psychological factors, stock price paths, and trading volume

Submitted to Management Sciencemanuscript MS-??

Psychological Factors, Stock Price Paths, andTrading Volume

Steven HuddartSmeal College of Business, Pennsylvania State University, University Park, PA 16802-3603, [email protected],

http://www.smeal.psu.edu/faculty/huddart

Mark LangKenan-Flagler Business School, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3490,

[email protected], http://public.kenan-flagler.unc.edu/faculty/langm/index.html

Michelle H. YetmanGraduate School of Management, University of California at Davis, Davis, CA 95616-8609, [email protected],

http://www.gsm.ucdavis.edu/Faculty/YetmanM/

We examine the relation between a stock’s trading volume and its past price series, which defines a trading

range, to provide large sample evidence that past price extremes influence investors’ trading decisions.

Volume is strikingly higher, in both economical and statistical terms, when price exits this range. This result

strengthens the longer the time since the stock price last achieved the price extreme and is robust across

model specifications and controls for past returns and news arrival. Volume spikes when price leaves the

trading range, then gradually subsides. Returns are reliably positive after the stock price exits the trading

range.

Key words : decision analysis, prospect theory, value function, reference point, behavioral finance

History :

1. Introduction

Prior literature suggests that investors focus on salient past stock prices in making trading decisions,

most notably the purchase price of a stock. However, experimental research indicates that price

levels other than the purchase price may affect investors’ decisions, particularly past extremes.

Consistent with that, research on stock option exercise provides evidence that employees and

traders are more likely to exercise options when stock prices exceed prior maximums. Similarly,

business publications often report information on the past trading range, reinforcing the notion

that past price levels may serve as important triggers for investors more generally.

Our goal in this paper is to provide large sample evidence on whether past extremes appear to

be important to investors’ trading decisions in practice. In particular, 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. 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.

1

Huddart, Lang, and Yetman: Psychological Factors, Price Paths, and Volume2 Article submitted to Management Science; manuscript no. MS-??

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.

The effect is more pronounced the longer the time since the prior extreme was attained, sug-

gesting 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, so that

the effect is most pronounced early after the prior extreme is reached and dissipates over time. The

effect exists 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.1

1 A candidate explanation for the high trading activity noted at price extremes is that traders who are hedging orreplicating the payoffs from derivative securities may be trading more heavily at such times. The derivatives thatmight cause such trades are not standard calls or puts since the deltas of calls and puts change smoothly as the priceof the underlying stock changes and do not depend on whether the stock is near a past price extreme. Thus, if theexplanation is hedging or replicating activity, one must look to more exotic derivatives for which hedge portfolioschange composition rapidly in the neighborhood of price extremes. The owner of a lookback call (put) has the rightto buy (sell) the underlying asset at the lowest (highest) price over the life of the option. A lookback straddle is along position in both a lookback call and a lookback put. Scenario B in Figure 6 of Fung and Hsieh (2001, p. 339)plots the delta of a lookback straddle on a stock whose price first rises, then falls, and finally rises past the priorextreme. This pattern of price movements over time defines the price breakouts we study. The lookback straddle’sdelta increases sharply before the extreme, indicating that replicators and hedgers are trading lots of shares witheach other. At the extreme, there is a kink so that the delta after the price extreme is nearly constant, indicatingthat replicators and hedgers are not trading. Thus, hedging and/or replication of a lookback straddle implies heavy

Huddart, Lang, and Yetman: Psychological Factors, Price Paths, and VolumeArticle submitted to Management Science; manuscript no. MS-?? 3

Finally, we document predictable returns after the stock price exits the past trading range. On

average, stocks breaking out from their past ranges experience positive risk-adjusted returns over

the following six months. The fact that the share price drift is upward whether the stock has fallen

below or risen above its trading range indicates that the effect is not due to momentum since

momentum would imply a continued drift downward for firms that have fallen below their 52-week

low. Further, the results for the 52-week low suggest that risk is unlikely to explain the effect since

the stock price path turns from negative to positive around the 52-week low.

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.

As discussed in the next section, much of the behavioral finance research has investigated purchase

price as a reference point for investors (Shefrin and Statman (1985) and Ferris, Haugen, and

Makhija (1988). However, research in psychology (Fredrickson and Kahneman, 1993) and evidence

from stock option exercise (Heath, Huddart and Lang, 1999) suggests that individuals also focus

on past extremes in decision-making. Consistent with that, the business press often refers to 52-

week highs and lows in discussions of stock valuations. To our knowledge, ours is the first paper

to provide large scale empirical evidence on the effects of prior maximums and minimums on the

trading behavior of investors in general. We provide strong evidence that the investors factor in

the past stock price range in their trading decisions.

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 potentially important determinants of trading volume. As Stat-

man, Thorley, and Vorkink (2003) 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. 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.

