Do Investors Integrate Losses and Segregate Gains? Mental Accounting and Investor Trading Decisions*
I test whether investors’ trading decisions are influenced by their preferences for framing gains and losses. I find that investors are more likely to bundle sales of losers than sales of winners on the same day, consistent with the hedonic editing hypothesis (Thaler 1985) that individuals prefer integrating losses and segregating gains. In addition, the extent to which mixed sales of winners and losers are consistent with the hedonic editing hypothesis is greater than what would be expected under random sales of stocks. These results suggest that mental accounting is likely to play a significant role in investors’ trading decisions.
I. Introduction
Recent studies have argued that prospect theory (Kahneman and Tversky 1979) and mental accounting (Thaler 1985) provide possible explanations for investor behavior (e.g., the disposition effect) and for outstanding asset pricing anomalies such as the equity premium puzzle, the value premium, and the momentum effect.1 However, there are relatively few empirical tests on whether and to what extent mental accounting affects investor decisions. This article tests the effects of mental accounting on investor trading decisions, which provides more direct insight into whether the joint implications of mental accounting and prospect theory provide plausible explanations for capital market anomalies.
In prospect theory, individuals evaluate outcomes using an S‐shaped value function. The value function is defined over gains and losses and shows diminishing sensitivity to both gains and losses. Mental accounting concerns the way investors evaluate outcomes using the value function. For example, whether investors evaluate the overall outcome or evaluate each outcome separately is a question of mental accounting. Diminishing sensitivity of the value function implies that individuals attain higher utility by evaluating losses together and gains separately. If investors try to evaluate outcomes in whatever way makes them happiest, they prefer integrating losses and segregating gains (the hedonic editing hypothesis; Thaler 1985).
Choices over the timing of events are likely to reflect preferences for integrating or segregating outcomes (e.g., Thaler and Johnson 1990): integration is easier if events occur on the same day, and segregation is easier if events occur on different days. If so, people prefer to have events occur on the same day if integration is desired. Similarly, people prefer to have events occur on different days if segregation is desired. When investors sell stocks, they choose whether to realize gains and losses together or separately. Therefore, stock sales by investors provide a natural setting to test the hedonic editing hypothesis. We can infer investors’ preferences for framing gains and losses by examining how they time the gains and losses from stocks sales.
Using the trading records of individual investors at a large discount brokerage house during 1991–96, I document that investors are more likely to bundle sales of stocks that are trading below their purchase prices (“losers”) on the same day than sales of stocks that are trading above their purchase prices (“winners”). Selling losers on the same day makes it easier for investors to aggregate their losses, and selling winners on different days makes it easier to segregate their gains. Therefore, investors’ selling behavior observed in this study can be interpreted as a consequence of their preferences for mentally aggregating or segregating events, preferences that are driven by their desire to perceive outcomes in more favorable ways.
I consider possible alternative explanations for why losers are more likely to be sold on the same day than winners. Tax‐loss selling strategies implemented near the end of the year, for example, may induce clustering of loss selling. Margin calls can trigger sales of multiple stocks that are likely to be losers. It is possible that investors have more losers than winners in their portfolios, increasing the chance of selling multiple losers than of selling multiple winners. Since the dollar value of a loser is likely to be smaller than the dollar value of a winner, an investor who has a fixed proceeds target may need to sell multiple losers, while selling one winner could suffice. Losers in a portfolio might be more correlated with each other than winners and therefore more likely to be sold together due to greater commonality. Good‐till‐cancel limit orders may take longer than a day to be executed, and investors’ greater use of limit orders for winners than for losers can spread out sales of winners relative to sales of losers. I examine these alternative hypotheses in univariate tests and also in multivariate tests. Some of the alternative stories provide a significant explanatory power but do not fully account for investors’ tendency to realize multiple losses than gains on the same day.
As an alternative testing approach, the probability of multiple stock sales is modeled under the assumption that the selling decision of each stock is independent. Under this assumption, the probability of multiple stock sales increases with the number of winners and with the number of losers in the portfolio, and the impact of an additional winner (loser) on the probability of multiple stock sales increases with the investor’s propensity to sell a winner (loser). Studies have documented that investors’ propensity to sell a winner is greater than their propensity to sell a loser (the disposition effect). If so, the impact of an additional winner on the probability of multiple stock sales should be larger than that of an additional loser if selling decisions are independent. However, the result shows that the effect of an additional loser on the probability of multiple stock sales is much larger than the effect of an additional winner, opposite of what is expected when sales decisions are independent and investors show disposition effect. Thus, this evidence suggests that selling decisions of losers are more positively correlated than selling decisions of winners.
For mixed outcomes of gains and losses, the hedonic editing hypothesis predicts individuals prefer integrating them unless the gain is very small relative to the loss. I find that the extent to which investors combine the sales of winners and losers in a way consistent with the hypothesis is greater than what we would expect if investors randomly chose which gains and losses to realize.
The contributions of this article can be summarized as follows. First, it develops testable hypotheses on investor trading behavior from the hedonic editing hypothesis (Thaler 1985) and provides evidence that investors’ stock selling decisions are consistent with the implications of prospect theory and mental accounting. A growing body of theoretical models are based on assumptions derived from psychological findings. However, as Hirshleifer (2001) points out, it is often not obvious how to translate preexisting evidence from psychological experiments into assumptions about investors in real financial settings (Hirshleifer 2001, 1577). This study tries to fill this gap by developing and testing a prediction from psychological theories on the behavior of market participants. Second, it complements recent studies on individual investor trading decisions, most of which have examined the trading decisions for each stock separately.2 In contrast, this article examines how selling decisions for multiple stocks interact with each other, even in the absence of common fundamental factors. Finally, the empirical finding of this article may have further implications on the study of equilibrium stock prices. Investors’ asymmetric selling decisions for their winners and losers can contribute to the asymmetry in the stock market. For example, empirical evidence shows that correlations of stock returns are higher in down markets than in up markets.3 Higher correlations of stock returns in down markets could be due to greater correlations in selling decisions on losers.4 In addition, investors’ selective adoption of different mental accounting systems may affect asset prices. Barberis and Huang (2001) consider two forms of mental accounting, one in which investors care about the gains and losses in the value of individual stocks (individual stock accounting) and the other in which investors care about the gains and losses in the value of the overall portfolio (portfolio accounting) and show that the form of mental accounting affects asset prices in a significant way. If investors mentally integrate losses and segregate gains, portfolio accounting (individual stock accounting) will be more prevalent in a down (up) market, implying different market behavior in up and down markets.
The remainder of the article is organized as follows. Section II reviews the literature on prospect theory and mental accounting. Section III lists the hypotheses to be tested, and Section IV describes the data and the empirical results. Section V discusses further implications of mental accounting principles and concludes the article.
