Capital Gains Taxes and Stock Return Volatility:

Evidence from Taxpayer Relief Act of 1997

Zhonglan Dai University of Texas at Dallas

Douglas A. Shackelford University of North Carolina and NBER

Harold H. Zhang University of Texas at Dallas

This version: January 15, 2008

We thank Kerry Back, Alex Butler, Michael Gallmeyer, Rick Green, Linda Krull, Harry Huizinga, Qin Lei, Jing Liu, Gregory Mankiw, Dave Mauer, Lillian Mills, Casey Schwab, Stephanie Sikes, Kam-Ming Wan, Steve Wei, Yexiao Xu, and seminar participants at Baruch College, Cheung Kong Graduate School of Business, the Southern Methodist University, Texas A&M University, the University of Texas at Dallas, the 2007 China International Conference in Finance, the 2007 NBER Summer Institute, the 2007 Oxford University Centre for Business Taxation Summer Symposium, and the 2007 Western Finance Association meetings for comments; and Scott Dyreng and Sudarshan Jayaraman for research assistance. Zhonglan Dai is at the School of Management, University of Texas at Dallas, Richardson, TX 75083, zdai@utdallas.edu, Douglas A. Shackelford is at the Kenan-Flagler Business School, University of North Carolina, Chapel Hill, NC 27599, doug_shack@unc,edu, and Harold H. Zhang is at the School of Management, University of Texas at Dallas, Richardson, TX 75083, harold.zhang@utdallas.edu. All errors are our own.

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Capital Gains Taxes and Stock Return Volatility:

Evidence from Taxpayer Relief Act of 1997

Abstract

This paper presents evidence consistent with capital gains tax changes inversely affecting

stock return volatility. We show that, since the government shares in the realized gains

and losses of assets held by taxable investors, a capital gains tax rate cut reduces risk

sharing between investors and the government. This reduction in risk sharing adversely

affects investors’ consumption smoothing, increasing consumption risk and leading to

higher asset return risk and volatility. Examining volatility before and after the 1997

reduction in the capital gains tax rate, we document a dramatic increase in the return

volatility of the market index and industry portfolios, even after controlling for all known

determinants of volatility. Furthermore, as predicted, non- or lower dividend-paying

stocks experience larger increases in return volatility than higher dividend-paying stocks

and stocks with large embedded capital losses have larger increases in return volatility

than stocks with small embedded capital losses. These empirical findings show that a

capital gains tax rate cut affects a firm’s return volatility differently depending on its

capital gains tax sensitivity.

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1. Introduction

This paper examines the effect of capital gains taxes on asset return volatility.

Previous studies of the effects of capital gains taxes on asset prices have focused on the

level of asset returns and on trading volume. This study extends that literature to consider

whether a 1997 reduction in the capital gains tax rate increased the volatility of stock

returns.

Our analysis relies on the role of financial markets in facilitating risk sharing

between investors and the government in the presence of capital gains taxes. Since the

government shares in the realized gains and losses of assets held by taxable investors, a

capital gains tax rate cut reduces risk sharing between investors and the government.

This reduction in risk sharing adversely affects investors’ consumption smoothing,

increasing consumption risk and leading to higher asset return risk and volatility.

Empirically it is difficult to design a test that directly links a reduction in the

capital gains tax rate to an increase in asset return volatility. Thus, we pursue an indirect

approach using equity returns from 1993 to 2002. First, we control for all of the factors

known to affect the volatility of stock returns. Second, we test whether the remaining

stock return volatility increased following a 1997 reduction in the capital gains tax rate.

Third, we test whether the volatility increased more for the stocks whose returns were

most affected by the tax cut.

We find that stock return volatility doubled after 1997. Known determinants of

stock return volatility only account for less than half of the increase. This leads us to

conjecture that the 1997 capital gains tax cut may have contributed to the increase in

volatility. Further tests show that the magnitudes of the increases in return volatility vary

in a predictable manner with characteristics of the stocks, such as dividend distribution

and embedded capital losses. These cross-firm results provide more compelling evidence

that the reduction in the capital gains tax rate boosted stock return volatility.

To our knowledge, this is the first study of the relation between asset return

volatility and the capital gains taxes. It builds on an increasing literature about how

capital gains taxes affect asset prices and trading volume. With regards to asset prices,

existing theoretical studies suggest that the effect of capital gains taxes on asset price is

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ambiguous because introducing capital gains taxes decreases both the demand and the

supply of assets. Consistent with this ambiguity, empirical investigations of the effect of

capital gains taxes have produced conflicting results. Several studies (Lang and

Shackelford (2000), Ayers, Lefanowicz, and Robinson (2003), among others) report that

the presence of capital gains taxes reduces stock price and current stock return, while

other studies document that imposing capital gains taxes increases stock price and current

stock return (Feldstein, Slemrod, and Yitzhaki (1980), Reese (1998), Klein (2001), Jin

(2005), among others).

With regards to capital gains taxes and trading volume, Dhaliwal and Li (2006)

report that tax-motivated trading activity creates excess trading volume around ex-

dividend days. Specifically, they find a concave relation between ex-dividend day

trading volume and institutional ownership, their measure of investor tax heterogeneity.

In other words, the more shareholders who face different tax rates (e.g., an even mix of

individuals and institutions), the more trading around ex-dividend dates, as differentially

taxed investors swap securities to minimize their tax liabilities.

In a recent study, Dai, Maydew, Shackelford, and Zhang (2008) investigate the

effect of capital gains taxes on asset price and trading volume by jointly considering the

impact on demand and supply of assets. Using the Taxpayer Relief Act of 1997 as the

event, they find that stock returns are higher in anticipation of a tax cut and stocks with

large embedded capital gains and high tax sensitive investor ownership experience a

lower return after the lower tax rate became effective. They also document that a capital

gains tax cut increases the trading volume the week before and immediately after the tax

cut announcement.

None of the existing studies, however, has examined the impact of capital gains

taxes on asset return volatility. Asset return volatility is one of the key determinants of

investors’ demand and supply of risky assets. Thus, if capital gains taxes affect asset

return volatility, then they affect investors’ demand and supply of risky assets and

ultimately asset returns.

In this paper, we first discuss the relation between the capital gains taxes and asset

return risk and volatility focusing on the risk sharing role of the capital gains taxes

between investors and the government. Based on our analysis, we develop hypotheses on

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the relation between capital gains taxes and asset return volatility. Then, we empirically

test the predictions using the Taxpayer Relief Act of 1997 as our event.

We hypothesize that after the reduction in the capital gains tax rate:

• Return volatility increased for the market index and industrial portfolios.

• Non- or lower dividend-paying stocks experienced a higher volatility increase

than higher dividend-paying stocks.

• Stocks with large embedded capital losses (gains) experienced a larger

increase in volatility than did stocks with small embedded capital losses

(gains).

The first prediction focuses on the effect of a capital gains tax rate cut on the

return volatility of portfolios and the market index. Thus, it represents the effect of a

capital gains tax rate cut on the volatility of the broad financial market. The next two

predictions focus on the effects of a capital gains tax rate cut on the return volatility of

stocks with different tax liabilities.

Our predictions reflect the roles played by the financial markets. From investors’

perspective, financial markets have two important functions: risk sharing and

consumption smoothing. Besides actively sharing risk with other market participants,

investors also share the risk of holding risky stocks with the government (passively)

through capital gains taxes. To demonstrate, if the investors’ asset holdings have

depreciated in value, then the investors’ after-tax losses are less than the decrease in the

market value of the asset because a fraction of the loss is borne by the government in the

form of reduced capital gains taxes or even tax rebate from the government. Therefore, a

cut in the capital gains tax rate reduces the risk sharing between investors and the

government.

This reduction in risk sharing causes investors to experience more volatile

consumption growth rates resulting in increased consumption risk. According to the

consumption capital asset pricing model (CCAPM), the risk of a portfolio of stocks is

determined by its equilibrium risk to consumption (Rubinstein (1976) and Breeden

(1979)). Thus, an increased consumption risk will lead to higher return risk and volatility

for a portfolio of stocks. While earlier empirical studies failed to provide supporting

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evidence using contemporaneous consumption growth, 1 more recent studies show a

strong positive relation between stock return risk and the ultimate consumption risk, as

measured by the consumption growth over the quarter of return and subsequent quarters

(Parker and Julliard (2005) and Tedongap (2007)).

The impact of a capital gains tax change on risk sharing, and thus its impact on

stock return volatility, should vary depending on the characteristics of particular stocks.

For example, suppose investors receive all returns as dividends, then capital gains taxes

are irrelevant and changes in the capital gains tax should have no impact on consumption

risk and return volatility. Conversely, if all future returns are expected to be taxed at the

new capital gains tax rate, then we would expect the rate change to substantially increase

consumption risk and return volatility. More generally, the capital gains tax change

should matter to the extent that investors anticipate the capital gains tax rate change

affecting future returns.

In our tests, we assume that firms will maintain their current dividend policy, and

thus, predict that, ceteris paribus, non- and lower dividend-paying stocks are subject to

greater risk than other firms, when capital gains tax rates are lower. Consequently, a

capital gains tax reduction will result in larger increases in return volatility for non- or

low-dividend stocks than for higher dividend-paying stocks.

Similarly, when investors sell, stocks with large embedded capital losses (gains)

trigger larger capital losses (gains) than stocks with little or no depreciation

(appreciation). Thus, a capital gains tax reduction causes stocks with larger, embedded

capital losses (gains) to become riskier because there is less risk sharing with the

government. Therefore, we predict that these stocks will experience higher volatility

increases when capital gains tax rates are cut. Furthermore, the effect is likely to be

stronger on portfolios of stocks with large embedded capital losses than stocks with

embedded capital gains because the losses are likely to have a larger impact on

consumption risk than gains. This can be attributed to a number of reasons. For example,

investors’ preferences may exhibit habit formation so that reduced consumption

associated with investment losses increases the investors’ risk aversion while increased

1 See Mankiw and Shapiro (1986), Breeden, Gibbons, and Litzenberger (1989), Campbell (1996), Cochrane (1996), Lettau and Ludvigson (2001), among others.

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consumption associated with investment gains reduces the investors’ risk aversion (see

Campbell and Cochrane (1999)).

We test these predictions by comparing stock return volatility before and after the

1997 reduction in the individual capital gains tax rate from 28 percent to 20 percent.

Using data from January 1993 to December 2002, we construct a market portfolio before

and after the legislation. After controlling for numerous factors which are widely

documented to be important determinants of stock return volatility and the state of the

economy, we find the volatility of monthly excess return of the value-weighted CRSP

stocks is more than 1.9 percentage points higher after the 1997 rate cut. This compares

with an average monthly volatility of 2.7 percent before 1997. Similarly, we find that the

monthly implied volatility for the Standard & Poors index options (VIX) increased by 2.1

percentage points after the capital gains tax cut, controlling for the non-tax determinants.

This compares with an average of 4.1 percent before 1997.

We repeat the analysis for five industry portfolios based on 4-digit SIC code:

consumer industry, manufacturing industry, high tech industry, healthcare industry, and

other industries. We find that the monthly return volatility is higher for all five portfolios

after the capital gains tax rate is reduced, once again controlling for variables often

identified to be important factors affecting return volatility. The increase in monthly

return volatility ranges from 1.6 percentage points for the manufacturing industry to 2.5

percentage points for the high tech industry.

Together, these results provide evidence that stock return volatility increased after

1997 for reasons other than those previously documented in the literature. We conjecture

that the 1997 cut in the capital gains tax rate partly explains the increases. However, it is

impossible to fully rule out other, non-tax factors (previously overlooked in the literature)

that arose around the time of the 1997 tax cut. This leads us to cross-sectional tests in an

attempt to address any problems potentially arising from omitted correlated variables.