Finally, our results on returns complement those in George and Hwang (2004), who examine the

relation between the prior trading range, momentum and future returns. Our approach is different

trade before the prior price maximum is reached and little trade afterwards. In contrast, our findings indicate nounusual volume before the prior maximum is reached and heavy trading afterwards. Hence, the explanation for ourabnormal volume does not appear to lie in trades undertaken to mimic lookback straddles. We thank David Hsiehfor suggesting these issues.


from George and Hwang (2004) in that they seek to better understand momentum investing and

focus on stocks that trade in the top 30 percent of the prior trading range. Since our volume

results suggest that the event of crossing outside the prior trading range appears to have specific

importance to investors, we instead focus on returns following that event. We document significant

positive returns, on average, for a stock whose price rises above its prior maximum price. Further,

we document that very similar volume and returns results hold, on average, for a stock whose price

falls below its prior minimum price, which suggests that what matters is trading outside the past

range, not the direction of the breakout.2

In the next section, we discuss the related research and motivate our enquiry. Then, we present

the data and analysis, followed by our conclusions.

2. 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 the-

ory. 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. One implication of the theory is that investors are more likely to trade when the

stock price crosses the reference point level because their risk tolerance changes. Closely related,

investors may focus on price levels because of a belief that past price ranges are informative about

likely future stock price directions.3

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 that investors focus on the status quo, which

empirical and experimental research in behavioral finance operationalizes as 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

2 George and Hwang (2004) examine returns in the bottom 30 percent of the prior distribution and do not findevidence of significant abnormal returns. Our design differs from theirs in that we focus on returns after the date onwhich the stock price crosses its prior minimum and document significantly positive returns following that date.

3 Dhar and Kumar (2001) note that the empirical behavioral finance literature typically does not differentiate betweenreference points and anchors (i.e., uninformative signals which people use in decision making) because the two areoften observationally equivalent. Following the prior literature, we do not attempt to differentiate the effects of beliefsfrom 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.


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, 1998),

futures traders (Heisler, 1994), subjects in a laboratory setting (Weber and Camerer, 1998) and

traders in 30 small stocks (Ferris et al., 1988).

While the notion that the purchase price affects investor behavior has empirical support, research

on learning and memory suggests that individuals are also likely to fixate on extreme observations

(Fredrickson and Kahneman, 1993; Fiske and Taylor, 1991). Closest to our study, Gneezy (1998)

examines trading behavior in an experimental setting, considering both purchase prices and previ-

ous 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 more salient

than the purchase price.

Research on stock options also suggests that the prior maximum is an important determinant in

financial decision-making. Heath et al. (1999) and Core and Guay (2001) examine employee stock

option exercise decisions 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. Poteshman and Serbin (2001) document similar early exercise behavior for

investors in traded options, focusing on cases in which early exercise is clearly irrational, with the

effect more pronounced for discount and full service customers than for firms’ proprietary traders.

Similarly, Huddart and Lang (2003) find that lower-level employees’ exercise decisions are more

sensitive to prior maximums relative to higher-level employees.

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. However, there

are several potentially important ways in which stock option exercise decisions differ from equity

trading decisions. For stock, the purchase price may serve as a reference point. For options, 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 market participants more generally. In a study of daily trade data from the Finnish stock


market, Grinblatt and Keloharju (2001) document that households and some types of institutions

have a greater propensity to sell stocks that they hold on days when the stock price is above the

highest price attained in the past month; also, on days when a domestic Finnish investor trades

stock, being at a monthly high increases the propensity to buy. Also, as noted earlier, Gneezy

(1998) finds that, in the laboratory, prior maximums serve as powerful reference points even in

the 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, the stock has split, or the current price is far from the purchase price.4

3. 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 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 An on-line supplement to

the paper illustrates our variable definitions in the context of a single stock price path.

4 The notion that investors are more likely to trade when prices move outside of prior trading ranges isalso consistent with the discussion of resistance and support levels in the business press. Some technical ana-lysts argue that stocks tend to trade within a range because investors are more likely to sell when shareprices reach past highs (creating “resistance”) and are more likely to buy as they fall toward past lows (cre-ating “support”). See, e.g., Shaun Taylor, “Support and Resistance,” Technical Analysis 101, June 18, 2001,http://www.investopedia.com/printable.asp?a=/articles/technical/061801.asp (accessed November 26, 2005).

5 As a practical matter, our results are not sensitive to shortening the time from the end of the benchmark perioduntil the observation week from four weeks to one week. When the benchmark period ends closer to the observationweek, the number of observations for which the stock price in the observation week is outside of the trading rangedecreases, but the regression coefficient estimates measuring the increased volume in such weeks remain consistentand strongly significant.


3.1. Sample

We base our analysis on a random sample of 1,000 firms drawn from the Center for Research in

Security Prices (CRSP) universe of common stocks listed on the NYSE, Amex, or Nasdaq exchanges

at some point in the period from 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, 1982 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.

3.2. 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,

VOLit = β0 +β1MVOLt + εit,

where VOLit 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. We use 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 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.

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 adjust-

ment. Further, we experimented with estimating residual cross correlations within industry, but

they were generally not significant.


Table 1 Descriptive statistics on regression variables.