II. Literature Review
A. Prospect Theory and Mental Accounting
Kahneman and Tversky (1979) propose prospect theory as a descriptive model of decision making. According to prospect theory, individuals maximize over a value function instead of the standard utility function. The value function is defined over gains and losses relative to a reference point rather than over levels of wealth. The function is concave for gains, convex for losses, and steeper for losses than for gains.
The prospect theory value function is defined over single outcomes. Then, a question arises as to how to use the value function to evaluate multiple outcomes: Do people evaluate the aggregated outcomes, or do they evaluate each outcome separately? This question is related to mental accounting (Thaler 1985), which refers to the way investors frame their financial decisions and evaluate the outcomes of their investments.
Thaler (1985) hypothesizes that people try to code outcomes to make themselves as happy as possible (the hedonic editing hypothesis). The hedonic editing hypothesis characterizes decision makers as value maximizers who mentally segregate or integrate outcomes depending on which mental representation is more desirable. For a joint outcome (x, y), people try to integrate outcomes when integrated evaluation yields higher value than separate evaluations, 
, and try to segregate outcomes when segregation yields higher value, 
. Under this assumption, Thaler (1985) derives mental accounting principles that determine whether segregation or integration is preferred. The principles indicate that individuals should segregate gains and integrate losses because the value function exhibits diminishing sensitivity as the magnitude of a gain or a loss becomes greater (figs. 1 and 2). Individuals can maximize their happiness by savoring gains one by one and minimize the pain by thinking about the overall loss rather than individual losses. For mixed outcomes, whether or not integration is preferred to segregation depends on the relative magnitudes of the gain and the loss. Since a loss hurts more than a gain of the same amount (loss aversion), it is better to combine a loss with a larger gain. Diminishing sensitivity of the value function implies that it is preferred to segregate a small gain as a “silver lining.”
Fig. 1.— Multiple gains—segregation preferred
Fig. 2.— Multiple losses—integration preferred
B. Test of the Hedonic Editing Hypothesis
In principle, individuals could divide or combine gains and losses completely arbitrarily in order to maximize their happiness. However, there are limits to the degree to which people can mentally segregate and integrate outcomes. Thaler and Johnson (1990) propose that temporal separation of events facilitates segregation of outcomes and temporal proximity facilitates integration. If so, the hedonic editing rules imply that people prefer to experience events on different days when segregation is preferred and on the same day when integration is preferred. Thus, we can test whether people engage in hedonic editing by looking at their choices over the timing of events.
Relatively few papers have tested the hedonic editing hypothesis. For mixed outcomes, Linville and Fischer (1991) find that people prefer to have a negative event with an offsetting positive event on the same days. Hirst, Joyce, and Schadewald (1994) find that people prefer to finance purchases of goods with loans whose terms correspond with the life of the good.5 For multiple gains, Thaler and Johnson (1990) and Linville and Fischer (1991) find people prefer to have positive events on different days.
However, the experimental evidence so far does not support the hedonic editing hypothesis on its prediction regarding multiple losses. Thaler and Johnson (1990) and Linville and Fischer (1991) find people prefer to have negative events on different days. These results are somewhat puzzling because people think aggregated losses are better than segregated ones (Thaler 1985). Thaler and Johnson (1990) argue that decision makers do not engage in active editing of outcomes and propose the quasi‐hedonic editing hypothesis, where hedonic editing rules are followed only part of the time. Linville and Fischer (1991) suggest that people have resources that are limited but renewable over time (e.g., renewed after a good night’s sleep) for dealing with emotionally impactful events.
If other factors such as limited daily gain‐savoring and loss‐buffering resources are also important determinants of preferences for experiencing events on the same day, a relative comparison of the preferences for combining positive events and negative events can help isolate the effect of mental accounting. Controlling for other determinants of timing choices is especially important when we use stock trading data to test the hedonic editing hypothesis, as mental accounting is one of many factors underlying investors’ trading decisions. Thus, the main test of the article is based on a relative comparison of investors’ propensities to sell multiple winners and losers to minimize the influence of other factors on stock selling decisions.
A few additional differences of this study from the previous ones are worth mentioning. While subjects in the previous experiments had no choice over the type of outcomes, investors construct their own choices of gains and losses to realize as well as the timing of the realizations. In addition, the previous results are based on responses to questions about hypothetical alternatives, while the results in this study are based on investors’ actual trading decisions.6
One may argue that a price drop is economically the same negative event regardless of whether the investor sells the stock or keeps it. However, people seem to perceive paper losses and realized losses differently, with the latter being taken more seriously.7 In addition, selling a stock at loss forces investors to admit that they have made mistakes in the past, which is a painful thing to do (Shefrin and Statman 1985). As long as it is painful to sell a stock at a loss, the pain will be minimized by selling losers at the same time according to the principles of mental accounting. Similarly, selling a stock at a gain will be registered as a positive event, so people will prefer selling winners on different days to maximize their happiness.
III. Hypotheses
The hedonic editing hypothesis implies that investors prefer to sell losers than winners on the same day. Therefore the main hypothesis of this article is posited as follows:
Hypothesis. Investors’ propensity to sell multiple stocks on the same day is greater when they realize losses than when they realize gains.
There are several alternative explanations for why investors may sell multiple losers on the same day more often than multiple winners.
Tax‐loss selling.—It is well known that tax‐loss selling is concentrated at the end of the year.8 If investors sell disproportionately more losers near the end of year for tax reasons, they may sell multiple losers on the same day.
Margin calls.—Margin calls force investors to liquidate their positions in some stocks, possibly leading to multiple stock sales. Since margin calls are triggered by stock price drops, disproportionately more losers than winners are likely to be sold from margin calls. Therefore, margin calls may contribute to the bundling of the sales of losers because such calls tend to result in sales of losers rather than sales of winners.
More losers than winners in the portfolio.—The number of stocks that an investor sells largely depends on his/her opportunity to do so. Investors with a large number of stocks are more likely to sell multiple stocks on the same day than those who have only a few stocks. Thus, the probability of selling multiple losers will be higher than that of selling multiple winners if investors have more losers than winners.
Difference in the preference for selling multiple stocks across investors.—It is possible that a certain group of investors always prefer selling multiple stocks per day, regardless of whether the stocks are winners or losers. If those investors happen to have more losers than winners, investor characteristics, not investors’ differential attitudes toward gains and losses, may drive the asymmetry in investors’ propensity to sell multiple stocks.