The cross-sectional tests exploit differences across stocks in dividend yields and

embedded capital losses and gains. In our first set of tests, as predicted, we find that the

portfolio of non-dividend paying stocks experiences higher volatility increase than

dividend-paying stocks, consistent with the prediction of our analysis. Specifically, after

the rate cut, non-dividend paying stocks experience 1.2 percentage points higher monthly

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return volatility than dividend-paying stocks, on average, after controlling for

documented determinants of stock return volatility, the state of the economy, both

domestic and foreign stock market performances, the debt-asset ratio, turnover, the

percentage bid-ask spread, size, earnings volatility, and growth option, among others.

This is above and beyond the 1.8 percentage points higher monthly return volatility of

non-dividend paying stocks relative to that of dividend paying stocks before the capital

gains tax cut.

In our second set of tests, as predicted, we find that stocks with large embedded

capital losses (i.e., losses in the upper 25 percentile) experience 1.1 percentage points

higher monthly return volatility increase than stocks with small embedded capital losses

(i.e., losses in the lower 25 percentile). This is in addition to the 1.8 percentage points

higher monthly return volatility of the large loss stock portfolio relative to that of the

small loss stock portfolio, and after controlling for all other determinants of return

volatility. However, contrary to expectations, we find no evidence that volatility varied

with the amount of embedded capital gains.

Finally, we repeat our cross-sectional tests (dividend yield and embedded losses

and gains), assuming capital gains taxes had been cut one, two and three years earlier, i.e.,

in 1996, 1995, and 1995, respectively. Using these hypothetical dates, we find no

evidence of higher volatility for non-dividend-paying stocks or those with large

embedded losses or gains. This provides some comfort that the changes in volatility

occurred in 1997.

It is worth noting that the stock return volatility increase associated with a capital

gains tax cut does not necessarily imply that investors are worse off when the capital

gains tax rate is lower. This is because a capital gains tax cut may increase the after-tax

stock return. Consequently, investors may experience the same or an improved return-

and-risk trade-off and thus face the same or better investment opportunities. However,

the findings in this paper does suggest that, when capital gains taxes are cut, taxable

individual investors incur costs, which, to our knowledge, have heretofore gone

unnoticed.

The paper is organized as follows. In section 2, we discuss the relation between

the capital gains taxes and stock return volatility and develop hypotheses about the

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effects of a capital gains tax cut on return volatility both for the broad market and the

cross-section of portfolios of individual stocks with different capital gains liabilities.

Section 3 presents empirical methodology to test the predictions of our analysis. Section

4 discusses the results of the empirical analysis. Section 5 provides closing remarks.

2. Capital Gains Taxes and Stock Return Volatility

Financial markets and the financial assets traded in those markets serve two

important roles for investors: consumption smoothing and risk sharing. Some individuals

earn more than they currently wish to spend; others spend more than they currently earn.

Trading in financial assets allows these individuals to shift their purchasing power from

high-earnings periods to low-earnings periods by buying financial assets in high-earning

periods and selling these assets to fund their consumption needs in low-earning periods.

Financial markets and the financial assets also allow investors to allocate risks among

themselves so that risk in their portfolio is commensurate with the return to the portfolio,

i.e., investors with high risk tolerance hold riskier assets, such as stocks, and those with

low risk tolerance hold more less risky assets, such as money market instruments. In an

economy without government taxation, market participants achieve consumption

smoothing and risk sharing through the trading of financial assets on financial markets.

However, through taxation and, in our case, capital gains taxation, the

government influences the consumption smoothing and risk sharing of market

participants. In the United States, capital gains taxes are levied upon selling an asset

based on the appreciation or depreciation on the asset. Specifically, in the case of

common stocks, if a stock has appreciated in value, the investor pays capital gains taxes

on the appreciation upon selling. Conversely, if the stock has depreciated in value upon

selling, the investor can use the realized losses to offset realized gains on other assets. If

the realized losses exceed the realized gains, the losses can be used to reduce the taxable

ordinary income up to a limit with the remaining losses carried forward to offset future

gains and ordinary income. (Because there are almost always capital gains available to

offset capital losses, we assume throughout the paper that all realized capital losses can

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be fully and immediately utilized to offset other realized capital gains.2) Thus, the tax

treatment of gains and losses on stocks offers a risk sharing mechanism between

investors and the government that affects the consumption smoothing of stock market

participants.

The fundamental insight of the Consumption Capital Asset Pricing Model

(CCAPM) is that the risk of an asset is determined by its equilibrium risk to consumption.

A higher consumption risk of an asset is associated with a higher risk of its return. For

portfolios with a large number of stocks, the return risk is often measured by its volatility,

implying a positive relation between the consumption growth risk and the stock return

volatility. Until recently, most empirical tests on the CCAPM found the relation between

the consumption risk and the stock return to be weak, when the consumption risk was

measured by the contemporaneous consumption growth rate on the stock returns. Recent

studies have found strong evidence for a positive relation between consumption risk and

stock returns, when the consumption risk is measured over a longer horizon. For example,

Parker and Julliard (2005) document that the ultimate risk to consumption, defined as the

covariance of asset returns and consumption growth over a horizon of three years can

explain from 44 to 73 percent of the variation in expected returns across portfolios of

stocks. Because a reduction in the capital gains tax rate adversely affects the risk sharing

between investors and the government and the consumption smoothing of stock market

participants, it will increase the consumption risk over the long horizon and consequently

lead to higher stock return volatility.

To facilitate the development of our hypotheses about the relation between the

capital gains taxes and stock return volatility, we focus on some extreme cases and then

offer insights on general situations. We start with the effect of the capital gains taxes on

2 Individuals, the only investors affected by the reduction in the capital gains tax rate studied in this paper, face no limit on the amount of capital losses that they can use to offset capital gains. If capital losses remain after offsetting all capital gains, then individuals can apply up to $3,000 of capital losses against ordinary income. In practice, this constraint is rarely binding (Poterba [1987] and Auerbach, Burman and Siegel [2000]). The Internal Revenue Service [1999a, 1999b] reports that in the year of the capital gains rate reduction (1997), individuals in the maximum tax bracket (39.6 percent), who accounted for 61 percent of all net capital gains, reported $169 billion of long-term capital gains and only $5 billion of long-term capital losses and $16 billion of short-term capital gains and only $8 billion of short-term capital losses. In short, individual investors had far more capital gains than they had capital losses to offset them. Thus, for our purposes, it is reasonable to assume that realized capital losses can be used to offset realized capital gains.

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the broad financial market and then discuss the implications of a change in the capital

gains taxes on return volatility across stocks. In all cases, we view capital gains taxes as

the mechanism through which the government “partner” shares the return of stock

investments with its taxable investor “partner.”

To begin, suppose the capital gains tax rate approaches 100 percent. The

government “partner” gets almost all the returns of investments made by taxable

investors. Consequently, the government bears almost all the risk, while the taxable

investors bear almost none. Conversely, suppose that the capital gains tax rate is zero.

Now, the taxable investor “partner” receives all the returns and bears all the risk. The

government collects no revenue and bears no risk.3

In reality, the capital gains tax rate is typically positive but well below 100

percent. When the capital gains tax rate increases, the government “partner” receives a

larger fraction of the return and bears more risk. The taxable investor “partner” receives a

lower fraction of the return and bears less risk. However, when the capital gains tax rate

is reduced, the government “partner” gets a smaller fraction of the return and bears less

risk, while the taxable investor “partner” receives a larger fraction of the return and bears

more risk. Because capital gains taxes apply to all stocks, a capital gains tax rate

reduction causes taxable investors to receive a larger fraction of returns on all stocks and

to bear more risk on all the stocks. This leads to more volatile consumption growth rates

for taxable investors. As a result, we have the following hypothesis on the relation

between the capital gains taxes and the return volatility for the broad stock market.

H1: A reduction in the capital gains tax rate will lead to higher return volatility

for the market index and industry portfolios.

Based on a firm’s characteristics, the impact of a capital gains tax rate change on

the risk sharing between taxable investors and the government may vary across stocks,

and, consequently, return volatility may vary across stocks. For instance, the impact of a

3 As a simple example, suppose an investor purchases a stock for $1 and intends to sell it three years later. There is 50 percent chance that the stock will be traded at $2 in three years and a 50 percent chance that the share will be worthless in three years. If the capital gains tax is zero, the investor will experience either a $1 after-tax gain or a $1 after-tax loss in three years. If the capital gains tax rate is 100 percent, the investor will have no after-tax gain or loss in three years, i.e., the investor will continue to have $1 of wealth. The reason is that in the case of a pre-tax gain of $1, the entire profit will be taxed. In the case of a pre-tax loss of $1, the loss will fully offset a $1 gain from another sale (which would otherwise have been fully taxed). As a result, the $1 loss reduces the investor’s total tax bill by $1.

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capital gains tax rate change on the risk sharing between taxable investors and the

government may vary across firms with different dividend yields.

For example, if taxable investors receive all returns from a firm as dividends, then

no income received is subject to capital gains taxes. Consequently, the government bears

no risk related to capital losses or gains and the capital gains taxes will have little direct

effect on stock return volatility. On the other hand, if the taxable investors receive no

dividends, then the entire return comes as capital gains. In that case, all income will be

subject to capital gains taxes and the government bears the maximum risk associated with

the capital gains. As a result, a capital gains tax change for these all-capital-gains firms

will have a large impact on the risk sharing between the taxable investors and the

government. This will affect the consumption risk of the taxable investors and the stock

return volatility. In general, the greater the percentage of profits taxed as capital gains,

the greater a cut in the capital gains tax rate reduces the amount that the government

shares in the risk and, thus, increases the return volatility of the stock. This leads to the

following hypothesis on the relation between stock return volatility and firms’ dividend

payouts.

H2: A reduction in the capital gains tax rate will increase the return volatility of

non- or lower dividend-paying stocks more than that of higher dividend-paying stocks.

Similarly, the impact of a capital gains tax rate change on the risk sharing

between taxable investors and the government and the consumption risk will likely vary

across firms with different embedded capital losses or gains. For example, if the sale

proceeds of a taxable investor in a stock are equal to his tax basis (i.e., the cost of

purchasing the stock), then the investor has no income subject to capital gains taxes upon

sale of the stock because he has neither gain nor loss. Furthermore, since there is no

income subject to capital gains taxes, the government bears no risk.

On the other hand, if the investor’s sale proceeds are equal to the gains (because

the cost of the stock was zero), then all proceeds are subject to the capital gains taxes.

Therefore, the government bears the maximum risk. Similarly, if the investor’s sale

proceeds are zero, then the loss is equal to the cost of purchasing the stock. In that case,

the full loss (which equals the tax basis) can be used to reduce the investor’s taxes, and,

again, the government bears the maximum risk.

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In short, when a stock has large embedded gains and losses, a capital gains tax

change will have a major impact on the risk sharing and consumption risk of the taxable

investors in those stocks. Thus, the effect of a capital gains tax change will have a greater

impact on the return volatility of these stocks than on other stocks. This leads to the

following hypothesis about the relation between stock return volatility and embedded

capital losses or gains in the case of a capital gains tax rate cut.

H3: A reduction in the capital gains tax rate will increase the stock return

volatility of firms with large embedded capital losses (gains) more than that of firms with

small embedded capital losses (gains).

In the next section, we discuss the empirical methodology used to test the three

hypotheses discussed above.