Number of Standard 25th 75th

Variable observations Mean Deviation Percentile Median Percentile

VOL 520,485 0.3437 0.5075 0.0672 0.1690 0.3910

ABNVOL 520,485 -0.0243 0.3809 -0.1644 -0.0547 0.0326

MAX 520,485 0.1279 0.3340 0.0000 0.0000 0.0000

MIN 520,485 0.0875 0.2825 0.0000 0.0000 0.0000

RET0 520,485 0.0020 0.0680 -0.0286 0.0000 0.0275

DIV 520,485 0.0362 0.1867 0.0000 0.0000 0.0000

EARNANN 520,485 0.0521 0.2222 0.0000 0.0000 0.0000

SDVOL 520,268 0.4607 0.2913 0.2551 0.3858 0.5845

REL PRC 520,485 33.9809 15.7355 21.3147 38.8446 49.2032

STORIES 212,941 1.3671 4.2561 0.0000 0.0000 0.0000

WORD ADJ 212,941 49.4782 142.0473 0.0000 0.0000 0.0000

ABVMAX 66,585 2.3006 1.2211 1.2000 2.4000 3.4000

BELMIN 45,531 2.3813 1.2138 1.4000 2.4000 3.6000

LHIGH 66,585 12.8646 12.0307 4.4286 7.0000 16.2857

LLOW 45,531 15.4633 13.6041 5.0000 8.4286 23.1429

The unit of observation is a firm-week. For a randomly selected sample of 1,000

firms, all firm-weeks in the period November 1, 1982 to December 31, 2002 with

available data are included. VOL is the average daily number of firm shares traded

as a percentage of firm shares outstanding in the observation week. ABNVOL is the

residual from firm-by-firm OLS regressions of VOL on market volume, where market

volume is measured as the average daily number of shares traded on the exchange

where the stock is listed (Nasdaq or NYSE/Amex), expressed as a percentage of the

number of shares outstanding for issues listed on that exchange in the observation

week. MAX (MIN) is an indicator variable that takes the value 1 if the closing stock

price for the observation week is above (below) the highest (lowest) price attained

in the year-long period ending 20 trading days before the last day of the observation

week. RET0 is the raw stock return, excluding dividends, over the observation week.

DIV and EARNANN are indicator variables taking the value 1 if a dividend record

date (from CRSP) or an earnings announcement (from COMPUSTAT), respectively,

occurs during the observation week. SDVOL is the annualized standard deviation

of stock returns computed from the 26 weekly observations prior to the observation

week. STORIES is the number of news stories reported in Dow Jones News Service

mentioning the firm during the week. WORD ADJ is the number of words in the

stories mentioning the firm in the week; where a story mentions multiple firms, the

number of words in the story is divided by the number of firms to assign the words

across the firms. ABVMAX (BELMIN) is the time in weeks that the daily closing

stock price has been above (below) the previous high (low), given the current price

is above (below) the prior high (low). LHIGH (LLOW) is the time in weeks since

the prior high (low) was reached, given the current price is above (below) the prior

high (low). All variables are winsorized at the 1% and 99% levels.


3.3. Descriptive statistics

Table 1 provides descriptive statistics on the regression variables. To mitigate the effects of extreme

values, we winsorize volumes, stock returns, stock volatilities, and news measures at the 1 percent

and 99 percent levels. Conclusions are not sensitive to winsorization. The mean value of VOL, is

0.34 percent, which implies annual volume of about 86 percent of shares outstanding. By construc-

tion, 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 percent of the observations, the firm-week closing stock price is above the prior

maximum; the mean value of MIN shows that in 8.75 percent of the observations, it is below the

prior minimum. Weekly stock returns excluding dividends, RET0, average 0.20 percent, implying

annual returns of about 10 percent. The median firm-week closing stock price is at the 52.8th per-

centile 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.

3.4. Second-stage regression analysis

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 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 et al.

(2003) 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 a proxy for information arrival, so controlling

for returns is at least a partial control for the effect of information on volume. Statman et al.

6 We specify an autoregressive model with 52 weekly lags, and apply a backstep procedure, which eliminates insignif-icant lag terms, to arrive at an appropriate lag structure. Results are similar using a Newey–West autocorrelationconsistent variance estimator (Newey and West, 1987)

7 The Statman et al. (2003) result is primarily for market volume rather than for individual stocks. We base ouranalysis on abnormal volume, controlling for the market, so it should not be affected by market volume.


(2003) 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.

Contemporaneous returns are strongly correlated with volume. Consistent with Statman et al.

(2003), 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 et al. (2003), 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 it is unlikely

that volume responds to news released three or 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.

From specification (1) of Table 2, the principal variables of interest, MAX and MIN, have positive

and highly significant coefficient estimates of 0.0749 and 0.0740, respectively. A change in abnor-

mal 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 outside its normal trading

range. The table reports two R2 statistics, one representing the fit of the model including lagged

volume and one the incremental R2 for the regressions. 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.


Table 2 Regression of ABNVOL on characteristics of the past price series and control variables.

