PSYCHOLOGICAL FACTORS, STOCK PRICE PATHS, AND TRADING VOLUME

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1 PSYCHOLOGICAL FACTORS, STOCK PRICE PATHS, AND TRADING VOLUME Steven Huddart, Pennsylvania State University Mark Lang, University of North Carolina at Chapel Hill and Michelle Yetman, University of Iowa We examine the relation between the trading volume of a stock, expressed as a percentage of shares outstanding, and the past stock price trading range. Volume is strikingly higher, in both economical and statistical terms, when the current price is above (below) the previous fifty-two week high (low). Results are robust to a wide range of controls, including returns and news events. An event study shows that volume spikes in the week when price leaves the prior trading range, then gradually returns to normal levels. The results suggest that behavioral factors affect investors trading decisions in equity markets. JEL Classification: C93 D70 D81 G10 Keywords: prospect theory, value function, reference point, behavioral finance this draft: May 8, 2003 Much of this paper was written while Mark Lang was visiting at the University of Queensland. We thank Robert Bloomfield, Dan Collins, Markus Glaser, Chip Heath, Bruce Johnson, Mort Pincus, Andrei Simonov, Martin Weber, Robert Yetman and seminar participants at the University of Iowa, the University of California at Davis, the University of Toronto, and the 2002 Review of Financial Studies/University of Mannheim Conference on Experimental & Behavioural Finance for helpful discussions. We thank Santhosh Gowda and Alan Jagolinzer for able research assistance. We particularly thank Brad Barber and Terrance Odean for providing us with their data on dates when companies are in the news. Send correspondence to: Steven Huddart Smeal College of Business Pennsylvania State University Box 1912 University Park, PA telephone: facsimile: huddart@psu.edu web:

2 In this paper, we examine the relation between a stock s weekly trading volume and aspects of the stock s past price series. Specifically, we focus on the extent to which volume is sensitive to whether the current price is outside the limits of the past range of prices at which the stock has traded. 1 In a pooled time series and cross-section regression analysis, we document a substantial increase in volume when a stock trades above the highest or below the lowest price attained during a 52-week benchmark period ending 20 trading days before the current week. This finding is difficult to reconcile with rational economic motives for trade and instead seems most consistent with behavioral research suggesting that investors focus on current prices relative to previous price extremes in making trading decisions. The spike in volume is robust to inclusion of controls for contemporaneous and prior stock returns, market-wide volume, earnings announcements, dividend record dates, and firm and date fixed effects. The 52-week high and low prices are significantly associated with volume while other deciles of the frequency distribution of past prices over the benchmark period typically are not. The increase in volume when the stock price is outside the limits of the prior trading range is distinct from a more general correlation between price and volume. In addition, for a subset of data for which we have access to a record of news events from the Dow Jones News Retrieval, results are robust to inclusion of controls for news. 1 As discussed later, in a relatively small number of cases, share price exactly equals the prior maximum or minimum. We treat such observations as falling outside the trading range. Results are not sensitive to whether we treat those observations as falling within or outside the trading range. 1

3 The effect is more pronounced the longer the time since the prior extreme was attained, suggesting that potential trades are pent up while the stock price is inside the limits of its trading range and are released when a stock moves outside the limits of its trading range. Further, trading volume tends to decrease the longer price is outside the limits of the past trading range, consistent with the notion that the effect is most pronounced early after the prior extreme is reached and dissipates over time. The effect is consistent for both NYSE/AMEX and NASDAQ stocks, but is stronger for NASDAQ stocks, perhaps reflecting differences in investor clienteles. Additionally, we conduct event studies of volume around the dates on which a firm s stock price moves above a previous high or below a previous low. Volume spikes in the week the stock price moves outside the limits of the previous trading range. The spikes in volume are robust to controls for returns, news events, and stock price volatility. The pattern is quite similar at each end of the trading range, although the spike is more pronounced when the stock price attains the prior high. After either event, volume remains elevated for several weeks, but gradually moves back toward normal levels. Our research contributes to the literature in several ways. First, it builds on research in behavioral finance suggesting that individuals focus on past stock price behavior in making trading decisions. For example, studies like Shefrin and Statman (1985) and Ferris et al. (1988) document investor trading behavior consistent with a focus on 2

