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Stock Volatility and Trading

Anna Agapova

Florida Atlantic University

777 Glades Rd

Boca Raton, FL 33431

aagapova@fau.edu

Margarita Kaprielyan

Florida Atlantic University

777 Glades Rd

Boca Raton, FL 33431

mkapriel@my.fau.edu

This version: October 2016

Contact author

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Stock Volatility and Trading

Abstract

Both, rational and behavioral models predict that stock volatility affects trading by investors.

Rational models of tax-induced trading predict that investors increase realization of capital losses

short term and capital gains long term (if at all) as stock volatility increases. Behavioral models

predict that disposition biases of holding on to losers and disposing of winners intensifies with

stock volatility. Even though the models have opposing predictions on how volatility affects

trading of stocks that increase or decrease in value, the theories need not be mutually exclusive.

We find that stock volatility increases trading in both losing stocks (tax-loss-harvesting

hypothesis) and wining stocks (disposition effect hypothesis).

JEL classification: G02, G10, G18

Key words: volatility, capital gains/losses, tax-induced trading, disposition effect

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1. Introduction

There is an anecdotal evidence that stock volatility affects investor trading. The latest

example of August 2015 events illustrates that at the peak of market volatility retail investors

substantially intensified trading in their brokerage stock accounts.1 However, it is not clear what

motivates the increase in trading sparked by volatility. On one hand, theories of tax-induced

trading (e.g., Constantinides, 1983, 1984) suggest a strategy of increased capital short-term loss

and long-term gain realization in more volatile stocks. On the other hand, behavioral theories

suggest that the effect of stock volatility on trading can be due to disposition effect (e.g., Kumar,

2009). Thus, it is an empirical question whether volatility indeed affects stock trading and which

of these theories drive the volatility effect on trading.

In a presence of capital gain taxes, a rational investor should use a timing option, and realize

capital gains immediately and defer capital gains Constantinides (1983). Additionally,

Constantinides (1984) shows that in a case of higher tax rates on short-term gains than on long-

term gains, profit maximizing investors should realize losses short term and gains long term, if at

all. He also establishes in the model and simulation that the strategy gives the best outcome in high

variance stocks. A competing behavioral theory of disposition effect, which is based on prospect

theory of Kahneman and Tversky (1979), suggests that investors are more reluctant to realize their

losses and more prone to dispose of winners. Theoretical behavioral finance models (Daniel,

Hirshleifer, and Subrahmanyam, 1998, 2001, Hirshleifer 2001) postulate that investor behavioral

biases intensify when stock are hard to value. In empirical tests of investor-level portfolio holdings

and trading data, Kumar (2009) finds that behavioral biases, such as disposition and

1 Wall Street Journal article from 091515 reports that on Aug. 24 the Dow Jones Industrial Average briefly dropped

by a record 1,000 points, and that August 2015 trading intensified in some brokerages by more than 40% in comparison

to the prior year. http://blogs.wsj.com/moneybeat/2015/09/15/retail-investors-set-trading-records-on-markets-most-

volatile-day/

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overconfidence biases, are stronger in stocks with higher valuation uncertainty measured with

idiosyncratic volatility, volume turnover, and firm age.

Even though the rational and behavioral models have opposing predictions on how

volatility affects trading of stocks that increase or decrease in value, the theories need not be

mutually exclusive. In a logit analysis of buy, sell and hold data of Finish investors, Grinblatt and

Keloharju (2001) find that the disposition effect and tax-loss selling are two major determinates of

the inclination to sell a stock owned by an investor.

This study provides new evidence that albeit presence of disposition effect throughout the

year, the abnormal trading predicted under tax-loss-selling hypothesis is also present and linked to

market and stock’s volatility. We find that as market volatility increases, so does the trading of

short-term and long-term losers, but not short-term or long-term winners; the finding consistent

with tax-induced trading behavior throughout the year. During large spikes in market volatility the

abnormal trading of losers (winners) intensifies (decreases), which is consistent with tax-

harvesting strategies; but when market uncertainty reaches very high levels (99th percentile), the

trading of winners also increases, which is consistent with the disposition effect.

Constantinides (1983) proves that the optimal liquidation policy is to realize losses

immediately and defer gain forever. Also, Constantinides (1984) shows that it is optimal to realize

losses immediately (short term) and gains long term with re-establishing the gaining stock position

to short-term basis, especially for high volatility stocks. Conditioning abnormal trading of losers

and winners on the stock volatility leads to findings consistent with Kumar (2009); the results

signal to disposition effect increasing in the stock volatility with higher marginal effect of stock’s

volatility on the trading of winners than losers. However, also consistent with Constantinides

(1984), the findings are in support of loss-harvesting increasing in the stock’s volatility throughout

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the year, with abnormal trading of losers increasing in volatility. Moreover, when we examine

turn-of-the-year trading patterns, the evidence shows that market environment plays a stronger role

in motivating the tax-loss harvesting strategies, while stock volatility drives the disposition effect.

Finally, to disentangle the disposition bias and tax-induced motivated trading, we examine

the trading behavior for long-term positions, while accounting for short-term disposition effect.

We find that abnormal trading of losers increases in the security’s idiosyncratic volatility if it is

also a short-term loser and unaffected if it is a short-term winner, which supports tax-harvesting

strategy but not the disposition effect. The findings support the conjecture that tax considerations

play a major role in the trading decisions of the investors not only at the end of the year, but also

throughout the year, and that the strategies implemented are affected by both the market and stock

volatilities.

The paper is organized as follows: Section 2 contains a literature review and hypotheses

development; Section 3 describes data selection process and the methodology; Section 4 presents

the empirical results; and Section 5 provides concluding remarks and implications of the study.

2. Related Literature and Hypotheses Development

Several studies find support for tax-induced trading at the turn-of-the year, with abnormal

trading of losers in December and winners in January, which is exaggerated in bull markets (Dyl

1977; D’Mello, Ferris, Hwang 2003; Lakonishok and Smidt, 1986. The tax-induced trading is also

evidenced by studies examining the trading behavior around the tax changes. Bolster, Lindsey,

and Mitrusi (1989) find increase in abnormal trading of winners in December of 1986 preceding

capital gain tax increase, while Seida and Wempe (2000) also find decrease in trading of losers in

December of 1986. Agapova and Volkov (2015) examine sensitivity of tax-induced trading of

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winners and losers in response to tax changes, and find that investors alter the trading of winners

and losers asymmetrically.

However, throughout the year, the evidence is strong for disposition effect (Ferris, Haugen

and Makhija, 1988; Ivkovich, Poterba, and Weisbenner, 2005), especially after 1986 when the

incentives to recognize the losses throughout the year decreased as the tax losses no longer expired

(D’Mello, Ferris, Hwang, 2003).

Constantinides (1983) demonstrates that an investor has a timing option, to recognize

capital losses short-term and defer recognition of capital gains, due to a differential in the tax

treatment of short-term versus long-term capital gains/losses. The model provides support for the

January anomaly and several studies find evidence of the abnormal trading of losers in December,

as well as abnormal trading of winners in January (Dyl, 1977; Lakonishok and Smidt, 1986; Sikes,

2014).

In a subsequent study, Constantinides (1984) introduces a second timing option and shows

that realization of short-term losses is always preferable, while realization of long-term gains in

order to re-establish the short-term status of the position is favorable for the stocks that exhibit

moderate to high volatility. The existence of such a timing option and its value depends on the

difference between tax rate on the short-term and long-term gains. The treatment of the capital

gain and losses in U.S. has varied through time. The Tax Reform of 1986 enacted an increase in

the long-term capital gain tax rates and thus provided a natural experiment environment to test tax

motivated investor behavior. Bolster et al. (1989) find that the abnormal trading of winners

increases in December prior to the law taking effect and decreases in January (contrary to the usual

pattern). However, the pattern for losers is not altered and the abnormal trading of losers persists

as in previous Decembers during a static tax regime. On the other hand, by using the data on

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individual trades, Seida and Wempe (2000) find that the trading pattern for losers is also altered

and the abnormal selling of losers on December 1986 is lower compared to other Decembers.

Moreover, they find that post-1986, the trading of losers (winners) increases (decreases), implying

that an increase in capital gain tax rates intensifies the “lock-in effect” rather than increases the tax

collections. 2

The Tax Payer Relief Act of 1997, which took an effect on May 7th, 1997, emphasized the

incentives for recognition of short-term losses and long-term gains due to reduction in long-term

capital gain tax rates.3 Subsequent Jobs and Growth Tax Relief Reconciliation Act of 2003

[JGTRRA of 2003] led to a further decrease in the long-term capital gain tax rates from 20% to

15%, with the change being retroactive. Although in 2012, JGTRRA of 2003 was expected to

expire at the end of the year, the preferential treatment of long-term capital gains was extended.

Short-term gains/losses are taxed at an ordinary income marginal tax rate, while long-term

gains/losses are taxed at lower rates, with a maximum of 23.9% for the highest net worth

individuals4, thus creating incentives to follow Constantinides (1984) strategy. These incentives

are exaggerated with the variability of the underlying security (Constantinides, 1984). Following

Constantinides (1984), the abnormal trading of stocks that generate positive cumulative capital

gain yields over the past year is expected to increase in the volatility of the stock. Although most

studies concentrate on measuring the evidence of tax-induced trading at the turn-of-the year, the

recognition of long-term gains is predicted to occur on the continuous basis conditional upon the

volatility of the stock. The increase in volatility increases the value of the timing option to liquidate

2 Lock-in effect – investors are unwilling to liquidate appreciated positions as tax rates increase, due to higher tax

liability. 3 Subsequently on January 1st, 2003, the long-term capital gain tax rate was further reduced after Jobs and Growth Tax

Relief Reconciliation Act of 2003 took effect 4 http://www.wsj.com/articles/got-losses-a-tax-break-could-soothe-the-pain-1440615934?alg=y

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the long-term “winning” position to re-establish the short-term status. Higher volatility leads to

higher probability the stock will decrease in value, thus the value of re-establishing the short-term

status to recognize loss in the future increases in the variability of the stock. Constantinides (1984)

simulates different trading strategies and finds that the strategy of realizing losses short-term for

high variance stocks leads to higher returns compared to the same strategy implemented for low

variance stocks. He also finds that the profitability of realizing losses short-term and gains long-

term for high variance stocks is higher than for lower variance stocks.

Hypothesis 1: Under tax-induced motives, the abnormal trading volume of losers (short-term and

long-term) increases in stock and market volatility, while abnormal trading of short-term winners

decreases and long-term winners increases in stock and market volatility.

Although tax considerations predict active trading of short-term and long-term losers and

long-term winners (with differential short-term versus long-term tax rates) and less trading of long-

term winners, the disposition effect predicts the opposite. The disposition effect is an empirical

finding that investors tend to dispose of winners and hold onto the losing stocks (Grinblatt and

Han, 2005). Disposition effect is explained by behavioral biases of the investors, such as mental

accounting and feelings of regret (Shefrin and Statman, 1985) or the prospect theory (Kahnman

and Tvesrky, 1979). Under the prospect theory, investors prefer sure gains over larger gains that

are merely probable and prefer larger probable losses over smaller sure losses (Kahnman and

Tvesrky, 1979). The theory explains the disposition effect, since the investors are risk-averse to

the gains and risk-seeking towards losses.