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

Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t

MAX 0.0749 41.7 0.0745 41.5 0.0835 26.3 0.0747 10.1 0.0785 13.6PCT90 0.0017 0.2PCT80 -0.0215 -3.0PCT70 -0.0244 -3.4PCT60 -0.0282 -3.9PCT50 -0.0322 -4.5PCT40 -0.0235 -3.2PCT30 -0.0278 -3.8PCT20 -0.017 -2.3PCT10 -0.0094 -1.3PCT0 0.0148 2.0MIN 0.0740 34.9 0.0735 34.6 0.0869 23.3 0.093 11.5 0.0959 13.0ABVMAX -0.0149 -8.1BELMIN -0.0105 -4.5LHIGH 0.0024 11.9LLOW 0.0007 3.2PRET0 2.0997 214.6 2.0741 212.3 2.5299 145.5 2.5451 141.7 2.5001 142.8NRET0 -1.4155 -116.5 -1.3888 -114.4 -1.6962 -78.4 -1.6726 -74.3 -1.6734 -76.8PRET1 0.7906 78.2 0.7962 77.2 0.9717 53.1 0.9839 52.4 0.9605 52.4NRET1 -0.4783 -38.0 -0.4891 -38.1 -0.6696 -29.2 -0.6463 -27.3 -0.6664 -29.1PRET2 0.2575 25.3 0.2645 25.6 0.3378 18.3 0.3494 18.6 0.3383 18.3NRET2 -0.0252 -2.0 -0.0369 -2.9 -0.0892 -3.9 -0.0675 -2.8 -0.0958 -4.1PRET3 0.1672 16.5 0.1725 16.8 0.1856 10.2 0.1974 10.6 0.2012 10.8NRET3 0.0981 7.8 0.0888 7.0 0.1384 6.1 0.1575 6.7 0.1233 5.3PRET4 0.1267 12.9 0.1319 13.3 0.1618 9.2 0.1691 9.4 0.1784 10.1NRET4 0.1083 9.0 0.0985 8.1 0.1353 6.2 0.1539 6.9 0.1246 5.7PRET5 0.0414 12.3 0.0423 12.4 0.0514 8.5 0.0513 8.2 0.0552 9.1NRET5 0.1114 18.1 0.1054 16.9 0.1463 12.8 0.1645 13.7 0.1449 12.6DIV 0.0124 6.0 0.0256 7.0 0.0256 7.0 0.0255 7.0EARNANN 0.0878 52.4 0.0886 31.4 0.0884 31.3 0.0887 31.4SDVOL -0.0245 -4.3 -0.0295 -2.7 -0.0254 -2.4 -0.0328 -3.1STORIES 0.0052 23.0 0.0052 23.0 0.0052 23.0WORD ADJ 0.0001 19.6 0.0001 19.6 0.0001 19.6

Regression R2 0.0989 0.1037 0.1327 0.1338 0.1339Total R2 0.4224 0.4255 0.4168 0.4219 0.4176

N 520,485 520,268 212,879 212,879 212,879

Variables are defined in Table 1 with the following additions. 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.

PCTi is an indicator variable that takes the value 1 if the closing stock price for the observation week

is above the percentile PCTi, but at or below the next percentile, where percentiles are calculated

relative to the distribution of prices over the year-long period ending 20 trading days before the last

day of the observation week. The exception is PCT90, which takes on the value 1 when the price is

above the 90th percentile and below the maximum. The coefficient estimate for each PCTi variable is

the difference from the mean of the PCTi estimates in the specification. Intercept and autoregressive

parameter estimates are not reported.


Further, the regression does not capture firm-specific news that may affect firm-specific volume,

except insofar as this news is reflected in the 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 percent of our sample weeks and 3.6 percent 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.

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 this 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 the Dow

Jones News Retrieval service that mention a firm (STORIES) and the number of words in those

articles deflated by the number of companies discussed (WORD ADJ). Because the database of

news variables covers only 1994-2000, we lose more than 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.

To rule out the possibility that we have misspecified the relation between news and volume with

our measures, 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 might be the

case that volume increases in anticipation of news or persists after the release of news. To address

this possibility, we replicate 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 percent

and 99 percent 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 percent and 5 percent 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 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.8

3.5. 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.

Specification (4) of Table 2 presents coefficient estimates from a regression that includes a set

of indicator variables, PCT0 through PCT90, that partition the prior price distribution by decile.

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 from

the previous specifications. 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

8 Conclusions should be drawn with caution because we were not able to replicate the Ferris et al. (1988) basic resultfor our sample. Given the potential for estimation error in the approach, it may be that their result is specific to thesample or time period. Their tests were based on a much smaller sample of firms (the thirty smallest NYSE/Amexfirms on CRSP) and a much shorter time period (1981–1985), so our analysis is not strictly comparable to theirs.


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 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

end-of-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) 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. The effect is not simply a consequence of well-performing firms or

firms with news having higher trading volume because the result obtains at the minimum as well

as at the maximum and in the presence of controls for past returns and news.

3.6. Effect of time elapsed since the extreme was attained

If traders focus on price relative to the prior trading range, pent-up sales and purchase demand

would 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

9 One potential concern is that volume might tend to be higher the more unusual is the price level regardless ofwhether the price is outside the prior trading range. To address that possibility, we construct a variable measuringthe distance of the observation week price from the median price over the benchmark period, defined as the absolutevalue of the difference between 0.50 and the location of the current price in the distribution of past prices, expressedas a percentile of the past price distribution. Thus, the variable ranges from 0.00 to 0.50, with firms trading at theprior maximum or minimum having a value of 0.50, firms trading at the prior median having a value of 0.00, andfirms trading at the 25th and 75th percentiles having values of 0.25. Results (not tabulated) are similar, suggestingthat our findings are not a manifestation of a more general increase in volume as price strays from the typical pricein the benchmark period. In addition, results are robust to inclusion of a control for share price, suggesting that theresult does not reflect a general relation between volume and share price.