4 reference points equal to the stock price at the time of purchase. Closest to our analysis, Heath et al. (1999), Core and Guay (2001), and Poteshman and Serbin (2001) provide evidence that current price relative to the past maximum helps explain financial decision-making in the context of option exercise. We provide evidence that extreme prices affect trading behavior in US equity markets as a whole. Second, we document that volume effects are similar for minimums and maximums, suggesting that it is trading outside the limits of a prior range rather than simply trading above a prior maximum that increases volume. Because patterns for volume at the maximum and minimum are similar, high- or low-priced stocks alone cannot drive the results. Third, our evidence suggests important new determinants of trading volume. As Statman and Thorley (1999) discuss, determinants of trading volume are poorly understood and models of rational utility-maximizing economic agents do not fit observed patterns well, but behavioral models offer novel testable predictions about determinants of volume. For example, Odean (1998b) develops a model in which trader overconfidence is reflected in high volume. Barber and Odean (2002) present evidence that small individual investors are net purchasers of stocks on days when stocks are in the news, experience extreme volume, or experience extreme returns. Our results are consistent with the notion that past extreme points in a stock s price path are salient cues that affect current trading decisions. 3

5 This observation is interesting in light of the prominence of past maximums and minimums the widely-reported 52-week high and low in the business press. The ubiquity of these statistics is surprising because there is little reason to believe that they are helpful in making investment decisions. The Wall Street Journal, for example, reports only a small set of data on each stock, so it is striking that statistics as apparently irrelevant as the prior maximum and minimum are reported. Prior extremes may be prominently reported because they satisfy some demand (i.e., investors are interested in knowing how current price compares to past trading ranges) and the media responds to that demand. Further, because the media report these data, investors may use them in reaching trading decisions because it is too difficult or costly to gather more relevant or useful information. The publication of the numbers makes them candidates for investor attention and may even suggest to investors that they are useful in decision-making. For example, an investor trying to decide when to sell a stock may view surpassing a prior high as an opportune time to sell. Similarly, an investor considering potential investments may view the stock trading below its historic low as a favorable time to buy. In the next section, we discuss the related research and motivate our enquiry. Then, we present the data and analysis, followed by our conclusions. 4

6 1. Background Much of the research in behavioral finance centers on the notion that investors focus on past stock price paths in making decisions. For example, investors may rely on past stock prices in setting reference points for making investment decisions. In the purest sense, a reference point is the inflection point of the value function defined within Kahneman and Tversky s (1979) prospect theory. They argue that standard expected utility theory does not explain many observed phenomena and propose instead an S- shaped value function that is convex to the left and concave to the right of a reference point. Individuals define gains and losses relative to the reference point, and are riskseeking when faced with loss outcomes and risk-averse when faced with gain outcomes. One implication of the theory is that investors are more likely to close positions above reference points than below. Similarly, investors may be more inclined to purchase stocks trading below their reference point because they are more risk-tolerant in that range. Closely related is the notion of beliefs based on past stock prices. For example, choosing to dispose of a stock based on whether current price exceeds some past salient stock price may reflect a belief in price reversion in which an investor sells (buys) stocks trading above (below) a past price because of a belief that stock price will eventually revert to that price. It is difficult to distinguish empirically between belief models and models based on the value function because investors may appear to be risk-seeking 5

7 at prices below the reference point (and hence, unwilling to liquidate their positions) because they believe the odds of price appreciation are greater. Similarly, investors may appear to be risk-averse at prices above the reference point when, in fact, they are responding to a belief that prices will revert. In fact, Dhar and Kumar (2001) note that the empirical behavioral finance literature typically does not differentiate between reference points and anchors (i.e., uninformative signals which people use in decision making) because the two are often observationally equivalent. 2 While the behavioral literature suggests that investors may focus on salient past price levels in making decisions, the theory does not prescribe the location of those price levels. Laboratory studies in the psychology literature often assume a reference point based on the status quo, while empirical and experimental research in behavioral finance focuses on the disposition effect, where the reference point is assumed to be the purchase price of the stock. Shefrin and Statman (1985) coined the term disposition effect and showed it to be an important determinant of trading behavior by investors at a retail brokerage. Evidence consistent with the disposition effect has been documented in a variety of settings including investors at a discount brokerage (Odean 1998a), futures traders (Heisler 1994), subjects in a laboratory setting (Weber and Camerer 1998) and traders in 30 small stocks (Ferris et al. 1988). 2 Following the prior literature, we do not attempt to differentiate the effects of beliefs from value functions and use the term reference points loosely to refer to prices salient to investor decision-making, either because of beliefs or value functions. 6

8 While the notion that the purchase price is a reference point has empirical support, research on learning and memory suggests that individuals are also likely to remember extreme observations (Fredrickson and Kahneman 1993; Fiske and Taylor 1991). As a result, individuals may focus on extreme observations when making investment decisions. Closest to our study, Gneezy (1998) examines trading behavior in an experimental setting, considering both purchase prices and previous extreme prices. He finds evidence that both purchase prices and prior maximum stock prices appear to precipitate trading, and that the prior maximum price may actually be a more salient reference point than the purchase price. Research on stock options provides confirming evidence that the prior maximum is an important determinant in financial decision-making. Heath et al. (1999) examine determinants of exercise using detailed option grant and exercise records for more than 50,000 employees at seven companies and find that exercise concentrates at times when the stock price is above the 52-week high, suggesting a greater willingness to liquidate positions when stocks are trading above a prior extreme. Core and Guay (2001) find consistent results for a broad cross-section of firm-level option exercise data. Poteshman and Serbin (2001) document similar early exercise behavior for investors in traded options, focusing on cases in which exercise is clearly irrational. They find that the effect is more pronounced for discount and full service customers than for firms proprietary traders, which they attribute to differences in sophistication. Similarly, Huddart and 7