The trading pattern observed during the months other than December and January provides

evidence for the disposition effect. Odean (1998) finds that individual investors on average sell

winners at a rate 50% higher than selling the losers. The disposition effect of holding on to losers

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and selling winners does not lead to excess profits for the investors, especially for investors with

taxable accounts (Odean, 1998). The effect is also found to be present among trading by the

institutional investors (Shapira and Venezia, 2001; Frazzini, 2006), while is more pronounced

among individual investors (Feng and Seasholes, 2005). However, during the months when most

investors rebalance for tax purposes, the evidence contrary to disposition effect is found.

Laknishok and Smidt (1986) find that abnormal trading for losers is higher than winners during

December. Seida and Wempe (2000) observe decrease in the trading of winners and increase in

the trading of losers post-1986 tax reform, which enacted an increase in the capital gain tax. The

findings support the tax-induced trading hypothesis, compared to the disposition effect hypothesis.

Predictions under the prospect theory are exaggerated by increase in uncertainty

surrounding the underlying security’s payoffs. According to Kahneman and Tversky (1979),

uncertain environment increases the desire to accept certain gains and decreases the undesirability

of possible losses. Kahneman & Tversky (1979) show that marginal utility of price increase in the

gain domain is lower than the marginal disutility of an equivalent downward price change. Thus,

after a gain, further gain would only increase utility marginally compared to a larger utility loss if

the gain is followed by a loss. However, in the loss domain, marginal disutility of a loss following

a loss is lower than the utility gained in case of an equivalent gain. Increase in market volatility

implies higher probabilities of gains and losses, thus exaggerating the risk-aversion in the gain

domain and risk-seeking in the loss domain. In other words, with the increase in market volatility,

investors are more likely to take a gamble in the loss domain and recognize sure gain in the gain

domain.

Increase in stock’s volatility also increases the desire to recognize sure gains and delay

losses, as higher stock volatility implies higher probabilities of stock price

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appreciation/depreciation. Thus, the disposition effect is also expected to increase in stock’s

volatility. Kumar (2009) finds that disposition effect is larger for stocks that exhibit higher

idiosyncratic volatility. Option theory also predicts holding onto the losers as the volatility

increases. At the end of holding period, an investor is faced with a decision of whether to liquidate

the stock or hold it. The decision to hold on the stock can be viewed as a call option, which is more

valuable with increase in the stock’s volatility. Increase in the volatility leads to an increase in

potential gamble payoffs. Since investors are risk-loving towards losses, increase in uncertainty

leads to desire to delay the loss recognition.

Hypothesis 2: Under the disposition bias, the abnormal trading of losers (short-term and long-

term) decreases in stock and market volatility, while abnormal trading of winner (short-term and

long-term) increases in stock and market volatility.

The tax-induced selling has also been shown to explain the January effect, the anomaly of

past losers outperforming winners in January. D’Mello et al. (2003) find that abnormal selling of

losers increases in December, while abnormal selling of winners increases in January. They show

that this trading pattern leads directly to the January anomaly observed in the stock returns and the

magnitude of the January effect is found to be stronger for the small firms (that are typically

characterized by higher volatility). The January effect is found to be stronger during high volatility

markets (Gu, 2003), but the causation of this phenomena is left unexplored. Even if throughout the

year, investors implement tax-loss harvesting strategies, at the turn of the year as most investors

close out the books, we would expect to see the tax motivated selling intensified for higher

volatility stocks and during higher volatility markets, based on Constantinides predictions. In a

case of the winners, increase in volatility would further delay the recognition of the gain that results

in the tax liability.

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Hypothesis 3: Trading volume of the losers in December is directly related to the stock and market

volatility, while the abnormal trading volume of the winners in January following high stock

market volatility is lower than abnormal trading in years characterized by lower volatility.

The increase in the abnormal trading volume of last year winners could be caused by the

tax-motivation of the investors, but also by the disposition effect, which is found to be exaggerated

for securities that are hard to value, measured by the idiosyncratic volatility (Kumar, 2009).

However, by examining abnormal trading of short-term and long-term winners’ sensitivity to

volatility allows to disentangle the two effects. The disposition effect is a short-term phenomenon,

while sale of long-term winners is preferable under the tax-loss-selling hypothesis put forth by

Constantinides (1984). If a stock appreciates in value long-term, but decreases in value short-term,

then the investor not engaging in tax strategy is expected to hold onto the stock. On the contrary,

an investor following a tax strategy is expected to liquidate the stock, in order to re-establish the

short-term status of the position. Recent decrease in the value of the stock may even provide

additional incentives to trade the long-term winner, in anticipation of short-term losses.

Hypothesis 4: Under tax induced strategy, the abnormal trading volume of long-term winners’

increases in stock’s and market volatility if the stock is a short-term loser. Under disposition bias,

the abnormal trading of long-term losers increases in stock and market volatility if the stock is a

short-term winner.

3. Data and Methodology

The sample consists of individual securities listed on NYSE/AMEX during January 1998

through December 2015. During the sample period, the long-term capital gain was lowered once

from 20% to 15%, with JGTRRA coming in effect on January 1, 2003, and there was unrealized

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anticipation of capital gain increase in December 2012.5 To avoid the micro-cap bias, all stocks

with prices less than $5 are omitted from the sample. Individual securities’ and S&P500 daily

returns, excluding dividends come from CRSP.

Using standard volume event methodology, described in Campbell and Wasley (1996), the

log-transformed cumulative abnormal relative volume (CAVLt) is estimated over [-21, 0] event

window, with event day 0 occurring on the last trading date of each month, as recorded in CRSP.

The abnormal relative volume is based on the estimation period [-252,-42], using value-weighted

CRSP trading volume of securities traded only on NYSE/AMEX.

We classify stocks into five (uneven) groups based on their performance distribution over

a long and a short run. Long-run classification is based on the long-term cumulative returns,

excluding dividends (long-term capital gains for tax purposes), over 13 month period, t - 14 months

to t-1 months, relative to a trading month t. Buy-and-hold return excluding dividends equals (Pricet-

1 /Pricet-14) – 1, with the closing prices on the last day of the trading day in a specific month, as

reported by CRSP. Summary statistics reveal that 10th percentile average long-term return is -

35.95% and 90th percentile average month return is 48% leading to the choice in rankings. The

securities are ranked each month into the following five groups: group 1 includes stocks with

returns < -36%; group 2 (-36%≤ BHR≤-8%); group 3 (-8% <BHR <20%); group 4 (28% ≤BHR

≤48%); group 5 with (BHR>48%). Securities in group 1 are extreme long-term losers, while

securities in group 5 are extreme long-term winners.

To account for abnormal trading in response to short-term unrealized loss/gains, securities

are also classified into five categories based on the past month returns (excluding dividends).

Summary statistics reveal that 10th percentile average month return is -9.79% and 90th percentile

5 The act was set to expire in January 2013; however, the preferential tax treatment of long-term capital gains was

extended.

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average month return is 11.13%2% leading to the following choice in rakings: Group 1S (1-month

return < -10%), Group 2S (-10%≤1-month return ≤-5%), Group 3S (-5%<1-month return <5%),

Group 4S (5%≤1-month return ≤10%) and Group 5S (1-month return >10%). Table 1 Panel A

reports descriptive statistics of the groups.

<Table 1 should be here>

Final sample consists of 12,968 unique securities, with maximum 216 monthly

observations from January 1998 through December 2015 period.

The following variables are used in the analysis below:6

IVOLt-1 = monthly idiosyncratic volatility of daily returns.

IVOL[t-1,t-13] = average monthly idiosyncratic volatility of returns.

Betat-1 = market beta in the previous month.

Beta[t-1,t-13] = average beta over a year ending prior to the abnormal trading month.

VOLt-1 = monthly standard deviation of daily returns, in the month prior to time t.

VOL[t-1, t-13] = annual standard deviation of daily returns, over a year ending a month prior to

abnormal trading month t.

S&PVOLt-1 = monthly standard deviation of S&P500 daily returns during a month prior to

abnormal trading volume.

ChangeS&PVOLt-1 = change in monthly standard deviation of S&P500 daily returns in the month

prior to the abnormal trading volume month.

S&PVOL[t-1,t-13] = annual standard deviation of S&P500 daily returns over the year prior to month

t.

6 We apply market model to the time-series of daily stock returns, requiring at least 17 observations per month, to

obtain monthly beta and monthly idiosyncratic volatility of daily returns. Using the same requirement of 17 days, we

also obtain monthly standard deviation of daily returns.

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VIXt-1 = VIX as reported at the end of the month prior to month t.

ChangeVIXt-1 = change in VIX over the month prior to month t.

S&PReturnt-1 = S&P500 returns in the month prior to month t.

S&PReturn[t-1,t-14] = S&P500 return over 13-month period ending one month prior to month t.

BidAski,t-1 is the average daily𝐴𝑠𝑘−𝐵𝑖𝑑

(𝐴𝑠𝑘+𝐵𝑖𝑑)/2 during the month previous to the abnormal trading

volume estimation window as reported by CRSP and controls for stock’s liquidity.

LogMV i,t-1 equals to the natural log of the stock’s market capitalization in the previous month,

estimated by multiplying shares outstanding by the closing price as reported by CRSP and controls

for the size effect that may influence the trading patterns.

DivYieldi,t-1 equals total dividends paid during previous year divided by the ending price, as

reported by CRSP.

Analystst-1 equals log(1+analyst coverage), where analyst coverage is the average number of

analysts covering the stock over the year prior to the year in which abnormal trading is measured.

December is an indicator variable and equals 1 if the observation occurs in December, and 0

otherwise. January is an indicator variable and equals 1 if the observation occurs in January, and

0 otherwise.

Summary statistics in Table 1 Panel B indicate that monthly standard deviation of an

average security in the market is 8.70%, while the 13-month volatility on average is 33.1%. Most

volatile (least volatile) stock exhibits monthly standard deviation of 34.43% (1.04%). Over the

sample period, total market volatility fluctuates from 1.18% to 23.33%, with the market suffering

the largest loss of 16.94% and maximum gain of 10.77%. Dividend yields vary significantly cross-

sectionally, with the highest yield of 21.76%, and median dividend yield of 1.63%. The size of the

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firms included in the sample also varies significantly from $47,562.50 to $581 billion. Analyst

coverage is on average 1.95, with the maximum (minimum) coverage of 3.8 (0.7).

4. Empirical Results

A. Market Volatility and Abnormal Trading

Table 2 presents the test results of the first model testing hypotheses 1 and 2: whether more

market volatility is associated with more trading in short-term losers, long-term losers and long-

term winners and decreased trading of short-term winners (tax induced strategy – Hypothesis 1)

or whether increased market volatility is associated with increased trading in winners and reduced

trading in losers (disposition effect – Hypothesis 2). The following regression model is applied

with control for time and stock fixed effects and robust standard errors:

CAVLt = α + β1MarketVOLt-1 + β2 S&PReturnt-1 + β3 LMVi,t-1 + β4 December + β5 January +

β6BidAski,t-1 + β7 DivYield i,t-1 + εi,t-1 (1)

where MarketVol is either S&PVOL or VIX.

Panel A reports results of the long-term return classification groups, while Panel B does so

for short-term return classification groups. For the long-term losers, S&PVOL and VIX coefficients

are positive and significant at least at 5 percent level, which is consistent with Hypothesis 1 that

investors employ tax-induced strategy, and realize loses more as market volatility increases. At the

same time, for the long-term winners, S&PVOL and VIX coefficients are negative and significant

at least at 1 percent level, i.e. less trading in winners as market volatility increases. The results are

in the same direction and significant for the short-term return classification groups. Thus, Table 2

results are consistent with Hypothesis 1 on tax-induced strategies, but do not show support for

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Hypothesis 2 of disposition effect presence in more volatile markets, as we observe less trading of

winning stocks in long or short term with increase of market volatility.