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 firm-weeks where price is below

(above) the prior high (low), LHIGH (LLOW) is set to zero. If investors delay trading until a new

extreme is reached, it seems reasonable to expect that 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 12.86 and 15.46 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.

Specification (5) of Table 2 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 LHIGH (the time since the previous high, conditioned

on being at the maximum) is positive and highly significant, suggesting that potential volume

accumulates between highs and is released when a stock crosses a prior high. 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

10 Results are robust for the full sample without news controls.


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.

3.7. Differences between Nasdaq and NYSE/Amex exchange-listed firms

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 Nasdaq investors tend to be less sophisticated, then prior research suggests

that they may be more heavily affected by psychological factors.

The results in Table 3 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 for

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.11 Further, the fact that the results are robust across exchanges provides

more comfort that results are not driven by a subset of stocks.

3.8. 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 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

11 One potential concern is that Nasdaq computes volume differently than NYSE, especially since 1992 (Atkins andDyl 1997). To address that possibility, we recompute volume in a number of ways, including rescaling it on an annualbasis by the ratio of Nasdaq/NYSE volume for our sample and computing it as a percentage of annual volume ratherthan shares outstanding. Results are robust, with Nasdaq firms showing consistently greater sensitivity to extremesthan NYSE/Amex firms.


Table 3 Regression of ABNVOL on MAX,

MIN, and controls, by stock

exchange.

NASDAQ NYSE/AMEX

Coeff. t Coeff. t

Intercept -0.2675 -25.0 -0.1455 -21.4

MAX 0.1233 23.6 0.0467 15.4

MIN 0.1076 17.6 0.0502 14.0

PRET0 2.7584 111.4 1.8426 85.9

NRET0 -1.7342 -55.5 -1.5867 -61.8

PRET1 1.0703 41.1 0.6529 29.0

NRET1 -0.6101 -18.4 -0.8080 -29.8

PRET2 0.3716 14.2 0.1998 8.8

NRET2 -0.0156 -0.5 -0.2682 -9.9

PRET3 0.2038 7.9 0.0764 3.4

NRET3 0.2413 7.3 -0.1259 -4.7

PRET4 0.1780 7.1 0.0882 4.1

NRET4 0.2021 6.4 -0.0569 -2.2

PRET5 0.0683 8.1 0.0067 0.9

NRET5 0.1826 11.0 0.0340 2.6

DIV 0.0083 1.1 0.0307 10.5

EARNANN 0.1122 25.3 0.0460 15.9

SDVOL -0.0060 -0.4 -0.0122 -0.9

STORIES 0.0084 20.2 0.0031 16.0

WORD ADJ 0.0002 17.2 0.0001 13.7

Regression R2 0.1466 0.1196

Total R2 0.4277 0.3990

N 116,885 95,994

See Table 1 for variable definitions. Autoregres-

sive parameter estimates are not reported.

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 2, specification (2) (excluding the MAX and MIN 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


Table 4 Regression of abnormal volume on indi-

cator variables for time relative to the

event week and control variables.

Event is trading Event is trading

above below

trading range trading range

Coeff. t Coeff. t

B10 -0.0103 -2.6 -0.0086 -2.0

B9 -0.0114 -2.7 -0.0047 -1.1

B8 -0.0139 -3.3 -0.0141 -3.1

B7 -0.0126 -2.9 -0.0175 -3.7

B6 -0.0188 -4.3 -0.0183 -3.9

B5 -0.0162 -3.7 -0.0205 -4.3

B4 -0.0174 -3.9 -0.0275 -5.7

B3 -0.0074 -1.7 -0.0176 -3.7

B2 0.0002 0.0 -0.0174 -3.6

B1 0.0184 4.1 -0.0033 -0.7

A0 0.1260 27.8 0.0722 14.6

A1 0.0955 21.1 0.0361 7.3

A2 0.0616 13.6 0.0112 2.3

A3 0.0410 9.1 0.0024 0.5

A4 0.0400 8.9 -0.0085 -1.8

A5 0.0385 8.7 -0.0074 -1.5

A6 0.0265 6.1 -0.0094 -2.0

A7 0.0268 6.2 -0.0108 -2.3

A8 0.0205 4.8 -0.0100 -2.2

A9 0.0209 5.0 -0.0034 -0.8

A10 0.0110 2.8 -0.0066 -1.6

Regression R2 0.1002 0.0988

Total R2 0.4234 0.4225

N 520,248 520,248

See Table 1 for variable definitions. Autoregressive

parameter estimates are not reported.

effects of returns, price volatility, earnings announcements and dividend record dates. We correct

for autocorrelation in volume as in Table 2.


Figure 1 Coefficient estimates from Table 4 regression of abnormal volume on indicator variables for event time.

