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THE JOURNAL OF FINANCE Ã¢â‚¬Â¢ VOL. LIII, NO. 5 Ã¢â‚¬Â¢ OCTOBER 1998

Are Investors Reluctant to Realize

Their Losses?

TERRANCE ODEAN*

ABSTRACT

I test the disposition effect, the tendency of investors to hold losing investments too

long and sell winning investments too soon, by analyzing trading records for 10,000

accounts at a large discount brokerage house. These investors demonstrate a strong

preference for realizing winners rather than losers. Their behavior does not appear

to be motivated by a desire to rebalance portfolios, or to avoid the higher trading

costs of low priced stocks. Nor is it justified by subsequent portfolio performance.

For taxable investments, it is suboptimal and leads to lower after-tax returns.

Tax-motivated selling is most evident in December.

THE TENDENCY TO HOLD LOSERS too long and sell winners too soon has been

labeled the disposition effect by Shefrin and Statman ~1985!. For taxable

investments the disposition effect predicts that people will behave quite differently than they would if they paid attention to tax consequences. To test

the disposition effect, I obtained the trading records from 1987 through 1993

for 10,000 accounts at a large discount brokerage house. An analysis of these

records shows that, overall, investors realize their gains more readily than

their losses. The analysis also indicates that many investors engage in taxmotivated selling, especially in December. Alternative explanations have been

proposed for why investors might realize their profitable investments while

retaining their losing investments. Investors may rationally, or irrationally,

believe that their current losers will in the future outperform their current

* University of California, Davis. This paper is based on my dissertation at the University of

California, Berkeley. I would like to thank an anonymous referee, Brad Barber, Peter Klein,

Hayne Leland, Richard Lyons, David Modest, John Nofsinger, James Poterba, Mark Rubinstein,

Paul Ruud, Richard Sansing, Richard Thaler, Brett Trueman, and participants at the Berkeley

Program in Finance, the NBER behavioral finance meeting, the Financial Management Association Conference, the American Finance Association meetings, and seminar participants at

UC Berkeley, the Yale School of Management, the University of California, Davis, the University of Southern California, the University of North Carolina, Duke University, the Wharton

School, Stanford University, the University of Oregon, Harvard University, the Massachusetts

Institute of Technology, the Amos Tuck School, the University of Chicago, the University of

British Columbia, Northwestern University, the University of Texas, UCLA, the University of

Michigan, and Columbia University for helpful comments. I would also like to thank Jeremy

Evnine and especially the discount brokerage house that provided the data necessary for this

study. Financial support from the Nasdaq Foundation is gratefully acknowledged.

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The Journal of Finance

Figure 1. Prospect theory value function.

winners. They may sell winners to rebalance their portfolios. Or they may

refrain from selling losers due to the higher transactions costs of trading at

lower prices. I find, however, that when the data are controlled for rebalancing and for share price, the disposition effect is still observed. And the

winning investments that investors choose to sell continue in subsequent

months to outperform the losers they keep.

The next section of the paper discusses the disposition effect and literature related to it. Section II describes the data set and Section III describes

the empirical study and its findings. Section IV discusses these findings and

Section V concludes.

I. The Disposition Effect

A. Prospect Theory

The disposition effect is one implication of extending Kahneman and TverskyÃ¢â‚¬â„¢s ~1979! prospect theory to investments. Under prospect theory, when

faced with choices involving simple two and three outcome lotteries, people

behave as if maximizing an Ã¢â‚¬Å“SÃ¢â‚¬Â-shaped value function ~see Figure 1!. This

value function is similar to a standard utility function except that it is defined on gains and losses rather than on levels of wealth. The function is

concave in the domain of gains and convex in the domain of losses. It is also

steeper for losses than for gains, which implies that people are generally

risk-averse. Critical to this value function is the reference point from which

gains and losses are measured. Usually the status quo is taken as the reference point; however, Ã¢â‚¬Å“there are situations in which gains and losses are

Are Investors Reluctant to Realize Their Losses?

1777

coded relative to an expectation or aspiration level that differs from the

status quo . . . . A person who has not made peace with his losses is likely to

accept gambles that would be unacceptable to him otherwiseÃ¢â‚¬Â ~Kahneman

and Tversky ~1979!!.

For example, suppose an investor purchases a stock that she believes to

have an expected return high enough to justify its risk. If the stock appreciates and the investor continues to use the purchase price as a reference

point, the stock price will then be in a more concave, more risk-averse, part

of the investorÃ¢â‚¬â„¢s value function. It may be that the stockÃ¢â‚¬â„¢s expected return

continues to justify its risk. However, if the investor somewhat lowers her

expectation of the stockÃ¢â‚¬â„¢s return, she will be likely to sell the stock. What if,

instead of appreciating, the stock declines? Then its price is in the convex,

risk-seeking, part of the value function. Here the investor will continue to

hold the stock even if its expected return falls lower than would have been

necessary for her to justify its original purchase. Thus the investorÃ¢â‚¬â„¢s belief

about expected return must fall further to motivate the sale of a stock that

has already declined than one that has appreciated. Similarly, consider an

investor who holds two stocks. One is up; the other is down. If the investor

is faced with a liquidity demand, and has no new information about either

stock, she is more likely to sell the stock that is up.

Throughout this study, investorsÃ¢â‚¬â„¢ reference points are assumed to be their

purchase prices. Though the results presented here appear to vindicate

that choice, it is likely that for some investments, particularly those held

for a long time over a wide range of prices, the purchase price may be only

one determinant of the reference point. The price path may also affect the

level of the reference point. For example, a homeowner who bought her

home for $100,000 just before a real-estate boom and had the home appraised for $200,000 after the boom may no longer feel she is Ã¢â‚¬Å“breaking

evenÃ¢â‚¬Â if she sells her home for $100,000 plus commissions. If purchase

price is a major component, though not the sole component, of reference

point, it may serve as a noisy proxy for the true reference point. Using the

proxy in place of the true reference point will make a case for the disposition effect more difficult to prove. It seems likely that if the true reference point were available the statistical evidence reported here would be

even stronger.

B. An Alternative Behavioral Theory

Investors might choose to hold their losers and sell their winners not because they are reluctant to realize losses but because they believe that todayÃ¢â‚¬â„¢s losers will soon outperform todayÃ¢â‚¬â„¢s winners. If future expected returns

for the losers are greater than those for the winners, the investorsÃ¢â‚¬â„¢ belief

would be justified and rational. If, however, future expected returns for losers are not greater than those for winners, but investors continue to believe

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they are despite persistent evidence to the contrary, this belief would be

irrational. In experimental settings Andreassen ~1988! finds that subjects

buy and sell stocks as if they expect short-term mean reversion.1

Most of the analysis presented here does not distinguish between prospect theory and an irrational belief in mean reversion as possible explanations for why investors hold losers and sell winners. It may be that investors

themselves do not always make a clear distinction. For example, an investor who will not sell a stock for a loss might convince himself that the

stock is likely to bounce back rather than admit his unwillingness to accept

a loss.

C. Taxes

InvestorsÃ¢â‚¬â„¢ reluctance to realize losses is at odds with optimal tax-loss selling for taxable investments. For tax purposes investors should postpone taxable gains by continuing to hold their profitable investments. They should

capture tax losses by selling their losing investments, though not necessarily

at a constant rate. Constantinides ~1984! shows that when there are transactions costs, and no distinction is made between the short-term and longterm tax rates ~as is approximately the case from 1987 to 1993 for U.S.

federal taxes2!, investors should gradually increase their tax-loss selling from

January to December. Dyl ~1977!, Lakonishok and Smidt ~1986!, and Badrinath and Lewellen ~1991! report evidence that investors do sell more losing

investments near the end of the year.