Smaller proceeds from losers than from winners.—The dollar value of a loser is likely to be smaller than the dollar value of a winner. This implies that the proceeds from selling a loser are likely to be smaller than the proceeds from selling a winner. If investors seek to achieve fixed proceeds from stock sales on a given day, they may need to sell multiple losers, while selling one winner could suffice.
Higher correlation among losers than among winners.—Losers in a portfolio might be more related with each other than winners, and related stocks are more likely to be sold together when news or events affect them at the same time. If stock return correlations of losers are greater than those of winners, or if losers are more likely than winners to belong to similar industries, losers are more likely to be sold on the same day than winners.
Delays in order execution.—Good‐till‐cancel limit orders may take longer than a day to be executed. If investors are more likely to use limit orders for winners than losers (Linnainmaa 2003), multiple sales orders submitted on the same day and executed on different days are more likely for the sales of winners than losers, contributing to the asymmetry in the observed investors’ propensity to sell multiple stocks. The next section describes the data and presents empirical tests designed to address these alternative explanations.
IV. Empirical Tests
A. Data Description
The data set of individual investor trades used in this study is from a large U.S. discount brokerage house. It contains the daily trading records of 158,034 accounts (78,000 households) from January 1991 to November 1996. The file has more than 3 million records of trades in common stocks, bonds, mutual funds, American Depositary Receipts (ADRs), and so forth. Each record contains an account identifier, the trade date, an internal security identifier and Committee on Uniform Security Identification Procedures (CUSIP) number, a buy‐sell indicator, the quantity traded, the commission paid, and the price at which the stocks are sold or bought.
The brokerage house labels households with more than $100,000 in equity at any point in time as “affluent,” households that executed more than 48 trades in any year as active “traders,” and the rest as “general.” If a household qualifies as active trader and affluent, it is considered an active trader. There are a total of 158,034 accounts that are cash, margin, or IRA/Keogh types. Only trades in common stocks are examined in this study. All trade records are adjusted for stock splits and stock dividends using the Center for Research in Security Prices (CRSP) event files. Multiple trades of the same stock from the same account on the same day are aggregated.
Following previous studies (e.g., Odean 1998 and Grinblatt and Keloharju 2000), I use the average purchase price as a reference point. When there are multiple purchases preceding a sale, the average purchase price is calculated as a split‐adjusted share volume‐weighted average. When a stock is sold, it is considered a winner if the sales price is greater than the average purchase price and a loser otherwise. Similarly, a stock that remains in the portfolio is considered a winner if the closing price is greater than the average purchase price and a loser otherwise.9 Sales records are discarded if there is no matching purchase record, since it is not possible to tell whether the sales are at losses or gains. As a consequence, sales of stocks that were purchased prior to January 1991 are not included in this study. Also, observations are dropped if the entire portfolio of stocks is liquidated, because the investor could be closing the account or selling all stocks in the portfolio because of liquidity needs.
Table 1 describes the sample of investor trades used in this study. Sales records from a total of 50,229 accounts are examined. Of these accounts, 17.2% are cash accounts, 49% are margin accounts, and 33.8% are IRA/Keogh accounts. The majority of accounts belong to general households (59.4%), and affluent and trader households account for 18.3% and 22.3%, respectively (panel A).
Panel B of table 1 reports the number of sales events by account type and client segment. Each day on which an investor placed a sell order is considered a sales event, and sales events from different accounts are treated as different observations.10 Of these sales events, 63.5% are from margin accounts, 11.1% from cash accounts, and 25.4% from retirement accounts. When sales events are classified by client segment, active traders account for the largest fraction of total sales events (50.3%).
Panel C describes the characteristics of investor portfolios on the days of stock sales, aggregated over all sales events. Investors’ portfolios are constructed from their purchase records since January 1991, and the profiles of investor portfolios are examined at the sales event level. The median portfolio size and the number of stocks in the portfolio over all sales events are $45,406 and five, respectively, for the entire sample. Investors on average have more winners than losers (median number of winners, three; median number of losers, two), and the dollar value of a winner is greater than that of a loser (the medians are $8,725 and $5,577, respectively).11
B. Proportion of Multiple Stock Sales Conditional on Gains or Losses
Figure 3 shows the distribution of the time interval between two consecutive stock sales from the same account separately for the sales of winners and for the sales of losers. There is not much difference between the sales of winners and the sales of losers for the intervals greater than 5 days, but there is a clear difference between them for the interval of 0–5 days. About 24% of sales of losers occur on the same day as another sale of losers, while 17% of sales of winners occur on the same day as another sale of winners. Figure 3 illustrates that the sales of losers tend to be bundled on the same day compared to the sales of winners.
Fig. 3.— Distribution of the interval between sales
Table 2 reports the number of sales events separately for those at gains and those at losses. To examine whether losses are more likely to be bundled than gains, sales events are classified by whether the sales are at gains or at losses and whether or not the investor sold multiple stocks on that day. I discard sales events with mixed sales of winners and losers in this cross‐classification analysis since they are associated with both gains and losses (mixed sales events are examined separately in Sec. IV.E). About 5.95% of the observations are deleted because they are mixed sales (25,337 out of 425,749 observations).
Panel A of table 2 documents the results for the entire sample. When investors are selling stocks at losses, they sell multiple losers in 10.44% of the cases, while they sell multiple winners in 8.48% of the cases where they realize gains. The difference between the two proportions is 1.96%, which is highly significant with a t‐statistic of 20.01.12 The results show that losses are more strongly associated with bundling than are gains. Panel B shows the results by client segment. Affluent households show the greatest difference between sales at losses and sales at gains in their propensities to sell multiple stocks (2.78%), and active trader households show the smallest difference (1.58%). All the differences are highly significant.
Tax‐loss selling.—It is well known that investors tend to realize losses near the end of the year to take advantage of tax deductions from capital losses. When sales events are classified by month, the difference is especially large in December. Investors sell multiple losers in 14.18% of the sales events at losses and sell multiple winners in 7.93% of the sales events at gains (difference, 6.25%; panel C, table 2) in December. The result suggests that tax‐loss selling is likely to cause clustering of loss selling. However, tax‐loss selling may not be the only cause since the difference between the two proportions is still significant (1.41%; t‐statistic, 13.82) from January–November.
An alternative way of addressing the tax‐loss selling hypothesis is to look at stock sales from retirement accounts (IRA/Keogh). Panel A of table 3 documents the results separately for taxable and retirement accounts. As expected, the difference between sales events at gains and sales events at losses in the proportions of multiple stock sales is larger for the taxable accounts (2.01%; t‐statistic, 17.58). However, the difference for the retirement accounts is also positive and highly significant (1.69%; t‐statistic, 8.87). Tax‐loss selling seems to play a role in the clustering of loss selling, but it does not explain why investors are more likely to sell multiple losers than winners on the same day from their retirement accounts.