Consistent with previous tax-loss-selling literature, the abnormal trading of losers is

significantly higher in December compared to other months. There is also more trading in more

liquid stocks as measured with bid-ask spread, which is negative and significant for all short-term

return groups, and in all but extreme losers for long-term returns. Less information asymmetry,

measured with analyst coverage, is negatively associated with trading in winning stocks, both long

and short term. However, more analyst coverage is positively associated with trading in long-term

losers. DivYieldi,t-1 is negative and highly significant all long-term return groups, expect for

extreme winners where it is insignificant. Overall, the results reported in Table 2 suggest that in

response to market volatility, investors increase trading of losers to harvest losses and decrease the

trading of winners.

<Table 2 should be here>

Next, we examine whether extreme values of market volatility measured with SPVOL and

VIX at 95th percentile and 99th percentile, i.e., variables equal 1 if the SPVOL (VIX) is in 95th (99th)

percentile, motivate more trading. Table 3 Panel A reports the results with VIX as a measure of

market volatility, while Panel B does so for SPVOL. The results show that with more extreme

volatility in the market, extreme losers, in the long and short run, exhibit even more trading.

However, for the extreme winners the picture is mixed. The trading continues to decrease in

extreme long and short term winners when market volatility is in its 95th percentile, measured with

both SPVOL and VIX. However, the trading in short term and long term winners increases in

extreme market volatility of 99th percentile measured with VIX, and long-term winners in extreme

values of SPVOL variable, yet short term winners’ trading declines in extreme values of SPVOL

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variable. The evidence is still mostly consistent with tax motivated strategy use in volatile markets,

yet there is some indication that for the extreme winners, disposition effect may be present in very

volatile markets.

<Table 3 should be here>

B. Individual Stock and Market Volatility and Abnormal Trading

However, trading decisions may be driven not by the overall increase in market volatility,

but by increase in the difficulty to value the individual stock. We expand the regression model to

include individual stock volatility measured with standard deviation of daily stock returns over

prior month period. To isolate the effect of aggregate market volatility on the abnormal trading,

market volatility is orthogonalized with respect to individual stock volatility. We used SPVOL as

a measure of market volatility in this model. The following regression model controls for time and

stock fixed effects and robust standard errors.

CAVLt = α + β1 VOLi,t-1 + β2 SPVOLt-1 + β3S&PReturnt-1 + β4 LogMVi,t-1 + β5 December +

β6January + β7BidAski,t-1 + β8 DivYield i,t-1 + εi,t-1 (2)

Table 4 reports the estimates of the extended regression model. Results in Panel A of the

table are based on the short-term measures of stock and market volatility over prior month prior to

abnormal trading volume measure, while results in Panel B are based on long-term measures of

stock and market volatility over (-13, -1) months prior to the trading. Short-term stock volatility is

positively associated with trading in all groups of stocks – winners and losers based on long-term

and short-term horizon, while SPVOL is negatively associated with trading in all groups of stocks.7

However, when measured with long-term measures of volatility (Panel B), the results flip between

VOL and SPVOL, i.e., VOL (SPVOL) is negative (positive) across all groups of stocks, except

7 Similar result is obtained with a use of VIX instead of SPVOL in the model. The results are not tabulated.

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extreme short-term winners. The coefficient on SPVOL for the short-term extreme winners remains

negative and highly significant. Thus, there is some evidence of prevalence of tax induced strategy

of holding on to short-term extreme winners, especially with increased volatility for the stock and

the market.

<Table 4 should be here>

When stock’s total volatility is separated into idiosyncratic volatility and beta during one

month before t in the extended model, as reported in Panel C of Table 4, the effect of SPVOL

remains the same as in the Panel A, i.e., it is negative in most of the groups and return measure

horizon, including extreme losers and winners. However, the effect of individual stock volatility

on abnormal trading is mostly driven by idiosyncratic stock volatility (IVOL), which is highly

positive and significant in this model, while Beta is negative in the short-term return groups and

mostly insignificant in long-term return groups. December and liquidity effects (Bid-Ask spread

and Analyst coverage) are in the same direction as in the models with only market volatility.

C. Individual Stock and Market Volatility, Short-term Return Status and Abnormal Trading

To test Hypothesis 4 we expand the models (1) and (2) to incorporate the status of the stock

in the short-term horizon. The results in Table 4 indicate that increase in individual stock volatility

(VOLi,t-1) is directly related to increase in trading of all stock groups. Since disposition effect could

be driving the marginal effect of volatility on the abnormal trading of winners, the Models (1) and

(2) are adjusted to include the effects of trading on short-term winners and losses. Short-term Loser

is an indicator variable equals 1 if the stock lost more than 10% in value in the previous month,

while Short-term Winner equals 1 if the stock gained more than 10% in value in the previous

month:

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CAVLt = α + β1VOLi,t-1 + β1Short-term Loser + β2Short-Term Winner + β3Short-term

Loser*VOLi,t-1 + β4Short-Term Winner*VOLi,t-1 + β5OrthMarketVOLt-1 + β6S&PReturnt-1 +

β7LogMVi,t-1 + β8December + β9January + β10BidAski,t-1 + β11DivYield i,t-1 + εi,t-1 (3)

Table 5 reports the results of Hypothesis 4 tests, conditioning for abnormal trading in

response to short-term unrealized losses and gains. Short-term winner or loser status of a stock has

a positive effect on abnormal trading of the stocks across all groups of long-term return (losers and

winners). Market volatility measured with SPVOL or VIX has the same effect as reported in Table

2, trading of losers increases with market volatility, while trading of winners decreases with market

volatility, which is consistent with tax-induced strategies (Hypothesis 1). Interaction term of Short-

term loser and Market Volatility (whether measured with SPVOL or VIX) is negative across all

groups of long-term return, which is consistent with disposition effect hypothesis that recent status

of a stock being a loser decreases abnormal trading with increased market volatility. Interaction

term S&PVOLt-1 *Short-term Winnert-1 is positive for group 5 (extreme long-term winners) and no

other group, which is consistent with disposition effect explanation that investors with such bias

increase trading of winners with increased market volatility. The results though is not present with

VIX measure of market volatility.

<Table 5 should be here>

Next, we examine whether short-term return status interacted with stock volatility

(idiosyncratic and beta), controlling for market volatility, has an effect on the stock trading activity.

Panel B of Table 5 reports the results. Results provide evidence for tax induced strategy

explanation - Short-Term Loser is positive for all but extreme long-term winner group, while

Short-Term Winner is negative for long-term loser group 1. However, Short-Term Winner is

20

positive for long-term winner groups 3 through 5, which is consistent with disposition effect that

investors tend to sell winners.

As predicted by prospect theory and also consistent by Kumar (2009), the abnormal trading

of short-term winners increases in the idiosyncratic volatility of the stock if it is a long-term winner

(coefficient on Short-Term Winner*IVOLi,t-1 is positive and significant at 1% for groups 3

through 5). However, after controlling for this short-term stock’s return, the abnormal trading of

long-term losers is positively related to increase in the security’s idiosyncratic volatility if it is a

short-term loser and unaffected if it is a short-term winner, which is consistent with tax induced

strategies. Coefficients on the interaction terms of Short-Term Loser*Betai,t-1 and Short-Term

Winner*Betai,t-1 are also consistent with tax-induced strategy explanation: Short-Term

Loser*Betai,t-1 is positive for groups 1, 3 and 5, i.e. trading increases in short-term losers with

increased stock beta whether it is losing or winning stock in a long-term; Short-Term

Winner*Betai,t-1 is positive for group 1, but negative for groups 3, 4 and 5, meaning overall losing

status increases trading of a stock with its systematic risk. The result is consistent with

Constantinides (1984) that trading of long-term winners is preferable in order to re-establish the

position. If the stock gains in value, but drops in value recently, the investor has more incentives

to re-establish the position in order to recognize potential tax loss in the future, while recognizing

reduced paper long-term gain.

D. Individual Stock Volatility Sorts and Abnormal Trading

According to Constantinides (1984), the individual stock volatility should play a major role

in a decision to execute the tax-trading strategy, as the profits increase from low to high volatility

stocks. We double sort stocks based on the stock’s return rank and the volatility decile. The results

21

of the sort are presented in Table 6. Panels A - C display the results of the sorts based on long-

term classification of losers and winners, with Group 1 (Group 5) including extreme losers

(winners), while Panel D - F display results based on short-term (previous month returns)

classification of losers (group 1S) and winners (group 5S). The stocks are sorted into volatility

deciles in an ascending order. To further separate the turn-of-the-year effects from the intra-year

trading, Table 6 presents results based on sorts over February through November, December and

January separately.

Across all groups (long-term winners and losers) lower volatility stocks are associated with

less than average trading volume during the calendar year (Panel A). The abnormal volume

generally increases from low volatility to high volatility stocks for each group. The effects of tax-

induced trading are evident for extreme losers with difference in abnormal trading between most

volatile and least volatile stocks of 2.04 and highly significant. For extreme winners, the same

trend is observed with a larger difference of 9.60, which is consistent with the predictions under

both tax-induced and disposition effect hypotheses.

Abnormal trading of losers in December, when investors typically increase implementation

of tax loss recognition, actually decreases from 1st (least volatile) to 2nd decile and increases from

9th to 10th volatility decile (Panel B). We interpret these results as evidence of both the disposition

effect and tax-induced trading in December. Under the disposition bias, investors are expected to

trade most volatile losers less, since the probability of large gamble payoff for these stocks is

higher. Holding onto to a long-term losing position of more than -36%, when monthly standard

deviation of that stock’s return is 2.38% (decile 1) has lower probability of large gamble payoff

than holding onto the same losing position when monthly standard deviation of that stock’s return

is 4.01% (decile 2). Under disposition effect, we would also see decrease in abnormal trading from

22

decile 9 to decile 10; however, we see an opposite pattern. Thus, we interpret the results as

domination of disposition bias for lowest volatility stocks and presence of tax-induced trading for

most volatile stocks. Since tax strategy is most profitable if the loser stock is liquidated short-term

(higher tax credit due to higher tax rate on short-term loss vs. long-term loss), analysis of abnormal

trading in December based on short-term loser/winner classification is provided in Panel E. The

results are similar to the results observed under long-term classification of losers.

Abnormal trading of long-term winners is also consistent with Constantinides (1984)

predictions. In the month of January, the abnormal trading of long-term winners is significantly

higher (5.37) for most volatile stocks than for least volatile stocks (Panel C). The abnormal trading

of short-term winners is pronounced in the extremes, with the difference between abnormal trading

in extremes insignificant (Panel F). It is important to note, then when we comparing the intrayear

abnormal trading of losers and winners in the same volatility decile (Group 1 vs. Group 5), almost

in every volatility decile, we see strong support of disposition effect, consistent with previous

studies. However, when we compare across volatility deciles, we observe evidence of tax-induced

trading. We conclude that when an investor holds two stocks characterized by similar volatility,

but one with positive returns and one with negative returns, she is likely to hold on to the losing

position and lock in her gain in the winning position. However, when she holds two positions with

similar performance, but different volatility, she weighs the payoff on the tax strategy versus a

probability of obtaining higher returns based on that stock’s recent volatility.