9 Lang (2003) compare option exercise behavior across levels in the organization and report that lower-level employees exercise decisions are more sensitive to prior maximums. Because employees typically cash out of the stock when they exercise their options, their basic decision of when to liquidate is similar to that faced by an investor holding a stock. Further, evidence in Heath et al. (1999) and Huddart and Lang (2003) suggests that the sensitivity of employee exercise decisions to prior price extremes is robust to controls for risk aversion and insider information. However, there are several potentially important ways in which employee stock option exercise decisions differ from equity trading decisions. In the latter case, the purchase price may serve as a reference point. In the former case, there is no corresponding purchase price since employees are granted stock options; employees do not purchase them and the stock price at the option grant date is not a plausible reference point, since exercise below that price is clearly uneconomic. Also, employees receiving stock options may differ from typical equity investors in terms of financial sophistication and training. Examining the effect of past lows on decision-making using options is problematic because options on stocks trading below a prior low are unlikely to be in the money. Equity trades, of course, are not affected by this moneyness consideration. However, there are reasons to believe that prior extremes might serve as powerful reference points for the market more generally. As noted earlier, Gneezy (1998) finds that, in the laboratory, prior maximums serve as powerful reference points even in the 8

10 face of the disposition effect. The 52-week high and low may be salient because they are commonly-reported statistics and may be more recent and relevant to traders than the purchase price, especially in cases where an investor has held the stock for so long that he no longer recalls the purchase price or the current trading price is far from the purchase price. 3 Though an analysis of aggregated trading data alone cannot identify exactly what psychological factors drive trade, it is nevertheless informative to document whether past trading ranges affect current trading decisions, and to calibrate this effect relative to other factors known to affect volume. The notion of trading in response to prior price extremes is particularly interesting because we know of no theory that predicts increased trade by utility-maximizing rational economic agents around a prior high or low Data and Analysis Our unit of observation is a firm-week. Our tests examine the association between volume and the location of the weekly closing stock price in the frequency distribution 3 The notion that investors are more likely to trade when prices move outside of prior trading ranges is also consistent with the discussion of resistance and support levels in the business press. Some technical analysts argue that stocks tend to trade within a range because investors are more likely to sell when share prices reach past highs (creating resistance ) and are more likely to buy as they fall toward past lows (creating support ). See, e.g., Shaun Taylor, Support and Resistance, Technical Analysis 101, June 18, 2001, (accessed April 30, 2003). 4 Since we cannot identify buyers and the sellers, an issue we cannot address with aggregate data is who takes the other side of the transaction if some investors trade based on price relative to prior extremes. While it might seem that the resulting order imbalance could destabilize stocks, that seems unlikely because our sample stocks are fairly large and liquid and the volume effects we document, while statistically and economically significant, are well within the range of ordinary volume for our stocks (e.g., moving volume from the median to the 75th percentile). Further, not all investors are likely to respond in the same way to a given cue; some investors may focus on the trading range while others trade for liquidity reasons or based on other factors. Also, sophisticated market participants may understand that volume at these events is less likely to represent informed trade than volume at other times, and so stand ready to buy or sell for negligible discounts or premiums. 9

11 of prices from a rolling benchmark period. We call the range of prices in the benchmark period the trading range, and focus on firm-weeks where the closing stock price is outside the trading range. Following Heath et al. (1999), we define the prior maximum (minimum) as the highest (lowest) daily closing stock price in the 52-week benchmark period ending 20 trading days (i.e., four weeks) before the last day of the observation week. Our choice of a 52-week period is based on its prominence in the business press and evidence in Heath et al. (1999) that it performs well relative to other benchmark periods in explaining option exercise. Excluding prices in the 20 days preceding the observation week is ad hoc, but reflects an assumption that reference points adjust gradually. This choice also increases the frequency of observations at the extremes; otherwise cases of stocks trading at extremes would be relatively rare because the reference point would reset immediately. 5 The appendix illustrates our variable definitions in the context of a single stock price path. 2.1 Sample We base our analysis on a random sample of 1,000 firms drawn from the CRSP universe of common stocks listed on the NYSE, AMEX, or NASDAQ exchanges at some point in the period November 1, 1982 to December 31, 2002 with at least five years of available price, volume, and return data. We begin our analysis on November 1, As a practical matter, our results are not sensitive to shortening the time from the end of the benchmark period until the observation week from four weeks to one week. When the benchmark period ends closer to the observation week, the number of observations for which the stock price in the observation week is outside of the trading range decreases, but the regression coefficient estimates measuring the increased volume in such weeks remain consistent and strongly significant. 10