Margin calls.—Stock price drops may trigger margin calls and force investors to sell some of the stocks in their portfolios. It is likely that there are more losers than winners in the accounts that just experienced margin calls; therefore, margin calls may result in sales of multiple losers more often than sales of multiple winners.
Panel B of table 3 reports results separately for accounts that allow margin trading and those that do not allow margin trading (cash and retirement accounts). The difference in the percentage of multiple stock sales is actually greater for nonmargin accounts (1.81% for margin accounts and 2.12% for nonmargin accounts), which indicates that margin calls are not the primary reason for clustering of loss selling.
Number of winners and losers and difference in preferences across investors.—Investors might simply have more losers than winners; therefore, they may sell multiple losers more often than multiple winners as they have more losers available for sale.13 It is also possible that a certain group of investors always prefer selling multiple stocks at a time regardless of whether the stocks are winners or losers. If those investors happen to have more losers rather than winners, multiple stock sales are more likely in loss sales events due to the greater presence of those investors in loss sales events. One such possibility is that frequent traders, who are more likely to execute multiple trades a day, have more losers than winners due to their overconfidence (Barber and Odean 2000). If so, we may observe more multiple stock sales in loss sales events because frequent traders are overrepresented in loss sales events.
Panel A of table 4 shows that the number of losers as a percentage of total number of stocks in a portfolio indeed increases with trading frequency and that frequent traders are more likely to sell multiple stocks a day. For the most frequent traders (group 5), 46.23% of the stocks in their portfolios are losers, and 10.8% of sales events are multiple sales events. For the least frequent traders (group 1), 39.56% of the stocks in their portfolios are losers, and 2.47% of sales events are multiple sales events. The investors in loss sales events trade on average 153.1 times, while investors in gain sales events trade on average 141.4 times during the sample period (untabulated), suggesting frequent traders comprise a greater part of loss sales events than gain sales events.
These results suggest that it is important to control for the difference in investors’ opportunities to sell winners and losers. Thus I restrict the sample to sales events on which investors have equal numbers of winners and losers. This restriction ensures that investors had equal opportunities to sell winners and losers and also controls for the possibility that differences in individual characteristics might be driving the results.
The results are qualitatively the same after imposing the restriction of equal numbers of winners and losers (panel B). The difference in the proportions of multiple stock sales is 1.64% with a t‐statistic of 8.91. Investors are more likely to sell multiple stocks when they realize losses than gains, even though they have equal opportunities to realize gains and losses. Also, the result rules out the possibility that the asymmetry is entirely driven by investors with more losers than winners who tend to sell multiple stocks, as those investors are excluded in this restricted sample.
Because I construct investors’ portfolios from their purchase records since 1991, stocks that were purchased prior to 1991 are not captured in the constructed portfolios. It is likely that there are more losers than winners among those stocks since investors tend to hold on to losers longer (e.g., Shefrin and Statman 1985; Odean 1998). Thus, the number of stocks in the portfolio is downward biased, and the downward bias is likely to be greater for the number of losers. Then the restriction of equal numbers of losers and winners may actually result in a sample with more losers than winners, biasing the results toward finding more bundling of losers.
To address this possible bias, panel C reports the results separately for the subperiods from 1991 to 1994 and from 1995 to 1996. When holding periods are calculated from round‐trip transactions, less than 1% of stocks are held for 4 years or longer. Thus, the bias from omitted stocks should be minimal in the later part of the sample period. It appears that the bias does not affect the result very much, as the difference in proportions does not change much in the later period (1.66% in the period 1991–94 vs. 1.60% in the period 1995–96).
Difference in sales proceeds.—Investors may sell stocks to meet liquidity needs. The number of stocks an investor needs to sell to reach a desired level of proceeds depends on the dollar value of each stock in her portfolio. Because the dollar value of a loser is on average smaller than the dollar value of a winner (table 1, panel C), investors may need to sell a larger number of losers than winners to reach the same level of proceeds. If so, stock sales for liquidity needs could be responsible for the observed pattern in investors’ selling behavior. To address this possibility, table 5 examines a subset of the sample that controls for the difference in the potential proceeds from sales of winners and losers.
For each sales event, the average dollar value per stock is calculated separately for winners and losers in the portfolio. Panel A of table 5 reports the results when the average dollar values of losers and winners in the same portfolio are close to each other (when the difference between the two is less than 10%); panel B reports the results when the average dollar value of losers is greater than the average dollar value of winners in the same portfolio. These restrictions do not eliminate the asymmetry in investors’ propensity to sell multiple stocks. The difference between gains and losses in the proportion of multiple sales is 1.12%, with a t‐statistic of 3.02 when winners and losers have similar dollar values. The difference is 1.00% (t‐statistic, 4.74) when losers have larger dollar values than winners.
Commonality among winners and among losers.—If losers in a portfolio are more related to each other than are winners, losers are more likely subject to common shocks, contributing to the clustering of loss selling. For example, it is possible that returns of losers are more highly correlated with each other than those of winners, or that the proportion of losers in similar industries is greater than that of winners. To investigate if losers are more related to each other than winners, table 6 reports various measures of relatedness separately for winners and for losers based on return correlations and industry membership.
For each sales event, the portfolio from which sales occur is divided into a winner and a loser portfolio. Indices of relatedness (RI) and the mean and maximum correlations (CORR, MXCORR) of the winner and of loser portfolios are calculated by pairwise comparisons of all possible pairs of winners and losers within each of their respective portfolios. Specifically, for sales event k, the index of relatedness and the mean and maximum correlations of the winner and loser portfolios are calculated as follows (denotes either W or L): 
where 
is an indicator variable equal to one if stock i and stock j belong to a same industry group, and 
is the correlation of daily stock returns of stocks i and j over 90 days prior to the sales event. 
(
) is the winner (loser) portfolio for sales event k. For the definition of industry groups, two alternative definitions based on 2‐digit SIC codes are used to make sure that the results are robust to different industry definitions. The index of relatedness using 12 industry groups following Ferson and Harvey (1991) is denoted RI(FH), and the index using 19 industry groups following Moskowitz and Grinblatt (1999) is denoted RI(MG). The index of relatedness and the mean and maximum correlations of winner and loser portfolios are first calculated at the sales event level, then averaged across sales events (
/
is the total number of winner/loser portfolios). 
Table 6 reports the indices of relatedness and the mean and maximum correlations of daily stock returns for winner and loser portfolios. The index of relatedness is higher and the mean and maximum correlations of returns are greater for winner portfolios than for loser portfolios, indicating that winners are more related to each other than are losers. The results are robust in relation to the number of stocks in the portfolio. If common shocks trigger multiple stock sales, they should increase the probability of multiple winner sales rather than that of multiple loser sales. Thus, we can dismiss the possibility that commonality among stocks is driving the asymmetry in investors’ propensity to sell multiple stocks.