<Table 6 should be here>

E. Stock and Market volatility and turn-of-the-year abnormal trading

Since most tax-loss-selling occurs in December, the marginal effect of market volatility on

abnormal trading of winners and losers should be more pronounced during the turn-of-the-year.

23

Model (1) is fitted separately for each group of stocks, with interaction terms between December

(January) and VIXt-1. Results are reported in Table 7 (Panel A). We observe that abnormal trading

of losers (Group 2 – returns between -36% and -8%) in December increases in implied market

volatility. We find no support for extreme loser December trading (long-term returns less than -

36%) increase in market volatility. Extreme winner trading in December also increases in market

volatility, but overall trading of long-term winners is lower in December. The results support the

volatility driven disposition effect on the winner side partially offsetting the tax-induced turn-of-

the year strategies.

The next set of results reported in Table 7 (Panel A) indicate that without controlling for

market conditions in December, individual stock volatility has no effect on loser/winner trading

patterns in December or January. However, when we control for market volatility at the turn-of-

the year in Panel B, we observe that long-term extreme losers’ abnormal trading in December

decreases in stock volatility, which is consistent with disposition effect. December abnormal

trading of losers (returns Group 2 – returns between -36% and -8%) increases with implied market

volatility and January trading of winners decreases in market volatility, as predicted under the tax-

induced hypothesis. Taken together, results signal that turn-of-the-year tax strategies are

conditioned on the market uncertainty, while stock volatility (difficulty valuing the stock) drives

the disposition effect.

<Table 7 should be here>

5. Conclusion

Disposition effect and tax-loss-selling hypotheses are competing models trying to explain

investor trading behavior. Using tax-induced strategies explanations and prospect theory that

24

explains the behavioral tendencies of investors to hold onto losers and dispose of winners

(disposition effect), this paper examines effect of market and individual securities’ volatility on

investors’ trading activities of losers and winners. Consistent with tax-induced strategies, spike in

market volatility leads to abnormal trading of long-term losers, but not winners. The positive

relation between market volatility and abnormal trading of losers is exaggerated during December,

when traders are more likely engage in tax-induced strategies. Finally, the results support the

predictions set forth by Constantinides (1984) that abnormal trading of long-term losers is

positively related to the volatility of the stock even after accounting for the short-term disposition

effect. We find an evidence of tax-induced strategy implementation on the winning positions, with

the positive relationship between the stock’s volatility and abnormal trading of winners increasing

if the stock is a short-term loser, which is inconsistent with disposition effect.

Whether disposition effect or tax-loss-selling dominates the trading decisions has been a

focus of many studies. This study finds support for both, as these theories are not mutually

exclusive. Most importantly, the evidence exists that tax-induced strategies take place throughout

the year, especially for high volatility stocks and during spikes in market volatility. Thus, what has

generally been thought of as a turn-of-the-year phenomenon, occurs throughout the year.

Moreover, the unexplained strong January effect during higher volatile markets could be a source

of tax-induced trading.

25

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27

Table 1. Summary Statistics CAVLt is log-transformed abnormal relative volume to the value-weighted CRSP-based log-transformed relative

volume, cumulative over [-21, 0] event window, with event day 0 occurring on the last trading date of each month.

VOLi,t-1 is monthly standard deviation of stock’s daily returns, excluding dividends, over previous month. S&PVOLt-1

is monthly standard deviation of S&P500 index daily returns over previous month. S&PReturnt-1 is monthly return on

S&P500 index as reported by CRSP over previous month. DivYieldi,t-1 is total dividends paid during previous year

divided by the ending price, as reported by CRSP. VIXt-1 is a measure of implied volatility over the next 30 days.

LogMVi,t-1 is natural log of market value, calculated as the closing price on the last trading day of the previous month

multiplied by total shares outstanding. BidAski,t-1 is (Ask – Bid)/(Ask+Bid)/2 during previous month, Analystst-1

equals log(1+analyst coverage).

Panel A

Groups 1 2 3 4 5

13 month return -50.04% -17.88% 7.26% 34.72% 99.79%

St. Dev. 10.73% 8.17% 7.98% 8.11% 47.78%

Max -35.00% -6.00% 23.00% 52.00% 204.26%

Min -69.20% -35.00% -6.00% 23.00% 52.00%

Number of observations 64,444 156,605 261,615 97,963 65,797

Groups 1 2 3 4 5

1-month return -16.43% -7.16% 0.17% 7.13% 17.81%

St. Dev. 5.37% 1.42% 2.58% 1.42% 7.14%

Max -10.00% -5.00% 5.00% 10.00% 33.38%

Min -26.89% -10.00% -5.00% 5.00% 10.00%

Number of observations 68,221 78,576 384,836 89,549 82,703

Panel B N Mean Median Std. Dev. Min Max

CAVL 700,051 0.131 -0.311 12.373 -39.557 43.985

VOLt-1 700,005 0.087 0.071 0.061 0.010 0.343

VOL[t-1, t-13] 661,547 0.332 0.289 0.203 0.057 1.169

IVOLt-1 699,648 0.073 0.059 0.053 0.007 0.291

IVOL[t-1,t-13] 645,444 0.074 0.065 0.044 0.009 0.231

Betat-1 699,660 0.736 0.704 0.759 -1.459 3.097

Beta[t-1,t-13] 645,444 0.749 0.737 0.567 -0.595 2.328

VIXt-1 745,589 20.93 19.470 7.923 10.42 59.89

S&PVOLt-1 745,589 0.049 0.043 0.029 0.012 0.233

ChangeVIXt-1 745,589 -0.060 -0.370 4.680 -15.28 20.50

ChangeS&PVOLt-1 745,589 0.000 -0.001 0.021 -0.063 0.097

S&PVOL[t-1,t-13] 745,589 0.181 0.178 0.077 0.095 0.454

BidAski,t-1 693,920 0.008 0.002 0.013 0.000 0.066

DivYieldi,t-1 712,527 0.030 0.016 0.039 0.000 0.218

S&PReturn[t-1,t-14] 745,589 0.082 0.114 0.180 -0.467 0.591

S&PReturnt-1 745,589 0.005 0.010 0.044 -0.169 0.108

LogMV i,t-1 708,909 13.255 13.255 2.091 3.862 20.078

Analystst-1 403,110 1.950 1.969 0.762 0.693 3.795

28

Table 2. Market Volatility Effect on Abnormal Trading The table presents results of cross-sectional regression of CAVLt, which is log-transformed abnormal relative volume to the value-weighted CRSP-based log-

transformed relative volume, cumulative over [-21, 0] event window, with event day 0 occurring on the last trading date of each month, on the following variables:

S&PVOLt-1 is monthly standard deviation of S&P500 index daily returns over previous month. VIXt-1 is a measure of implied volatility over the next 30 days.

S&PReturnt-1 is monthly return on S&P500 index as reported by CRSP over previous month. LogMVi,t-1 is natural log of market value, calculated as the closing

price on the last trading day of the previous month multiplied by total shares outstanding. December (January) equals 1 if observation occurs in December (January),

and 0 otherwise. BidAski,t-1 is (Ask – Bid)/(Ask+Bid)/2 during previous month. DivYieldi,t-1 is total dividends paid during previous year divided by the ending price,

Analystst-1 equals log(1+analyst coverage). The model controls for year fixed effects. The models are fitted separately for each group of stocks: Group 1 (ret < -

20%); Group 2 (-20%≤ ret≤-10%); Group 3 (-10% <ret <10%); Group 4 (10% ≤ret ≤20%); Group 5 with (ret>20%). t-statistics are reported in parenthesis and a

robust to heteroskedasticity using White (1980) method. *, ** and *** indicate statistical significance at less than the 10%, 5%, and 1% levels, respectively.

Panel A Long-term Winners and Losers

group 1

loser group 2 group 3 group 4

group 5

winner

group 1

loser group 2 group 3 group 4

group 5

winner

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Intercept 20.95*** 10.67*** 10.25*** 19.23*** 15.74*** 20.73*** 9.841*** 10.39*** 20.16*** 18.12***

(7.31) (4.67) (5.38) (8.23) (5.22) (7.03) (4.27) (5.41) (8.47) (5.91)

S&PVOLt-1 6.198*** 13.73*** 5.754*** 5.164** -11.65***

(3.00) (8.64) (3.46) (2.00) (-3.01)

VIXt-1 0.0213** 0.055*** 0.008 -0.023* -0.110***

(2.10) (6.92) (1.01) (-1.88) (-5.76)

S&PReturnt-1 4.483*** 2.371*** 1.791*** 0.186 5.461*** 4.789*** 3.427*** 1.310* -1.764 1.377

(5.43) (3.42) (2.73) (0.18) (4.53) (4.99) (4.27) (1.80) (-1.58) (0.94)

LogMV i,t-1 -1.738*** -0.883*** -0.625*** -1.120*** -0.885*** -1.741*** -0.877*** -0.628*** -1.130*** -0.904***

(-8.24) (-5.17) (-4.54) (-6.49) (-3.89) (-8.20) (-5.13) (-4.56) (-6.53) (-3.97)

December 3.221*** 2.404*** 0.029 -1.169*** -1.174*** 3.223*** 2.358*** 0.022 -1.175*** -1.137***

(17.88) (19.63) (0.34) (-9.82) (-6.87) (17.99) (19.42) (0.26) (-9.87) (-6.68)

January 0.836*** 0.822*** -0.0961 -0.428*** -1.546*** 0.842*** 0.725*** -0.132 -0.431*** -1.362***

(5.45) (7.30) (-1.17) (-3.82) (-10.79) (5.50) (6.48) (-1.61) (-3.84) (-9.47)

BidAski,t-1 -14.95 -39.00*** -66.58*** -78.26*** -129.3*** -14.14 -37.82*** -65.46*** -76.15*** -127.1***

(-1.36) (-4.43) (-7.47) (-5.88) (-7.32) (-1.29) (-4.30) (-7.35) (-5.74) (-7.21)

DivYieldi,t-1 -8.249*** -4.272** -4.287* -9.476*** 8.161 -8.334*** -4.324** -4.331* -9.486*** 8.111

(-2.96) (-2.07) (-1.89) (-3.19) (1.40) (-2.99) (-2.10) (-1.91) (-3.19) (1.40)

Analystst-1 0.978*** 0.143 -0.481*** -0.862*** -1.912*** 0.979*** 0.142 -0.483*** -0.859*** -1.915***

(2.96) (0.72) (-3.05) (-4.04) (-5.57) (2.96) (0.71) (-3.06) (-4.03) (-5.59)

N 45,692 88,540 124,873 67,754 62,647 45,692 88,540 124,873 67,754 62,647

adj. R2 0.03 0.02 0.01 0.02 0.04 0.03 0.02 0.01 0.02 0.05

29

Panel B Short-term Winners and Losers

group 1

loser group 2 group 3 group 4

group 5

winner

group 1

loser group 2 group 3 group 4

group 5

winner

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Intercept 6.387*** -0.258 9.128*** 16.10*** 20.35*** 5.901*** -0.421 9.231*** 16.31*** 21.92***

(3.13) (-0.12) (5.80) (8.52) (10.07) (2.83) (-0.19) (5.77) (8.47) (10.61)

S&PVOLt-1 11.35*** 10.44*** 8.089*** 10.13*** -8.547***

(6.17) (5.06) (5.45) (4.23) (-3.33)

VIXt-1 0.0416*** 0.0307*** 0.0152** 0.0152 -0.0635***

(4.44) (3.16) (2.15) (1.38) (-5.60)