Shefrin and Statman ~1985! propose that investors choose to sell their

losers in December as a self-control measure. They reason that investors are

reluctant to sell for a loss but recognize the tax benefits of doing so. The end

of the year is the deadline for realizing these losses. So each year, investors

postpone realizing losses until December when they require themselves to

sell losers before the deadline passes.

A sophisticated investor could reconcile tax-loss selling with her aversion

to realize losses though a tax-swap. By selling her losing stock and purchasing a stock with similar risk characteristics, she could realize a taxloss while maintaining the same risk exposure. Thaler ~1985! argues that

1

SubjectsÃ¢â‚¬â„¢ tendencies to trade as if making regressive predictions diminish when their attention is focused on price changes rather than price levels ~Andreassen ~1988!! and when

casual attributions for price trends, such as might normally be provided by the media, are made

available ~Andreassen ~1987, 1990!!.

2

Prior to 1987 long-term capital gains tax rates were 40 percent of the short-term capital

gains tax rates; from 1987 to 1993 long-term and short-term gains were taxed at the same

marginal rates for lower income taxpayers. The maximum short-term rate at times exceeded

the maximum long-term rate. In 1987 the maximum short-term rate was 38.5 percent and the

maximum long-term rate was 28 percent. From 1988 to 1990 the highest income taxpayers paid

a marginal rate of 28 percent on both long-term and short-term gains. In 1991 and 1992 the

maximum long-term and short term-rates were 28 percent and 31 percent. In 1993 the maximum long-term and short-term rates were 28 percent and 39.6 percent.

Are Investors Reluctant to Realize Their Losses?

1779

people tend to segregate different gambles into separate mental accounts.

These are then evaluated separately for gains and losses. A tax-swap requires closing such an account for a loss, which people are reluctant

to do.

D. Previous Studies

Previous research3 offers some support for the hypothesis that investors

sell winners more readily than losers, but this research is generally unable

to distinguish among various motivations investors might have for doing

so. Investors may be behaviorally motivated to hold losers and sell winners, that is, they may have value functions like those described in prospect theory or they may incorrectly expect mean-reverting prices. There

are also rational reasons why investors may choose to hold their losers and

sell their winners: ~1! Investors who do not hold the market portfolio may

respond to large price increases by selling some of the appreciated stock to

restore diversification to their portfolios ~Lakonishok and Smidt ~1986!!;

~2! Investors who purchase stocks on favorable information may sell if the

price goes up, rationally believing that price now ref lects this information, and may continue to hold if the price goes down, rationally believing that their information is not yet incorporated into price ~Lakonishok

and Smidt ~1986!!; and ~3! Because trading costs tend to be higher for

lower priced stocks, and because losing investments are more likely to be

lower priced than winning investments, investors may refrain from selling

losers simply to avoid the higher trading costs of low-priced stocks ~Harris

~1988!!.

The contribution of this paper is to demonstrate, with market data, that a

particular class of investors ~those with discount brokerage accounts! sell

winners more readily than losers. Even when the alternative rational motivations listed above are controlled for, these investors continue to prefer

selling winners and holding losers. Their behavior is consistent with prospect theory; it is also consistent with a ~mistaken! belief that their winners

and losers will mean revert.

Starr-McCluer ~1995! finds that 15 percent of the stock-owning households interviewed in

the 1989 and 1992 Surveys of Consumer Finances have paper losses of 20 percent or more. She

estimates that in the majority of cases the tax advantages of realizing these losses would more

than offset the trading costs and time costs of doing so. Heisler ~1994! documents loss aversion

in a small sample of futures speculators. In a study of individual federal tax returns, Poterba

~1987! finds that although many investors do offset their capital gains with losses, more than

60 percent of the investors with gains or losses realized only gains. Weber and Camerer ~1995!

report experimental evidence of the disposition effect. Lakonishok and Smidt ~1986! and Ferris,

Haugen, and Makhija ~1988! find a positive correlation between price change and volume. Bremer

and Kato ~1996! find the same correlation for Japanese stocks. Such a correlation could be

caused by investors who prefer to sell winners and hold losers, but it could also be the result of

buyersÃ¢â‚¬â„¢ trading preferences.

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The Journal of Finance

II. The Data

The data for this study are provided by a nationwide discount brokerage

house. From all accounts active in 1987 ~those with at least one transaction!,

10,000 customer accounts are randomly selected. The data are in three files:

a trades file, a security number to CUSIP file, and a positions file. Only the

first two files are used in this study. The trades file includes the records of

all trades made in the 10,000 accounts from January 1987 through December 1993. This file has 162,948 records, each record is made up of an account

identifier, the trade date, the brokerage houseÃ¢â‚¬â„¢s internal number for the

security traded, a buy-sell indicator, the quantity traded, the commission

paid, and the principal amount. Multiple buys or sells of the same stock, in

the same account, on the same day, are aggregated. The security number to

CUSIP table translates the brokerage houseÃ¢â‚¬â„¢s internal numbers into CUSIP

numbers. The positions file contains monthly position information for the

10,000 accounts from January 1988 through December 1993. Each of its

1,258,135 records is made up of the account identifier, year, month, internal

security number, equity, and quantity. Accounts that were closed between

January 1987 and December 1993 are not replaced; thus the data set may

have some survivorship bias in favor of more successful investors. The data

do not distinguish different account types. Therefore it is not possible to

separate taxable accounts from tax-free accounts. Given the large sample

size, we can expect the sample proportions of different account types to be

close to the proportions for all of the brokerageÃ¢â‚¬â„¢s accounts. At the beginning

of the data period, 20 percent of the brokerageÃ¢â‚¬â„¢s accounts were either IRA or

Keogh accounts, and these accounts were responsible for 17.5 percent of all

trades. The inclusion of these tax-exempt accounts will reduce tax-motivated

trading in the data set, but with 80 percent of the accounts taxable, taxmotivated selling is easily detectable.

There are two data sets similar to this one described in the literature.

Schlarbaum et al. ~1978! and others analyze trading records for 2500 accounts at a large retail brokerage house for the period January 1964 to

December 1970; Badrinath and Lewellen ~1991! and others analyze a second

data set provided by the same retail broker for 3000 accounts over the period

January 1971 to September 1979. The data set studied here differs from

these primarily in that it is more recent and comes from a discount broker.

By examining discount brokerage records I can rule out the retail broker as

an inf luence on observed trading patterns.

Badrinath and Lewellen ~1991! look for evidence of tax-motivated trading

and find that the ratio of stocks sold for a loss to those sold for a gain rises

as the year progresses. Using a somewhat different measure, I also find

evidence that investors increase their tax-motivated selling as the year progresses. However the focus of this paper, unlike that of Badrinath and Lewellen, is to test the disposition effect. As the next section describes, this is done

by analyzing the rates at which investors realize gains and losses relative to

their opportunities to do so.

Are Investors Reluctant to Realize Their Losses?

1781

III. Empirical Study

A. Methodology

This study tests whether investors sell their winners too soon and hold

losers too long. It also investigates tax-motivated trading in December. To

determine whether investors sell winners more readily than losers, it is not

sufficient to look at the number of securities sold for gains versus the number sold for losses. Suppose investors are indifferent to selling winners or

losers. Then in an upward-moving market they will have more winners in

their portfolios and will tend to sell more winners than losers even though

they had no preference for doing so.4 To test whether investors are disposed

to selling winners and holding losers, we must look at the frequency with

which they sell winners and losers relative to their opportunities to sell

each.