Delays in order execution.—It may take longer than a day for good‐till‐cancel limit orders to be executed.14 Some sales may be counted as separate events when they are from limit orders submitted on the same day but executed over different days. Linnainmaa (2003) finds that investors are more likely to submit limit orders when they realize gains than losses. If so, investors may appear to realize gains over different days relative to losses even though they are equally likely to bundle sales of winners and sales of losers.
Because the data set does not have information on whether a trade is from a limit order or from a market order, I perform three different tests to control for the possible effects of stale limit orders. First, I look at sales events in which sales prices are lower than closing prices of the previous trading day and also sales quantities are smaller than the previous day’s trading volumes (panel A of table 7). If a stock is sold at a price lower than the closing price of the previous trading day, and if there was enough trading volume on the previous day, it is probably safe to assume that the order was placed and executed on the same day. If the order had been placed on the previous day or earlier, it would have been executed on the previous day, which closed with a higher price than the limit price.
Second, I examine sales events in which none of the sales are at round or half dollars (panel B). Goetzmann and Zhu (2003) argue that limit orders are more likely to take place at round dollars or half dollars since investors are more likely to use rounding when setting limit order prices. Under this assumption, sales events examined in panel B are likely to consist of market orders. Finally, sales events that are far apart from other sales events from the same account are examined in panel C. Delays in order execution create a problem when one sales event with multiple sales based on the timing of order submission is counted as two or more sales events with a single sale based on the timing of order execution. Panel C identifies sales events that are not likely to be associated with this kind of double counting. The interval between order submission and execution is probably less than a few days in most cases. If sales events are double counted due to delays in limit order execution, those double‐counted sales events are likely to be within a few days of each other. If there is no other sales event in the 15‐day window around the sales event [−7,7], it is not likely to be associated with double counting due to stale limit orders.15 Table 7 shows that the results are qualitatively the same after excluding sales events that are possibly contaminated by stale limit orders. Therefore, delays in limit order execution do not appear to explain the asymmetry.
Account level analysis.—So far, the propensity to sell multiple stocks is calculated by aggregating across sales events from all accounts. As an alternative, the propensity to sell multiple stocks is calculated at the account level in table 8. The propensity to sell multiple stocks when the account realizes losses and when it realizes gains and the difference between the two are calculated for each account and then aggregated across accounts.
Let 
(
) be the number of sales events when account i sells multiple losers (one loser). Similarly, 
(
) is the number of sales events when account i sells multiple winners (one winner). For each account with at least five sales events, the difference in the propensity to sell multiple stocks is calculated, and the differences are averaged across accounts: 
The account level analysis yields results very similar to the aggregated result. On average, the propensity to sell multiple stocks is larger when investors realize losses rather than gains, and the average difference is 1.96%.
C. Logistic Analysis of the Determinants of Multiple Stock Sales
A logistic regression approach allows simultaneous examination of many determinants of multiple stock sales. The following logistic model is used to examine whether or not realizing losses increases the propensity to sell multiple stocks: 
where 
is the logistic cumulative distribution function. For each sales event, the dependent variable takes the value of one if multiple stocks are sold and zero if only one stock is sold. LOSS is an indicator variable that takes the value of one if the sales are at losses and zero if they are at gains. The 
’s are control variables. As in the previous section, sales events in which investors sell both a winner and a loser are dropped from the analysis.
For control variables, a dummy variable for sales events from margin accounts (MARGIN) and a dummy variable for sales events from taxable accounts (TAX) are included because margin trading and tax‐loss selling can contribute to the multiple stock sales. Also included are a dummy for sales in December (DEC), a natural log of the number of stocks in the portfolio (Log[NSTOCK]), the value‐weighted average of the holding period returns of stocks in the portfolio (VWHPRET), the average of the squared daily market returns calculated over days [−60, −1] (MKTVOL), four market return variables (MKTRET), and four portfolio return variables (PFRET) that cover the sales date and 20 trading days prior to the sales event date (days 0, −1, [−5, −2], [−20, −6]).16 Other control variables are the average dollar value of a stock in the portfolio (DPOSI); a dummy variable equal to one if the account makes purchases on the same day (PURCHASE); and two dummy variables that represent the client segment, one for the active traders (TRADER) and the other for the affluent households (AFFLUENT). The total number of stock sales from all accounts on the same day (NTSALES) is included as a proxy for the overall selling activity on that day. Also included are interaction terms of LOSS with a taxable account dummy and with a December sales dummy (
, 
, 
).
Table 9 reports maximum likelihood estimates of regression coefficients and their robust standard errors. The results in table 9 confirm the univariate results. Investors are more likely to sell multiple stocks when they realize losses, after controlling for the effect of the number of stocks in the portfolio, account and household characteristics, the average dollar value of the stocks in the portfolio, overall selling activity during the day, market volatility, and the current and past portfolio and market returns. The coefficient for the variable LOSS is positive and significant at the 1% level across all models. Since interaction terms of the LOSS variable with the DEC and TAX dummies are included as well, the coefficient of LOSS represents the effect of realizing losses on the probability of multiple stock sales in non‐December months for nontaxable accounts. The coefficient estimate of 
is positive and highly significant, confirming the results in tables 2 and 3 that tax‐loss selling in December increases the probability of multiple stock sales.
The value‐weighted holding period return of the portfolio, VWHPRET, is negatively related to the probability of multiple stock sales. VWHPRET is closely related to whether the investor realizes losses or gains at the sales event, therefore likely to take away significance from the LOSS dummy. However, the LOSS variable remains significantly positive after controlling for the holding period returns and portfolio returns prior to and on the sales events. Adverse market movements prior to the sales, especially on the sales date, increase the probability of multiple stock sales. It also appears that investors sell multiple stocks in highly volatile markets and on days when there is a high level of selling activity, as the coefficients for MKTVOL and NTSALES are positive and significant. Also, the coefficient of the PURCHASE dummy is positive and highly significant. It is possible that sales with accompanying purchases occur when investors rebalance their portfolios, and portfolio rebalancing is likely to result in multiple stock sales. In the last column, I replace Log(NSTOCK) with a set of dummies, one for each number of stocks up to 
, and one for 
, to account for a possible nonlinear effect of Log(NSTOCK) on the probability of multiple stock sales.17 Using a set of dummies for the number of stocks increases the model fit but does not change the results very much.
