Stock Volatility and Trading

Transcription

1 Stock Volatility and Trading Anna Agapova Florida Atlantic University 777 Glades Rd Boca Raton, FL Margarita Kaprielyan Florida Atlantic University 777 Glades Rd Boca Raton, FL This version: October 2016 Contact author 1

2 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 2

3 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 longterm 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 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. 3

4 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 taxharvesting strategies; but when market uncertainty reaches very high levels (99 th 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 4

5 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, 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 Agapova and Volkov (2015) examine sensitivity of tax-induced trading of 5

6 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 6

7 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 7 th, 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 individuals 4, 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 1 st, 2003, the long-term capital gain tax rate was further reduced after Jobs and Growth Tax Relief Reconciliation Act of 2003 took effect 4 7

8 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 longterm 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 longterm 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 8

9 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 9

10 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 longterm) 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. 10

11 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 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 11

12 anticipation of capital gain increase in December 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 10 th percentile average long-term return is % and 90 th 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 10 th percentile average month return is -9.79% and 90 th percentile 5 The act was set to expire in January 2013; however, the preferential tax treatment of long-term capital gains was extended. 12

13 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. 13

14 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 daily Ask 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 crosssectionally, with the highest yield of 21.76%, and median dividend yield of 1.63%. The size of the 14

15 firms included in the sample also varies significantly from $47, 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 longterm 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 15

16 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 95 th percentile and 99 th percentile, i.e., variables equal 1 if the SPVOL (VIX) is in 95 th (99 th ) 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 95 th percentile, measured with both SPVOL and VIX. However, the trading in short term and long term winners increases in extreme market volatility of 99 th 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 16

17 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. 17

18 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: 18

19 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 Shortterm 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 19

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 20

21 of the sort are presented in Table 6. Panels A - C display the results of the sorts based on longterm 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 taxinduced 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 1 st (least volatile) to 2 nd decile and increases from 9 th to 10 th 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 21

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. 22

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-ofthe 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-ofthe 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 taxinduced 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 23

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. 24

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27 Table 1. Summary Statistics CAVL t 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. VOL i,t-1 is monthly standard deviation of stock s daily returns, excluding dividends, over previous month. S&PVOL t-1 is monthly standard deviation of S&P500 index daily returns over previous month. S&PReturn t-1 is monthly return on S&P500 index as reported by CRSP over previous month. DivYield i,t-1 is total dividends paid during previous year divided by the ending price, as reported by CRSP. VIX t-1 is a measure of implied volatility over the next 30 days. LogMV i,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. BidAsk i,t-1 is (Ask Bid)/(Ask+Bid)/2 during previous month, Analystst-1 equals log(1+analyst coverage). Panel A Groups month return % % 7.26% 34.72% 99.79% St. Dev % 8.17% 7.98% 8.11% 47.78% Max % -6.00% 23.00% 52.00% % Min % % -6.00% 23.00% 52.00% Number of observations 64, , ,615 97,963 65,797 Groups month return % -7.16% 0.17% 7.13% 17.81% St. Dev. 5.37% 1.42% 2.58% 1.42% 7.14% Max % -5.00% 5.00% 10.00% 33.38% Min % % -5.00% 5.00% 10.00% Number of observations 68,221 78, ,836 89,549 82,703 Panel B N Mean Median Std. Dev. Min Max CAVL 700, VOL t-1 700, VOL [t-1, t-13] 661, IVOL t-1 699, IVOL [t-1,t-13] 645, Beta t-1 699, Beta [t-1,t-13] 645, VIX t-1 745, S&PVOL t-1 745, ChangeVIX t-1 745, ChangeS&PVOL t-1 745, S&PVOL [t-1,t-13] 745, BidAsk i,t-1 693, DivYield i,t-1 712, S&PReturn [t-1,t-14] 745, S&PReturn t-1 745, LogMV i,t-1 708, Analysts t-1 403,