12 because that is the first date for which NASDAQ volume is available on CRSP. We limit the sample to 1,000 firms to keep the resulting dataset tractable. Because we use weekly observations for 1,000 firms over a period of 20 years, there are over 500,000 firm-week observations in total. We include stocks listed on any of the three major US exchanges so that findings apply to US equities generally. 2.2 First-stage regression Our tests examine the association between volume and the location of the weekly closing stock price in the frequency distribution of prices from a rolling benchmark period. Our primary analysis is performed in two stages, similar to Ferris et al. (1988). In the first-stage regression, we define abnormal trading volume, ABNVOL, for a given firm-week to be the residual from firm-by-firm regressions of average daily firm volume for the week on average daily market volume for the week, VOL it = β 0 + β 1 MVOL t + ɛ it, where VOL it is the average daily number of firm i shares traded as a percentage of firm shares outstanding in week t, and MVOL is the average daily number of market shares traded as a percentage of the number of market shares outstanding in week t. Weuse the NASDAQ (NYSE) market volume for firms trading on the NASDAQ (NYSE or AMEX). The dependent variable in our second-stage regressions is ABNVOL. In these 11

13 regressions, we examine the relation between a stock s market-adjusted volume and aspects of the stock s past price series across all sample firms and years. In constructing ABNVOL, we could have focused on a value-weighted measure of share volume, but we chose shares traded to abstract from the effects of share price. Implicitly, our choice assumes that investors make decisions based on numbers of shares rather than dollar values. Results are not sensitive to the choice of dollar- or equalweighted measures of market volume. Additionally, results are robust to other volume measures that we discuss in the other analyses section. We use average daily volume over a week since daily volume is likely to be highly correlated and monthly volume may be too aggregated to detect specific effects. Because of concerns about remaining correlation in volume, we adjust for autocorrelation in all of our analyses. 6 While cross correlation is also a potential issue, it should be mitigated by our first-stage market model adjustment. Further, we experimented with estimating residual cross correlations within industry, but they were generally not significant. As we discuss later, results are also robust to firm and date fixed effects. 2.3 Descriptive statistics [Table 1] Table 1 provides descriptive statistics on the regression variables. To mitigate the effects of extreme values, we winsorize volumes, stock returns, stock volatilities, and 6 We specify an autoregressive model with 52 weekly lags, and apply a backstep procedure, which eliminates insignificant lag terms, to arrive at an appropriate lag structure. Results are similar using a Newey West autocorrelation consistent variance estimator (Newey and West, 1987). 12

14 news measures at the 1% and 99% levels. Conclusions are not sensitive to winsorization. The mean value of VOL, is 0.34%, which implies annual volume of about 86% of shares outstanding. By construction, abnormal volume for our sample, ABNVOL, is nearly 0; the small difference from 0 is due to winsorization. The key explanatory variables for the second-stage regression are the indicator variables MAX and MIN. These variables distinguish firm-weeks when the stock price is outside its trading range. MAX (MIN) is 1 when the closing price for the observation firm-week is at or above the prior high (at or below the prior low), and 0 otherwise. The mean value of MAX in table 1 shows that in 12.79% of the observations, the firm-week closing stock price is above the prior maximum; the mean value of MIN shows that in 8.75% of the observations, it is below the prior minimum. Weekly stock returns excluding dividends, RET0, for the sample average 0.20%, implying annual returns of about 10%. The median firm-week closing stock price is at the 52.8th percentile of the prior price distribution (not tabulated), which is attributable to the generally rising stock prices during the sample period. Other variables are described as they are introduced into the analysis. 2.4 Second-stage regression analysis [Table 2] Table 2 reports the basic regression of abnormal volume on the indicator variables, MAX and MIN. We include contemporaneous and prior returns as control variables in 13

15 the regression because prior research indicates that volume is associated with contemporaneous and past returns. For example, Heath et al. (1999) document a relation between past returns and stock option exercise, which they attribute to a belief in mean reversion of price in the short run. Similarly, Statman and Thorley (1999) argue that elevated volume reflects overconfidence induced by past investment success. 7 In particular, our concern is that MAX and MIN are correlated with prior return, so a significant coefficient on MAX or MIN in the absence of controls for stock returns might simply reflect the already-documented relationship between returns and volume. Because information arrival affects returns and volume, stock returns also serve as proxy for information arrival, so controlling for returns is at least a partial control for the effect of information on volume. Statman and Thorley (1999) suggest that the relation between volume and returns may be asymmetric, with negative returns reducing volume more than positive returns increase it, while Barber and Odean (2002) show that retail investors are more likely to trade when returns are large in absolute value. These considerations lead us to include contemporaneous and lagged returns in the regression and to split returns by sign. RET0 is the raw stock return, excluding dividends, over the observation week. The variable NRETi is min(0, RETi). The variable PRETi is max(0, RETi). For i = 1 to 4, RETi is the return over week i relative to the observation week. RET5 is the return over weeks 5 to 26 relative to the observation week. 7 The Statman and Thorley (1999) result is primarily for market volume rather than for individual stocks. We base our analysis on abnormal volume, controlling for the market, so it should not be affected by market volume. 14