S&PReturnt-1 23.86*** 17.08*** 4.678*** -7.548*** -15.35*** 24.64*** 17.17*** 4.232*** -7.853*** -16.11***

(19.58) (13.39) (7.07) (-6.10) (-12.06) (16.83) (11.90) (5.81) (-6.17) (-12.52)

LogMV i,t-1 -0.325** 0.105 -0.529*** -0.922*** -0.850*** -0.329** 0.0976 -0.536*** -0.931*** -0.878***

(-2.15) (0.67) (-4.74) (-6.83) (-5.65) (-2.17) (0.62) (-4.79) (-6.89) (-5.82)

December 2.418*** 2.077*** 0.498*** -0.472*** -0.650*** 2.417*** 2.088*** 0.494*** -0.494*** -0.591***

(12.27) (11.83) (6.40) (-3.60) (-4.11) (12.18) (11.95) (6.36) (-3.77) (-3.75)

January 0.248 0.208 0.117 -0.344*** -0.211 0.171 0.138 0.0728 -0.395*** -0.135

(1.07) (1.13) (1.63) (-2.71) (-1.37) (0.73) (0.75) (1.01) (-3.09) (-0.88)

BidAski,t-1 -66.10*** -66.38*** -94.56*** -106.3*** -106.8*** -65.86*** -65.47*** -93.26*** -103.9*** -106.7***

(-6.40) (-6.44) (-12.74) (-9.44) (-10.70) (-6.36) (-6.35) (-12.57) (-9.22) (-10.77)

DivYieldi,t-1 -0.533 -0.801 -4.502*** -2.369 -3.977 -0.583 -0.837 -4.538*** -2.476 -4.073

(-0.19) (-0.33) (-2.71) (-1.02) (-1.55) (-0.21) (-0.35) (-2.73) (-1.06) (-1.59)

Analystst-1 -0.144 -0.442** -0.808*** -1.576*** -2.959*** -0.144 -0.435** -0.806*** -1.570*** -2.942***

(-0.64) (-2.20) (-6.07) (-8.83) (-13.02) (-0.65) (-2.17) (-6.05) (-8.79) (-12.95)

N 46,751 48,165 176,540 57,687 60,363 46,751 48,165 176,540 57,687 60,363

adj. R2 0.032 0.02 0.013 0.025 0.04 0.032 0.02 0.012 0.024 0.04

30

Table 3. Extreme Market Volatility Effect on Abnormal Trading

The table presents results of cross-sectional regression of CAVLt, which is log-transformed abnormal relative volume to the value-weighted CRSP-based log-

transformed relative volume, cumulative over [-21, 0] event window, with event day 0 occurring on the last trading date of each month, on the following variables:

S&PVOLt-1 is monthly standard deviation of S&P500 index daily returns over previous month. VIXt-1 is a measure of implied volatility over the next 30 days.

S&PReturnt-1 is monthly return on S&P500 index as reported by CRSP over previous month. LogMVi,t-1 is natural log of market value, calculated as the closing

price on the last trading day of the previous month multiplied by total shares outstanding. December (January) equals 1 if observation occurs in December (January),

and 0 otherwise. BidAski,t-1 is (Ask – Bid)/(Ask+Bid)/2 during previous month. DivYieldi,t-1 is total dividends paid during previous year divided by the ending price,

Analystst-1 equals log(1+analyst coverage). The model controls for year fixed effects. The models are fitted separately for each group of stocks: Group 1 (ret < -

20%); Group 2 (-20%≤ ret≤-10%); Group 3 (-10% <ret <10%); Group 4 (10% ≤ret ≤20%); Group 5 with (ret>20%). t-statistics are reported in parenthesis and a

robust to heteroskedasticity using White (1980) method. *, ** and *** indicate statistical significance at less than the 10%, 5%, and 1% levels, respectively.

Extreme Loser Extreme Winner

Long Short Long Short

Panel A (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

Intercept 20.73*** 21.36*** 21.43*** 5.901*** 6.531*** 6.764*** 18.12*** 15.42*** 15.06*** 21.92*** 19.92*** 19.58***

(7.03) (7.45) (7.58) (2.83) (3.20) (3.33) (5.91) (5.12) (5.00) (10.61) (9.88) (9.73)

VIXt-1 0.021** 0.042*** -0.11*** -0.064***

(2.10) (4.44) (-5.76) (-5.60) 95th%ile 0.370* 1.304*** -1.54*** -0.50**

VIXt-1 (1.71) (6.33) (-2.87) (-2.01) 99th%ile 1.695*** 2.828*** 3.996* 2.314***

VIXt-1 (4.81) (9.62) (1.70) (2.93)

S&PReturnt-1 4.789*** 4.015*** 4.517*** 24.64*** 24.60*** 23.12*** 1.377 6.179*** 7.357*** -16.11*** -15.2*** -14.68***

(4.99) (4.79) (5.39) (16.83) (19.65) (20.84) (0.94) (5.48) (6.72) (-12.52) (-11.96) (-11.47)

LogMV i,t-1 -1.74*** -1.75*** -1.74*** -0.33** -0.33** -0.30** -0.90*** -0.89*** -0.87*** -0.88*** -0.84*** -0.82***

(-8.20) (-8.27) (-8.30) (-2.17) (-2.11) (-1.97) (-3.97) (-3.92) (-3.84) (-5.82) (-5.60) (-5.47)

December 3.22*** 3.29*** 2.30*** 2.42*** 2.49*** 2.10*** -1.14*** -1.16*** -1.15*** -0.59*** -0.63*** -0.69***

(17.99) (18.16) (15.79) (12.18) (12.81) (10.36) (-6.68) (-6.80) (-6.78) (-3.75) (-3.99) (-4.31)

January 0.842*** 0.835*** 0.873*** 0.171 0.17 0.213 -1.36*** -1.49*** -1.49*** -0.135 -0.174 -0.191

(5.50) (5.45) (5.65) (0.73) (0.73) (0.92) (-9.47) (-10.47) (-10.49) (-0.88) (-1.13) (-1.24)

BidAski,t-1 -14.14 -13.16 -13.91 -65.9*** -65.5*** -64.6*** -127*** -131*** -133*** -106.7*** -109*** -110***

(-1.29) (-1.20) (-1.27) (-6.36) (-6.35) (-6.27) (-7.21) (-7.49) (-7.56) (-10.77) (-11.04) (-11.12)

DivYieldi,t-1 -8.33*** -8.41*** -8.45*** -0.58 -0.50 -0.67 8.11 8.18 8.35 -4.07 -3.92 -3.80

(-2.99) (-3.01) (-3.03) (-0.21) (-0.18) (-0.24) (1.40) (1.41) (1.43) (-1.59) (-1.52) (-1.48)

Analystst-1 0.98*** 0.98*** 0.98*** -0.144 -0.15 -0.161 -1.92*** -1.91*** -1.90*** -2.94*** -2.96*** -2.97***

(2.96) (2.96) (2.96) (-0.65) (-0.67) (-0.72) (-5.59) (-5.55) (-5.54) (-12.95) (-13.02) (-13.08)

N 45,692 45,692 45,692 46,751 46,751 46,751 62,647 62,647 62,647 60,363 60,363 60,363

adj. R2 0.03 0.03 0.03 0.03 0.03 0.03 0.05 0.04 0.04 0.04 0.04 0.04

31

Extreme Loser Extreme Winner

Long Short Long Short

Panel B (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

Intercept 20.95*** 21.48*** 21.63*** 6.387*** 7.160*** 7.109*** 15.74*** 15.49*** 15.03*** 20.35*** 20.58*** 19.81***

(7.31) (7.54) (7.65) (3.13) (3.53) (3.52) (5.22) (5.14) (4.99) (10.07) (10.22) (9.85)

SPVOLt-1 6.20*** 11.35*** -11.7*** -8.55***

(3.00) (6.17) (-3.01) (-3.33) 95th%ile 0.29 0.72*** -2.36*** -2.00*** SPVOLt-1 (1.50) (3.99) (-5.53) (-8.23) 99th%ile 0.988** 2.606*** 3.436** -2.186***

SPVOLt-1 (2.39) (8.39) (2.14) (-2.86)

S&PReturnt-1 4.48*** 3.71*** 4.07*** 23.86*** 21.38*** 23.09*** 5.461*** 6.47*** 7.46*** -15.35*** -16.0*** -15.73***

(5.43) (4.47) (4.82) (19.58) (19.46) (20.82) (4.53) (5.86) (6.79) (-12.06) (-12.52) (-12.23)

LogMV i,t-1 -1.74*** -1.75*** -1.76*** -0.33** -0.35** -0.33** -0.89*** -0.90*** -0.87*** -0.85*** -0.88*** -0.84***

(-8.24) (-8.32) (-8.38) (-2.15) (-2.29) (-2.16) (-3.89) (-3.94) (-3.83) (-5.65) (-5.83) (-5.58)

December 3.22*** 3.30*** 3.16*** 2.42*** 2.55*** 2.24*** -1.17*** -1.18*** -1.15*** -0.65*** -0.66*** -0.56***

(17.88) (18.25) (16.89) (12.27) (13.10) (11.31) (-6.87) (-6.92) (-6.78) (-4.11) (-4.16) (-3.52)

January 0.84*** 0.84*** 0.88*** 0.25 0.236 0.26 -1.55*** -1.51*** -1.49*** -0.211 -0.10 -0.20

(5.45) (5.47) (5.67) (1.07) (1.01) (1.12) (-10.79) (-10.63) (-10.47) (-1.37) (-0.67) (-1.29)

BidAski,t-1 -15.0 -12.6 -13.6 -66.1*** -62.4*** -65.3*** -129*** -133*** -133*** -107*** -108*** -109***

(-1.36) (-1.16) (-1.24) (-6.40) (-6.05) (-6.34) (-7.32) (-7.59) (-7.56) (-10.70) (-10.94) (-11.06)

DivYieldi,t-1 -8.25*** -8.44*** -8.45*** -0.53 -0.68 -0.53 8.16 8.26 8.35 -3.98 -4.06 -3.83

(-2.96) (-3.02) (-3.03) (-0.19) (-0.24) (-0.19) (1.40) (1.42) (1.43) (-1.55) (-1.58) (-1.49)

Analystst-1 0.98*** 0.98*** 0.98*** -0.14 -0.13 -0.14 -1.91*** -1.91*** -1.90*** -2.96*** -2.95*** -2.97***

(2.96) (2.96) (2.98) (-0.64) (-0.59) (-0.64) (-5.57) (-5.55) (-5.54) (-13.02) (-12.97) (-13.05)

N 45,692 45,692 45,692 46,751 46,751 46,751 62,647 62,647 62,647 60,363 60,363 60,363

adj. R2 0.03 0.03 0.03 0.03 0.03 0.03 0.04 0.04 0.04 0.04 0.04 0.04

32

Table 4. Stock and Market Volatility Effect on Abnormal Trading The table presents results of cross-sectional regression of CAVLt, which is log-transformed abnormal relative volume to the value-weighted CRSP-based log-

transformed relative volume, cumulative over [-21, 0] event window, with event day 0 occurring on the last trading date of each month, on the following variables:

S&PVOLt-1 is orthogonalzied monthly standard deviation of S&P500 index daily returns over previous month. S&PReturnt-1 is monthly return on S&P500 index

as reported by CRSP over previous month. LogMVi,t-1 is natural log of market value, calculated as the closing price on the last trading day of the previous month

multiplied by total shares outstanding. December (January) equals 1 if observation occurs in December (January), and 0 otherwise. BidAski,t-1 is (Ask –

Bid)/(Ask+Bid)/2 during previous month. DivYieldi,t-1 is total dividends paid during previous year divided by the ending price, Analystst-1 equals log(1+analyst

coverage). The model controls for year fixed effects. The models are fitted separately for each group of stocks: Group 1 (ret < -20%); Group 2 (-20%≤ ret≤-10%);

Group 3 (-10% <ret <10%); Group 4 (10% ≤ret ≤20%); Group 5 with (ret>20%). t-statistics are reported in parenthesis and a robust to heteroskedasticity using

White (1980) method. *, ** and *** indicate statistical significance at less than the 10%, 5%, and 1% levels, respectively.