3. Empirical Methodology

We use the Taxpayer Relief Act of 1997 (TRA97) as our event to empirically test

the impact of a change in the capital gains tax rate on stock return volatility. TRA97

lowered the maximum tax rate on capital gains for individual investors from 28 percent to

20 percent for assets held more than 18 months. TRA97 is particularly attractive for an

event study because the capital gains tax cut was large and relatively unexpected, and the

bill included few other changes that might confound our analysis. Little information was

released about the Taxpayer Relief Act of 1997 (TRA97), until Wednesday, April 30,

1997, when the Congressional Budget Office (CBO) surprisingly announced that the

estimate of the 1997 deficit had been reduced by $45 billion. Two days later, on May 2,

the President and Congressional leaders announced an agreement to balance the budget

by 2002 and, among other things, reduce the capital gains tax rate. These announcements

greatly increased the probability of a capital gains tax cut. On Wednesday, May 7, 1997,

Senate Finance Chairman William Roth and House Ways and Means Chairman William

Archer jointly announced that the effective date on any reduction in the capital gains tax

rate would be May 7, 1997. As promised, the lower tax rate on long-term capital gains

(eventually set at 20 percent) became retroactively effective to May 7, 1997, when the

President signed the legislation on August 5, 1997.

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Using TRA97 as the event that changed capital gains tax rates, we examine the

time series of return volatilities for various stock portfolios including:

• the value-weighted market index,

• the implied volatility of Standard & Poors index options (VIX),

• five industry portfolios classified based on 4-digit SIC code (consumer,

manufacturing, high tech, health, and others),

• constructed portfolios based on firms’ dividend distributions, and

• constructed portfolios based on the past 18 months price changes.4

The primary focus of our empirical analysis is on the constructed portfolios based

on firms’ dividend distributions and past price changes, which exploit cross-sectional

differences in dividends and past price movements to test H2 and H3, respectively. As

discussed above, the reason for the focus on the cross-sectional tests is that unaccounted

for, non-tax factors potentially boosted the return volatility of the market and industry

stock portfolios, which are used to test H1. That said, we are unaware of any cross-

temporal changes that would have coincided with passage of TRA97. Nonetheless, we

expect tests of H2 and H3 to provide more compelling evidence about the impact of the

capital gains taxes on stock return volatility than tests of H1.

To test H2 (that a capital gains tax rate cut leads to a larger increase in the return

volatility of non- or lower dividend-paying stocks than that of higher dividend-paying

stocks), we use the firm’s dividend distribution in the prior year to construct a non-

dividend paying portfolio and a dividend-paying portfolio. For the dividend-paying

stocks, we further form a low dividend yield portfolio and a high dividend yield portfolio

using the median dividend yield as a threshold. To mitigate any confounding effects on

return volatility from reducing the capital gains tax rate on stocks with large price

changes, we restrict our attention to stocks with share price changes (either positive or

negative) of less than 5 percent over the last 18 months.

To test H3 (that a capital gains tax cut increases the return volatility of stocks with

large embedded capital losses or gains more than stocks with small embedded losses or

gains), we dichotomize the non-dividend paying stocks into those whose share prices

4 We use 18-month price changes to form our portfolios because TRA97 established 18 months as the minimum holding period for investors to apply the lower long-term capital gains tax rate.

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have declined over the last 18 months and those whose share prices have increased over

the same period. Then, we divide the stocks whose share prices have declined into

quartiles based on the amount of their price depreciation. We call these quartiles, loss

portfolios. Similarly, we divide the stocks whose share prices have risen into quartiles

based on the amount of their appreciation. These quartiles are termed gain portfolios. We

limit our analysis to non-dividend paying stocks to mitigate any confounding effects on

stock return volatility arising from a firm’s dividend distribution.

For all of our tests, we use daily returns to construct monthly volatility measure.

The sampling period used in our empirical analysis spans from January 1993 to

December 2002. To avoid the transient effect caused by the capital gains tax cut

announcement, we exclude observations from April to September of 1997 from our

analysis.

Let itjr be the return on stock (or industry) portfolio i on day j in month t and itσ be

stock (or industry) portfolio i’s return volatility in month t. We construct the monthly

stock (or industry) portfolio return volatility for each portfolio-month as follows

,)(

1

2∑=

−=tJ

j

ititjit rrσ (1)

where ∑=

=tJ

j

itj

t

it rJ

r1

1is the sample mean return for stock (or industry) portfolio i in month

t, tJ is the number of observations in month t. For the market index, we construct the

monthly market return volatility for each month t, ,tσ as follows

∑ ∑=

−

=

+ −−+−=t tJ

j

J

j

tjtttjttjt rrrrrr1

1

1

)1(

2 ))((2)(σ , (2)

where tjr is the market excess return on day j of month t and ∑=

=tJ

j

tjt

t rJ

r

1

1 is the sample

mean excess return for the market index in month t. Note that the market return volatility

(including the extra cross-product terms in the expression) adjusts for the first-order

autocorrelation in daily returns associated with nonsynchronous trading among stocks

15

included in the index.5 We also use the implied volatility for the Standard & Poors index

options (VIX) at month t as an alternative measure for the volatility of the market

portfolio.

To test our hypotheses on the effect of the capital gains tax rate cut on stock

return volatility, we introduce two dummy variables: Post and HVP. Dummy variable

tPost takes value 0 on and before 3/31/1997 and value 1 on and after 10/1/1997. Note

that this is different from a standard event study on stock returns which focuses on the

announcement effect. We exclude the “announcement” months from our examination

because we are interested in the change of the volatility level around the event. Dummy

variable HVPi takes the value of 0 if portfolio i is a pre-selected benchmark portfolio and

the value of 1 for an alternative portfolio believed to have a higher volatility than the pre-

selected benchmark portfolio. Another important difference between stock returns and

the volatility of stock returns is that the latter has significant persistence. To allow for the

serial correlation in stock return volatility, we use lagged demeaned volatility as

explanatory variable in our analysis.

Specifically, to test the change in return volatility for different stock portfolios

under hypothesis 1, we use the following specifications:

For market index and the implied volatility index

,'111

)(

1

tt

q

j

f

jtj

f

jt

p

j

j

q

j

jtjjt

p

j

jtt XrrPost εγζσξδσρβασ +++∆++∆++= ∑∑∑∑=

−−

==

−−

=

(3)

For industry portfolios i

,'1

)()(

1

111

)()(

1

itt

n

j

jtijjti

m

j

j

q

j

f

jtj

f

jt

p

j

j

q

j

jtjjt

p

j

jtit

Xr

rrPost

εγησθ

ζσξδσρβασ

+++∆+

+∆++∆++=

∑∑

∑∑∑∑

=

−−

=

=

−−

==

−−

= (4)

For constructed portfolio i

5 Similar measures are used in French, Schwert and Stambaugh (1987) and Guo and Whitelaw (2006), among others.

16

,''1

)()(

1

111

)()(

1

ititt

n

j

jtijjti

m

j

j

q

j

f

jtj

f

jt

p

j

j

q

j

jtjjt

p

j

jtit

ZXr

rrPost

εϕγησθ

ζσξδσρβασ

++++∆+

+∆++∆++=

∑∑

∑∑∑∑

=

−−

=

=

−−

==

−−

= (5)

where ∑=

−=∆T

k

kttT

1

1σσσ is the demeaned volatility measure for the market index,

subscript j refers to its lags, and subscript k refers to the months, f

jt−∆σ and f

jtr − represent

lagged demeaned return volatility and monthly average of daily return for foreign stock

markets, respectively, )( jti −∆σ and )( jtir − are lagged demeaned industry (or constructed)

portfolio volatility and monthly average of daily return for industry (or constructed)

portfolio, respectively, tX refers to a vector of aggregate control variables, and

itZ represents a vector of characteristics specific to constructed portfolio i as of time t.

Existing empirical asset pricing studies suggest that stock return volatility exhibits

persistence and that large negative stock price changes tend to be followed by periods of

high stock return volatility. The latter is sometimes referred to as the leverage effect. To

control for these effects, we allow stock return volatility to depend on lagged return

volatility and stock returns. As the capital markets become more integrated, we also

consider the impact of foreign stock market return and volatility on domestic stock return

volatility by including f

jt−∆σ and f

jtr − as control variables. For the industry and

constructed portfolios, our specifications also account for volatility persistence and

leverage effect at the portfolio level.

For both the market index and industry portfolios, we expect the return volatility

to be higher after the capital gains tax rate is cut. This implies that the estimated

coefficient for Post is positive, i.e., .0>β On the return volatility of stock portfolios

constructed above, we predict that portfolios of non- or lower dividend-paying stocks and

portfolios with large embedded capital gains or losses will experience more return

volatility after the capital gains tax cut, compared with other firms. For these portfolios,

we expect the estimated coefficient for the dummy variable Post to be positive, i.e.,

.0>β However, for portfolios of high dividend-paying stocks or portfolios of stocks with

small embedded gains or losses, a capital gains tax cut may have a negligible effect on

17

the return volatility of these portfolios. The estimated coefficient for the dummy variable

Post on these portfolios may be insignificant.

To test the cross-sectional implications stated in H2 and H3, we need to compare

the return volatility increases for different portfolios. This is achieved by estimating the

following panel regression model utilizing observations for both the benchmark portfolio

and the alternative portfolio:

.1

)()(

111

1

)()(

1

321

ititit

n

j

jtijjti

m

j

j

q

j

f

jtj

f

jt

p

j

j

q

j

jtjjt

p

j

jititit

ZXrr

rHVPPostHVPPost

εϕγησθζσξ

δσρβββασ

++++∆++∆+

+∆+×+++=

∑∑∑∑

∑∑

=

−−

==

−−

=

=

−−

= (6)

This specification allows us to test H2 and H3 by examining the coefficient

estimate for the interaction term, HVPPost × . For H2, we choose the dividend-paying

portfolio as the benchmark portfolio and the non-dividend paying portfolio as the

alternative portfolio. We expect the non-dividend paying portfolio to experience a larger

increase in return volatility than the dividend-paying portfolio does. This implies that the

interaction term HVPPost × will have a positive coefficient because HVP takes a value

of one for the non-dividend paying portfolio and a positive coefficient indicates a higher

volatility for the HVP portfolio. Consequently, testing H2 is equivalent to testing if

.03 >β

Similarly, for H3, we choose the portfolio with the smaller embedded losses

(gains) as the benchmark portfolio and the portfolio with the larger embedded losses

(gains) as the alternative portfolio. We predict that the portfolio of stocks with larger

embedded losses (gains) will experience a greater increase in return volatility than the

portfolio of stocks with smaller embedded losses (gains). Thus, we expect the coefficient

estimate for HVPPost × to be positive, i.e., .03 >β

This specification also allows us to test whether the benchmark portfolio

experiences a volatility increase after the capital gains tax rate cut ( 1β ) and whether the

alternative portfolio indeed has a higher volatility over the benchmark portfolio prior to

the capital gains tax cut ( 2β ). A positive coefficient estimate for 1β indicates a higher

return volatility for the benchmark portfolio after the capital gains tax rate cut, and a

18

positive coefficient estimate for 2β shows that the alternative portfolio has a higher

return volatility than the benchmark portfolio before the capital gains tax rate cut.

It is important to control for variables which may affect stock return volatility.

Based on the capital asset pricing theory, Lettau and Ludvigson (2001) propose using the

consumption-wealth ratio (CAY) as a determinant for stock returns. They show that the

CAY variable is a better predictor than are the dividend yield, the term premium, the

default premium, and other previously widely used predictors combined. Campbell and

Shiller (1988) document that stochastically detrended risk free rate (RREL) is an

important predictor for stock returns. We also include the growth rate of the industrial

production to account for the state of the economic activities. In summary, our regression

analysis includes the following aggregate control variables:

CAY --- the consumption-wealth ratio,

RREL --- the stochastically detrended risk free rate,

GIP --- the industrial production growth rate (GIP).