16 Contemporaneous returns are strongly correlated with volume. Consistent with Statman and Thorley (1999), the sign on positive returns is positive and the sign on negative returns (coded as negative values) is negative for the contemporaneous and previous week s returns. The likely explanation for the opposite signs on contemporaneous returns is that volume tends to be high when there is news that moves stock prices either positively or negatively. The previous week s return is also significant, consistent with Beaver (1968) who suggests that volume can remain elevated for a week or more following a news release. Also consistent with Statman and Thorley (1999), for returns more than three weeks prior to the sample week the sign on both positive and negative returns is positive, suggesting that volume tends to be higher for firms that are performing well. Since is unlikely that volume responds to news released three of more weeks in the past, the correlation between volume and past returns seems more consistent with behavioral explanations, such as trading by momentum investors who are attracted to stocks that have performed relatively well in the recent past. The principal variables of interest, MAX and MIN, are positive and highly significant with coefficient estimates of and , respectively. From table 1, a change in abnormal volume of that magnitude is enough to move from the median to about the 75th percentile, indicating a substantial increase in volume when the stock price moves to outside its normal trading range. The table reports two R 2 statistics, one representing the fit of the model including lagged volume and one the incremental R 2 for the re- 15

17 gressions. Despite the fact that the overall magnitude of the effect based on the coefficient estimate is substantial and the t-statistic is large due to the large number of observations, the explanatory power of the regression is relatively low. In part, this is because we control for market volume in the first-stage regressions. Controlling for market volume biases against finding the predicted results since it eliminates the effect of cases in which market volume is generally high because a disproportionate share of stocks are trading outside of prior trading ranges. However, analysis of ABNVOL focuses attention on firm-specific effects. Further, the regression does not capture firm-specific news that is likely to affect firm-specific volume, except as it is reflected in returns variables. We return to this issue later. One potential concern with specification (1) of table 2 is that the preceding results might be driven by the effect of earnings announcements or dividend record dates. In particular, volume is likely to be higher around earnings announcements because of the arrival of new information and around dividend record dates because of tax-based dividend capture strategies. DIV and EARNANN are indicator variables taking the value 1 if a dividend record date or an earnings announcement, respectively, occurs during the observation week. From table 1, firms announced earnings recorded by COMPUSTAT in about 5.2% of our sample weeks and 3.6% of sample firm-weeks include dividend record dates recorded by CRSP. While this seems too infrequent to drive the empirical results, we re-estimate the regression including indicator variables for earnings announcements and dividend record dates. 16

18 Finally, the volatility of returns may affect volume for at least two reasons. First, increased return volatility may reflect increased uncertainty in the market, which may lead to additional trading. Second, prospect theory suggests that higher volatility may affect decisions to sell. We define stock volatility, SDVOL, as the annualized standard deviation of stock returns computed from the 26 weekly observations prior to the observation week. Specification (2) in table 2 reports results controlling for earnings announcements, dividend record dates, and return volatility. As expected, volume is on average higher around dividend record and earnings announcement dates. The standard deviation of past returns is negatively correlated with volume, suggesting that return volatility drives out volume. Most importantly, the indicator variables for prior extremes remain highly significant and only drop very slightly with inclusion of the additional variables. It might be that the significant coefficients on MAX and MIN capture the arrival of news other than earnings. As noted earlier, Barber and Odean (2002) present evidence that individual investors are net purchasers of stocks on days when stocks are in the news. As a consequence, the analysis might be confounded by the inclusion of other news dates that are not controlled by inclusion of returns, earnings announcements and dividend record dates. To address that possibility, we include measures of news from Barber and Odean (2002) for the subset of our sample for which their data are available. We include two variables the number of stories published in the week on 17