Panel A Long Short Long Short Long Short Long Short Long Short

Group 1: Extreme Losers Group 2 Group 3 Group 4 Group 5: Extreme Winners

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Intercept 13.06*** -0.0698 9.481*** -1.158 9.247*** 7.757*** 17.06*** 14.00*** 11.58*** 12.46***

(4.60) (-0.03) (4.14) (-0.51) (4.88) (4.95) (7.35) (7.37) (3.93) (5.96)

VOLt-1 1.416*** 1.893*** 1.663*** 1.484*** 1.881*** 1.527*** 2.203*** 1.351*** 2.137*** 1.464***

(18.54) (29.24) (14.92) (6.32) (27.57) (22.56) (22.91) (14.18) (12.38) (15.52)

S&PVOLt-1 -0.622*** -0.650*** -0.279*** -0.308*** -0.499*** -0.338*** -0.643*** -0.250*** -1.266*** -1.053***

(-9.85) (-11.73) (-4.38) (-2.59) (-10.01) (-7.15) (-8.27) (-3.34) (-10.28) (-12.96)

S&PReturnt-1 0.649 16.82*** -0.0696 13.82*** -0.136 3.394*** -1.486 -7.639*** 3.854*** -14.19***

(0.78) (14.05) (-0.10) (9.89) (-0.21) (5.15) (-1.46) (-6.17) (3.18) (-11.15)

LogMV i,t-1 -1.134*** 0.166 -0.755*** 0.204 -0.534*** -0.394*** -0.959*** -0.737*** -0.686*** -0.331**

(-5.38) (1.10) (-4.40) (1.24) (-3.88) (-3.50) (-5.56) (-5.40) (-3.08) (-2.12)

December 2.850*** 1.799*** 2.189*** 1.850*** -0.0651 0.413*** -1.187*** -0.508*** -1.230*** -0.778***

(15.94) (9.33) (18.02) (10.29) (-0.77) (5.35) (-10.03) (-3.88) (-7.38) (-4.97)

January 0.731*** 0.0998 0.714*** 0.0841 -0.0666 0.0991 -0.339*** -0.309** -1.489*** -0.191

(4.84) (0.44) (6.38) (0.45) (-0.81) (1.39) (-3.05) (-2.44) (-10.58) (-1.26)

BidAski,t-1 -38.15*** -87.56*** -52.22*** -76.07*** -76.60*** -104.1*** -93.54*** -115.0*** -156.7*** -129.8***

(-3.50) (-8.50) (-5.91) (-7.28) (-8.52) (-13.88) (-7.02) (-10.20) (-8.83) (-12.88)

DivYieldi,t-1 -8.692*** -2.602 -4.068** -1.457 -3.179 -4.502*** -7.863*** -2.544 8.949 -7.098***

(-3.25) (-0.98) (-1.97) (-0.60) (-1.40) (-2.70) (-2.64) (-1.10) (1.58) (-2.86)

Analystst-1 0.715** -0.363* 0.147 -0.426** -0.408** -0.814*** -0.771*** -1.613*** -1.715*** -3.104***

(2.21) (-1.66) (0.74) (-2.12) (-2.57) (-6.10) (-3.63) (-9.01) (-5.12) (-13.72)

N 45,692 46,751 88,540 48,165 124,873 176,540 67,754 57,687 62,647 60,363

adj. R2 0.06 0.07 0.03 0.03 0.02 0.02 0.04 0.03 0.08 0.07

33

Panel B Long Short Long Short Long Short Long Short Long Short

Group 1: Extreme Losers Group 2 Group 3 Group 4 Group 5: Extreme Winners

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Intercept 24.66*** 8.520*** 12.73*** 3.189 11.75*** 12.97*** 21.86*** 19.80*** 25.15*** 20.88***

(8.31) (4.14) (5.50) (1.50) (6.13) (8.59) (9.33) (10.08) (7.92) (10.04)

VOL[t-1, t-13] -0.804*** -0.135 -0.944*** -1.140*** -0.916*** -1.034*** -1.167*** -1.020*** -0.851*** -0.269**

(-5.03) (-0.92) (-7.43) (-8.51) (-7.20) (-10.75) (-6.76) (-7.25) (-4.12) (-2.03)

S&PVOL[t-1, t-13] 0.799*** 1.546*** 0.755*** 0.966*** 0.474*** 0.677*** 0.569*** 0.291* 0.312 -0.943***

(4.50) (10.13) (6.06) (6.16) (4.15) (7.43) (3.44) (1.89) (1.11) (-5.10)

S&PReturn[t-1, t-13] 2.857*** 11.27*** 1.547** 4.617*** 0.0547 1.423*** -2.210*** -0.575 1.419* -0.354

(3.08) (15.26) (2.57) (6.64) (0.12) (3.64) (-3.73) (-1.04) (1.90) (-0.53)

LogMV i,t-1 -2.024*** -0.594*** -1.008*** -0.133 -0.723*** -0.739*** -1.257*** -1.095*** -1.295*** -0.865***

(-9.15) (-3.87) (-5.80) (-0.86) (-5.20) (-6.79) (-7.25) (-7.74) (-5.36) (-5.54)

December 3.333*** 2.853*** 2.438*** 2.304*** 0.0529 0.471*** -1.159*** -0.587*** -1.572*** -0.854***

(17.36) (14.06) (19.67) (13.21) (0.62) (6.10) (-9.78) (-4.38) (-9.46) (-5.31)

January 0.747*** 0.675*** 0.743*** 0.695*** -0.122 0.264*** -0.457*** -0.167 -0.249* 0.198

(4.72) (2.93) (6.50) (3.89) (-1.49) (3.75) (-4.05) (-1.34) (-1.65) (1.31)

BidAski,t-1 -5.783 -63.29*** -32.06*** -54.73*** -61.74*** -86.92*** -70.44*** -94.03*** -99.28*** -108.8***

(-0.53) (-6.11) (-3.66) (-5.32) (-6.95) (-11.94) (-5.34) (-8.52) (-5.60) (-10.88)

DivYieldi,t-1 -6.876** -1.701 -4.150** -1.985 -4.696** -8.241*** -9.599*** -4.979** -10.30* -6.528**

(-2.43) (-0.61) (-2.02) (-0.86) (-2.06) (-5.30) (-3.22) (-2.17) (-1.86) (-2.53)

Analystst-1 1.064*** -0.316 0.125 -0.736*** -0.503*** -1.099*** -0.860*** -1.805*** -2.927*** -3.320***

(3.19) (-1.40) (0.63) (-3.69) (-3.19) (-8.43) (-4.05) (-10.27) (-8.50) (-14.31)

N 45,692 45,559 88,540 47,058 124,873 173,132 67,754 56,549 54,190 58,751

adj. R2 0.04 0.03 0.02 0.02 0.01 0.02 0.02 0.03 0.05 0.04

34

Panel C Long Short Long Short Long Short Long Short Long Short

Group 1: Extreme Losers Group 2 Group 3 Group 4 Group 5: Extreme Winners

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Intercept 9.033*** -3.918* 5.803** -4.785** 6.151*** 5.060*** 13.34*** 11.73*** 7.014** 8.653***

(3.13) (-1.91) (2.54) (-2.15) (3.24) (3.18) (5.70) (6.06) (2.38) (4.15)

IVOLt-1 34.45*** 39.79*** 31.56*** 31.42*** 35.74*** 29.23*** 42.25*** 24.99*** 52.10*** 40.89***

(28.14) (34.89) (29.82) (18.85) (31.93) (25.66) (27.15) (14.99) (29.54) (31.94)

Betat-1 -0.0788 0.234*** -0.120** 0.042 -0.275*** -0.141*** -0.373*** -0.283*** 0.0509 -0.358***

(-0.96) (3.01) (-2.01) (0.51) (-4.96) (-3.03) (-5.15) (-3.85) (0.67) (-5.23)

S&PVOLt-1 -13.18*** -9.487*** -1.478 -3.904* -8.156*** -4.654*** -10.38*** -1.801 -34.74*** -29.65***

(-6.42) (-5.04) (-0.90) (-1.78) (-4.81) (-2.99) (-3.94) (-0.72) (-9.03) (-11.32)

S&PReturnt-1 1.081 16.01*** -0.0484 12.60*** -0.172 3.252*** -2.084** -6.826*** 2.529** -11.85***

(1.33) (13.30) (-0.07) (9.82) (-0.26) (4.95) (-2.05) (-5.51) (2.12) (-9.38)

LogMV i,t-1 -1.032*** 0.189 -0.676*** 0.287* -0.476*** -0.347*** -0.874*** -0.705*** -0.566** -0.218

(-4.92) (1.26) (-3.96) (1.81) (-3.47) (-3.07) (-5.07) (-5.15) (-2.55) (-1.41)

December 3.019*** 1.969*** 2.260*** 1.883*** -0.0183 0.463*** -1.146*** -0.461*** -1.159*** -0.722***

(16.97) (10.19) (18.75) (10.76) (-0.22) (6.02) (-9.71) (-3.52) (-6.97) (-4.64)

January 0.744*** 0.151 0.798*** 0.119 -0.0279 0.130* -0.333*** -0.297** -1.483*** -0.169

(4.95) (0.67) (7.17) (0.65) (-0.34) (1.82) (-3.01) (-2.34) (-10.53) (-1.11)

BidAski,t-1 -41.62*** -89.23*** -54.60*** -78.19*** -82.08*** -109.1*** -102.0*** -119.9*** -163.1*** -139.9***

(-3.80) (-8.64) (-6.20) (-7.57) (-9.09) (-14.45) (-7.64) (-10.63) (-9.24) (-13.86)

DivYieldi,t-1 -8.550*** -2.458 -3.818* -1.056 -3.212 -4.375*** -8.426*** -2.277 9.590* -6.500***

(-3.21) (-0.92) (-1.87) (-0.44) (-1.42) (-2.64) (-2.84) (-0.98) (1.71) (-2.62)

Analystst-1 0.709** -0.276 0.18 -0.417** -0.394** -0.795*** -0.761*** -1.584*** -1.622*** -3.035***

(2.21) (-1.26) (0.91) (-2.08) (-2.49) (-5.99) (-3.60) (-8.85) (-4.84) (-13.39)

N 45,691 46,750 88,540 48,165 124,873 176,540 67,754 57,687 62,646 60,362

adj. R2 0.06 0.07 0.03 0.03 0.03 0.02 0.04 0.03 0.08 0.07

35

Table 5. Stock and Market Volatility Effect on Abnormal Trading Controlling for the Prior Month Short-term Return The table report results of cross-sectional regression of CAVLt, log-transformed abnormal relative volume to the value-weighted CRSP-based log-transformed

relative volume, cumulative over [-21, 0] event window, with event day 0 occurring on the last trading date of each month, on the following variables: S&PVOLt-1

is monthly standard deviation of S&P500 index daily returns over previous month. VIXt-1 is a measure of implied volatility over the next 30 days. S&PReturnt-1 is

monthly return on S&P500 index. LogMVi,t-1 is natural log of market value. December (January) equals 1 if observation occurs in December (January), and 0

otherwise. BidAski,t-1 is (Ask – Bid)/(Ask+Bid)/2 during previous month. DivYieldi,t-1 is total dividends paid during previous year divided by the ending price, Analystst-1 equals log(1+analyst coverage) The model controls for time and stock fixed effects and robust standard errors. The groups are formed based on long-

term return. t-statistics are reported in parenthesis. *, ** and *** indicate statistical significance at less than the 10%, 5%, and 1% levels, respectively.