Campbell, Lettau, Malkiel, and Xu (2001) document an increase in firm

idiosyncratic volatility relative to market volatility from 1962 to 1997.6 They suggest

several factors as possible explanations. These factors include changing discount rates, a

shift towards reliance on external as opposed to internal capital markets, firms’ growth

potentials, changes in executive compensation, firms’ leverage position, and the

increased share of institutional ownership. Cohen, Hall, and Viceira (2000) find the

changes in executive compensation have a statistically significant effect on the risks of

their firms’ activities. But the effect is small in magnitude. Dai, Maydew, Shackelford,

and Zhang (2007) find that turnover has a significant effect on stock returns. Xu and

Malkiel (2003) and Cao, Simins, and Zhao (2006) document that firms’ growth options

have significant effect on idiosyncratic risk of equity. In addition, both the New York

Stock Exchange and the Nasdaq reduced the tick size for stock trading between June

1997 and August 1997, the same time that TRA97 was being finalized. To capture

possible effects on the return volatility of our constructed portfolios associated with these

variables, we include the value-weighted firm’s debt-asset ratio (D/A), turnover in the

most recent past month (Turnover), the average monthly bid-ask spread in the most

6 Similar results are also documented in Pastor and Veronesi (2006) for the more recent periods until 2002.

19

recent past month (BidAskSpread), price-earnings ratio as a proxy for growth option (P/E

ratio), and the average individual ownership in the most recent past quarter (IND) in the

regression analysis for each constructed portfolio. In addition, since the capital gains tax

change will not likely to affect earnings and stock return volatility are related to earnings

volatility, we also control for the earnings volatility (CV earnings) measured by the

coefficient of variation in quarterly earnings. The logarithm of market capitalization of

the portfolio (Size) is also included as a control. In summary, the list of control variables

specific to each constructed portfolios are as follows:

D/A --- the value weighted averages of firms’ debt-asset ratios,

Turnover --- the value weighted averages of individual stock turnover,

BidAskSpread --- the value weighted average of individual stocks’ percentage bid-

ask spread,

P/E ratio --- the value weighted average of individual stocks’ price-earnings

ratios,

IND --- the value weighted average of individual ownership of stocks in the

portfolio,

CV earnings --- the value weighted average of firm’s quarterly earnings’

coefficient of variation,

Size --- the logarithm of the market value of the portfolio.

For all specifications (equations (3) to (6)), we also include monthly dummies to

account for calendar effect.

Finally, recall that the 1997 capital gains tax rate reduction only applies to

individual investors. It follows that companies owned solely by individuals should have

experienced an increase in stock return volatility while companies owned solely by other

stockholders (e.g., pensions) should not have been affected by the legislation. More

generally, the capital gains tax rate change should only affect stock return volatility if the

marginal investor is an individual. Since the marginal investor is unobservable, we test

whether return volatility is increasing in individual stock ownership. Specifically, we

divide the non-dividend paying and dividend paying portfolios, according to the median

detrended individual ownership in each month, to form four portfolios:

• non-dividend paying, low individual ownership portfolio,

20

• non-dividend paying, high individual ownership portfolio,

• dividend-paying, low individual ownership portfolio, and

• dividend-paying, high individual ownership portfolio.

We then apply regression analysis to the four portfolios as we do for all other constructed

portfolios.

Unfortunately, our measure of tax-sensitive investors using individual stock

ownership is flawed. First, the returns on many institutional holdings are subject to the

individual income tax (e.g., street name holdings by brokerage houses on behalf of

individual investors). Thus, we measure tax-sensitive investors with measurement errors.

Second, Gompers and Metrick (2001) and Xu and Malkiel (2003) document that

institutional ownership increases idiosyncratic volatility. Since they find a positive

correlation between institutional ownership and volatility and we predict a negative

relation, our tests are biased against rejecting the null. (Note that the null is that there is

no relation between institutional ownership and volatility, while we predict that volatility

will rise with the number of investors in the firm affected by the legislation). In

summary, rejecting the null hypothesis will provide strong evidence that the 1997 rate

reduction increased volativity. Unfortunately, we may fail to reject the null because our

tests lack sufficient power to discriminate between the extant finding and our prediction.

4. Empirical Analysis

4.1. Sample and Summary Statistics

To empirically test the effect of TRA97 on stock return volatility, we use all

stocks included in the CRSP data base. The excess return on the market index is

constructed as the market return of the value-weighted portfolio of stocks included in the

CRSP data base after the risk free rate is subtracted. The monthly implied volatility index

for the Standard & Poors index options (VIX) is the average implied annualized volatility

for different call and put options on the index with expiration date in a month. The

returns for the foreign equity markets are based on the Morgan Stanley Capital Markets

International (MSCI) ACWIsm ex USA Index. This is a free float-adjusted market

capitalization index designed to measure equity market performance in all global

developed and emerging markets outside of the United States. The five industry

21

portfolios are formed using the 4-digit SIC code and consist of the (1) consumer industry

(consumer durables, non-durables, wholesale, retail, and some services, such as laundries

and repair shops), (2) manufacturing industry (manufacturing, energy, and utilities), (3)

high tech industry (business equipment, telephone and television transmission), (4) health

care industry (healthcare, medical equipment, and drugs), and (5) other industries (mines,

construction, building materials, transportation, hotels, business services, entertainment,

finance).7 We construct monthly excess returns and volatility for non-dividend paying

and dividend-paying portfolios, low dividend yield and high dividend yield portfolios,

quartile gain portfolios, and quartile loss portfolios as discussed in the previous section.

These are value-weighted portfolios using daily individual stock return data.8 As noted

above, the investigation period is from January 1993 to December 2002, excluding April

through September of 1997. This sample period enables to have about the same number

of observations before and after the announcement, while avoiding any potentially

confounding effects arising during the legislative deliberations.

For the aggregate control variables, we obtain the consumption-wealth ratio

(CAY) from Martin Lettau’s website. Since the consumption-wealth ratio is at quarterly

frequency, we use linear interpolation to obtain monthly observations. The stochastically

detrended risk free rate is constructed by removing the average risk free rate in the prior

twelve months from the risk free rate in month t as in Campbell and Shiller (1988). The

growth rate of the industrial production is calculated using the monthly industrial

production index obtained from the Federal Reserve Bank of St. Louis.

We obtain daily individual stock return data from the daily CRSP data base.

Dividend and stock price are extracted from the monthly CRSP data base. We compute a

firm’s dividend yield based on dividend distribution in the prior year and the stock price

in the most recent month. We construct the embedded capital gains and losses using a

firm’s most recent 18 month stock price change prior to month t.9 To obtain measures of

investor ownership, we use institutional investors’ ownership information submitted by

7 The excess return on the value-weighted market index and returns on industry portfolios are obtained from Kenneth French’s website. 8 To remove the influence from extreme values, we winsorize observations at the bottom and the top 5 percent for each portfolio. 9 We also performed the analysis for the loss and gain portfolios using price changes in the past 12 months. The results are very similar to that for the 18 month price changes.

22

investment management companies to the Security Exchanges Commission on Form 13-

F.10 We compute the individual investor ownership on stock i at time t (INDit) as follows:

INDit = 1 – the percentage of shares owned by institutional investors at time t.

We compute a firm’s debt-asset ratio using data from the COMPUSTAT data

base. Because the COMPUSTAT data base is only available at quarterly frequency, we

assume that a firm’s debt-asset ratio remains the same within the quarter. Monthly

individual stock turnover is constructed by dividing the monthly trading volume by the

shares outstanding at the end of the month.11 The average monthly percentage bid-ask

spread for individual stocks is constructed using the transaction level Trade And Quote

(TAQ) data base.12 For the measure on firms’ growth options, we use the ratio of the end-

of-month price to the lagged earnings per share.13 The earnings volatility measure, we

use the coefficient of variation calculated using 24 quarterly earnings in the previous six

years.14 Firm size is measured by the end-of-month price multiplied by the total shares

outstanding for each firm. For each portfolio, we compute the monthly value weighted

averages of firms’ debt-asset ratios, turnover, percentage bid-ask spreads, price-earnings

ratios, the detrended individual ownership, the coefficient of variation for quarterly

earnings, and the logarithmic market value of the portfolio.

Table 1 presents the summary statistics for the market and industry portfolios and

economy-wide control variables used in our regression analysis in Panel A and the

univariate tests of mean return volatility changes for the market and industry portfolios in

Panel B. The dataset consists of 120 monthly time series observations from January 1993

to December 2002. The average daily excess return for the value-weighted market

portfolio is 0.019 percent with a standard deviation of 0.22 percent. The monthly

volatility of the market excess return has a mean of 4.3 percent with a standard deviation

of 2.3 percent. For the same time period, average daily return for the foreign equity

10 We thank Rabih Mousssawei for providing us the institutional stock ownership data. 11 Ideally, we would use the monthly trading volume for individual investors only. However, this information is unobservable. Thus, we assume that the differences, in any, between individuals’ turnover and other investors’ turnover do not affect the study’s inferences. 12 We thank Kam-Ming Wan for providing us the monthly bid-ask spread data on individual stocks. 13 We also used alternative measures such as the market value to book value ratio and the forecasted operating income growth rate on individual firms obtained from the IBES database as a proxy. The results are qualitatively similar. 14 The coefficient of variation is defined as the standard deviation scaled by the sample average.

23

markets is 0.012 percent with a standard deviation of 0.21 percent. The average monthly

volatility for the foreign equity markets is less than the U.S. equity market at 3.7 percent

with a standard deviation of 1.6 percent. The monthly implied volatility has a mean of 5.9

percent with a standard deviation of 2.0 percent.15

The industry portfolios have average daily returns ranging from 0.032 percent for

the manufacturing to 0.053 percent for the healthcare. The manufacturing industry has the

lowest standard deviation of 0.19 percent and the high tech industry has the highest

standard deviation of 0.40 percent. Consistent with the daily statistics and our intuition,

the monthly return volatility is the lowest for the manufacturing industry with an average

of 3.5 percent and a standard deviation of 1.7 percent, and is the highest for the high tech

industry with an average of 6.9 percent and a standard deviation of 3.8 percent. The CAY

variable has an average of 0.033 percent and a standard deviation of 2.1 percent. The

stochastically detrended risk free rate has a monthly average of -0.008 percent and a

standard deviation of 0.071 percent. Over the sample period, the industrial production

grew at 0.28 percent per month on average with a standard deviation of 0.53 percent.

The univariate test results in Table 1, Panel B suggest that both the market and

industry portfolios experienced dramatic increases in return volatility during the

investigation period. Specifically, the monthly average of return volatility for the market

portfolio increased from 2.7 percent before the capital gains tax rate cut to 5.6 percent

after the capital gains tax rate cut. Similarly, the implied volatility also increased from 4.2

percent to 7.3 percent. For industry portfolios, the monthly average of return volatility

increased the least for manufacturing industry from 2.2 percent to 4.5 percent and the

most for the high technology industry from 3.9 percent to 9.4 percent. All increases are

statistically greater than zero. The question facing this study is the extent to which these

dramatic increases in stock return volatility are attributable to the 1997 reduction in the

capital gains tax rate

Table 2 reports the summary statistics for the constructed portfolios based on a

firm’s dividend distribution in Panel A and the embedded capital losses (gains) in the past

18 months in Panel B (C), and the univariate tests for the mean volatility changes for the

15 Because the raw VIX data are for annual return volatility of the Standard & Poors index, we scale the VIX by the square root of 12 to obtain monthly return volatility measure.