19 the Dow Jones News Retrieval service that mention a firm (STORIES) and the number of words in those articles deflated by number of companies discussed (WORD ADJ). Because the database of news variables covers only , we lose more that half our observations for this subsample. As noted in table 1, the mean number of stories about a firm in a given week is 1.4 but the median is zero, indicating that stories tend to cluster in a given week. The mean number of words in articles in which a firm is mentioned in a given week is 49, but again the median is zero. The results (reported in table 2, specification (3)) indicate that, as expected, volume is significantly higher for firms with news in the event week. However, the prior maximum and minimum variables remain significant and, in fact, increase in magnitude for this subsample and set of controls. The coefficient estimates on MAX and MIN indicate the effect on abnormal volume associated with moving outside the trading range is as great as the effect associated with an earnings announcement, more than three times the effect associated with a dividend record date, and an order of magnitude greater than the effect associated with a mention of the company name in the business press. It is possible that we have misspecified the relation between news and volume with our measures. To address that possibility, we replicate the analysis excluding all weeks in which there was a news story about a firm. While the sample size drops, results (not tabulated) are very similar. Further, it may be the case that volume increases in anticipation of news or persists after the release of news. As a result, we replicate 18

20 the analysis excluding news weeks, as well as the preceding week and following week. Results (not tabulated) are again very similar. Alternatively, it could be that volume is nonlinear in returns, and price tends to exit the prior trading range through a particularly large positive or negative return. Thus, the indicator variables MAX and MIN might be significantly associated with extreme volume because they are correlated with extreme returns. In our primary analysis, we winsorize returns and volume at the 1% and 99% levels, which should mitigate this issue. We also replicate the analysis including both return and return squared as explanatory variables with similar results (not tabulated). In addition, various rules for eliminating observations with extreme returns do not affect inference: regression analysis of subsamples that exclude observations with contemporaneous returns in excess of 10% and 5% in absolute value yield very similar results (not tabulated). Finally, it is possible that the disposition effect might affect results for the prior maximum since more investors are above their purchase price when above the maximum than at other levels (although this should not affect results for the minimum). Even for the maximum, this seems unlikely, however, since the prior maximum is unlikely to be highly correlated with investors purchase prices. It is not possible to explicitly incorporate controls for the disposition effect since we do not observe investors purchase prices, but Ferris et al. (1988) suggest an approach for estimating them. For a given sample day s price, they form eight equal price bands, four above and four below, and 19

21 accumulate volume in each price band over the prior year to create eight variables. They regress the sample day s volume on the eight prior volume variables, using past volume to estimate the price at which most investors likely purchased their stock. This approach likely measures the disposition effect with error because there is no way to know if investors who purchased in previous volume spikes sold in the interim or if investors selling today bought more than one year ago. Nevertheless, we compute similar variables for each firm-week and included them in our regression. Again, results (not tabulated) are unaffected by inclusion of the controls Comparison with other percentiles of the past price distribution Another potential concern is that other percentiles of the price distribution might have explanatory power. For example, investors might focus on a measure of central tendency like the median, or there might be spikes in volume across other percentiles of the prior trading range. While it seems unlikely that most investors would know percentiles of the prior distribution like the median since they are generally not reported, it is possible that they have a general sense for central tendency over the prior year. [Table 3] Table 3 presents coefficient estimates from a regression that includes a set of indicator variables, PCT0 through PCT90, that partition the prior price distribution into 8 Conclusions should be drawn with caution because we were not able to replicate the Ferris et al. (1988) basic result for our sample. Given the potential for estimation error in the approach, it may be that their result is specific to the sample or time period. Their tests were based on a much smaller sample of firms (the thirty smallest NYSE/AMEX firms on CRSP) and a much shorter time period (1981 to 1985), so our analysis is not strictly comparable to theirs. 20

22 deciles. For example, PCT0 takes on a value of one if price is above the prior minimum and at or below the 10th percentile of the past price distribution, and is zero otherwise; PCT10 takes on a value of one if price is above the 10th percentile of the past price distribution and at or below the 20th percentile of the past price distribution and is zero otherwise; and so on. The exception is PCT90, which takes on a value of one if the price is above the 90th percentile but below the prior maximum, since MAX takes on a value of one for a firm trading at or above the prior maximum. The coefficient estimates on these indicator variables measure the effect on volume of the location of the observation firm-week stock price in the distribution of past stock prices. For expositional convenience, observations are adjusted by the mean volume across all percentiles, so coefficient estimates can be interpreted as the weighted-average volume in a given price percentile relative to the average across all percentiles. Results for the control variables and for the maximum and minimum are similar to those in table 2. There are clear spikes at the maximum and minimum. More to the point, there is no clear evidence of spikes within the trading range. There is some evidence of an increase in volume for PCT0 and PCT90, but that is not surprising for several reasons. First, we have made numerous assumptions to operationalize our measures. For example, we assume that it is the 52-week extremes that matter and that people adjust their reference points over a period of four weeks. Any misspecification of those assumed date limits, even for a subset of investors, would cause observations close 21

