922)
2
Size
2.4932
(0.2631)
2.5899
(0.2448)
Size3
-0.0799
(0.4684)
-0.0847
(0.4419)
4
Size
0.0008
(0.6722)
0.0009
(0.6412)
D/A
-0.3244
(0.3566)
-0.3428
(0.3315)
Post*TSO
-
49
InsOwn
0.3631
(0.3257)
0.2480
(0.4807)
Turnover
2.8033
(0.0001)
2.8169
(0.0001)
BidAskSpread
0.8303
(0.0001)
0.8298
(0.0001)
∆σ t −1
0.0725
(0.0002)
0.0719
(0.0002)
∆σ t −2
-7.3089
(0.0001)
-7.2611
(0.0001)
CAYt-1
0.2068
(0.0001)
0.2062
(0.0001)
CAYt-2
24.6361
(0.0001)
24.5601
(0.0001)
GIPt-1
12.2117
(0.0440)
11.9108
(0.0493)
GIPt-2
-0.3984
(0.0021)
-0.4024
(0.0018)
RRELt-1
64.8671
(0.0001)
64.6122
(0.0001)
RRELt-2
16.2698
(0.0006)
16.1564
(0.0007)
rt −1
0.2169
(0.7393)
0.2087
(0.7490)
rt − 2
-1.0011
(0.0001)
-1.0083
(0.0001)
∆σ i ( t −1)
0.0954
(0.0001)
0.0955
(0.0001)
∆σ i ( t − 2 )
0.0354
(0.0001)
0.0355
(0.0001)
ri ( t −1)
-0.5295
(0.0001)
-0.5306
(0.0001)
ri ( t −2 )
-0.2414
(0.0001)
-0.2427
(0.0001)
N
101,682
101,682
-2 res. Loglikelihood
638,477
638,489
50