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Are Investors Reluctant to Realize Their Losses?

 

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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 justif ied 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.

T too long and sell winners too soon has beenHE TENDENCY TO HOLD LOSERS

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

investments the disposition effect predicts that people will behave quite dif- ferently 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 tax- motivated 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 f inance meeting, the Financial Management Asso- ciation Conference, the American Finance Association meetings, and seminar participants at UC Berkeley, the Yale School of Management, the University of California, Davis, the Univer- sity 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.

THE JOURNAL OF FINANCE • VOL. LIII, NO. 5 • OCTOBER 1998

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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 rebal- ancing 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 litera- ture 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 Tver- sky’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 “S”-shaped value function see Figure 1 . This~ !

value function is similar to a standard utility function except that it is de- fined 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 ref- erence point; however, “there are situations in which gains and losses are

Figure 1. Prospect theory value function.

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coded relative to an expectation or aspiration level that differs from the status qu person who has not made peace with his losses is likely too . . . . A accept gambles that would be unacceptable to him otherwise” 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 appre- ciates 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 investor’s value function. It may be that the stock’s expected return continues to justify its risk. However, if the investor somewhat lowers her expectation of the stock’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 investor’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, investors’ 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 ap- praised for $200,000 after the boom may no longer feel she is “breaking even” 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 dispo- sition effect more difficult to prove. It seems likely that if the true refer- ence 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 be- cause they are reluctant to realize losses but because they believe that to- day’s losers will soon outperform today’s winners. If future expected returns for the losers are greater than those for the winners, the investors’ belief would be justified and rational. If, however, future expected returns for los- ers 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 pros- pect theory and an irrational belief in mean reversion as possible explana- tions for why investors hold losers and sell winners. It may be that investors themselves do not always make a clear distinction. For example, an in- vestor 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

Investors’ reluctance to realize losses is at odds with optimal tax-loss sell- ing for taxable investments. For tax purposes investors should postpone tax- able 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 trans-~ !

actions costs, and no distinction is made between the short-term and long- term 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 Badri-~ ! ~ !

nath 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 pur- chasing a stock with similar risk characteristics, she could realize a tax- loss while maintaining the same risk exposure. Thaler 1985 argues that~ !

1 Subjects’ tendencies to trade as if making regressive predictions diminish when their at- tention 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 maxi- mum long-term and short-term rates were 28 percent and 39.6 percent.

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people tend to segregate different gambles into separate mental accounts. These are then evaluated separately for gains and losses. A tax-swap re- quires 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 win- ners, that is, they may have value functions like those described in pros- pect 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 informa- tion, and may continue to hold if the price goes down, rationally believ- ing 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 moti- vations listed above are controlled for, these investors continue to prefer selling winners and holding losers. Their behavior is consistent with pros- pect theory; it is also consistent with a mistaken belief that their winners~ !

and losers will mean revert.

3 Starr-McCluer 1995 f inds 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 f inds 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 buyers’ trading preferences.

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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 Decem- ber 1993. This file has 162,948 records, each record is made up of an account identifier, the trade date, the brokerage house’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 house’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 brokerage’s accounts. At the beginning of the data period, 20 percent of the brokerage’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, tax- motivated 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 ac-~ !

counts 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 pro- gresses. However the focus of this paper, unlike that of Badrinath and Lewel- len, 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.

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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 num- ber 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 account’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 in- vestor’s total portfolio. In most accounts there will be securities that were purchased before January 1987 for which the purchase price is not avail- able, 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 investor’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.

4 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 port- folio. 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 weren’t, they are counted as paper gains. D, E, and G are paper losses. So for these two investors over these two days, two re- alized 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 Paper Gains

 Proportion of Gains Realized PGR~ ! ~1!

Realized Losses

Realized Losses Paper Losses

 Proportion of Losses Realized PLR~ ! ~2!

In the example PGR 1 2 and PLR 1 4. A large difference in the propor- 0  0

tion of gains realized PGR and the proportion of losses realized PLR in-~ ! ~ !

dicates 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 peo-

ple sell gains more readily than losses and of the specification of the refer- ence 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 remem- ber 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.

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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 Proportion of Gains Realized

in December Proportion of Losses Realized Proportion of Gains Realized 

in January–November.

The null hypothesis here is: PLR PGR in December PLR 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 -statistic greater than t

35. The second null hypothesis, PLR PGR in December PLR PGR in  

Table I

PGR and PLR for the Entire Data Set This table compares the aggregate Proportion of Gains Realized PGR to the aggregate Pro-~ !

portion 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 1987–~

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 real- ized 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 -statistics test the null hypotheses that the differences in proportions are equal to zerot

assuming that all realized gains, paper gains, realized losses, and paper losses result from independent decisions.

Entire Year December Jan.–Nov.

PLR 0.098 0.128 0.094 PGR 0.148 0.108 0.152 Difference in proportions 0.050 0.020 0.058 

t-statistic 35 4.3 38 

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

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 assump- tion 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 won’t bias the observed proportions. For Hypotheses 1 and 2 the null hypotheses are re- jected 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 paper—that investors realize gains too soon and hold losers too long—i

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