23 to our measures of the prior maximum and minimum to be significant. Similarly, the price ranges may be measured with error. We define the range with respect to the endof-week price, but it is possible that the price exceeded a prior extreme during the week but fell back by the end. Finally, it is possible that investors may not draw a bright line around a single price. For example, an investor may be aware of the general range of a price extreme (e.g., around $50/share, as opposed to $50.75), and therefore may not differentiate between share prices in the tight neighborhood of a prior high or low. Most important for our purposes, the changes in volume between the 10th and 20th percentiles and between the 90th and 100th percentiles are dwarfed by the effect of moving outside the trading range, indicating that the effect of being at a maximum or minimum is much larger than other movements within the trading range. 9 The preceding suggests that volume increases when a stock moves outside its normal trading range. While we cannot be certain what causes it, several observations are worth noting. First, the result for the maximum is very consistent with the literature on stock options where the direction of trade can be explicitly identified and incentives can be better controlled. Further, it is consistent with laboratory research by Gneezy (1998) 9 One potential concern is that volume might tend to be higher the more unusual is the price level regardless of whether the price is outside the prior trading range. To address that possibility, we construct avariable measuring the distance of the observation week price from the median price over the benchmark period, defined as the absolute value of the difference between 0.50 and the location of the current price in the distribution of past prices, expressed as a percentile of the past price distribution. Thus, the variable ranges from 0.00 to 0.50, with firms trading at the prior maximum or minimum having a value of 0.50, firms trading at the prior median having a value of 0.00, and firms trading at the 25th and 75th percentiles having values of Results (not tabulated) are similar, suggesting that our findings are not a manifestation of a more general increase in volume as price strays from the typical price in the benchmark period. In addition, results are robust to inclusion of a control for share price, suggesting that the result does not reflect a general relation between volume and share price. 22

24 and archival studies of individual trader choices including Dhar and Kumar (2001). It seems clear that something occurs at the extremes that increases trading volume. Further, the controls for past returns and news, and the fact that the result obtains at the minimum as well as at the maximum, suggest that it is not simply a reflection of the fact that well-performing firms or firms with news have higher trading volume. 2.6 Effect of time elapsed since the extreme was attained To the extent that traders focus on price relative to the prior trading range, one might expect pent-up sales and purchase demand to accumulate the longer the firm has traded in the range. As a result, one might expect the increase in volume when price breaks through the previous range to be a function of the length of time since the last extreme. For example, one can imagine investors waiting in the wings to liquidate positions for diversification or liquidity reasons until the price reaches the prior high. Similarly, investors may wait to purchase shares until the price reaches a new low. The longer the lag before the new maximum or minimum, the greater the accumulated backlog of shares and, hence, the greater the volume when price crosses the prior high. To examine this relationship we include variables in the regression specification that measure the time in weeks since the prior maximum (minimum) was reached, given the price is above (below) the prior high (low), which we label LHIGH (LLOW). For firmweeks where price is below (above) the prior high (low), LHIGH (LLOW) is set to zero. Further, it seems reasonable to expect that if investors delay trading until a new extreme 23

25 is reached, volume will tend to increase when the new level is reached and drop off the longer the share price remains above (below) the previous high (low). Because the greatest response to a new extreme may well occur shortly after the extreme is reached, we include the variables ABVMAX (BELMIN) which measure the time in weeks the share price has been above (below) the prior maximum (minimum). Table 1 reports descriptive statistics on LHIGH, LLOW, ABVMAX and BELMIN. We present the statistics for firm-weeks outside the limits of the trading range (i.e., LHIGH and ABVMAX descriptive statistics are computed over the 65,585 firm-weeks where the closing weekly stock price is above the upper limit of the trading range and LLOW and BELMIN statistics are computed over the 45,531 firm-weeks where the closing weekly stock price is below the lower limit of the trading range.) The means of LHIGH and LLOW are and weeks, respectively. Since the interquartile range of each of these variables is more than 11 weeks, there is substantial variation in the times since the putative reference points were set. Given the current price is outside the limits of the trading range, it may have been there for several weeks as evidenced by the values of ABVMAX and BELMIN at the 75th percentile, 3.40 and 3.60, respectively. [Table 4] Table 4 presents regression results including the variables for time since prior maximum (minimum) and time above (below) current maximum (minimum) along with all controls. 10 The coefficient estimate on the LHIGH (the time since the previous high 10 Results are robust for the full sample without news controls. 24