D. Modeling Stock Sales as Independent Bernoulli Trials
As an alternative approach, the probability of observing multiple stock sales is modeled under the assumption that the decision to sell one stock is independent of the decision to sell other stocks. This provides a benchmark for what we should expect about the probability of multiple stock sales if there is no dependency, that is, if there is no intentional bundling or separating of sales.
Suppose that whether or not a stock is sold on a given day is modeled as an independent Bernoulli trial.18 Then the probability of multiple stock sales from an investor on a given day is a function of the number of winner and loser stocks in the portfolio and the propensity of the investor to sell each winner and loser. If the investor has 
winners and 
losers in her portfolio and the probability that she sells each winner (loser) is 
, then the probability of multiple stock sales on a sales event can be written as follows: 
Figure 4 shows the logit of the probability of multiple sales as a function of 
and 
when 
and 
.19 It shows that the logit of the probability of multiple stock sales increases with the number of winners (
) and the number of losers (
) almost linearly except for the lowest values of 
and 
. Alternative views of the figure are also presented by fixing 
at five. The probability of multiple stock sales increases more rapidly with the number of winners than with the number of losers, since investors are more likely to sell a winner than a loser (
).
Fig. 4.— Logit of the probability of multiple stock sales as a function of the number of winners (
) and losers (
) (
, 
)
Suppose we estimate the following logit model: 
where Λ is the logistic cumulative distribution function, equivalent to modeling the logit of 
as a linear function of 
and 
. The estimated coefficients for the number of winners and the number of losers (
and 
) are related to investors’ propensities to sell a winner and a loser, respectively. If investors are more likely to sell a winner than to sell a loser, as the disposition effect implies (
; e.g., Odean 1998), and that the decision to sell each stock is independent, we expect 
. But if we observe 
, this indicates that sales decisions of losers are positively correlated or at least that sales decisions of losers are more positively (less negatively) correlated than sales decisions of winners.
Table 10 presents the coefficient estimates the following model: 
where the 
’s are control variables similar to those used in table 9. This specification allows for mixed sales of winners and losers, therefore I include mixed sales in this analysis. Table 10 shows that the estimate of 
is always greater than the estimate of 
across different specifications. Chi‐square test statistics for the equality of these two coefficients reject the null hypothesis 
at the 1% level. If there is no dependency in the sales decisions of different stocks, 
is greater than 
when 
. However, a vast amount of empirical evidence on the disposition effect (see n. 1) shows that a loser is less likely to be sold than a winner (
). The results in table 10 provide further evidence that selling decisions of losers are more positively correlated with each other than are the selling decisions of winners.
E. Mixed Sales Events
According to the hedonic editing hypothesis, whether or not investors prefer to integrate or separate mixed outcomes of gains and losses depends on the relative magnitudes of the gains and losses. When the net gain is positive (the gain is larger than the loss), integration is preferred. When the net gain is negative, segregation is preferred if the gain is relatively very small, and integration is preferred otherwise. Therefore, the hedonic editing rule for mixed outcomes can be summarized as follows: for 
and 
, 
when 
(segregation preferred), and 
when 
(integration preferred).
To test whether investors follow the hedonic editing rule when they realize gains and losses together, I check whether the combined outcome is preferred to separate outcomes under the hedonic editing hypothesis for each mixed sales event.20 Specifically, I compare the percentage of mixed sales events consistent with the hypothesis with the corresponding percentage for a sample of hypothetical mixed sales events. A mixed sales event is consistent with the hedonic editing hypothesis if the magnitude of the gain and the loss is such that integration is preferred under the hedonic editing hypothesis (
).
For each mixed sales event on which 
winners and 
losers are sold, I randomly select 
winners and 
losers from the investor’s entire portfolio to construct a hypothetical mixed sales event. A set of hypothetical mixed sales events, one hypothetical event for each actual event, comprise a hypothetical sample. Then the percentage of mixed sales events consistent with the hypothesis is calculated for each hypothetical sample, for a total of 1,000 such samples. If investors try to follow hedonic editing rules, the percentage of mixed sales events consistent with the hypothesis should be higher than what is expected when investors random sell the same number of winners and losers.
How small should the gain be relative to the loss to make investors prefer segregation? It depends on the curvature and steepness of the value function. Since it is not clear what the cutoff value k is, I consider different cutoff values, ranging from 0.01 to 0.15.21 Table 11 shows that investors are more likely to combine sales of winners and losers so that the combined outcome is more desirable than separate outcomes according to the mental accounting principles. Regardless of the cutoff value employed, the percentage of sales events consistent with the hypothesis is greater than what is expected if investors randomly selected which gains and losses to realize. For instance, with the cutoff value of 0.1 (i.e., segregation is preferred when the size of gain is smaller than one‐tenth of the size of loss, and integration is preferred otherwise), 92.12% of mixed sales events are consistent with the hypothesis for the original sample, while 89.95% of mixed sales are consistent with the hypothesis for hypothetical samples (
). The result from mixed sales events provides additional evidence that mental accounting has a significant effect on investors’ selling decisions.
V. Conclusion
This article examines whether mental accounting of multiple outcomes influences the way investors sell stocks. I find that investors are more likely to sell multiple stocks when they realize losses than gains, consistent with the hedonic editing hypothesis (Thaler 1985) that individuals prefer integrating losses and segregating gains. Also, the way investors combine sales of winners and losers shows that investors select which gains and losses to realize together so that the combined outcome is more desirable than segregated outcomes. These results suggest that mental accounting plays a significant role in investors’ trading decisions.
Previous studies have examined how mental accounting of multiple outcomes affects the behavior of market participants in various contexts. Shefrin and Statman (1993) suggest that the design of financial products may be guided by the mental accounting principles. They describe how brokers promote covered calls by framing the cash flow of a covered call into three mental accounts or “three sources of profit”—the call premium, the dividend, and the capital gain on the stock. By segregating gains, brokers can make covered calls more attractive to their clients.
Loughran and Ritter (2002) offer a possible explanation for why issuers seem willing to leave large amounts of money on the table during initial public offerings (IPOs). They argue that the loss from underpricing will be aggregated with a larger gain from the retained shares. Issuers will therefore not be upset by the large initial underpricing. Based on the idea of Loughran and Ritter (2002), Ljungqvist and Wilhelm (2005) use the combined value of the loss from underpricing and the gain from retained shares as a behavioral measure of the IPO decision‐maker’s satisfaction with the underwriter and find that their behavioral measure has an explanatory power for the choices of underwriter and fees in subsequent offerings.