By going through each accountÃ¢â‚¬â„¢s trading records in chronological order, I

construct for each date a portfolio of securities for which the purchase date

and price are known. Clearly this portfolio represents only part of each investorÃ¢â‚¬â„¢s total portfolio. In most accounts there will be securities that were

purchased before January 1987 for which the purchase price is not available, and investors may also have other accounts that are not part of the

data set. Though the portfolios constructed from the data set are only part

of each investorÃ¢â‚¬â„¢s total portfolio, it is unlikely that the selection process will

bias these partial portfolios toward stocks for which investors have unusual

preferences for realizing gains or losses.

I obtain information on splits and dividends as well as other price data

needed for this study from the 1993 Center for Research in Security Prices

daily stock file for NYSE, AMEX, and Nasdaq stocks. The study is limited to

stocks for which this information is available. Of the 10,000 accounts, 6,380

trade stocks in the CRSP file for a total of 97,483 transactions.

Each day that a sale takes place in a portfolio of two or more stocks, I

compare the selling price for each stock sold to its average purchase price to

determine whether that stock is sold for a gain or a loss. Each stock that is

in that portfolio at the beginning of that day, but is not sold, is considered to

be a paper ~unrealized! gain or loss ~or neither!. Whether it is a paper gain

or loss is determined by comparing its high and low price for that day ~as

obtained from CRSP! to its average purchase price. If both its daily high and

low are above its average purchase price it is counted as a paper gain; if they

are both below its average purchase price it is counted as a paper loss; if its

average purchase price lies between the high and the low, neither a gain or

loss is counted. On days when no sales take place in an account, no gains or

losses, realized or paper, are counted.

In Badrinath and Lewellen ~1991! 49 percent of all round-trip sales are for a loss. In my

database only 43 percent of such sales are for a loss. The difference could be due to different

trading practices by retail and discount investors, but quite likely it simply ref lects the greater

rise in prices during the period I examine.

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Suppose, for example, that an investor has five stocks in his portfolio, A,

B, C, D, and E. A and B are worth more than he paid for them; C, D, and E

are worth less. Another investor has three stocks F, G, and H in her portfolio. F and G are worth more than she paid for them; H is worth less. On

a particular day the first investor sells shares of A and of C. The next day

the other investor sells shares of F. The sales of A and F are counted as

realized gains. The sale of C is a realized loss. Since B and G could have

been sold for a profit but werenÃ¢â‚¬â„¢t, they are counted as paper gains. D, E, and

G are paper losses. So for these two investors over these two days, two realized gains, one realized loss, two paper gains, and three paper losses are

counted. Realized gains, paper gains, realized losses, and paper losses are

summed for each account and across accounts. Then two ratios are calculated:

Realized Gains

Realized Gains 1 Paper Gains

Realized Losses

Realized Losses 1 Paper Losses

5 Proportion of Gains Realized ~PGR!

~1!

5 Proportion of Losses Realized ~PLR!

~2!

In the example PGR 5 102 and PLR 5 104. A large difference in the proportion of gains realized ~PGR! and the proportion of losses realized ~PLR! indicates that investors are more willing to realize either gains or losses.

Any test of the disposition effect is a joint test of the hypothesis that people sell gains more readily than losses and of the specification of the reference point from which gains and losses are determined. Some possible choices

of a reference point for stocks are the average purchase price, the highest

purchase price, the first purchase price, or the most recent purchase price.

The findings of this study are essentially the same for each choice; results

are reported for average purchase price. Commissions and dividends may or

may not be considered when determining reference points, and profits and

losses. Although investors may not consider commissions when they remember what they paid for a stock, commissions do affect capital gains and losses.

And because the normative standard to which the disposition effect is being

contrasted is optimal tax-motivated selling, commissions are added to the

purchase price and deducted from the sales price in this study except where

otherwise noted. Dividends are not included when determining which sales

are profitable because they do not affect capital gains and losses for tax

purposes. The primary finding of the paper, that investors are reluctant to

sell their losers and prefer to sell winners, is unaffected by the inclusion or

exclusion of commissions or dividends. In determining whether the stocks

that are not sold on a particular day could have been sold for a gain or a

loss, the commission for the potential sale is assumed to be the average

commission per share paid when the stock was purchased.5 All gains and

losses are calculated after adjusting for splits.

5

If, for potential sales, the commission is instead assumed to be the same percentage of

principal as paid when the stock was purchased, the results do not significantly change.

Are Investors Reluctant to Realize Their Losses?

1783

Table I

PGR and PLR for the Entire Data Set

This table compares the aggregate Proportion of Gains Realized ~PGR! to the aggregate Proportion of Losses Realized ~PLR!, where PGR is the number of realized gains divided by the

number of realized gains plus the number of paper ~unrealized! gains, and PLR is the number

of realized losses divided by the number of realized losses plus the number of paper ~unrealized!

losses. Realized gains, paper gains, losses, and paper losses are aggregated over time ~1987Ã¢â‚¬â€œ

1993! and across all accounts in the data set. PGR and PLR are reported for the entire year, for

December only, and for January through November. For the entire year there are 13,883 realized gains, 79,658 paper gains, 11,930 realized losses, and 110,348 paper losses. For December

there are 866 realized gains, 7,131 paper gains, 1,555 realized losses, and 10,604 paper losses.

The t-statistics test the null hypotheses that the differences in proportions are equal to zero

assuming that all realized gains, paper gains, realized losses, and paper losses result from

independent decisions.

PLR

PGR

Difference in proportions

t-statistic

Entire Year

December

Jan.Ã¢â‚¬â€œNov.

0.098

0.148

20.050

235

0.128

0.108

0.020

4.3

0.094

0.152

20.058

238

There are two hypotheses to be tested. The first is that investors tend to

sell their winners and hold their losers. Stated in terms of realization rates

for gains and losses this is:

HYPOTHESIS 1: Proportion of Gains Realized . Proportion of Losses Realized

(for the entire year).

The null hypothesis in this case is that PGR # PLR. The second hypothesis

is that in December investors are more willing to sell losers and less willing

to sell winners than during the rest of the year. That is:

HYPOTHESIS 2: Proportion of Losses Realized 2 Proportion of Gains Realized

in December . Proportion of Losses Realized 2 Proportion of Gains Realized

in JanuaryÃ¢â‚¬â€œNovember.

The null hypothesis here is: PLR 2 PGR in December # PLR 2 PGR in

January through November.

B. Results

Table I reports the PGR realized and the PLR realized for the entire year,

for January through November, and for December. We see that for the entire

year investors do sell a higher proportion of their winners than of their

losers. For both Hypothesis 1 and Hypothesis 2 the null hypotheses can be

rejected with a high degree of statistical significance. A one-tailed test of the

first null hypothesis, PGR # PLR, is rejected with a t-statistic greater than

35. The second null hypothesis, PLR 2 PGR in December # PLR 2 PGR in

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January through November, is also rejected ~t equals 16!. These tests count

each sale for a gain, sale for a loss, paper gain on the day of a sale, and

paper loss on the day of a sale as separate independent observations.6 These

observations are aggregated across investors. This independence assumption will not hold perfectly. For example, suppose an investor chooses not to

sell the same stock on repeated occasions. It is likely that the decision not to

sell on one date is not independent of the decision not to sell on another

date. Alternatively, two investors may be motivated to sell the same stock

on, or about, the same day because they receive the same information. This

lack of independence will inf late the test statistics, though it wonÃ¢â‚¬â„¢t bias the

observed proportions. For Hypotheses 1 and 2 the null hypotheses are rejected with such a high degree of statistical significance that some lack of

independence is not problematic. In the following discussion, the data are, at

times, divided into several partitions ~e.g., Figure 2 and Table VI!. Where

t-statistics for individual partitions approach the conventional thresholds of

statistical significance, they should be viewed with some skepticism.