24

constructed portfolios in Panel D. Specifically, Panel A presents the summary statistics

for the non-dividend paying, dividend-paying, low dividend yield, and high dividend

yield portfolios. To focus on dividend-paying dimension, we restrict to those stocks with

price changes less than 5 percent in the past 18 months. The non-dividend paying

portfolio has an average daily return of 0.010 percent with a standard deviation of 0.30

percent. The dividend-paying portfolio has a mean daily return of 0.031 percent with

standard deviation of 0.17 percent. Consistent with results on the non-dividend and

dividend paying portfolios, the low dividend yield portfolio has a lower mean return of

0.024 percent with standard deviation of 0.20 percent while the high dividend yield

portfolio has a higher mean return of 0.037 percent with standard deviation of 0.18

percent. The monthly return volatility for the non-dividend paying portfolio has a mean

of 5.9 percent with a standard deviation of 2.5 percent. Both statistics are much higher

than those for the dividend-paying portfolio which has a mean of 3.5 percent with a

standard deviation of 1.4 percent. The low dividend yield portfolio has a mean return

volatility of 4.1 with a standard deviation of 1.5 percent while the corresponding statistics

are lower at 3.5 percent and 1.3 percent for the high dividend yield portfolio,

respectively.

Panels B and C present summary statistics for the losses and gain portfolios,

respectively. To focus on the embedded price change dimension, we restrict the analysis

to stocks that have not paid dividends. Recall that we dichotomize the non-dividend

paying stocks into depreciated and appreciated stocks and further divide the two groups

into quartiles. For the loss portfolios, the average daily return is the highest at 0.044

percent for the quartile portfolio with the largest embedded capital losses (the upper 25

percentile). For the quartile portfolio with the smallest embedded capital losses (the lower

25 percentile) the average daily return is lower at 0.014 percent. The average monthly

return volatility increases from 5.8 percent for the smallest loss portfolio to 7.6 percent

for the largest loss portfolio.

For the gain portfolios, the average daily returns range from 0.0008 percent for

the quartile portfolio with the smallest embedded capital gains (lowest 25th percentile) to

0.078 percent for the quartile portfolio with the largest embedded capital gains (upper

25th percentile). The quartile portfolio with the largest embedded capital gains also has

25

the highest monthly return volatility of 7.9 percent while the quartile portfolio with the

smallest embedded capital gains has a lower monthly return volatility at 5.4 percent.

Overall, the results on the gains and loss portfolios provide empirical evidence that higher

return is associated with higher risk.

Consistent with the return volatility increases for the market index and industry

portfolios (in Table 1, Panel B), the univariate test results in Panel D indicate that all

constructed portfolios have experienced significant return volatility increases. Moreover,

there are also differences in the increases in return volatility across different portfolios.

Non-dividend paying stocks see a larger return volatility increase than dividend paying

stocks (3.1 percent for non-dividend paying stock portfolio versus 1.8 percent of dividend

paying stock portfolio). However, among dividend paying stocks, the amount by which

return volatility increased did not vary with the dividend yield (the low dividend yield

portfolio increased by 1.84, while the high dividend yield portfolio increased by 1.85).

The quartile portfolio of stocks with the largest embedded capital losses

experienced a 5.3 percent return volatility increase compared to 3.1 percent volatility

increase for the quartile portfolio of stocks with the smallest embedded capital losses.

However, the return volatility increases are similar for portfolios of stocks with different

embedded capital gains (2.9 percent for the portfolio of stocks with the smallest gains

versus 2.4 percent for portfolios of stocks with the largest gains).

Table 3 presents the summary statistics for the portfolio control variables

including the value-weighted averages of firms’ debt-to-asset ratio (D/A), turnover

(Turnover), percentage bid and ask spread (BidAskSpread), price-earnings ratio (P/E

ratio), individual ownership (IND), coefficient of variation for quarterly earnings (CV

earnings), and the logarithm of market value of the portfolio (Size). Panel A reports the

summary statistics for the non-dividend and dividend paying portfolios. The non-

dividend paying portfolio has a lower average debt/asset ratio (D/A=0.49) and a higher

standard deviation (0.12) than dividend-paying portfolios (0.64 and 0.05, respectively for

the portfolio of all dividend-paying stocks, 0.60 and 0.06 for low yield portfolio and 0.69

and 0.06 for high yield portfolio) with a higher standard deviation. This is consistent with

dividend-paying firms utilizing more debt financing to gain the tax benefit associated

with issuing debt, although formal analysis of that relation, if any, is beyond the scope of

26

this paper. The non-dividend paying portfolio also has a much higher average turnover

(16.1 percent) than dividend-paying portfolios (6.3 percent for all dividend-paying

stocks, 7.1 percent for low yield portfolio and 5.7 percent for high yield portfolio). The

average bid-ask spread is higher for the non-dividend paying stocks at 0.68 percent than

for the dividend paying stocks at 0.30 percent. The average price-earnings ratio is 20 for

non-dividend paying stocks and 31 for dividend paying stocks. The lower P/E ratio for

the non-dividend paying stocks may be the result of restricting the stocks to be included

in the portfolios with price changes less than 5 percent. The average individual investor

ownership is 44 percent for the non-dividend paying stocks and slightly higher at 47

percent for dividend paying stocks. The earnings volatility measured by the coefficient of

variation in the past 24 quarters is substantially higher at 3.1 for non-dividend paying

stocks than 0.7 for dividend paying stocks. Finally, the average size is larger for dividend

paying stocks than for non-dividend paying stocks.

Panel B shows the summary statistics for the portfolio control variables for the

loss portfolios. The debt/asset ratio (D/A) stays in a narrow range between 0.46 and 0.47.

The turnover rate is 16 percent for the smallest loss portfolio and 20 percent for the

largest loss portfolio. The average percentage bid-ask spread increases steadily from 65

basis points for the smallest loss portfolio to 133 basis points for the largest loss portfolio.

The price-earnings ratio declines from 21 for the portfolio of stocks with smallest losses

to around 6 for stocks with largest losses. The average individual investor ownership

increases from 46 percent for the smallest loss portfolio to 59 percent for the largest loss

portfolio. Except for the smallest loss portfolio, the earnings volatility measured by the

coefficient of variation is negative and the magnitude increases as the embedded losses

increase. Finally, the logarithm of market value declines from 15 for the smallest loss

portfolio to 13 for the largest loss portfolio.

Panel C shows the same summary statistics for the gain portfolios. The debt/asset

ratio steadily decreases from 0.49 to 0.40 as the embedded capital gains increase. The

turnover rate is 17 percent for the smallest gain portfolio and 25 percent for the largest

gain portfolio. The average percentage bid-ask spread is hump-shaped. The smallest gain

portfolio has a spread of 0.68. The interquartile portfolios have values of 0.96 and 0.82.

The largest gain portfolio is only 0.49. The P/E ratio increases steadily from 29 for the

27

portfolio with the smallest gains to 38 for the portfolio with the largest gains. The

individual investor ownership remains in a narrow range between 42 to 45 percent.

Contrary to the loss portfolios, the earnings volatility becomes more positive as the

embedded gains increase, ranging from -5.7 for the portfolio with the smallest gains to

1.1 for the portfolio with the largest gains. Finally, there is little difference in market

value across gain portfolios.

4.2. Time series analysis of the capital gains tax effect on stock return volatility

This section discusses our time series analysis of the effect of a capital gains tax

cut on stock return volatility. Table 4 reports the coefficient estimate for the dummy

variable Post for the market index, implied volatility of Standard & Poors index options,

industry and constructed portfolios using equations (3) to (5).

As predicted, the volatility of the market excess return is higher after the capital

gains tax rate is reduced. We find that the monthly volatility of the market excess return

is 1.9 percentage points higher after the capital gains tax cut than before the capital gains

tax cut, after controlling for domestic and foreign equity market performances and the

aggregate economic variables. This estimated regression coefficient is statistically

significant at the 5 percent level. The 1.9 percentage point increase also is economically

significant. It accounts for 66 percent of the difference between the pre-TRA97 average

volatility of 2.7 and the post-TRA97 average of 5.6 (see Table 1, Panel B). Restated, this

implies that the non-tax factors from previous studies account for only 34 percent of the

overall increase in volatility after 1997. In other words, a substantial portion of the

increase in stock return volatility from the period, 1993 to 1997, to the period, 1997 to

2002, cannot be accounted for with documented factors. This leaves us to ponder the

change around 1997 that led to dramatic increases in volatility. Because the capital gains

taxes were cut in 1997, we conjecture that at least a portion of the increase in volatility

was attributable to TRA97.

We find similar results using the implied volatility for the S&P index options. The

implied volatility is higher by 2.1 percentage points, after the capital gains tax rate

reduction. The coefficient is highly statistically significant. Using the same computation

as above, we conclude that the non-tax factors in our analysis only account for 32 percent

28

of the difference between the pre-TRA97 average volatility of 4.2 and the post-TRA97

average of 7.3 (see Table 1, Panel B).16

For the five industry portfolios, the estimated coefficients for the categorical

variable, Post, is always significantly greater than zero. This indicates that, for every

industry, the return volatility is higher after the capital gains tax cut, controlling for

domestic and foreign equity market performances and the aggregate economic variables.

Specifically, the monthly return volatility is higher by 2.1 percentage points for the

consumer industry, 1.6 percentage points for the manufacturing industry, 2.5 percentage

points for the high tech industry, 2.1 percentage points for the healthcare industry, and

2.4 percentage points for all other industries after the capital gains tax cut than before the

capital gains tax cut. When we compare the regression coefficient with the increase in

overall return volatility in Table 1, Panel B, we find that the non-tax factors in our

regression analysis only accounts for 22 percent of the volatility increase for the

consumer industry, 30 percent for the manufacturing industry, 55 percent for the high

tech industry, 16 percent for the healthcare industry, and 25 percent for all other

industries. In short, as with the market excess return and the S&P index options, we find

that much of the increase in volatility from 1993 to 2002 cannot be explained by

previously documented reasons.

For the constructed portfolios, the estimated regression coefficient for the dummy

variable, Post, is always positive. After controlling for domestic and foreign equity

market performances, the aggregate economic variable, and portfolio specific

characteristics, we find that the coefficient is statistically significant for the non-dividend

paying and dividend paying portfolios and three of the loss portfolios, but never

significantly greater than zero for any of the gain portfolios.

As predicted, following TRA97, the non-dividend paying portfolio experienced a

greater increase in volatility than the dividend paying portfolio. The coefficient for the

non-dividend paying portfolio is 2.5 percentage points, compared with 1.9 percentage

points for all dividend-paying stocks. Also consistent with our prediction, the low

dividend yield portfolio experienced a higher volatility increase (2.4) than the high

dividend yield portfolio does (1.5).

16 We compute the 32 percent from 1-[2.1%/(7.3%-4.2%)].

29

The estimated coefficients for the Post dummy are positive in all four quartile loss

portfolios, consistent with a higher return volatility after the capital gains tax cut than

before the tax cut. As expected, the increase in return volatility is largest for the portfolio

with the largest losses (6.4 percentage points). With the exception of the second lowest

quartile, the return volatility increase is higher as the embedded losses increase. For the

gain portfolios, while the estimated coefficient is positive for the dummy variable Post, it

is insignificant at the 5 percent test level. Nonetheless, both the magnitude of the

estimates and the significance increase as the embedded gains increase.

For our time series regressions, the lagged consumption-wealth ratio (CAY) in

general has a significant positive effect on the return volatility. Lagged returns for each

portfolio have a negative effect on the return volatility of the portfolio, lending support to

the leverage effect. Past return volatility of the portfolio also has a positive effect on

current return volatility, implying some return persistence. We also find that turnover has

a positive effect on dividend paying portfolios and gain portfolios.

To summarize, we find that returns were about twice as volatile from 1997 to

2002 as they were from 1993 to 1997. After analyzing the volatility of the market excess

return, the implied volatility of S&P index options, and the return volatility across

industries, we estimate that less than half of the increase can be attributed to non-tax

influences on stock return volatility identified in prior studies. This leaves us to infer that

something around 1997 caused a substantial increase in stock return volatility. The factor

we identify and study in this paper that may have contributed to the increase in volatility

is the 1997 capital gains tax rate reduction.