If investors are more likely to integrate concurrent events, firms may have an incentive to strategically time their disclosures to take advantage of investor preferences. Companies sometimes manage their income statements by accounting choices to make poor results look even worse (“take a big bath”). It has been argued that this method is often utilized in a bad year to artificially enhance next year’s earnings. Several explanations have been offered for firms’ incentives to smooth earnings. However, it is somewhat puzzling why firms smooth earnings and also occasionally take big baths. Mental accounting of multiple outcomes provides an alternative explanation for the coexistence of these seemingly opposite behaviors.22 The mental accounting principles indicate that stock prices will be, on average, higher if the manager spreads out good news over time by income smoothing. In contrast, for sufficiently bad news, it is better to report a big loss and possibly improved profits in a later period rather than two separate losses. These previous studies and the new evidence in this article suggest that mental accounting may be an important factor underlying firm and investor behavior.
References
- Ang, Andrew, and Joseph Chen. 2002. Asymmetric correlations of equity portfolios. Journal of Financial Economics 63:443–94.
- Badrinath, S., and Wilber Lewellen. 1991. Evidence on tax‐motivated securities trading behavior. Journal of Finance 46:369–82.
- Barber, Brad, and Terrance Odean. 2000. Trading is hazardous to your wealth: The common stock investment performance of individual investors. Journal of Finance 55:773–806.
- ———. 2002. Online investors: Do the slow die first? Review of Financial Studies 15:455–87.
- ———. 2005. All that glitters: The effect of attention and news on the buying behavior of individual and institutional investors. Working paper, Graduate School of Management and Haas School of Business, University of California, Berkeley.
- Barberis, Nicholas, and Ming Huang. 2001. Mental accounting, loss aversion, and individual stock returns. Journal of Finance 56:1247–92.
- Barberis, Nicholas, Ming Huang, and Jesus Santos. 2001. Prospect theory and asset prices. Quarterly Journal of Economics 141:1–53.
- Benartzi, Shlomo, and Richard Thaler. 1995. Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics 110:73–92.
- Dhar, Ravi, and Alok Kumar. 2002. A non‐random walk down the main street: Impact of price trends on trading decisions of individual investors. Working paper, Yale University, New Haven, CT.
- Dhar, Ravi, and Ning Zhu. 2002. Up close and personal: An individual level analysis of the disposition effect. Working paper 02‐20, Yale International Center for Finance, New Haven, CT.
- Ferris, Stephen P., Robert A. Haugen, and Anil K. Makhija. 1988. Predicting contemporary volume with historic volume at differential price levels: Evidence supporting the disposition effect. Journal of Finance 43:677–97.
- Ferson, Wayne E., and Campbell R. Harvey. 1991. The variation of economic risk premiums. Journal of Political Economy 99:385–415.
- Genesove, David, and Christopher Mayer. 2001. Loss aversion and seller behavior: Evidence from the housing market. Quarterly Journal of Economics 116:1233–60.
- Goetzmann, William N., and Ning Zhu. 2003. Rain or shine: Where is the weather effect? Working Paper no. 9465, National Bureau of Economic Research, Cambridge, MA.
- Grinblatt, Mark, and Bing Han. 2006. Disposition effect and momentum. Journal of Financial Economics 78, no. 2:311–33.
- Grinblatt, Mark, and Matti Keloharju. 2000. The investment behavior and performance of various investor types: A study of Finland’s unique data set. Journal of Financial Economics 55:43–67.
- ———. 2001a. How distance, language and culture influence stock holdings and trades. Journal of Finance 56:1053–73.
- ———. 2001b. What makes investors trade? Journal of Finance 56:589–616.
- Harris, Lawrence, and Joel Hasbrouck. 1996. Market vs. limit orders: The super DOT evidence on order submission strategy. Journal of Financial and Quantitative Analysis 31:213–31.
- Hirshleifer, David. 2001. Investor psychology and asset pricing. Journal of Finance 64:1533–97.
- Hirshleifer, David, James Myers, Linda A. Myers, and Siew Hong Teoh. 2003. Do individual investors drive post‐earnings announcement drift? Working paper, Fisher College of Business, Ohio State University, and University of Illinois at Urbana‐Champaign.
- Hirst, D. Eric, Edward J. Joyce, and Michael S. Schadewald. 1994. Mental accounting and outcome contiguity in consumer borrowing decisions. Organizational Behavior and Human Decision Processes 58:136–52.
- Hong, Dong, and Alok Kumar. 2002. What induces noise trading around public announcement events? Working paper, Cornell University, Department of Economics, Ithaca, NY.
- Kahneman, Daniel, and Jackie Snell. 1990. Predicting utility. In Insights in decision making: A tribute to Hillel J. Einhorn, ed. R. M. Hogarth. Chicago: University of Chicago Press.
- Kahneman, Daniel, and Amos Tversky. 1979. Prospect theory: An analysis of decision under risk. Econometrica 47:263–91.
- Kirschenheiter, Michael, and Nahum D. Melumad. 2002. Can “big bath” and earnings smoothing coexist as equilibrium financial reporting strategies? Journal of Accounting Research 40:761–96.
- Koch, Timothy W., and Larry D. Wall. 2000. The use of accruals to manage reported earnings: Theory and evidence. Working Paper 2000‐23, Federal Reserve Bank of Atlanta.
- Kumar, Alok. 2005. Style switching and stock returns. Working paper, University of Notre Dame, Mendoza School of Business, South Bend, IN.
- Kyle, Albert, and Wei Xiong. 2001. Contagion as a wealth effect. Journal of Finance 56:1401–40.
- Lakonishok, Josef, and Seymour Smidt. 1986. Volume for winners and losers: Taxation and other motives for stock trading. Journal of Finance 41:951–74.
- Linnainmaa, Juhani. 2003. Who makes the limit order book? Implications on contrarian strategies and the disposition effect. Working paper, University of California, Los Angeles.
- Linville, Patricia W., and Gregory W. Fischer. 1991. Preferences for separating or combining events. Journal of Personality and Social Psychology 60:5–23.
- Ljungqvist, Alexander, and William J. Wilhelm. 2005. Does prospect theory explain IPO market behavior? Journal of Finance 60, no. 4:1759–90.
- Locke, Peter R., and Steven C. Mann. 2005. Professional trader discipline and trader disposition. Journal of Financial Economics 76, no. 2:401–44.
- Longin, Francois, and Bruno Solnik. 2001. Extreme correlation of international equity markets. Journal of Finance 56:649–76.
- Loughran, Tim, and Jay R. Ritter. 2002. Why don’t issuers get upset about leaving money on the table in IPOs? Review of Financial Studies 15:413–43.
- Moskowitz, Tobias J., and Mark Grinblatt. 1999. Do industries explain momentum? Journal of Finance 54:1249–90.
- Odean, Terrance. 1998. Are investors reluctant to realize their losses? Journal of Finance 53:1775–98.