To gain some perspective into how critical the independence assumptions

made above are to the primary finding of this paperÃ¢â‚¬â€that investors realize

gains too soon and hold losers too longÃ¢â‚¬â€it is instructive to look at an alternative test. Suppose that instead of assuming that independence exists at a

transactional level we assume only that it exists at an account level. That is,

we assume that the proportions of gains and losses realized in each account

are independent of those realized in other accounts. PGR and PLR are then

estimated for each account and their difference, PGR Ã¢â‚¬â€œ PLR, is calculated for

each account. The average account PGR is 0.57, the average account PLR is

0.36, the average of PGR 2 PLR is 0.21, and the hypothesis that the mean

of PGR 2 PLR is less than or equal to zero is rejected with a t-statistic of

19.7 This alternative test also attempts to control for dependence caused by

common information. To do this the sale of a stock is only counted if no sale

has been previously counted for that stock in any account within a week

before or after the sale date. That is, no two sales of the same stock within

a week of each other are counted. Similarly, no two unrealized paper losses

or gains of the same stock within a week of each other are counted. This test

provides an alternative to the one reported in Table I and throughout the

rest of the paper, but it is not without drawbacks. The previous test, in

6

To calculate the t-statistics in Table I, the standard error for the difference in the proportions PGR and PLR is:

!

PGR~1 2 PGR!

nrg 1 npg

1

PLR~1 2 PLR!

nrl 1 npl

where nrg , npg , nrl , and npl are the number of realized gains, paper gains, realized losses, and

paper losses.

7

An account is included in this test only if the denominators for both PGR and for PLR are

nonzero for that account. There are 1893 such accounts. These same accounts are used to

calculate share-based and dollar-based PGR and PLR.

Are Investors Reluctant to Realize Their Losses?

1785

Figure 2. Ratio of the Proportion of Gains Realized (PGR) to the Proportion of Losses

Realized (PLR) for each month. PGR is the number of realized gains divided by the number

of realized gains plus the number of paper ~unrealized! gains, and PLR is the number of realized losses divided by the number of realized losses plus the number of paper ~unrealized!

losses. Realized gains, paper gains, losses, and paper losses are aggregated over time ~1987Ã¢â‚¬â€œ

1993! and across all accounts in the data set.

effect, weights each account by the number of realized and paper gains and

losses in that account. This alternative test weights each account equally,

which means we ignore the fact that accounts with more transactions provide more accurate estimates of their actual PGR and PLR. In other words,

by treating each account the same, we assume that the observed account

PGRs and PLRs are homoskedastic when they are clearly heteroskedastic.

However, to properly weight for this heteroskedasticity we need to know the

degree of independence of transactions within accounts, which is exactly the

issue this test is intended to circumvent. It is presented here simply to demonstrate that when a different set of independence assumptions is made, the

null to Hypothesis 1 is still rejected at a very significant level.

It should be noted that the PGR and the PLR measures are dependent on

the average size of the portfolios from which they are calculated. When the

portfolio sizes are large, both of these proportions will be smaller. Thus these

proportions are smaller for traders who trade frequently and generally have

larger portfolios than for those who trade less frequently. When PGR and

PLR are calculated for Table I, the accounts with more trades weigh more

heavily than those with fewer trades. In the alternative specification described in the last paragraph all accounts are weighted equally. For this

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reason PGR and PLR are both larger in the alternative specification than in

Table I. Of primary interest is not the individual values of PGR and PLR,

but their values relative to each other.

Throughout this paper PGR and PLR are calculated in terms of trades and

potential trades. An alternative specification is to calculate them in terms of

number of shares traded and potential number of shares traded. When gains,

losses, paper gains, and paper losses are aggregated across accounts before

calculating PGR and PLR, as is done throughout most of this paper, measuring in shares further complicates the question of independence. However,

if PGR and PLR are first calculated for each account and then the mean of

PGR 2 PLR is calculatedÃ¢â‚¬â€as in the alternative test described in the previous paragraphÃ¢â‚¬â€independence is assumed only between accounts. When this

alternative test is done for PGR and PLR based on shares rather than trades,

the results are virtually unchanged: average PGR is 0.58, average PLR is

0.36, and the null hypothesis that the mean of PGR 2 PLR is less than or

equal to zero is rejected with a t-statistic of 18.8

Suppose investors frequently realize small gains and less frequently

take large losses. It is then possible that they are selling similar proportions of the values of their gains and losses, though realizing gains at a

higher rate on a trade-counted basis. This is, however, not the case. I

calculate the average PGR and PLR per account by measuring losses, gains,

potential losses, and potential gains in terms of dollars rather than shares

or trades. When, as before, no two sales or potential sales of the same

stock within a week of each other are counted, the average dollar-based

PGR is 0.58 and the average dollar-based PLR is 0.42. The hypothesis that

the mean of PGR 2 PLR is less than or equal to zero is rejected with a

t-statistic of 13.9

In Table I the ratio of PGR to PLR for the entire year is a little over 1.5,

indicating that a stock that is up in value is more than 50 percent more

likely to be sold from day to day than a stock that is down. In Weber and

CamererÃ¢â‚¬â„¢s ~1995! experimental studies of the disposition effect, a stock that

is up is also about 50 percent more likely to be sold than one that is down.

Figure 2 charts the ratio of PGR to PLR for each month. This ratio declines

from 2.1 in January to 0.85 in December. This decline is consistent with

ConstantinidesÃ¢â‚¬â„¢ tax-loss selling model and suggests that at least some investors pay attention to tax-motivated selling throughout the year. From January through November, however, the observed ratio of PGR to PLR is greater

8

As in the previous test no two sales or potential sales of the same stock within a week of

each other are counted here. If sales and potential within a week of each other are also counted,

share-based PGR is 0.51 and share-based PLR is 0.31.

9

To examine this issue from another perspective, I look at each year in each portfolio and

tally the total number of years for which both potential gains and potential losses are present

in the portfolio and either net gains or net losses are realized. Net dollar gains are realized for

2,116 of these years and net dollar losses for 1,477 years. This indicates that, in most cases,

large losses are not offsetting small gains.

Are Investors Reluctant to Realize Their Losses?

1787

than 1 and the hypothesis that the population ratio is less than or equal to

1 is rejected in each of these months with t-statistics ranging from 3.6 in

November to 18 in January.10

To test the robustness of these results the data set is partitioned into two

time periods and also into two groups of traders. Table II displays results

when the data set is partitioned into stocks sold from 1987 to 1990 and 1990

to 1993, and when it is partitioned into the decile of traders who trade most

frequently and the nine deciles of traders who trade least frequently. In the

data set, the most active 10 percent of the traders account for 57 percent of

all stock trades. In both time periods and for both the frequent and the

infrequent traders, a significantly greater proportion of all possible gains

than of all possible losses is realized throughout the year ~t greater than 22,

in all cases!. In December, losses are realized at a higher rate relative to

gains than during the rest of the year, indicating that investors are realizing

tax losses in December. Due to how portfolios are reconstructed over time,

average portfolio sizes are larger for the later years of the sample. PGR and

PLR are therefore smaller for the second temporal partition, just as they are

smaller for the partition of frequent traders.

One reason investors might choose to sell winners rather than losers is

that they anticipate a change in the tax law under which capital gains rates

will rise. The tax law of 1986 made such a change. If investors sold off

winners in anticipation of higher tax rates, they might have entered 1987

with a larger percentage of losers in their portfolio than usual. Because such

stocks are purchased prior to 1987 they would not show up in the portfolios

reconstructed here. It is possible therefore that the rate at which winners

are being realized relative to losers is lower in the investorsÃ¢â‚¬â„¢ total portfolio

than in the partial reconstructed portfolios. As old stocks are sold and new

ones purchased the partial portfolios become more and more representative

of the total portfolio. We would expect that if a sell-off of winners in anticipation of the 1986 tax law affects the observed rate at which gains and

losses are realized in the partial portfolios, that effect would be greater in

the first part of the sample period than in the last part. However the ratio

PGR0PLR is virtually the same for the periods 1987 to 1990 and 1991 to 1993.