(a) (b)

(A) (B)

Note. Bars plot the coefficient estimates for event-time indicator variables from the regression reported in Table 4 of

abnormal volume, ABNVOL, on indicator and control variables. In panel A, the event is the stock moves above the

trading range. In panel B, the event is the stock moves below the trading range.

Regression coefficients for the variables of interest are reported in Table 4 and plotted in Fig. 1.12

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 is crossed. 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.

This result confirms the conclusions from the earlier pooled analysis and provides further assur-

ance that the preceding results are driven by the stock price paths of individual firms rather than

differences across firms.

3.9. 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

12 Coefficients on the control variables (not reported) are very similar to those in Table 2.


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.

Another potential concern is that our analysis is detecting inter-firm rather than intra-firm

differences. For example, it is possible that some sample firms tend to trade more frequently above

prior maximums or below prior minimums and also tend to have higher volume for reasons other

than their current stock price relative to past price levels. If so, our interpretation of the link

between price level and trading volume would be incorrect. The event study analysis suggests that

this is not the case because results are robust in a comparison of a given firm over time. However,

to ensure that our results reflect differences within firms over time rather than across firms, we

replicate the analysis using firm fixed effects. In addition, it could be that our analysis reflects

periods in which volume is elevated and firms are trading at high prices for reasons not captured

by our control variables. That seems unlikely here because our sample is randomly selected and we

explicitly adjust out the market volume effects. However, to ensure that cross correlation of that

type does not drive our empirical results, we replicate our analysis using date fixed effects.

Finally, because of concerns about nonindependence of observations in our panel data, we repli-

cate all of our analysis using the Fama–MacBeth approach where we estimate each regression model

by week and evaluate the significance of the weekly coefficients across the time series. We find that

all variables of interest remain significant at conventional levels and all inferences remain the same.

4. Returns analysisThe preceding analyses suggest that stocks crossing outside a prior trading range experience abnor-

mal volume. Because the elevated volume suggests increased investor interest, a related question

is whether breaking out of a prior trading range is associated with predictable future returns. To

investigate that question, we identify the date on which the stock breaks out of the prior trading

range and track the stock for the subsequent six months to assess whether breaking out of the

trading range appears to predict future returns. To compute returns, we follow the calendar-time

portfolio approach where we place a firm-week into one of three portfolios: MAX (MIN) portfolio

if the firm-week is within 26 weeks of passing a 52-week max (min) or COMPARISON if the firm-

week does not fit into either the MAX or MIN portfolio.13 Next, for each portfolio we calculate the

13 We include delisting returns in the portfolios, but inferences remain unchanged when excluding these returns.


weekly value-weighted portfolio returns.14 Finally, for each portfolio, we adjust the weekly returns

for risk factors by regressing the weekly value-weighted returns on the Fama and French (1993) and

Carhart (1997) risk factors, including the overall market return (WKMKTRF), the performance of

small stocks relative to big stocks (WKSMB), the performance of value stocks relative to growth

stocks (WKHML), and the momentum factor (UMD).15

In untabulated results, we find that stocks crossing the prior maximum (minimum) earn raw

weekly returns of 0.21% (0.22%) over the comparison portfolio, which are both significantly different

from zero at conventional levels. Table 5 reports results controlling for the risk factors. Controlling

for the market return, stocks crossing the prior maximum earn excess returns of 0.18% per week or

a total of 4.68% over the ensuing six months. Results are very similar controlling for either three or

four risk factors, with average weekly returns of 0.19% and 0.14%, respectively. Further, the positive

returns for both approaches are significantly different from zero and from the COMPARISON

portfolio at conventional levels. While the magnitude of incremental returns is strongest in the

month immediately following the period where the maximum is crossed (untabulated analysis),

they remain elevated over the following five months and, as George and Hwang (2004) also find,

there is no evidence of reversal.

Results are at least as striking for firms crossing the prior minimum. We document average

weekly abnormal returns of 0.21% over the six months following the point at which they move

outside of the prior trading range, cumulating to nearly 5.5% over the six months. These positive

returns are significantly different from zero and from the COMPARISON portfolio at conventional

levels. Results are even stronger for the four factor model, reflecting the fact that the controls

for momentum increase the risk-adjusted returns because firms crossing the minimum tend to be

bouncing back from low returns. Again, the largest returns occur in the first month after the

crossing date, but the returns continue to be elevated over the following five months, providing no

evidence of reversals.

Fig. 2 plots cumulative returns from the 3-factor model over the six months following the date

on which the stock crosses outside the prior trading range. Stock returns appear to increase fairly

consistently over the months following the event, gradually leveling out after about five months.

14 We compute value-weighed returns rather than equal-weighed returns because (1) equal weighting leads to over-stated portfolio returns because of the bid-ask bounce and (2) value-weighted returns better measure the economicsignificance of a trading strategy—see Barber et al. (2001), Blume and Stambaugh (1983), Barber and Lyon (1997),Canina et al. (1998), and Lyon et al. (1999).

15 We collected the risk factors from Kenneth French’s website:http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html.


Table 5 Analysis of returns in the 26 weeks after a stock moves outside

its past trading range.