In an attempt to better link the increase in volatility to the reduction in capital

gains taxes, we turn to cross-firm tests based on dividend yields and embedded losses and

gains. We expect the capital gains tax reduction to affect firms differently depending on

their dividend yields and embedded depreciation or appreciation. If the cross-firm

increases in volatility correspond with the cross-firm differences in the impact of the

capital gains tax, then we will have more confidence that TRA97 actually was a factor in

the increase in stock return volatility after 1997. Consistent with TRA97 contributing to

the increase in volatility, the findings above show volatility moved indirectly with

dividend yield and more for firms with larger embedded losses. We find less evidence

30

that volatility was greater for firms with larger embedded gains. The next section extends

these cross-firm tests in an attempt to provide further evidence that the capital gains tax

cut in 1997 contributed to stock return volatility increase.

4.3. The cross-sectional test on the effect of a tax cut on return volatility

To test the cross-firm effect of a capital gains tax change on return volatility of

portfolios of stocks with different sensitivities to the capital gains tax rate cut, we

estimate the panel regression model specified in equation (6). The specification requires

that we identify a benchmark portfolio and an alternative portfolio with possibly a higher

return volatility.17 We start by comparing non-dividend paying portfolios and dividend

paying portfolios. Both our intuition and time series analysis results suggest that non-

dividend paying stocks have a higher return volatility than dividend paying stocks. We

thus choose the portfolio of non-dividend paying stocks as the alternative portfolio and

the dividend paying, the low yield, and the high yield portfolio as benchmark portfolios.

Table 5 presents the estimation results. As predicted, the coefficient estimate for

the interaction term, HVPPost × , is positive and statistically significant, when the

benchmark portfolio consists of all dividend paying stocks or high-yield stocks. The

estimated coefficient indicates that the portfolio of non-dividend paying stocks

experiences 1.2 percentage points (Column 1) higher monthly return volatility than the

portfolio of all dividend-paying stocks and 1.6 percentage points (Column 3) higher

monthly return volatility than the portfolio of high-yield stocks. The statistical

significance is less when the benchmark portfolio consists of only low-yield stocks (p=

0.06). This is not surprising because low-yield stocks are more similar to non-dividend

paying stocks than high-yield stocks. Still, the estimated coefficient shows that the

portfolio of non-dividend paying stocks has almost 0.8 percentage points (Column 2)

more monthly return volatility than the portfolio of low-yield stocks. The estimated

higher monthly return volatility for the non-dividend paying stocks than the dividend

paying stocks after the capital gains tax cut is above and beyond the 1.8 percentage points

higher monthly return volatility of non-dividend paying stocks relative to dividend

17 We use the PROC MIXED Procedure in SAS to estimate our panel regression model. Our estimation method utilizes the clustered estimate for the standard errors.

31

paying stocks before the capital gains tax cut as indicated by the estimated coefficient for

.2β

Table 6 presents the results from the cross-sectional tests of the return volatility

increases on portfolios of stocks with different embedded capital losses (or gains). Our

discussions in Section 2 and the time series analysis on the return volatility of different

portfolios of stocks suggest that stocks with large embedded capital losses (or gains) have

larger return volatility increase relative to stocks with small embedded capital losses (or

gains). Therefore, we choose the portfolio of stocks with the lowest 25 percentile capital

losses (gains) as the benchmark portfolio and the portfolio of stocks with the highest 25

percentile of capital losses (gains) as the alternative portfolio.

For the loss portfolios, the coefficient estimate for the interaction term,

HVPPost × , is positive and statistically significant on the margin at the 5 percent test

level. The estimated coefficient implies that, after the reduction in the capital gains tax

rate, the monthly return volatility of the portfolio of stocks with the largest 25 percentile

embedded capital losses was 1.1 percentage points higher than that of stocks with the

lowest 25 percentile embedded capital losses. This is in addition to the 1.8 percentage

points higher monthly return volatility of large loss stock portfolio relative to the small

loss stock portfolio before the capital gains tax rate cut as indicated by the estimated

coefficient estimate for .2β The result is consistent with investors holding stocks with

large embedded capital losses suffering more reduction in risk sharing with the

government and incurring a larger consumption risk increase after the capital gains tax

rate cut.

For the gain portfolios, we choose the portfolio of stocks with the largest 25

percentile embedded capital gains as the alternative portfolio and the portfolio of stocks

with the lowest 25 percentile embedded capital gains as the benchmark portfolio. The

coefficient estimates for HVPPost × is positive, but insignificant. This is contrary to

expectations that firms with larger embedded gains would experience a greater reaction in

stock return volatility following TRA97. These findings imply that the adverse effect on

the risk sharing between investors and government is not nearly as severe when investors

have large embedded capital gains as when they have large embedded capital losses.

Restated, the results are consistent with a capital gains tax rate cut not increasing the

32

consumption risk as much when investors have large embedded capital gains as when

they have large embedded capital losses.

Overall, the empirical results on the cross-sectional tests discussed above suggest

that, after the capital gains tax rate reduction, the non-dividend paying portfolio

experienced a higher return volatility increase relative to the dividend-paying portfolios.

The results also are consistent with the capital gains tax rate cut increasing the return

volatility of stocks with large embedded capital losses more than that of stocks with small

embedded capital losses. However, we find no similar evidence for embedded capital

gains.

4.4. Comparisons with other years before TRA97

As a robustness check, we repeat the cross-firm tests for other years before

TRA97, when the capital gains tax rate was not reduced. Finding similar relations for the

interaction term, HVPPost × , in years without a capital gains tax rate cut will raise

concerns about the inferences drawn above.

Using the same sample and regression variables, we conduct the same panel

regression analysis, assuming hypothetically that the event window was the same months

from April to September but in 1994, 1995 and 1996. 18 In other words, in these

robustness tests, we redefine Post as months following September 1994, September 1995,

and September 1996, respectively.

Table 7 reports the results of the cross-sectional tests on portfolios of stocks with

different sensitivity to a capital gains tax cut assuming hypothetically that the capital

gains tax rate cut took place in either 1994, 1995, or 1996. None of the coefficients on the

interaction term, HVPPost × , are significantly greater than zero in any of the nine

regressions. For the non-dividend paying versus dividend paying portfolios (Panel A),

the coefficient estimate for HVPPost × remains positive for all three regressions, but

insignificant. For the losses portfolios (Panel B), the estimated coefficients for the

interaction term HVPPost × is positive in 1994 and 1996, but negative in 1995. For the

gain portfolios (Panel C), the coefficients on HVPPost × are always negative. In short,

18 We do not perform the robustness check for time periods after TRA97 because the tax effect on return volatility has already taken place and return volatility in subsequent years are higher.

33

none of these robustness tests provide any evidence that the inferences drawn above are

spurious.

The findings in Table 7 provide comfort about the inferences that we drew from

Tables 5 and 6. Stock return volatility increased significantly more for non-dividend

paying stock (than for dividend paying stocks) and for stocks with large embedded losses

(than for stocks with small embedded losses) after 1997. We do not observe similar

increases after 1994, 1995 and 1996. This implies that whatever caused the stock return

volatility to increase had not occurred before 1997. These robustness tests cannot fully

rule out that some other non-tax event in 1997 was the driver of higher stock return

volatility after 1997, but it provides further support for the hypothesis that the capital

gains tax rate cuts in 1997 increased stock return volatility thereafter.

4.5. Investor ownership and the effect of a capital gains tax cut on return volatility

The capital gains rate reduction in the TRA97 only applies to income reported on

personal tax returns, i.e., capital gains from the selling of shares held directly by

individuals or held indirectly by individuals in flow-through entities, such as mutual

funds, partnerships, trusts, S corporations, or limited liability corporations that pass

income to investors’ personal tax returns. Capital gains taxes are not levied on tax-

deferred accounts (e.g., qualified retirement plans, including pensions, IRAs and 401(k)),

tax-exempt organizations, and foreigners. C corporations pay capital gains taxes;

however, the rate reduction in TRA97 did not apply to corporations. Thus, portfolios of

stocks with more tax sensitive investor ownership (i.e., stocks with returns that are

expected to trigger capital gains taxes that will be reported on personal tax returns) may

have experienced higher return volatility than portfolios of stocks with less tax sensitive

investor ownership.

We now examine if investor ownership has additional effect on the return

volatility increase associated with the capital gains tax cut. To achieve this objective, we

use a measure of individual investor ownership as a proxy for tax sensitive ownership and

then form portfolios based on the tax sensitive ownership measure. Specifically, we

compute the detrended individual investor ownership and then sort individual stocks

included in the non-dividend paying portfolio and the dividend-paying portfolio

34

constructed above into four portfolios based on the median detrended individual investor

ownership. They are (a) non-dividend paying, low individual ownership portfolio; (b)

non-dividend paying, high individual ownership portfolio; (c) dividend-paying, low

individual ownership portfolio; and (d) dividend-paying, high individual ownership

portfolio. We then perform both the time series regression using equation (5) and the

panel regression analysis using equation (6) to analyze the effect of the capital gains tax

cut on the return volatility of portfolios with different levels of individual investor

ownership.

There is a problem with this specification that deserves mentioning before we

discuss our findings. As discussed in Section 3, Gompers and Metrick (2001) and Xu and

Malkiel (2003) document that institutional ownership increases idiosyncratic volatility.

Based on their findings, we include a measure of institutional ownership as a control in

our earlier tests. Now, we are identifying individual ownership as a factor in determining

the extent to which capital gains taxes affect stock return volatility. Consequently, we

have one firm characteristic, the individual-institutional mix of the shareholders, serving

two roles in the determination of stock return volatility. This dual capacity potentially

undermines our ability to conduct this robustness test and may account for any inability

to reject the null hypothesis.

Turning to the results, Panel A in Table 8 shows summary statistics from the time

series regression of the relation between stock return volatility and individual ownership.

The first two columns show the results for the two non-dividend paying portfolios. The

last two columns show the results for the two dividend paying portfolios. All four Post

coefficient estimates are positive. Each is significant at the 5 percent test level, except

for the non-dividend paying, high individual ownership portfolio, which is significant at

the 10 percent level. However, contrary to expectations, in both cases, the portfolios with

the higher level of individual ownership have smaller estimated coefficients for the Post

dummy than the portfolios with the lower level of individual ownership. That said,

neither difference is statistically significant. Thus, these results provide no evidence that

the level of individual ownership affected the impact of the capital gains tax rate on stock

return volatility.

35

In Panel B, we report the results for the cross-sectional tests on the return

volatility increases for different portfolios. Column 1 shows the comparison between the

non-dividend versus dividend paying portfolios with low individual ownership while

Column 2 shows the comparison for the two portfolios with high individual ownership. In

both cases, we use the dividend paying portfolio as the benchmark portfolio and the non-

dividend paying portfolio as the alternative portfolio. In both columns, the coefficient

estimate for the variable of interest, HVPPost × , is positive. However, contrary to

expectations, the coefficient is only significant for the low individual ownership

portfolios. As in Panel A, these results provide no evidence that the level of individual

ownership affected the impact of the capital gains tax rate on stock return volatility.

Together, these tests provide no evidence that higher levels of individual investor

ownership contributed to higher stock return volatility following TRA97. There are

several possible explanations for this failure to reject the null hypothesis. First, as

discussed above, the fact that idiosyncratic volatility increases in institutional ownership

(Gompers and Metrick (2001) and Xu and Malkiel (2003)) may mean that our

institutional ownership measure is confounded by non-tax effects and thus a poor

measure of tax-sensitive stock ownership. Second, from a theoretical perspective, as long

as the marginal investor of a stock is tax sensitive, the stock return volatility will respond

to a capital gains tax change, regardless of the percentage of individual investor

ownership on the stock. Third, the individual investor ownership may not be a good

proxy for the tax sensitive ownership because of measurement error. As discussed in

other studies (e.g., Blouin, Raedy and Shackelford, 2007), 13-F filings crudely measure

the amount of capital gains that will be reported in individual tax returns. Finally,

individual investors are subject to the “disposition effect” and may not be tax-savvy.