10

In Tables IÃ¢â‚¬â€œVI, realized and unrealized losses are tabulated on days that sales took place

in portfolios of two or more stocks. One objection to this formulation is that for portfolios that

hold only winners or only losers an investor cannot choose whether to sell a winner or to sell a

loser, but only which winner or loser to sell. Another objection is that if an investor has net

capital losses of more than $3,000 for the current year ~in non-tax-deferred accounts! it may be

normative for that investor to choose to sell a winner rather than a loser. I have repeated the

analyses reported in the tables subject to the additional constraints that there be at least one

winner and one loser in a portfolio on the day of a sale for that day to be counted and that the

net realized capital losses for the year to date in the portfolio be less than $3,000. When these

constraints are imposed, the difference in PGR and PLR is, for each analysis, greater. For

example, for the entire sample and the entire year ~as in Table I! there are 10,111 realized

gains, 71,817 paper gains, 5,977 realized losses, and 94,419 paper losses. Thus the PLR is

0.060; the PGR is 0.123; their difference is 0.063; and the t-statistic for the difference in proportions is 47.

1788

The Journal of Finance

Table II

PGR and PLR Partitioned by Period and Trading Activity

This table compares the aggregate Proportion of Gains Realized ~PGR! to the aggregate Proportion of Losses Realized ~PLR!, where PGR is the number of realized gains divided by the

number of realized gains plus the number of paper ~unrealized! gains, and PLR is the number

of realized losses divided by the number of realized losses plus the number of paper ~unrealized!

losses. The data are partitioned into the periods 1987Ã¢â‚¬â€œ1990 and 1990Ã¢â‚¬â€œ1993 and into the 10

percent of the accounts that trade most frequently and the 90 percent that trade least frequently. For 1987Ã¢â‚¬â€œ1990 there are 7,280 realized gains, 28,998 paper gains, 7,253 realized losses,

and 50,540 paper losses. For 1990Ã¢â‚¬â€œ1993 there are 6,603 realized gains, 50,660 paper gains,

4,677 realized losses, and 59,808 paper losses. For frequent traders there are 10,186 realized

gains, 75,182 paper gains, 8,886 realized losses, and 103,096 paper. For infrequent traders

there are 3,697 realized gains, 4,476 paper gains, 3,042 realized losses, and 7,251 paper losses.

The t-statistics test the null hypotheses that the differences in proportions are equal to zero

assuming that all realized gains, paper gains, realized losses, and paper losses result from

independent decisions.

1987Ã¢â‚¬â€œ1990

1991Ã¢â‚¬â€œ1993

Frequent

Traders

Infrequent

Traders

Entire year PLR

Entire year PGR

Difference in proportions

t-statistic

0.126

0.201

20.075

230

0.072

0.115

20.043

225

0.079

0.119

20.040

229

0.296

0.452

20.156

222

December PLR

December PGR

Difference in proportions

t-statistic

0.143

0.129

0.014

1.9

0.110

0.097

0.013

2.3

0.095

0.084

0.010

2.3

0.379

0.309

0.070

3.5

Jan.Ã¢â‚¬â€œNov. PLR

Jan.Ã¢â‚¬â€œNov. PGR

Difference in proportions

t-statistic

0.123

0.207

20.084

232

0.069

0.117

20.048

227

0.078

0.123

20.045

231

0.282

0.469

20.187

225

Table III reports the average returns since the day of purchase for realized

and paper winners and losers. In December the losses that are realized are

of much greater magnitude than those realized throughout the rest of the

year. This is additional evidence that some investors do engage in taxmotivated selling in December.

Lakonishok and Smidt ~1986! suggest that investors might sell winners

and hold on to losers in an effort to rebalance their portfolios. We expect

that investors who are rebalancing will sell a portion, but not all, of their

shares of winning stocks. A sale of the entire holding of a stock is most likely

not motivated by the desire to rebalance. So to eliminate trades that may be

motivated by a desire to rebalance, I calculate PGR and PLR using only

sales that are of an accountÃ¢â‚¬â„¢s entire position in a stock ~and using paper

gains and losses on the days of those sales!. There may be some cases where

shares of a stock are already in the portfolio before 1987 and then additional

shares are purchased. For these, the sale of all shares purchased after 1987

Are Investors Reluctant to Realize Their Losses?

1789

Table III

Average Returns

This table reports the mean return realized on stocks sold for a gain and on stocks sold for a

loss. It also reports mean return that could be realized by stocks that are not sold on days that

other stocks in the same portfolio are sold. These stocks are classified as paper gains and paper

losses. For all accounts over the entire year, there are 13,883 realized gains, 79,658 paper gains,

11,930 realized losses, and 110,348 paper losses. For all accounts during the month of December, there are 866 realized gains, 7,131 paper gains, 1,555 realized losses, and 10,604 paper

losses.

Return

Return

Return

Return

on

on

on

on

realized gains

paper gains

realized losses

paper losses

Jan.Ã¢â‚¬â€œNov.

December

Entire Year

0.275

0.463

20.208

20.391

0.316

0.500

20.366

20.417

0.277

0.466

20.228

20.393

may not amount to the sale of all shares held. So this removal of sales that

could be motivated by diversification is not perfect. Even so, if the preference for selling winners is due to rebalancing, removing most rebalancingmotivated trades will greatly reduce the preference for selling winners.

In Table IV, for the entire year, when partial sales are ignored the preference for selling winners rather than losers is not substantially changed.

The tendency to sell winners and hold losers does not appear to be the result

of rebalancing. When partial sales are ignored, investors realize losses in

December at an even higher rate relative to realizing gains. Perhaps this is

because investors who are intentionally realizing tax losses choose to sell

their entire position in the losing stock.

Investors who sell winners for the purpose of rebalancing their portfolios

are likely to make new purchases. In an alternative effort to eliminate trades

that may be motivated by a desire to rebalance, I calculate PGR and PLR

using only sales for which there is no new purchase into a portfolio on the

sale date or during the following three weeks ~and using paper gains and

losses on the days of those sales!. Table V reports that when sales motivated

by a desire to rebalance are eliminated in this way, investors continue to

prefer to sell winners. Once again, investors realize losses at a higher rate

than gains in December.

Another reason investors might sell winners and hold losers is that they

expect the losers to outperform the winners in the future. An investor who

buys a stock because of favorable information may sell that stock when it

goes up because she believes her information is now ref lected in the price.

On the other hand, if the stock goes down she may continue to hold it, believing that the market has not yet come to appreciate her information.

Investors could also choose to sell winners and hold losers simply because they believe prices mean revert. I test whether such beliefs are justified, ex post.

1790

The Journal of Finance

Table IV

PGR and PLR When the Entire Position in a Stock Is Sold

This table compares the aggregate Proportion of Gains Realized ~PGR! to the aggregate Proportion of Losses Realized ~PLR!, where PGR is the number of realized gains divided by the

number of realized gains plus the number of paper ~unrealized! gains, and PLR is the number

of realized losses divided by the number of realized losses plus the number of paper ~unrealized!

losses. In this table losses and gains are counted only if a portfolioÃ¢â‚¬â„¢s total position in a stock was

sold that day. Paper ~unrealized! gains and losses are counted only if the portfolioÃ¢â‚¬â„¢s total position in another stock held in the portfolio was sold that day. Realized gains, paper gains, losses,

and paper losses are aggregated over time ~1987Ã¢â‚¬â€œ1993! and across all accounts in the dataset.