Specification (1) (2) (3)

Coeff. t Coeff. t Coeff. t

MAX Portfolio:

Intercept 0.0018 4.8 0.0019 5.7 0.0014 4.1

WKMKTRF 0.8177 46.9 0.8341 51.4 0.8406 53.1

WKSMB 0.3780 14.6 0.3693 14.6

WKHML 0.0000 0.8 0.0000 1.1

UMD 0.0005 7.4

Adjusted R2 0.6876 0.7430 0.7562

MIN Portfolio:

Intercept 0.0021 3.3 0.0021 3.4 0.0032 5.3

WKMKTRF 0.7850 27.3 0.8288 29.1 0.8158 29.6

WKSMB 0.3516 7.7 0.3692 8.4

WKHML 0.0003 5.3 0.0003 5.2

UMD -0.0011 -8.6

Adjusted R2 0.4269 0.4661 0.5025

COMPARISON Portfolio:

Intercept -0.0004 -1.0 -0.0004 -1.1 -0.0002 -0.5

WKMKTRF 0.9392 50.8 0.9463 50.1 0.9436 50.0

WKSMB -0.0565 -1.9 -0.0528 -1.8

WKHML 0.0001 2.3 0.0001 2.3

UMD -0.0002 -2.6

Adjusted R2 0.7207 0.7232 0.7247

Difference in Intercept

MAX − COMPARISON 0.0022 4.0 0.0024 4.5 0.0016 3.0

MIN − COMPARISON 0.0024 3.3 0.0025 3.5 0.0034 4.7

Regression of 999 weekly value-weighted portfolio returns on risk fac-

tors, where the MAX (MIN) portfolio comprises the 26 firm-weeks after

a firm’s stock price passes a 52-week maximum (minimum), and COM-

PARISON comprises all other firm-weeks. The risk factors are the overall

market return, WKMKTRF; the performance of small stocks relative to

big stocks, WKSMB; the performance of value stocks relative to growth

stocks, WKHML; and the momentum factor, UMD.


Figure 2 Cumulative abnormal returns after a stock moves outside of the past trading range.

(a) (b)

(A) (B)

Note. Lines plot the cumulative abnormal return for 26 weeks after a stock moves outside its past trading range. In

panel A, the event is the stock moves above the trading range. In panel B, the event is the stock moves below the

trading range.

One potential concern with the returns results is that Gervais, Kaniel and Mingelgrin (2001)

document a positive relation between high volume and future returns. Given that we document

increased volume when a stock moves outside a prior range, it is possible that our returns results

may reflect a more general relation between volume and returns. To address that possibility, we

replicated our returns analysis by first adjusting firm returns for the effects of firm-specific volume

over the preceding weeks. Consistent with the results in Gervais et al. (2001), we find a signifi-

cant positive relation between returns and previous volume. However, our results of interest (not

tabulated) are very similar to those reported in Table 5.16

While our analysis cannot isolate the factors that drive the future stock returns, they do suggest

that moving outside a prior trading range is associated not only with predictable volume patterns,

but also with predictable returns.

5. Conclusions

We identify new determinants of market volume. While prior research has focused on the disposition

effect, our results suggest that extreme prices in a stock’s past price path affect investors’ trading

decisions in equity markets. Across a broad sample of stocks, volume fluctuates depending on the

location of the current price in the distribution of prices over the prior year: volume is higher

when the stock price is above the 52-week high or below the 52-week low, suggesting that the

prior extremes are salient in decision-making. While our results do not imply that all investors use

these cues or that some investors always use these cues, the 52-week high and low appear to be

16 Also, our results are similar when we use firm returns adjusted for the effects of size and lagged return (similar tothe method of George and Hwang, 2004).


salient enough to some investors that this phenomenon can be observed in aggregate volume data.

Statman et al. (2003) note that determinants of trading volume are poorly understood, and that

observed patterns of volume do not accord well with economic models. It is significant, therefore,

that what appears to be a behavioral determinant of volume has an effect as large as or larger

than the effects of prominent information events, including earnings announcements, and tax-based

trading strategies, such as dividend capture. Further, the event of crossing outside of a prior trading

range is associated with predictable future abnormal returns.

Earlier research, e.g., Heath et al. (1999), has found that the prior maximum affects the exercise

behavior of stock option holders. The stock option setting differs from the equity setting because

there is no “purchase price” to serve as an obvious reference point, and the financial sophistication

and motivations of stock option holders may differ from those of active investors. Thus, our paper

complements research on options by documenting a similar effect in the equity-trading arena.

Analyzing financial decision-making in the context of options has the advantage of a tighter-

controlled setting where the direction of trade is clear. The fact that our results are consistent

with those from the stock option setting provides some assurance that our findings are not driven

by omitted variables unique to equity trading. Further, our results suggest that similar behavioral

phenomena importantly affect investor behavior across financial decision-making contexts, not

limited to stock option exercise decisions.

Prior stock option research has not focused on the effect of the minimum because options on

stocks trading below prior minimums are not typically in the money. We find that minimums have

similar effects to maximums, suggesting that trading range is an important determinant of volume,

and that it is the price relative to the trading range that matters, rather than price per se.

ReferencesAtkins, A., E. Dyl. 1997. Market structure and reported trading volume: NASDAQ versus the NYSE. J.