5. Conclusion

We analyze the impact of capital gains taxes on the volatility of stock returns. Our

analysis predicts that reducing capital gains taxes increases the stock return volatility

because a capital gains tax cut reduces the risk sharing role of financial markets between

investors and the government and increases the consumption risk. Using the Tax Relief

Act of 1997, we empirically test the predictions on the stock return volatility of a capital

36

gains tax cut. Our time series regression analysis uncovers that the return volatility

increases for the market index, the implied volatility of Standard & Poors index options,

and industry portfolios, after controlling for all known determinants of stock return

volatility. These findings are consistent with something happening in 1997 that increased

stock return volatility. We conjecture that the 1997 reduction in the capital gains tax rate

accounted for at least some of the increase in volatility.

To provide more compelling evidence that the 1997 tax cut affected volatility

(and mitigate concerns about omitted correlated variables), we turn to cross-sectional

tests. We hypothesize that the effect of a capital gains tax change on stock return

volatility should vary depending upon dividend distribution and the size of the embedded

capital losses (or gains). We find that non- and lower dividend-paying stocks experience

a larger increase in return volatility than high dividend-paying stocks. We also find that

stocks with large embedded capital losses exhibit a larger increase in return volatility

after a capital gains tax rate reduction than stocks with small embedded capital losses.

However, we do not find a similar relation with embedded capital gains. We also show

that the different return volatilities for portfolios of stocks did not exist before 1997.

It is difficult, if not impossible, to construct a test that provides strong direct

evidence that a reduction in the capital gains tax rate caused stock return volatility to

increase. Our approach has been to control for every other possible determinant of stock

return volatility and see if the remaining volatility shows the footprints of taxes. We infer

from the findings in this study that the volatility left after controlling for every known

determinant appears to reflect the influence of the 1997 capital gains tax rate cut. Stock

return volatility was substantially greater after 1997. Furthermore, firms most affected by

the rate reduction showed the greatest change in volatility. Specifically, non-dividend

paying firms had a greater increase in volatility than dividend paying firms and firms

with large embedded capital losses experienced a greater increase in volatility than firms

with small embedded losses. Since we are unable to provide direct evidence that the tax

cut increased stock return volatility, we are cautious in our conclusions. However, we are

left without an alternative explanation for the surge in volatility following the rate

reductions in 1997, in particular, why portfolios of stocks with different sensitivities to

the capital gains taxes experience different increases in return volatility. Thus, we infer

37

from these findings that the 1997 reduction in the capital gains tax rate contributed to an

increase in stock return volatility in subsequent years.

In closing, while a capital gains tax cut may increase stock return volatility,

investors are not necessarily worse off. From an investor’s perspective, the expected

investment opportunities or the risk and return trade-off are the key consideration for

long-term investment decisions. A capital gains tax cut also may increase investors’ 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.

38

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41

Table 1 Market and Industry Portfolios and Aggregate Control Variables

Panel A of this table provides summary statistics for the market, industry portfolio and aggregate control variables. Panel B provides univariate tests on the mean volatility change before and after TRA97 for the

market and industry portfolios. marketr is the monthly average daily excess return of value-weighted CRSP

stock index; marketσ is the monthly volatility of the excess return of the value-weighted CRSP stock index;

foreignr is the monthly average daily excess return of value-weighted Morgan Stanley Capital International

(MSCI) world stock index excluding the United States; foreignσ is the monthly volatility of the excess

return of the value-weighted MSCI world stock index excluding the United States; VIXt is the monthly

implied volatility for the Standard & Poors index options at month t, ,industryr is the monthly average daily

gross return for the five industry portfolio as defined in Fama and French: consumer; manufacturing; high

technology; heathcare and all others; industryσ is the monthly volatility for each of the five industry

portfolios; CAY is the demeaned consumption-wealth ratio; RREL is the stochastically detrended risk free rate; and GIP is the growth rate of industrial production. The sample period covers January of 1993 to December of 2002. Note that observations between April and September of 1997 are excluded in the calculation of volatility mean in the univariate tests.

Panel A: Summary Statistics

Variable Mean Median Std Min Max

Market Portfolio and Implied Volatility

marketr 0.01887 0.05250 0.22370 -0.81762 0.40600

marketσ 4.28393 3.72106 2.31162 1.14089 13.47769

foreignr 0.01169 0.03063 0.21066 -0.71839 0.46165

foreignσ 3.65546 3.32699 1.57619 1.37693 9.22375

VIXt 5.92684 6.06362 1.99210 3.06862 12.78254

Industry Portfolios

consumerr 0.03760 0.05174 0.19744 -0.66238 0.52261

ingmanufacturr 0.03235 0.04138 0.18795 -0.70867 0.58095

hightechr 0.04220 0.07952 0.39592 -1.30000 0.83739

healthcarer 0.05329 0.08731 0.22793 -0.61524 0.56191

otherr 0.04477 0.07728 0.22639 -0.99524 0.61304

consumerσ 4.20179 3.95541 2.01454 1.36115 11.09683

ingmanufacturσ 3.47898 3.15529 1.71258 1.23093 11.20402

hightechσ 6.87807 5.86460 3.80486 2.01788 18.76379

healthcareσ 5.24268 4.73629 2.32152 1.67003 14.57388

otherσ 4.43622 3.93285 2.34291 1.22332 12.91087

Aggregate Controls

CAY 0.00033 0.00116 0.02076 -0.04622 0.03312

RREL -0.00757 -0.00887 0.07144 -0.20375 0.14783

GIP 0.00282 0.00314 0.00528 -0.00836 0.02163

42

Panel B: Univariate Tests for the mean volatility change for market and industry portfolios

Mean volatility Pre-TRA97 Post-TRA97 Difference p-value

marketσ 2.7090 5.6008 2.8918 0.0001

VIXt 4.1519 7.3328 3.1809 0.0001

consumerσ 2.7161 5.4143 2.6982 0.0001

ingmanufacturσ 2.2179 4.4929 2.2750 0.0001

hightechσ 3.9430 9.4113 5.4683 0.0001

healthcareσ 3.8496 6.3451 2.4955 0.0001

otherσ 2.6695 5.9034 3.2339 0.0001

43

Table 2 Summary Statistics for Constructed Portfolios

Panel A reports the monthly average of daily returns and monthly volatility for non-dividend paying, dividend-paying, low dividend yield, and high dividend yield portfolios constructed based on whether a firm pays dividends and the magnitude of dividend yield in the past year. We only include stocks with price

changes (gains or losses) in the prior 18 months being less than 5 percent. r is the monthly average of daily return for month t. σ is the monthly volatility at month t. We use the subscript “ND” to represent the

non-dividend paying portfolio, “D” for the dividend paying portfolio, “LY” for the low dividend yield portfolio (with dividend yield in the lower 50 percentile), and “HY” for the high dividend yield portfolio (with dividend yield in the upper 50 percentile), respectively. Panel B reports the monthly average of daily returns and monthly volatility for four quartile loss portfolios constructed based on a firm’s stock price depreciation in the past 18 months up to month t in ascending order with portfolio 1 corresponding to the smallest embedded capital losses and portfolio 4 the largest embedded capital losses. Panel C reports the monthly average of daily returns and monthly volatility for four quartile gain portfolios constructed based on a firm’s stock price appreciation in the past 18 months up to month t in ascending order with portfolio 1 corresponding to the smallest embedded capital gains and portfolio 4 the largest embedded capital gains.

tr% denotes the average daily return for month t for the quartile portfolios and t%σ denotes the monthly

volatility of the quartile portfolios at month t. For both the gains and loss portfolios, we exclude dividend-paying stocks to mitigate possible confounding effect on stock return volatility from a firm’s dividend distribution. The sample period covers January of 1993 to December of 2002.

Variable Mean Median Std Min Max

Panel A: Non-Dividend and Dividend Paying Portfolios

NDr 0.01020 0.00690 0.29672 -1.24217 1.01549

Dr 0.03126 0.04418 0.17322 -0.50811 0.43754

LYr 0.02438 0.03442 0.19979 -0.59497 0.54784

HYr 0.03713 0.04691 0.17608 -0.55451 0.47131

NDσ 5.89013 5.11680 2.51470 2.33783 16.10004

Dσ 3.49784 3.28363 1.36005 1.46585 8.02294

LYσ 4.05311 3.87738 1.49104 1.63227 8.75432

HYσ 3.51169 3.30966 1.34652 1.45658 8.37397

Panel B: Loss Portfolios (smallest to largest losses)

tr %25 0.01382 0.04874 0.29515 -1.08488 0.73012

tr %50 -0.01582 0.01873 0.37703 -1.40639 0.94808

tr %75 0.02781 0.02734 0.40893 -1.26344 1.54829

tr %100 0.04368 0.05614 0.55178 -1.93861 2.03547

t%25σ 5.75504 5.01138 2.34971 2.21929 14.06575

t%50σ 6.40039 5.29427 3.44350 1.65766 17.11815

t%75σ 7.14459 5.74115 3.67043 2.22324 17.40801

t%100σ 7.60548 5.95752 4.33132 2.85232 20.48670

44

Panel C: Gain portfolios ( smallest to largest gains)

tr %25 0.00079 0.01519 0.29946 -0.99960 0.91874

tr %50 0.02260 0.02076 0.28016 -0.93593 0.69403

tr %75 0.04010 0.04708 0.29947 -0.97831 0.91414

tr %100 0.07830 0.09727 0.41447 -1.80513 1.04318

t%25σ 5.44185 4.81950 2.25315 1.64414 11.62200

t%50σ 5.35551 4.57299 2.51103 1.62656 14.87364

t%75σ 6.00811 5.30272 2.48089 2.22233 14.54936

t%100σ 7.87081 7.03272 3.15716 3.52583 17.62147

Panel D: Univariate Tests for the mean volatility change for constructed portfolios

Mean volatility Pre-TRA97 Post-TRA97 Difference p-value

Non-dividend and dividend paying portfolios

NDσ 4.2028 7.2952 3.0924 0.0001

Dσ 2.5230 4.3327 1.8097 0.0001

LYσ 3.0796 4.9237 1.8441 0.0001

HYσ 2.5083 4.3583 1.8500 0.0001

Loss portfolios

t%25σ 4.0982 7.1851 3.0869 0.0001

t%50σ 4.0956 8.4404 4.3448 0.0001

t%75σ 4.9036 9.1382 4.2346 0.0001

t%100σ 4.7921 10.0737 5.2816 0.0001

Gain portfolios

t%25σ 3.8700 6.7648 2.8948 0.0001

t%50σ 3.7845 6.7189 2.9344 0.0001

t%75σ 4.7062 7.1358 2.4296 0.0001

t%100σ 6.6287 8.9819 2.3532 0.0001

45

Table 3 Summary Statistics for Portfolio Control Variables

This table reports the value-weighted monthly averages for the debt/asset ratio (D/A), turnover (Turnover), percentage bid-ask spread (BidAskSpread), price-earnings ratio (P/E ratio), individual investor ownership (IND), coefficient of variation for quarterly earnings (CV earnings), and logarithm of market value (Size) for each portfolio constructed the same as in Table 2. The sample period covers January of 1993 to December of 2002. For brevity, we report only mean and standard deviation.