PGR and PLR are reported for the entire year and for December only. For the entire year there

are 10,967 realized gains, 36,033 paper gains, 9,476 realized losses, and 51,502 paper losses.

For December there are 666 realized gains, 3,440 paper gains, 1,171 realized losses, and 4,759

paper losses. The t-statistics test the null hypotheses that the differences in proportions are

equal to zero assuming that all realized gains, paper gains, realized losses, and paper losses

result from independent decisions.

PLR

PGR

Difference in proportions

t-statistic

Entire Year

December

0.155

0.233

20.078

232

0.197

0.162

0.035

4.6

Table VI reports excess returns for periods following the sale of a winning

stock or the observation of a paper loss. Three investment horizons are examined: 84 trading days, which is the approximate median in sample holding period for stocks,11 254 trading days ~one year!, which is Benartzi and

ThalerÃ¢â‚¬â„¢s ~1995! estimate of the average investorÃ¢â‚¬â„¢s investment horizon, and

504 trading days ~two years!, which is how often, on average, New York

Stock Exchange equities turned over during this period. Returns are calculated in excess of the CRSP value-weighted index. For winners that are sold,

the average excess return over the following year is 3.4 percent more than it

is for losers that are not sold. Investors who sell winners and hold losers

because they expect the losers to outperform the winners in the future are,

on average, mistaken. The superior returns to former winners noted here

are consistent with Jegadeesh and TitmanÃ¢â‚¬â„¢s ~1993! finding of price momentum in security returns at horizons of up to eighteen months, though DeBondt and Thaler ~1985, 1987! find price reversals at longer horizons of

three to five years.12

11

Note that the in-sample median holding period is a downwardly biased estimate of the

true median holding period since stocks held for long periods are more likely to be bought

before or sold after the data period and therefore not counted in the sample averages. The

average turnover rate for equity in these accounts is 6.5 percent per month, which corresponds

to an average holding period of about 15 months.

12

At the time of this study CRSP data were available through 1994. For this reason two-year

subsequent returns are not calculated for sales dates in 1993.

Are Investors Reluctant to Realize Their Losses?

1791

Table V

PGR and PLR When No New Stock Is Purchased

Within Three Weeks of Sale

This table compares the aggregate Proportion of Gains Realized ~PGR! to the aggregate Proportion of Losses Realized ~PLR!, where PGR is the number of realized gains divided by the

number of realized gains plus the number of paper ~unrealized! gains, and PLR is the number

of realized losses divided by the number of realized losses plus the number of paper ~unrealized!

losses. In this table losses and gains are counted only if a no new purchase was made into a

portfolio on the day of the sale or within three weeks following the sale. Paper ~unrealized!

gains and losses are counted for days on which qualifying sales were made. Realized gains,

paper gains, losses, and paper losses are aggregated over time ~1987Ã¢â‚¬â€œ1993! and across all accounts in the dataset. PGR and PLR are reported for the entire year and for December only. For

the entire year there are 8,336 realized gains, 10,240 paper gains, 7,553 realized losses, and

19,370 paper losses. For December there are 590 realized gains, 1,024 paper gains, 1,194 realized losses, and 1,863 paper losses. The t-statistics test the null hypotheses that the differences

in proportions are equal to zero assuming that all realized gains, paper gains, realized losses,

and paper losses result from independent decisions.

PLR

PGR

Difference in proportions

t-statistic

Entire Year

December

0.281

0.449

20.168

236

0.391

0.366

0.015

1.6

The average excess returns to winners sold in Table VI are determined by

calculating excess buy-and-hold returns over the periods subsequent to each

profitable sale of each stock and then taking an average that weighs each

observation equally. Many stocks are sold for a profit on more than one date;

sometimes the same stock is sold for a profit on the same date by more than

one investor. Each of these sales is counted as a separate observation. The

same procedure applies to paper losses. The p-values in Table VI are estimated by bootstrapping an empirical distribution for the difference in average excess buy-and-hold returns to realized winners and paper losses. This

empirical distribution is generated under the null hypothesis that subsequent excess returns to realized winners and paper losers are drawn from

the same underlying distribution. The methodology is similar to that of Brock,

Lakonishok, and LeBaron ~1992! and Ikenberry, Lakonishok, and Vermaelen

~1995!. Lyon, Barber, and Tsai ~1998! test the acceptance and rejection rates

for this methodology and find that it performs well in random samples. For

each stock in the sample for which CRSP return data are available, a replacement stock is drawn ~with replacement! from the set of all CRSP stocks

of the same size decile and same book-to-market quintile as the original

stock. Using the replacement stocks together with the original observation

dates, average excess buy-and-hold returns are calculated for the 84, 252,

and 502 trading days following the dates on which sales for a profit or paper

losses are observed. These averages, and their differences, constitute one

observation from the empirical distribution. One thousand such observa-

1792

The Journal of Finance

Table VI

Ex Post Returns

This table compares average returns in excess of the CRSP value-weighted index to stocks that

are sold for a profit ~winning stocks sold! and to stocks that could be, but are not, sold for a loss

~paper losses!. Returns are measured over the 84, 252, and 504 trading days subsequent to the

sale of a realized winner and subsequent to days on which sales of other stocks take place in the

portfolio of a paper loser. p-values refer to the frequency with which differences in excess returns over the same periods in the empirical ~bootstrapped! distributions exceed the difference

in excess returns observed in the data.

Performance over

Next 84

Trading Days

Average excess return on

winning stocks sold

Average excess return on

paper losses

Difference in excess returns

~ p-values!

Performance over

Next 252

Trading Days

Performance over

Next 504

Trading Days

0.0047

0.0235

0.0645

20.0056

0.0103

~0.002!

20.0106

0.0341

~0.001!

0.0287

0.0358

~0.014!

tions are made. The null hypothesis is rejected at the a percent level if the

average subsequent excess return to realized winners minus that to paper

losers in the data set is greater than the ~1 2 a! percentile average excess

return to realized winners minus that to paper losers observed in the empirical distribution.

We saw in Table III ~column 3! that investors are more likely to realize

smaller, rather than larger, gains and losses. It may be that, due to regret

aversion, investors are most loath to realize their greatest losses, and, due to

tax consequences, they postpone realizing their greatest gains. Lower price

ranges are likely to have a greater proportion of large losers and a smaller

proportion of large winners than upper price ranges. Investors will therefore

have a greater propensity to not sell losers in lower price ranges, and to not

sell winners in higher price ranges.

Harris ~1988! suggests that investorsÃ¢â‚¬â„¢ reticence to sell losers may be due to

their sensitivity to higher trading costs at lower stock prices. Table VII reports PGR and PLR for different price ranges and return ranges for January

through November. Stocks with a price less than or equal to $10, with prices

greater than $10 and less than or equal to $25, and with prices higher than

$25, represent, respectively, 36 percent, 35 percent, and 29 percent of the

data set. Partitioning on magnitude of return controls for the disproportionate numbers of large losers in the lower price range and of large winners in

the top price range. The ranges for absolute value of return are: 0 to 0.15, 0.15

to 0.30, 0.30 to 0.50, and greater than 0.50. We see that in fourteen of fifteen

partitions winners are realized at a higher rate than losers. This difference is

statistically significant in thirteen partitions. When comparing winners and

losers of similar magnitude, investors appear to prefer to sell winners and

hold losers even when trading costs for both are about the same.

Are Investors Reluctant to Realize Their Losses?