Panel A Market VOL=SPVOL Market VOL = VIX

Loser Winner Loser Winner

(1) (2) (3) (4) (5) (1) (2) (3) (4) (5)

Intercept 14.22*** 8.084*** 9.051*** 18.08*** 16.26*** 14.00*** 7.468*** 9.567*** 19.37*** 18.65***

(5.00) (3.54) (4.76) (7.75) (5.43) (4.79) (3.24) (4.99) (8.15) (6.14)

Short-term Losert-1 3.972*** 3.709*** 3.897*** 3.281*** 1.937*** 4.710*** 4.604*** 4.802*** 3.636*** 2.245***

(19.38) (21.82) (18.24) (9.51) (5.02) (16.53) (18.57) (16.28) (7.34) (4.31)

Short-term winnert-1 0.803*** 0.984*** 1.895*** 2.301*** 3.094*** 0.805** 0.885*** 1.754*** 2.421*** 3.496***

(3.10) (4.79) (9.30) (9.23) (10.74) (2.23) (3.08) (6.05) (6.97) (8.44)

Market VOLt-1 5.768** 12.52*** 4.673*** 2.277 -10.9*** 0.03** 0.05*** -0.004 -0.04*** -0.1***

(2.44) (6.70) (2.60) (0.80) (-2.62) (2.38) (5.63) (-0.49) (-3.16) (-5.62)

Market VOLt-1 *STLosert-1 -4.024* -8.8*** -21.9*** -21.3*** -17.9*** -0.04*** -0.06*** -0.09*** -0.07*** -0.05**

(-1.73) (-4.05) (-7.05) (-4.00) (-2.76) (-4.00) (-6.35) (-7.86) (-3.15) (-2.39)

Market VOLt-1 *STWinnert-1 -3.3 -5.805* -4.253 6.322 17.94*** -0.008 -0.0091 -0.0015 0.009 0.019

(-1.02) (-1.81) (-1.11) (1.14) (2.82) (-0.62) (-0.77) (-0.11) (0.51) (0.92)

S&PReturnt-1 14.09*** 7.61*** 1.65** -3.87*** -3.67*** 13.39*** 7.61*** 0.259 -6.32*** -8.04***

(14.85) (10.04) (2.34) (-3.68) (-2.96) (12.48) (8.79) (0.33) (-5.51) (-5.37)

LogMV i,t-1 -1.36*** -0.76*** -0.58*** -1.08*** -1.01*** -1.36*** -0.76*** -0.59*** -1.09*** -1.02***

(-6.48) (-4.45) (-4.24) (-6.25) (-4.46) (-6.48) (-4.43) (-4.30) (-6.31) (-4.52)

December 3.22*** 2.46*** 0.069 -1.11*** -1.12*** 3.24*** 2.42*** 0.071 -1.11*** -1.11***

(18.02) (20.30) (0.81) (-9.34) (-6.66) (18.22) (20.18) (0.84) (-9.38) (-6.63)

January 0.88*** 0.93*** -0.034 -0.39*** -1.55*** 0.87*** 0.85*** -0.043 -0.36*** -1.38***

(5.78) (8.34) (-0.41) (-3.51) (-10.92) (5.74) (7.64) (-0.52) (-3.25) (-9.68)

BidAski,t-1 -7.75 -34.3*** -66.3*** -80.9*** -137*** -6.73 -33.4*** -65.4*** -78.4*** -133***

(-0.72) (-3.93) (-7.44) (-6.10) (-7.89) (-0.62) (-3.83) (-7.34) (-5.92) (-7.67)

DivYieldi,t-1 -6.51** -3.02 -3.85* -9.06*** 8.132 -6.56** -3.05 -3.93* -9.08*** 8.1

(-2.38) (-1.47) (-1.69) (-3.05) (1.42) (-2.39) (-1.49) (-1.73) (-3.06) (1.42)

Analystst-1 0.85*** 0.12 -0.43*** -0.79*** -1.71*** 0.85*** 0.12 -0.43*** -0.79*** -1.72***

(2.60) (0.58) (-2.74) (-3.71) (-5.06) (2.60) (0.58) (-2.74) (-3.69) (-5.11)

N 45,692 88,540 124,873 67,754 62,647 45,692 88,540 124,873 67,754 62,647

adj. R2 0.06 0.03 0.02 0.03 0.07 0.06 0.03 0.02 0.03 0.07

36

Panel B Loser Winner

(1) (2) (3) (4) (5)

Intercept 5.424* 4.620** 6.258*** 14.15*** 10.23***

(1.87) (2.02) (3.29) (6.02) (3.49)

IVOLt-1 25.47*** 25.97*** 27.31*** 26.60*** 29.46***

(16.03) (19.23) (20.02) (13.99) (14.30)

Betat-1 -0.322*** -0.152** -0.229*** -0.233*** 0.142

(-3.12) (-2.21) (-3.72) (-2.91) (1.59)

Short-term Loser 2.058*** 2.300*** 2.065*** 1.167** -0.0974

(6.81) (9.04) (6.84) (2.48) (-0.20)

Short-term Winner -0.841** -0.261 0.994*** 1.022*** 1.513***

(-2.27) (-0.92) (4.20) (3.47) (4.90)

IVOLt-1_STLoser 5.755*** 3.216 -3.582 2.668 -3.107

(3.11) (1.61) (-1.42) (0.76) (-0.98)

IVOLt-1_STWinner 0.699 1.942 6.380*** 16.74*** 17.67***

(0.32) (0.90) (3.01) (5.94) (7.53)

BETAt-1_STLoser 0.257* 0.0484 0.382** 0.1 0.762***

(1.91) (0.37) (2.45) (0.48) (3.98)

BETAt-1_STWinner 0.398*** 0.0389 -0.685*** -0.769*** -0.676***

(2.69) (0.31) (-5.61) (-4.83) (-5.32)

VIXt-1 -0.730*** -0.202*** -0.456*** -0.653*** -1.472***

(-9.43) (-3.19) (-7.50) (-6.71) (-10.39)

S&PReturnt-1 7.197*** 4.755*** -0.686 -6.551*** -8.593***

(6.86) (5.53) (-0.90) (-5.77) (-5.87)

LogMV i,t-1 -0.764*** -0.598*** -0.478*** -0.894*** -0.776***

(-3.65) (-3.51) (-3.48) (-5.17) (-3.52)

December 3.176*** 2.361*** 0.0339 -1.091*** -1.063***

(18.05) (19.78) (0.40) (-9.26) (-6.45)

January 0.798*** 0.916*** 0.101 -0.201* -1.143***

(5.36) (8.30) (1.24) (-1.83) (-8.07)

BidAski,t-1 -30.93*** -47.84*** -80.63*** -102.2*** -165.1***

(-2.87) (-5.46) (-8.93) (-7.67) (-9.52)

DivYieldi,t-1 -7.163*** -2.742 -3.114 -8.438*** 9.382*

(-2.72) (-1.34) (-1.37) (-2.85) (1.69)

Analystst-1 0.598* 0.143 -0.381** -0.742*** -1.502***

(1.87) (0.73) (-2.41) (-3.51) (-4.55)

N 45,691 88,540 124,873 67,754 62,646

adj. R2 0.09 0.04 0.03 0.05 0.10

37

Table 6 The values presented in Panels A through F are average CAVLt for each rank, with stocks double sorted on cumulative

returns over 13 months prior to time t (Panels A – C) and over 1 month prior to time t (Panels D – F). Difference in

the means between the most volatile (10th decile) and least volatile (1st decile) is presented below the sort returns in

each Panel and tested using t-test. *, ** and *** indicate statistical significance at less than the 10%, 5%, and 1%

levels, respectively.

Long-term Winners/Losers

Panel A

February – November

Volatility

Decile

Group1 Group 2 Group3 Group4 Group5 Group1 - Group5 t-test

1 -0.83 -2.22 -1.26 0.17 -3.51 2.68 (2.11)

2 -2.74 -1.95 -1.16 0.70 -1.58 -1.16 (-1.90)

3 -2.79 -1.80 -0.94 0.67 -1.79 -1.00 (-2.30)

4 -2.14 -1.56 -0.92 0.47 -1.85 -0.28 (-0.79)

5 -2.16 -1.19 -0.57 0.66 -1.64 -0.52 (-1.70)

6 -1.64 -1.23 -0.27 0.81 -0.90 -0.73 (-2.81)

7 -1.14 -0.85 -0.18 0.90 0.08 -1.22 (-5.63)

8 -1.61 -0.64 0.31 1.46 0.80 -2.41 (-11.99)

9 -0.82 -0.50 0.56 2.03 1.82 -2.65 (-14.95)

10 1.21 1.51 2.80 5.14 6.09 -4.88 (-27.65)

(10) - (1) 2.04 3.74 4.06 4.97 9.60

t-test (2.75) (23.65) (29.98) (15.92) (36.80)

Panel B

December

Volatility

Decile

Group1 Group 2 Group3 Group4 Group5 Group1 - Group5 t-test

1 11.68 12.13 2.08 1.20 0.22 11.46 (2.98)

2 6.67 9.91 0.95 0.39 3.73 2.94 (1.56)

3 2.62 5.60 1.36 0.64 2.12 0.51 (-0.36)

4 3.28 4.31 1.15 0.49 1.34 1.94 (-1.74)

5 3.79 3.56 1.08 0.74 0.56 3.23 (-3.31)

6 2.76 2.15 0.71 0.23 (0.30) 3.05 (-3.76)

7 2.67 1.90 0.74 0.84 0.68 1.99 (2.79)

8 3.64 2.48 1.01 0.35 0.84 2.79 (5.27)

9 2.67 1.94 0.97 1.19 2.06 0.62 (0.98)

10 5.73 4.04 2.69 3.63 6.31 (0.58) (-0.98)

(10) - (1) (5.96) (8.08) 0.60 2.43 6.09

t-test (-2.60) (-14.39) (1.42) (2.77) (7.38)

Panel C

January

Volatility

Decile

Group1 Group 2 Group3 Group4 Group5 Group1 - Group5 t-test

1 -0.37 2.45 2.00 -0.22 1.16 -1.54 (-0.48)

2 -0.97 3.04 1.52 2.40 1.95 -2.92 (-1.74)

3 0.73 1.60 1.66 1.50 1.35 -0.62 (-0.54)

4 -0.04 1.28 1.35 0.89 0.32 -0.36 (-0.35)

5 -0.57 1.29 0.88 0.81 0.54 -1.11 (-1.31)

6 0.55 0.65 0.41 1.22 -0.03 0.57 (0.70)