- ———. 1999. Do investors trade too much? American Economic Review 89:1279–98.
- Ortega, Bob. 1998. In Sam we trust: The untold story of Sam Walton and how Wal‐Mart is devouring America. New York: Times Business.
- Poterba, James M., and Scott J. Weisbenner. 2001. Capital gains tax rules, tax‐loss trading, and turn‐of‐the‐year returns. Journal of Finance 56:353–68.
- Ritter, Jay R. 1988. The buying and selling behavior of individual investors at the turn of the year. Journal of Finance 43:701–17.
- Shapira, Zur, and Itzhak Venezia. 2001. Patterns of behavior of professionally managed and independent investors. Journal of Banking and Finance 25:1573–87.
- Shefrin, Hersh, and Meir Statman. 1985. The disposition to sell winners too early and ride losers too long: Theory and evidence. Journal of Finance 40:777–90.
- ———. 1993. Behavioral aspects of the design and marketing of financial products. Financial Management 22:123–34.
- Thaler, Richard H. 1985. Mental accounting and consumer choice. Marketing Science 4:199–214.
- Thaler, Richard H., and Eric J. Johnson. 1990. Gambling with the house money and trying to break even: The effects of prior outcomes on risky choice. Management Science 36:643–60.
- Weber, Martin, and Colin Camerer. 2000. The disposition effect in securities trading: An experimental analysis. Journal of Economic Behavior and Organization 33:167–84.
- Zhu, Ning. 2002. The local bias of individual investors. Working Paper no. 02‐30, Yale ICF, New Haven, CT.
-
* I thank an anonymous referee, Hal Arkes, Natasha Burns, Werner DeBondt, Anand Goel, Bing Han, Danling Jiang, Shane Johnson, Alok Kumar, Juhani Linnainmaa, Terrance Odean, Kelley Pace, Carrie Pan, John Persons, Chip Ryan, Meir Statman, René Stulz, Jüergen Symanzik, Siew Hong Teoh, Ingrid Werner, and seminar participants at CUNY‐Baruch, DePaul University, Drexel University, HKUST, Louisiana State University, National University of Singapore, Ohio State University, Queen’s University, SUNY‐Buffalo, University of Georgia, University of Virginia–McIntire, and the Society for Judgment and Decision Making annual meetings in Minneapolis, for helpful comments. I am especially grateful to David Hirshleifer for his encouragement, many insightful comments, and help with the data. I thank the National Science Foundation (SES‐033905) for financial support. All remaining errors are mine. Contact the author at slim1@depaul.edu.
-
1. On the disposition effect, e.g., see Shefrin and Statman (1985), Ferris, Haugen, and Makhija (1988), Odean (1998), Locke and Mann (2000), Weber and Camerer (2000), Genesove and Mayer (2001), Grinblatt and Keloharju (2001b), Shapira and Venezia (2001), Dhar and Zhu (2002); on the equity premium puzzle, the value premium, and the momentum effect, see, e.g., Benartzi and Thaler (1995), Barberis and Huang (2001), Barberis, Huang, and Santos (2001), Grinblatt and Han (forthcoming).
-
2. For example, Odean (1998, 1999), Barber and Odean (2000, 2002, 2005), Grinblatt and Keloharju (2001a, 2001b), Dhar and Kumar (2002), Hong and Kumar (2002), Zhu (2002), Hirshleifer et al. (2003), and Kumar (2005).
-
3. For example, Longin and Solnik (2001) and Ang and Chen (2002).
-
4. Kyle and Xiong (2001) show that simultaneous liquidation of unrelated securities due to wealth effects can lead to financial contagion.
-
5. As consumer purchases are voluntary, the costs of the goods (losses) are likely to be smaller than their benefits (gains).
-
6. It is also possible that the difference of the results in this study from the previous ones is partly due to the difference between predicted utility and decision utility discussed in Kahneman and Snell (1990). Predicted utility is the anticipation of the hedonic quality of a future experience, and decision utility is the sign and weight associated with a consequence in a decision context. Kahneman and Snell (1990) find that a majority of subjects predicted their experience with painful treatments would get worse over time, while their choices over treatment schedules are rather consistent with decreasing marginal disutility. Thaler and Johnson (1990) ask subjects how they would feel about an additional loss, which measures the predicted utility of multiple losses, while investors’ trading decisions reflect their decision utility.
-
7. When Sam Walton lost $1.7 billion during the great stock market crash of October 19, 1987, he responded, “It’s paper anyway” (Ortega 1998).
-
8. Evidence for tax‐loss selling near the end of the year can also be found in, e.g., Lakonishok and Smidt (1986), Ritter (1988), Badrinath and Lewellen (1991), Odean (1998), and Poterba and Weisbenner (2001).
-
9. The results are not sensitive to the way winners and losers are defined. The results are qualitatively the same when the first or the most recent purchase price is used as a reference point, when commissions are added to the purchase price and subtracted from the sales price, and when stocks sold at reference prices are considered winners or dropped from the analysis.
-
10. Suppose there are only two accounts in the sample, account 1 and account 2. Account 1 sold stock A and stock B on October 9, 1991, and stock C on November 14, 1992. Account 2 sold stock B and stock C on November 14, 1992. In this hypothetical example, the number of sales events is three (two from account 1 and one from account 2).
-
11. Since portfolios are constructed from the purchase records since 1991, the number of stocks and the portfolio sizes reported in table 1 are not very accurate. Barber and Odean (2000) report that the mean household holds 4.3 stocks worth $47,334, and the median household holds 2.61 stocks worth $16,210, which are calculated from the month‐end position statements. It seems averaging over sales events instead of examining month‐end positions inflates the numbers by disproportionately representing portfolios of the investors who trade frequently and have larger portfolios.
-
12. The standard errors are calculated under the assumption that all sales events are independent.
-
13. However, table 1 shows that investors actually have more winners than losers.
-
14. In the sample of Harris and Hasbrouck (1996), about 82% of limit orders are day orders that are automatically canceled if not executed until the close, and 17% of limit orders are good‐till‐cancel orders.
-
15. The results are almost the same when I use longer windows like [−14,14].
-
16. Grinblatt and Keloharju (2000) find that returns beyond a month (about 20 trading days) in the past appear to have little impact on the decision to sell a stock.
-
17.
for less than 5% of the sample. -
18. Odean’s (1998) proportion of gains realized and proportion of losses realized methodology is based on the same assumption.
-
20. I thank an anonymous referee for suggesting such a test.
-
21. Thaler (1985) used an example with
and 
and found that subjects prefer segregated outcomes. -
22. For rational explanations, see Koch and Wall (2000) and Kirschenheiter and Melumad (2002).