1793

Table VII

PGR and PLR Partitioned by Price and Return

This table compares the aggregate Proportion of Gains Realized ~PGR! to the aggregate Proportion of Losses Realized ~PLR!, where PGR is the number of realized gains divided by the

number of realized gains plus the number of paper ~unrealized! gains, and PLR is the number

of realized losses divided by the number of realized losses plus the number of paper ~unrealized!

losses. The data are partitioned on stock price and on absolute value of the return to date ~R!,

for all accounts, 1987Ã¢â‚¬â€œ1993, January through November only. The t-statistics test the null hypotheses that the differences in proportions are equal to zero assuming that all realized gains,

paper gains, realized losses, and paper losses result from independent decisions.

6R6 # 0.15

0.15 , |R| # 0.30

0.30 , |R| # 0.50

0.50 # |R|

Price # $10

PLR

PGR

Difference

t-statistic

0.141

0.267

20.126

13.0

0.129

0.257

20.128

10.2

0.109

0.295

20.186

11.7

0.030

0.282

20.252

17.5

$10 # Price # $25

PLR

PGR

Difference

t-statistic

0.138

0.222

20.084

16.9

0.105

0.186

20.081

13.1

0.076

0.172

20.096

13.1

0.058

0.135

20.077

11.3

$25 # Price

PLR

PGR

Difference

t-statistic

0.125

0.197

20.072

19.4

0.104

0.126

20.022

4.5

0.104

0.081

0.023

23.2

0.049

0.055

20.006

0.61

There is another way to contrast the hypothesis that losses are realized

more slowly due to the higher transactions costs with the two behavioral

hypotheses. We can look at the rates at which investors purchase additional

shares of stocks they already own. The proportion of gains purchased again

~PGPA! and the proportion of losses purchased again ~PLPA! can be calculated in a manner analogous to how PGR and PLR are calculated. When a

stock already in the portfolio is purchased again it is counted as a gain

purchased again or a loss purchased again. On days when purchases are

made, stocks already in the portfolio for which additional shares are not

repurchased are counted as gains or losses potentially purchased again. Thus:

Gains Purchased Again

Gains Purchased Gains Potentially

1

Again

Purchased Again

Losses Purchased Again

Losses Purchased Losses Potentially

1

Again

Purchased Again

5

Proportion of Gains

~PGPA!

Purchased Again

5

Proportion of Losses

~PGPA! ~4!

Purchased Again

~3!

1794

The Journal of Finance

When these proportions are calculated, additional purchases of a particular

stock in a particular account are not counted if they take place within one

week of a previous purchase of the stock. This is done to avoid the possibility

of counting a purchase order filled over more than one day as an additional

purchase.

If investors avoid the higher transactions cost of low priced stocks we

would expect PLPA to be less than PGPA. If, however, investors are more

risk seeking for losing investments ~prospect theory! or if they believe prices

will revert ~as do AndreassenÃ¢â‚¬â„¢s subjects!, then PLPA will be greater than

PGPA. This is the case. For the entire sample PLPA 5 0.135 and PGPA 5

0.094. If we assume that all decisions to purchase or not purchase additional

stock are independent, the hypothesis that these two proportions are equal

can be rejected with a t-statistic of 19. This supports the two behavioral

theories, but not the transaction cost hypothesis.13

In Table III we saw that investors tend to sell their larger gains and losses

at a slower rate than their smaller gains and losses. Prospect theory does

not predict that investors realize their large gains more slowly than their

small gains. Nor does a belief in mean reversion predict this. If, however,

investors believe that stocks that perform moderately well will revert, but

those that perform unusually well will trend,14 they might sell their small

winners and hold their larger ones. These beliefs could then also lead them

to buy fewer additional shares of small winners and more additional shares

of larger winners. To test this I partition winning investments into large or

small winners using the mean unrealized winnersÃ¢â‚¬â„¢ return of 0.47 as a break

point ~see Table III!. Similarly I partition losers into large and small losers

using -0.39 as a break point. Small winners are repurchased at a rate of

0.112, large winners are repurchased at a rate of 0.043. Small losers are

repurchased at a rate of 0.172 and large losers at 0.067. The difference in

the rates at which large and small gains are realized is highly significant

~t equals 26, assuming independence!; so, too, is the difference in the rate at

which large and small losses are realized ~t equals 39!. These investors do

not tend to buy additional shares of big winners. This is not consistent with

the hypothesis that they believe small winners will revert but large winners

will perform well, however other factors may be working against the hypothesis. Investors who are in the habit of buying additional shares of stocks

they already own may reach their limit of additional purchases before these

stocks have an opportunity to make large gains ~or losses!. Regret aversion

may also inf luence investors to not buy additional shares of big winners. For

example, suppose an investor buys 100 shares of stock A at $100 per share.

Then stock A appreciates to $150. The investor may believe stock A will

13

For the same reasons as discussed in Section III B, these decisions will not always be

independent. So the t-statistic of 19 overstates the actual statistical significance.

14

In this vein Barberis, Shleifer, and Vishny ~1996! develop a model in which investors

believe that earnings switch between two regimes, one mean reverting and the other trend

following.

Are Investors Reluctant to Realize Their Losses?

1795

continue to appreciate but he may still refrain from buying an additional

100 shares, for if he does purchase more shares, he will more poignantly

regret that he didnÃ¢â‚¬â„¢t buy them at $100 per share to begin with. The greater

the difference between the original and additional purchase prices, the greater

is this potential regret.

The results presented so far are not able to distinguish between the two

behavioral hypotheses. Both prospect theory and a belief in mean reversion

predict that investors will hold their losers too long and sell their winners

too soon. Both predict that investors will purchase more additional shares of

losers than of winners. However a belief in mean reversion should apply to

stocks that an investor does not already own as well as those she does, but

prospect theory applies only to the stocks she owns. Thus a belief in mean

reversion implies that investors will tend to buy stocks that had previously

declined even if they donÃ¢â‚¬â„¢t already own these stocks, and prospect theory

makes no prediction in this case. Odean ~1997! finds that this same group of

investors tends to buy stocks that have, on average, outperformed the CRSP

value-weighted index by about 25 percent over the previous two years.

This would appear inconsistent with a simple belief in mean reversion.

~It is, though, consistent with a belief that big winners will continue to perform well.!

IV. Discussion

This paper examines the behavior of individual investors and finds that

investors exhibit disposition effects; that is, they realize their profitable stocks

investments at a much higher rate than their unprofitable ones, except in

December. The extent to which this behavior affects market prices depends

on the trading activities of other market participants such as professional

traders and institutional investors. If the disposition effect holds in aggregate it may contribute to the positive relationship between price change and

volume identified by Lakonishok and Smidt ~1986! and by Ferris et al. ~1988!.

The disposition effect could also be a cause of the positive correlation between price changes and volume in other markets such as residential real

estate. Case and Shiller ~1988! report evidence of disposition effects from

interviews with homeowners in boom and post-boom real estate markets.

By affecting supply, the disposition effect may also contribute to market

stability near prices at which substantial trading has previously taken place.

If many investors buy a stock at a particular price, that price may become

their reference point. If the stock falls below this reference point, these investors will be averse to selling for a loss, reducing the supply of potential

sellers. A reduced supply of potential sellers could slow further price decreases. On the other hand, if the stock rises above the reference point, these

investors will be more willing to sell, increasing the supply of potential sellers, and possibly slowing further price increases. If these investors have

private information about the future prospects of a company whose stock

1796

The Journal of Finance

they hold, the disposition effect may slow the rate at which this information

is incorporated into price. For example, investors with negative information

may be unwilling to sell a stock if its price is below their reference point. In

not selling the stock, these investors will fail to signal their negative information to the market, and there could be a delay before that information is

ref lected in prices.