26 conditioned at being at the maximum) is positive and strongly significant, suggesting that potential volume accumulates between highs and is released when a stock crosses a prior high. 11 Similarly, the variable for time spent at the maximum, ABVMAX, is strongly negative, suggesting that the volume effects of exceeding a prior maximum are initially high and dissipate the longer the stock price remains above the prior maximum. Again, the results are consistent with a recent high cueing some investors to trade shares. As those investors stores of shares are exhausted, volume drops off even though the price remains high. Results for the minimums are consistent with those for the maximums, but weaker. The coefficient on LLOW is significantly positive as with LHIGH, suggesting that the volume reaction is larger the longer it has been since the prior minimum was set, but the coefficient magnitude is smaller. Similarly, the coefficient on BELMIN is negative and significant, but smaller than the coefficient on ABVMAX. Finally, we examine whether the strength of the relation differs between NASDAQ and NYSE/AMEX firms. Examining the exchanges separately provides some indication of the robustness of results to subsamples of firms. If the holders of NASDAQ tend to be less sophisticated, then prior research suggests that they may be more heavily affected by psychological factors. 11 The fact that volume is higher the longer the time since the prior maximum also suggests that it is not simply the case that investors set reservation prices and then trade only at those prices. If investors chose reservation prices based on other factors, one could observe increased trading volume at new price levels because more reservation prices are exceeded. However, if that were the case, one would expect to see relatively lower volume the longer the time since the prior maximum because more investors would have reset there reservation prices since the last high and a higher proportion of new investors would have come in with different reservation prices. 25

27 [Table 5] The results in table 5 indicate that the effect is strongly significant for both the NASDAQ and NYSE/AMEX subsamples. However, the effect is stronger for NASDAQ firms; the coefficients on both MAX and MIN for NASDAQ firms are more than double the corresponding coefficients NYSE/AMEX firms. While we cannot be sure what causes the results to vary across exchanges, the results suggest that NASDAQ stocks are more sensitive to the effects of past extreme prices. Consistent with this, the returns relation for longer lags is also stronger for the NASDAQ than for the NYSE/AMEX firms, with coefficient estimates for the NASDAQ sample substantially larger than for the NYSE/AMEX sample. 12 Further, the fact that the results are robust across exchanges provides more comfort that results are not driven by a subset of stocks. 2.7 Event study The preceding analysis pools time series and cross-section. An alternative approach to investigate the effect of extreme prices is to directly compare volume around weeks on which a firm s stock price breaks through a previous high or low. We identify a subset of observations in which a firm breaks through a previous extreme and examine volume around that date using a regression framework. We identify stocks where price moves outside the prior maximum or minimum and track them for 10 weeks before and 12 One potential concern is that NASDAQ computes volume differently than NYSE, especially since 1992 (Atkins and Dyl 1997). To address that possibility, we recompute volume in a number of ways, including rescaling it on an annual basis by the ratio of NASDAQ/NYSE volume for our sample and computing it as a percentage of annual volume rather than shares outstanding. Results are robust, with NASDAQ firms showing consistently greater sensitivity to extremes than NYSE/AMEX firms. 26

28 10 weeks after crossing the threshold. Thus, our sample includes the 21-week window centered on the week in which the stock exceeds the prior maximum, or falls below the prior minimum. To avoid overlapping event windows, we require event-weeks for a given firm to be at least 21 weeks apart. To ensure that results are not driven by other factors, we estimate a regression with the controls in table 3, specification 2 (excluding the MAX, MIN, and PCT variables), but supplemented with indicator variables for each week relative to the week when the extreme is reached. As a result, the coefficient estimates measure volume in a particular week after controlling for the normal effects of returns, price volatility, earnings announcements and dividend record dates. We correct for autocorrelation in volume as in table 3. [Table 6] [Figure 1] Regression coefficients for the variables of interest are reported in table 6 and plotted in figure For the maximum, volume increases slightly in the weeks leading up to crossing the prior maximum, and then spikes sharply in the week the prior maximum iscrossed. The volume remains elevated, but gradually declines over the following weeks. The pattern for minimums is similar, although not as pronounced. Volume shows a strong spike in the week that a prior minimum is breached, remains elevated for the next two weeks, then returns to normal levels. 13 Coefficients on the control variables (not reported) are very similar to those in table 3, specification 2. 27

29 This result confirms the conclusions from the earlier pooled analysis and provides further assurance that the preceding results are driven by the stock price paths of individual firms rather than differences across firms. 2.8 Other analyses To investigate whether our results are sensitive to our variable definitions, we conducted a variety of untabulated specification checks. In all cases results are robust. To ensure that our results are not sensitive to the control for market volume, we replicate our analysis using raw volume. In addition, we re-estimated the regression using raw volume as a dependent variable and including market volume as a control in a one-stage regression (effectively constraining the market volume relation to be the same across all stocks). To ensure that the right-skewness of volume does not affect the results, we replicate the analysis using the natural logarithm of abnormal volume in place of abnormal volume. In addition, to ensure that nonlinearity or extreme observations do not drive the results, we replicate the analysis using ranks of variables in place of the variables. As discussed earlier, another potential approach for measuring volume is based on past average volume rather than percent of shares outstanding. For example, Barber and Odean (2002) scale volume by average volume for the stock. We implemented a similar approach, scaling weekly volume by average volume during the year for the stock, both with and without a control for analogously scaled market volume. 28