Panel A: Non-Dividend and Dividend paying Portfolios

Non-Div. Paying Div. Paying Low-Yield High-Yield

mean std mean std mean std mean std

D/A 0.4943 0.1206 0.6370 0.0494 0.5996 0.0646 0.6914 0.0634

Turnover 0.1611 0.0678 0.0627 0.0190 0.0707 0.0246 0.0566 0.0180

BidAskSpread 0.6815 0.3484 0.3023 0.1283 0.3510 0.1751 0.2822 0.1093

P/E ratio 20.0411 35.9818 31.1732 64.5378 25.4008 46.2705 37.6375 145.3361

IND 0.4405 0.0952 0.4714 0.0540 0.4445 0.0652 0.4946 0.0575

CV earnings 3.0734 14.6450 0.6817 0.8714 0.8408 1.7461 0.5604 1.1522

Size 14.8446 1.2549 16.5291 0.9074 16.5517 1.1110 16.0920 0.7767

Panel B: Loss portfolios ( smallest to largest losses)

Port. 1 (25%) Port. 2 (50%) Port. 3 (75%) Port. 4 (100%)

mean std mean std mean std mean std

D/A 0.4763 0.0971 0.4607 0.1049 0.4635 0.1040 0.4604 0.0948

Turnover 0.1633 0.0554 0.1663 0.0635 0.1844 0.0644 0.1968 0.0654

BidAskSpread 0.6515 0.3483 0.8152 0.4884 0.9455 0.4933 1.3275 0.7072

P/E ratio 20.5068 24.5023 21.7288 36.9862 13.5860 27.6493 5.6140 35.4093

IND 0.4591 0.0768 0.4913 0.0973 0.5040 0.0999 0.5920 0.0999

CV earnings 5.2095 18.1340 -1.9583 19.1837 -3.0090 24.3061 -4.8815 67.5841

Size 15.1925 1.4664 14.8591 1.5998 14.4564 1.4629 13.4353 1.8123

Panel C: Gain portfolios ( smallest to largest gains)

Port. 1 (25%) Port. 2 (50%) Port. 3 (75%) Port. 4 (100%)

mean std mean std mean std mean std

D/A 0.4925 0.0811 0.4867 0.0748 0.4294 0.0812 0.4050 0.0770

Turnover 0.1667 0.0537 0.1539 0.0543 0.1822 0.0657 0.2459 0.0594

BidAskSpread 0.6842 0.6761 0.9672 0.9808 0.8209 0.8089 0.4874 0.3098

P/E ratio 28.6664 24.0376 31.6232 22.6895 34.1299 23.6667 37.7229 15.7612

IND 0.4232 0.0870 0.4470 0.1008 0.4284 0.1045 0.4204 0.0844

CV earnings -5.6750 57.1063 -2.0627 27.6997 0.4420 4.3358 1.1467 4.2161

Size 15.1664 1.0915 15.5426 1.1167 15.8103 1.1679 15.9727 1.7030

46

Table 4 Time series regression analysis on stock return volatility increases

This table reports the test results of time series analysis on the effect of TRA 97 on stock return volatility.

The tests are conducted for the excess return of the value-weighted CRSP stock market index ( marketσ ), the

implied volatility of the S&P index options (VIXt), five industry portfolios including the consumer, manufacturing, high tech, healthcare, and others, and the constructed portfolios with different sensitivity to the capital gains tax rate cut using equations (3), (4), and (5). The sample period covers January of 1993 to December of 2002. Post is a dummy variable which takes value of 1 if the observation is after 10/1/1997 and 0 if it is

before 3/31/1997. The p-value for dummy variable post is based on one-sided test.

Variable Estimate Std. Error t-statistic Prob. 0>β Adj. R

2

Market and Industry Portfolios

marketσ 1.8992 1.0070 1.89 0.0314 0.4715

VIXt 2.1048 0.6599 3.19 0.0010 0.7592

consumerσ 2.0813 0.7796 2.67 0.0046 0.5953

ingmanufacturσ 1.6252 0.6938 2.34 0.0108 0.6335

hightechσ 2.5370 1.3615 1.86 0.0330 0.6875

healthcareσ 2.1204 0.9871 2.15 0.0174 0.5503

otherσ 2.3549 0.8769 2.69 0.0044 0.6232

Non-Dividend and Dividend Paying Portfolios

NDσ 2.4814 1.4388 1.72 0.0444 0.4675

Dσ 1.9205 0.8203 2.34 0.0110 0.5940

LYσ 2.4224 0.8547 2.83 0.0030 0.5654

HYσ 1.5206 0.6318 2.41 0.0093 0.6485

Loss portfolios (smallest to largest losses)

t%25σ 2.7938 1.5760 1.77 0.0402 0.5630

t%50σ 1.1549 1.4666 0.79 0.2168 0.6985

t%75σ 3.7202 1.9391 1.92 0.0295 0.6801

t%100σ 6.3805 1.7908 3.56 0.0003 0.7505

Gain portfolios (smallest to largest gains)

t%25σ 0.5297 1.1435 0.46 0.3223 0.4795

t%50σ 1.1499 1.1708 0.98 0.1646 0.5449

t%75σ 1.3680 1.1771 1.16 0.1245 0.6076

t%100σ 2.0770 1.5822 1.31 0.0967 0.5711

47

Table 5 Cross-Sectional Tests on Volatility Increases for Non-Dividend versus

Dividend Paying Portfolios

This table reports the cross-sectional test results on the effect of TRA97 on the monthly volatility of the excess return of the value-weighted portfolios formed based on whether a stock pays dividends and the magnitude of dividend yield in the prior year. To mitigate the effect of large embedded capital gains or losses on stock return volatility, we only include stocks with price changes in the past 18 months prior to current month to be less than 5 percent. See tables 1, 2 and 3 for variable definitions. The sample period covers January of 1993 to December of 2002. Post is a dummy variable which takes value of 1 if the observation is after 10/1/1997 and 0 if it is before 3/31/1997. The numbers in parentheses are p-values. The p-value for variables post, HVP and PostxHVP are based on one-sided test.

Variable Predicted ND vs. D ND vs. LY ND vs. HY

Post 2.1128 1.5824 1.7799

(0.0003) (0.0120) (0.0005)

HVP 1.7657 1.1199 1.7699

(0.0030) (0.0190) (0.0075)

PostxHVP + 1.1591 0.7928 1.6196

(0.0177) (0.0612) (0.0021)

D/A 0.3834 -1.0165 2.1152

(0.7765) (0.4388) (0.0772)

Turnover -3.1389 -2.7996 0.1785

(0.3747) (0.4151) (0.9591)

BidAskSpread 0.2811 -0.3501 0.4603

(0.8010) (0.7482) (0.6519)

P/E ratio 0.0026 -0.0020 0.0001

(0.0977) (0.3633) (0.8995)

IND 0.0175 0.0350 -0.0611

(0.7552) (0.5014) (0.1880)

CV earnings -0.0024 0.0015 -0.0041

(0.8564) (0.9107) (0.7540)

Size -0.1170 -0.2777 0.0767

(0.5200) (0.1282) (0.6449)

N 224 224 224

-2 log likelihood 743.3 767.9 731.8

48

Table 6 Cross-Sectional Test of Volatility Increases for Losses and Gain portfolios

This table reports the cross-sectional test results on the effect of TRA97 on the monthly volatility of the excess return of the value-weighted portfolios formed based on the price depreciation (appreciation) in the past 18 months prior to current month. Only non-dividend paying stocks in the past year are included. See tables 1, 2 and 3 for variable definitions. The sample period covers January of 1993 to December of 2002. Post is a dummy variable which takes value of 1 if the observation is after 10/1/1997 and 0 if it is before 3/31/1997. The numbers in parentheses are p-values. The p-value for variables post, HVP and PostxHVP are based on one-sided test.

Variable Predicted LgL. vs. SmL. LgG. vs. SmG.

Post 2.6979 0.5528

(0.0013) (0.2551)

HVP 1.8396 1.1116

(0.0042) (0.0319)

PostxHVP + 1.0952 0.0348

(0.0527) (0.4760)

D/A 3.4841 -2.3868

(0.0647) (0.3375)

Turnover 4.0660 7.2320

(0.1957) (0.0616)

BidAskSpread 0.1074 0.0201

(0.8851) (0.9369)

P/E ratio -0.0017 0.0077

(0.7274) (0.2645)

IND -0.0617 -0.0627

(0.3121) (0.3479)

CV earnings 0.0036 -0.0027

(0.2304) (0.3535)

Size 0.2287 0.3043

(0.2630) (0.1081)

N 224 224

-2 log likelihood 860.0 857.8

49

Table 7 Robustness Check on Cross-Sectional Volatility Increase Test

This table reports the robustness test results of volatility increase for different portfolios. Post is a dummy variable which takes value of 1 if the observation is after 10/1/1997 and 0 if it is before 3/31/1997. HVP is a dummy variable which takes value of 0 if the observation is in a benchmark portfolio and 1 if it is in an alternative portfolio. The last

column reports the probability of a one-sided test on a positive coefficient for .HVPPost× The sample period

covers January of 1993 to December of 2002.

Break point Variable Estimate Std. Error t-statistic Prob

0=β

Panel A: Non-dividend paying Vs. dividend-paying portfolios

4/1994 – 9/1994 PostxHVP 1.0380 0.7424 1.40 0.1637

4/1995 – 9/1995 PostxHVP 0.9496 0.5928 1.60 0.1109

4/1996 – 9/1996 PostxHVP 0.8098 0.5260 1.54 0.1254

Panel B: Large losses (upper 25%) Vs. small losses (lower 25%) portfolios

4/1994 – 9/1994 PostxHVP 0.1372 0.9827 0.14 0.8891

4/1995 – 9/1995 PostxHVP -0.5003 0.8189 -0.61 0.5420

4/1996 – 9/1996 PostxHVP 0.0397 0.7701 0.05 0.9590

Panel C: Large gains (upper 25%) Vs. small gain (lower 25%) portfolios

4/1994 – 9/1994 PostxHVP -0.0974 0.8800 -0.11 0.9120

4/1995 – 9/1995 PostxHVP -0.0395 0.6626 -0.06 0.9526

4/1996 – 9/1996 PostxHVP -0.2536 0.5971 -0.42 0.6715

50

Table 8 Test for Volatility Changes for Non-Dividend and Dividend Paying

Portfolios with Low and High Individual Ownership

This table reports the test results of time series and cross-sectional analyses on the effect of TRA97 on the monthly volatility of the excess return of the value-weighted portfolios formed based on a stock’s dividend distribution in the prior year and the detrended individual ownership in the most recent past quarter. Stocks with detrended individual ownership in the lower 50 percentile are included in the low individual ownership portfolios (Low IND) and stocks with detrended individual ownership is the upper 50 percentile are included in the high individual ownership portfolios (High IND). The price change in the past 18 months prior to current month is restricted to less than 5 percent. The sample period covers January of 1993 to December of 2002. Post is a dummy variable which takes value of 1 if the observation is after 10/1/1997 and 0 if it is before 3/31/1997. The numbers in parentheses are p-values based on one-sided test.

Panel A: Time Series Analysis

Variable Dividend Paying Dividend Paying

Pred.

sign

Non-dividend

Low IND Port.

Non-dividend

High IND Port. Low IND Port. High IND Port.

Post + 3.4382 2.9993 1.6843 1.1574

(0.0109) (0.0350) (0.0273) (0.0941)

N 112 112 112 112

Adj. R2 0.2904 0.4245 0.4671 0.5852

Panel B: Cross-Sectional Analysis

Variable

Pred.

sign

Non-dividend vs. dividend paying

With low individual ownership

Non-dividend vs. dividend paying

With high individual ownership

Post + 1.6873 1.5943

(0.0041) (0.0040)

HVP + 1.8652 2.9475

(0.0012) (0.0001)

PostxHVP + 1.3540 0.1345

(0.0083) (0.3973)

N

-2 log likelihood

224

798.5

224

776.5