Financial Research 20(3) 291–304.

Barber, B., T. Odean. 2002. All that glitters: the effect of attention and news on the buying behavior of

individual and institutional investors. Unpublished working paper, University of California, Berkeley,

CA.

Barber, B. M., R. Lehavy, M. McNichols, B. Trueman. 2001. Can investors profit from the prophets? Security

analyst recommendations and stock returns. J. Finance 56(2) 531–564.

Barber, B. M., J. D. Lyon. 1997. Detecting long-run abnormal stock returns: the empirical power and

specification of test statistics. J. Financial Economics 43(3) 341–372.


Beaver, W. 1968. The information content of annual earnings announcements. J. Accounting Research 6(Sup-

plement) 67–92.

Blume, M. E., R. F. Stambaugh. 1983. Biases in computed returns: an application to the size effect. J.

Financial Economics 12(3) 387–404.

Canina, L., R. Michaely, R. H. Thaler, K. L. Womack. 1998. Caveat compounder: a warning about using the

daily CRSP equal-weighted index to compute long-run excess returns. J. Finance 53(1) 403–416.

Carhart, M. M. 1997. On persistence in mutual fund performance. J. Finance 52(1) 57–82.

Core, J., W. Guay. 2001. Stock option plans for non-executive employees. J. Financial Economics 61(2)

253–287.

Dhar, R., A. Kumar. 2001. A non-random walk down the Main Street: impact of price trends on trading

decisions of individual investors. Working paper, Yale School of Management, New Haven, CT.

Fama, E., K. French. 1993. Common risk factors in the returns on stocks and bonds. J. Financial Economics

33(1) 3–56.

Ferris, S., R. Haugen, A. Makhija. 1988. Predicting contemporary volume with historic volume at differential

price levels: evidence supporting the disposition effect. J. Finance 43(3) 677–697.

Fiske, S. P., S. E. Taylor. 1991. Social Cognition, 2nd ed. McGraw-Hill, New York, NY.

Fredrickson, B., D. Kahneman. 1993. Duration neglect in retrospective evaluations of affective episodes. J.

Personality and Social Psychology 65(1) 45–55.

Fung, W., D. Hsieh. 2001. The risk in hedge fund strategies: theory and evidence from trend followers. R.

Financial Stud. 14(2) 313–341.

George, T. J., C.-Y. Hwang. 2004. The 52-week high and momentum investing. J. Finance 59(5) 2145–2176.

Gneezy, U. 1998. Updating the reference level: experimental evidence. Working paper, University of Haifa,

Israel.

Gervais, S., R. Kaniel, D. H. Mingelgrin. 2001. The high-volume return premium. J. Finance 56(3) 877–919.

Grinblatt, M., M. Keloharju. 2001. What makes investors trade? J. Finance 56(2) 589–616.

Heath, C., S. Huddart, M. Lang. 1999. Psychological factors and stock option exercise. Q. J. Economics

114(2) 601–627.

Heisler, J. 1994. Loss aversion in a futures market: an empirical test. R. Futures Markets 13(3) 793–822.

Huddart, S., M. Lang. 2003. Information distribution within firms: evidence from stock option exercises. J.

Accounting & Economics 34(1–3) 3–31.

Kahneman, D., A. Tversky. 1979. Prospect theory: an analysis of decision under risk. Econometrica 47(2)

263–292.

Lyon, J. D., B. M. Barber, C.-L. Tsai. 1999. Improved methods for tests of longrun abnormal stock returns.

J. Finance 54(1) 165–201.


Newey, W. K., K. D. West. 1987. A simple, positive semi-definite, heteroscedasticity and autocorrelation

consistent covariance matrix. Econometrica 55(3) 703–708.

Odean, T., 1998. Are investors reluctant to realize their losses? Journal of Finance 53(5) 1775–1798.

Poteshman, A., V. Serbin. 2003. Clearly irrational financial market behavior: evidence from the early exercise

of exchange traded stock options. J. Finance 58(1) 37–70

Shefrin, H., M. Statman. 1985. The disposition to sell winners early and ride losers too long: theory and

evidence. J. Finance 40(3) 777–790.

Statman, M., S. Thorley, K. Vorkink. 2003. Investor overconfidence and trading volume. Unpublished working

paper, Santa Clara University, CA.

Weber, M., C. Camerer. 1998. The disposition effect in securities trading: an experimental analysis. J.

Economic Behavior and Organization 33(2) 167–184.

Acknowledgments

Much of this paper was written while Mark Lang was visiting at the University of Queensland. We thank

Brad Barber, Robert Bloomfield, Dan Collins, Markus Glaser, Chip Heath, David Hsieh, Bruce Johnson,

Owen Lamont, Stefan Nagel, Mort Pincus, Andrei Simonov, Martin Weber, Robert Yetman, Ning Zhu and

seminar participants at the American Finance Association annual meetings, the Conference on Experimental

& Behavioural Finance at the University of Mannheim, the University of California at Davis, the University

of Iowa, and the University of Toronto for helpful discussions. We thank Maya Atanasova, 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. Steven Huddart acknowledges

financial support from the Smeal Competitive Research Grant Fund.

psychological factors, stock price paths, and trading volume

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