7 -1.19 -0.44 0.73 0.75 0.92 -2.11 (-3.08)

8 0.57 0.62 0.86 0.67 0.13 0.44 (0.68)

9 1.21 0.77 1.05 2.30 1.48 -0.26 (-0.49)

10 1.91 2.74 3.23 5.65 6.53 -4.63 (-7.53)

(10) - (1) 2.28 0.28 1.23 5.86 5.37

t-test (1.22) (0.51) (2.85) (7.11) (6.48)

38

Panel D

February – November

Volatility

Decile

Group1 Group 2 Group3 Group4 Group5 Group1 - Group5 t-test

1 4.60 1.00 -1.83 0.43 3.62 0.98 (0.59)

2 0.26 -1.29 -1.53 0.25 1.39 -1.13 (-1.89)

3 -0.56 -1.32 -1.33 -0.25 0.85 -1.41 (-3.52)

4 -0.48 -1.36 -1.30 -0.24 0.22 -0.69 (-2.23)

5 -0.60 -0.91 -1.19 -0.15 1.13 -1.73 (-6.64)

6 -0.04 -0.73 -0.99 -0.06 0.85 -0.89 (-3.98)

7 0.45 -0.64 -0.64 -0.28 0.98 -0.53 (-2.79)

8 0.20 -0.43 -0.49 0.23 1.75 -1.55 (-8.68)

9 0.91 -0.19 -0.25 0.25 2.34 -1.43 (-8.8)

10 3.51 1.50 1.10 2.14 6.38 -2.87 (-17.57)

(10) - (1) -1.09 0.50 2.93 1.71 2.75

t-test (-1.31) (1.32) (22.59) (4.88) (1.92)

Panel E

December

Volatility

Decile

Group1 Group 2 Group 3 Group 4 Group 5 Group1 - Group5 t-test

1 18.91 16.64 3.23 2.01 2.31 16.59 (3.69)

2 8.69 9.03 2.92 1.23 2.19 6.50 (2.98)

3 3.03 5.82 2.01 0.44 3.87 -0.85 (-0.63)

4 3.98 5.49 1.50 0.39 0.65 3.33 (3.36)

5 5.79 4.02 1.14 0.51 1.53 4.26 (5.08)

6 4.28 2.69 0.42 -0.20 1.33 2.94 (4.01)

7 4.32 3.39 0.41 -0.04 1.31 3.01 (4.58)

8 5.14 2.56 0.46 0.06 1.82 3.32 (6.42)

9 4.53 1.91 0.51 0.55 2.24 2.29 (4.23)

10 6.93 3.18 2.98 1.96 6.06 0.87 (1.66)

(10) - (1) -11.98 -13.46 -0.25 -0.05 3.74

t-test (-6.06) (-11.11) (-0.55) (-0.04) (0.95)

Panel F

January

Volatility

Decile

Group1 Group 2 Group3 Group4 Group5 Group1 - Group5 t-test

1 5.12 4.43 1.64 1.98 8.53 -3.41 (-0.87)

2 5.18 3.05 1.61 2.94 3.86 1.32 (0.62)

3 1.43 2.32 1.37 1.53 2.84 -1.41 (-0.93)

4 -0.34 2.15 0.74 1.10 2.89 -3.23 (-2.43)

5 2.12 1.43 0.45 0.28 2.71 -0.58 (-0.56)

6 0.82 1.34 0.36 -0.11 1.60 -0.78 (-0.88)

7 0.05 0.94 -0.10 -0.41 1.89 -1.84 (-2.52)

8 1.20 0.82 0.13 -0.21 1.69 -0.49 (-0.74)

9 1.93 1.04 0.46 0.89 2.50 -0.57 (-0.97)

10 4.12 1.75 1.99 2.91 7.44 -3.31 (-5.52)

(10) - (1) -0.99 -2.69 0.35 0.93 -1.09

t-test (-0.27) (-1.89) (0.87) (1.12) (-0.40)

39

Table 7 Stock and Market Volatility and Turn-of-the-year Abnormal Trading The table reports results of cross-sectional regression of CAVLt, log-transformed abnormal relative volume to the value-weighted CRSP-based log-transformed

relative volume, cumulative over [-21, 0] event window, with event day 0 occurring on the last trading date of each month variables: VIXt-1 is a measure of implied

volatility over the next 30 days (orthogonal to VOLt-1, when both included). VOLt-1 is monthly standard deviation of daily returns over previous month. S&PReturnt-

1 is monthly return on S&P500 index as reported by CRSP over previous month. LogMVi,t-1 is natural log of market value. December (January) equals 1 if

observation occurs in December (January), and 0 otherwise. BidAski,t-1 is (Ask – Bid)/(Ask+Bid)/2 during previous month. DivYieldi,t-1 is total dividends paid

during previous year divided by the ending price, Analystst-1 equals log(1+analyst coverage) . The model controls for time and stock fixed effects and robust

standard errors. The groups are formed based on long-term return: group 1 includes stocks with returns < -36%; group 2 (-36%≤ BHR≤-8%); group 3 (-8% <BHR

<20%); group 4 (28% ≤BHR ≤48%); group 5 with (BHR>48%). t-statistics are reported in parenthesis. *, ** and *** indicate statistical significance at less than

the 10%, 5%, and 1% levels, respectively.

Panel A Loser Winner Loser Winner

(1) (2) (3) (4) (5) (1) (2) (3) (4) (5)

Intercept 20.75*** 10.22*** 10.58*** 20.18*** 18.08*** 13.88*** 8.156*** 8.851*** 17.17*** 13.53***

(7.03) (4.44) (5.50) (8.48) (5.88) (4.74) (3.55) (4.62) (7.24) (4.53)

Dec_VIXt-1 -0.0152 0.0457*** 0.0885*** 0.0642*** 0.0833***

(-1.39) (4.62) (7.48) (3.45) (2.96)

Jan_VIXt-1 0.0565*** 0.0881*** 0.0649*** 0.00625 -0.0261

(3.59) (6.19) (4.39) (0.26) (-0.89)

Dec_VOLt-1

-1.571 -0.538 3.921* -3.312 4.366 (-0.84) (-0.28) (1.96) (-1.04) (1.35)

Jan_VOLt-1

-2.11 1.82 3.488 -0.783 -1.145 (-1.16) (0.84) (1.50) (-0.24) (-0.39)

VOLt-1

31.48*** 27.50*** 29.29*** 35.72*** 47.16*** (27.22) (28.06) (27.84) (24.23) (28.10)

VIXt-1 0.0238** 0.0443*** -0.00256 -0.0286** -0.114*** -0.116*** -0.0503*** -0.0813*** -0.123*** -0.256*** (2.27) (5.45) (-0.34) (-2.34) (-6.08) (-10.89) (-5.83) (-10.13) (-9.53) (-13.26)

S&PReturnt-1 5.013*** 3.055*** 0.994 -1.946* 1.246 -3.445*** -1.407* -1.773** -4.151*** -1.703 (5.03) (3.77) (1.37) (-1.74) (0.85) (-3.51) (-1.72) (-2.45) (-3.75) (-1.18)

LogMV i,t-1 -1.749*** -0.884*** -0.626*** -1.124*** -0.894*** -1.199*** -0.745*** -0.543*** -0.974*** -0.692*** (-8.23) (-5.17) (-4.54) (-6.49) (-3.92) (-5.67) (-4.37) (-3.95) (-5.63) (-3.12)

December 3.653*** 1.305*** -1.703*** -2.368*** -2.753*** 3.321*** 2.288*** -0.348** -0.856*** -1.577*** (9.12) (4.98) (-7.13) (-6.63) (-5.05) (8.50) (9.17) (-1.98) (-3.10) (-4.12)

January -0.657 -1.269*** -1.404*** -0.544 -0.833 1.087*** 0.608** -0.165 -0.0256 -0.757** (-1.41) (-3.71) (-4.74) (-1.19) (-1.42) (3.23) (2.48) (-0.91) (-0.10) (-2.30)

BidAski,t-1 -14.79 -38.75*** -66.24*** -76.13*** -126.5*** -40.97*** -52.17*** -78.08*** -95.00*** -160.5*** (-1.34) (-4.40) (-7.42) (-5.73) (-7.17) (-3.75) (-5.92) (-8.67) (-7.14) (-9.11)

DivYieldi,t-1 -8.203*** -4.228** -4.323* -9.507*** 7.93 -8.142*** -3.689* -3.144 -7.843*** 9.825* (-2.94) (-2.05) (-1.90) (-3.20) (1.37) (-3.03) (-1.80) (-1.38) (-2.63) (1.75)

Analystst-1 0.981*** 0.145 -0.487*** -0.862*** -1.920*** 0.728** 0.15 -0.404** -0.768*** -1.646*** (2.97) (0.73) (-3.08) (-4.04) (-5.60) (2.25) (0.76) (-2.54) (-3.62) (-4.91)

N 45692 88540 124873 67754 62647 45692 88540 124873 67754 62647

Adj. R2 0.032 0.017 0.009 0.02 0.045 0.064 0.033 0.023 0.038 0.08

40

Panel B Loser

Winner

(1) (2) (3) (4) (5)

Intercept 14.24*** 9.888*** 9.729*** 17.67*** 12.68***

(4.97) (4.32) (5.12) (7.58) (4.29)

Dec_VIXt-1 0.0183 0.473*** 0.696*** 0.731*** 0.614*** (0.15) (4.32) (6.88) (4.72) (2.78)

Jan_VIXt-1 0.16 0.289** 0.269** -0.113 -0.473** (1.00) (2.25) (2.18) (-0.58) (-2.03)

Dec_VOLt-1 -0.294** -0.253 0.166 -0.337 0.746*** (-2.44) (-1.34) (1.14) (-1.46) (3.11)

Jan_VOLt-1 -0.234* 0.165 0.157 -0.137 -0.132 (-1.73) (0.92) (0.85) (-0.61) (-0.54)

VOLt-1 1.406*** 1.621*** 1.788*** 2.143*** 1.935*** (16.97) (13.61) (25.44) (20.93) (10.35)

VIXt-1 -0.765*** -0.371*** -0.642*** -0.934*** -1.719*** (-8.78) (-4.58) (-10.85) (-9.83) (-11.43)

S&PReturnt-1 -2.297** -1.271 -1.970*** -4.321*** -1.394 (-2.20) (-1.43) (-2.71) (-3.89) (-0.95)

LogMV i,t-1 -1.176*** -0.766*** -0.542*** -0.968*** -0.699*** (-5.56) (-4.46) (-3.94) (-5.60) (-3.13)

December 3.395*** 2.258*** 0.102 -0.950*** -1.138*** (14.14) (17.17) (1.16) (-7.41) (-5.51)

January 0.963*** 0.713*** 0.148 -0.136 -1.058*** (4.56) (6.14) (1.61) (-1.07) (-6.21)

BidAski,t-1 -38.76*** -53.09*** -78.07*** -94.27*** -156.8*** (-3.55) (-6.00) (-8.67) (-7.06) (-8.84)

DivYieldi,t-1 -8.643*** -3.979* -3.315 -7.864*** 8.948 (-3.23) (-1.92) (-1.46) (-2.64) (1.59)

Analystst-1 0.727** 0.147 -0.415*** -0.774*** -1.719*** (2.24) (0.75) (-2.61) (-3.65) (-5.13)

N 45692 88540 124873 67754 62647

Adj. R2 0.063 0.032 0.023 0.039 0.077