Though the disposition effect may inf luence market prices, its economic

significance is likely to be greatest for individual investors. To get a rough

idea of the economic costs of the loss aversion, let us imagine that a hypothetical investor is choosing to sell one of two stocks. The first of these stocks

behaves like the average realized winner in this data set and the other like

the average paper loser. The investor wishes to sell $1,000 worth of stock

after commissions and that happens to be what his position in each stock is

currently worth. Suppose he is averse to realizing losses and so sells the

winning stock. If his experience is similar to that of the average investor in

this data set, his return on the sale will be 0.277 ~Table III, third column!.

Since the stock is currently worth $1000, its purchase price must have been

$783, and his capital gain is $217. If he instead chooses to sell $1,000 worth

of the losing stock, his return will be 2 0.393, with a purchase price of $1,647,

and a capital loss of $647. One year later the ~losing! stock that he held will

have, on average, a return 1 percent below the market ~Table VI!; the winning stock that he sold will have, on average, a return 2.4 percent above the

market. Marginal tax rates for capital gains for investors in this sample

vary from 0 to 28 percent, plus state taxes. Assume that our investorÃ¢â‚¬â„¢s marginal tax rate is 15 percent and that he has taxable gains against which to

offset losses. Then by choosing to sell the winning stock rather than the

loser, he gives up an immediate tax savings of $130. Suppose that whichever

stock the investor does not sell now, he will sell in one year; then the investor is paying $130 in taxes one year earlier than he otherwise would. If he

can expect a return of 8 percent on his money, choosing not to defer these

taxes costs him about $10. In addition to this, over the next year the investorÃ¢â‚¬â„¢s return on the stock he holds ~the loser! is $34 less than if he had held

the other stock ~the winner!. Using $1,000 as a basis, and including the

value of the immediate tax savings ~$10! as well as the anticipated difference in capital gains ~$34!, the investorÃ¢â‚¬â„¢s return is about 4.4 percent higher

over the next year if he sells the loser rather than the winner. The benefits

of deferring taxes may be even higher if the investor chooses to delay realizing his gains for more than one year. On the other hand, a habit of regular

loss realizations may reduce the magnitude of available capital losses.

The trading records analyzed in this paper are obtained from a discount

brokerage house. This avoids the need to consider agency issues that inf luence institutional investors or to disentangle the decisions and motivations

of individual investors from those of their retail brokers. It would be illuminating to repeat this study with data on institutional trading and with data

from a retail brokerage house.

Are Investors Reluctant to Realize Their Losses?

1797

V. Conclusion

This paper finds that individual investors demonstrate a significant preference for selling winners and holding losers, except in December when taxmotivated selling prevails. This investor behavior does not appear to be

motivated by a desire to rebalance portfolios or by a reluctance to incur the

higher trading costs of low priced stocks. Nor is it justified by subsequent

portfolio performance. It leads, in fact, to lower returns, particularly so for

taxable accounts.

REFERENCES

Andreassen, Paul, 1987, On the social psychology of the stock market: Aggregate attributional

effects and the regressiveness of prediction, Journal of Personality and Social Psychology

53, 490Ã¢â‚¬â€œ496.

Andreassen, Paul, 1988, Explaining the price-volume relationship: The difference between price

changes and changing prices, Organizational Behavior and Human Decision Processes 41,

371Ã¢â‚¬â€œ389.

Andreassen, Paul, 1990, Judgmental extrapolation and market overreaction: On the use and

disuse of news, Journal of Behavioral Decision Making 3, 153Ã¢â‚¬â€œ174.

Badrinath, S., and Wilber Lewellen, 1991, Evidence on tax-motivated securities trading behavior, Journal of Finance 46, 369-382.

Barberis, Nicholas, Andre Shleifer, and Robert Vishny, 1996, A model of investor sentiment with

both underreaction and overreaction, Working paper, University of Chicago.

Benartzi, Shlomo, and Richard Thaler, 1995, Myopic loss aversion and the equity premium

puzzle, Quarterly Journal of Economics 110, 73Ã¢â‚¬â€œ92.

Bremer, Marc, and Kato Kiyoshi, 1996, Trading volume for winners and losers on the Tokyo

Exchange, Journal of Financial and Quantitative Analysis 31, 127Ã¢â‚¬â€œ142.

Brock, William, Josef Lakonishok, and Blake LeBaron, 1992, Simple technical trading rules and

the stochastic properties of stock returns, Journal of Finance 47, 1731Ã¢â‚¬â€œ1764.

Case, Karl, and Robert Shiller, 1988, The behavior of home buyers in boom and post-boom

markets, New England Economic Review November0December, 29Ã¢â‚¬â€œ46.

Constantinides, George, 1984, Optimal stock trading with personal taxes: Implications for prices

and the abnormal January returns, Journal of Financial Economics 13, 65Ã¢â‚¬â€œ69.

DeBondt, Werner, and Richard Thaler, 1985, Does the stock market overreact?, Journal of Finance 40, 793Ã¢â‚¬â€œ807.

DeBondt, Werner, and Richard Thaler, 1987, Further evidence on investor overreaction and

stock market seasonality, Journal of Finance 42, 557Ã¢â‚¬â€œ581.

Dyl, Edward, 1977, Capital gains taxation and the year-end stock market behavior, Journal of

Finance 32, 165Ã¢â‚¬â€œ175.

Ferris, Stephen, Robert Haugen, and Anil Makhija, 1988, Predicting contemporary volume with

historic volume at differential price levels: Evidence supporting the disposition effect, Journal of Finance 43, 677Ã¢â‚¬â€œ697.

Harris, Lawrence, 1988, Discussion of predicting contemporary volume with historic volume at

differential price levels: Evidence supporting the disposition effect, Journal of Finance 43,

698Ã¢â‚¬â€œ699.

Heisler, Jeffrey, 1994, Loss aversion in a futures market: An empirical test, Review of Futures

Markets 13, 793Ã¢â‚¬â€œ822.

Ikenberry, David, Josef Lakonishok, and Theo Vermaelen, 1995, Market underreaction to open

market share repurchases, Journal of Financial Economics 39, 181Ã¢â‚¬â€œ208.

Jegadeesh, Narasimhan, and Sheridan Titman, 1993, Returns to buying winners and selling

losers: Implications for stock market efficiency, Journal of Finance 48, 65Ã¢â‚¬â€œ91.

1798

The Journal of Finance

Kahneman, Daniel, and Amos Tversky, 1979, Prospect theory: An analysis of decision under

risk, Econometrica 46, 171Ã¢â‚¬â€œ185.

Lakonishok, Josef, and Seymour Smidt, 1986, Volume for winners and losers: Taxation and

other motives for stock trading, Journal of Finance 41, 951Ã¢â‚¬â€œ974.

Lyon, John, Brad Barber, and Chih-Ling Tsai, 1998, Improved methods for tests of long-run

abnormal stock returns, Journal of Finance, forthcoming.

New York Stock Exchange Fact Book, 1995, ~New York Stock Exchange, Inc., New York, N.Y.!.

Odean, Terrance, 1997, Do investors trade too much?, Working paper, University of California,

Davis.

Poterba, James, 1987, How burdensome are capital gains taxes? Evidence from the United

States, Journal of Public Economics 33, 157Ã¢â‚¬â€œ172.

Schlarbaum, Gary, Wilber Lewellen, and Ronald Lease, 1978, Realized returns on common stock

investments: The experience of individual investors, Journal of Business 51, 299Ã¢â‚¬â€œ325.

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, 777Ã¢â‚¬â€œ790.

Starr-McCluer, Martha, 1995, Tax losses and the stock portfolios of individual investors, Working paper, Federal Reserve Board of Governors.

Thaler, Richard, 1985, Mental accounting and consumer choice, Marketing Science 4, 199Ã¢â‚¬â€œ214.

Weber, Martin, and Colin Camerer, 1998, The disposition effect in securities trading: An experimental analysis, forthcoming Journal of Economic Behavior and Organization.

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