The Disposition Effect: Selling Winners and Holding Losers

Individual investors have a strong preference for selling stocks that have

increased in value since bought (winners) relative to stocks that have decreased in value

since bought (losers). Shefrin and Statman (1985) labeled this behavior the “disposition

effect”—investors are disposed to sell winners and hold losers. In this section, we begin

by illustrating the basic effect. We then survey the empirical and experimental work

documenting the disposition effect, which we summarize in Table 2. We close by

discussing possible explanations for the disposition effect.

3.1. The Evidence

The disposition effect is a remarkably consistent and robust phenomenon. Before

diving into the literature on this topic, we illustrate the basic effect using data from the

LDB dataset and the Finnish dataset from 1995 to 2008. (The analysis of the Finnish

dataset was provided to us by Noah Stoffman.) Specifically, we estimate models of the

form

where h(t,x(t)) is the hazard rate at time t conditional on a set of p observed predictors as

of period t (denoted x(t)). The baseline hazard rate, h0(t), is the hazard rate when all

predictors take on a value of zero. The ! coefficients are estimated from the data. The

hazard rate is the probability density function of the hazard event at time t conditional on

survival to time t (i.e., not observing the hazard event prior to t).

!

h(t, x(t)) = h0 (t)exp("1x1 + ...+ " p x p )

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In our analyses, the hazard event is the sale of a stock, and time is measured in days

subsequent to the original purchase. The hazard rate for a particular stock being sold by a

particular investor is conditional on the covariates for that stock and investor at time t.

For each kth covariate, we report estimates of the hazard ratio assuming a one-unit

increase in the covariate:

Note that the hazard ratio, exp(!k), is the ratio of hazard rates for two stocks with the

same covariates except that xk is one unit larger for the stock whose hazard rate is given

in the numerator. Thus, if xk is a dummy variable, the hazard ratio is the ratio of the

hazard when the dummy variable takes on a value of 1 to the hazard when its value is 0

and all other covariates are the same.

The Cox model makes no assumptions about how the baseline hazard rate

changes over time and does not estimate the baseline hazard rate. The model does assume

that hazard ratios do not change with time. For example, the model makes no

assumptions about how the unconditional rate of selling stocks changes from day 50 to

day 100, but the model does assume that if a winner is sold at a 20% higher rate than a

loser on day 50, then the winner will also be sold at a 20% higher rate than a loser on day

100.

To analyze how the magnitude of the return since a stock was purchased affects

the hazard rate of selling the stock, we create dummy variables for 4% wide return

categories. These return categories are:

r " -42%, -42% < r " -38%, …, -2% < r " 2%, …, 58% < r " 62%, 62% < r.

For example, we create a dummy variable that is one if the return at the time of the sale is

greater than -2% and less than or equal to 2%. These covariates are time varying since the

return since purchase can change daily.

!

exp("k ) = h0(t)exp("1x1 + ...+ "k (xk +1) + ...+ " p x p )

h0(t)exp("1x1 + ...+ "k xk + ...+ " p x p )

HD

For the LDB dataset, we estimate one model for the full sample period (1991 to

1996) and base confidence intervals on the estimated standard errors for the single model.

For the Finnish dataset, separate models are estimated for each sample year (1995 to

2008) and then the results are averaged across years. Confidence intervals are based on

the time-series standard errors of coefficient estimates (i.e., an adaptation of the FamaMacbeth

approach to calculating standard errors that assumes serial independence in the

estimated coefficients).4

In Figure 1, Panel A, we plot the hazard ratio for selling (y axis) for various levels

of return since the stock was purchased (x axis) using data from the large discount

brokerage covering the period 1991 to 1996. In Panel B, results using the Finnish data

are plotted. The general patterns of the hazard ratios are remarkably consistent.

Consider the large discount broker (Panel A). The default hazard rate is the

omitted return category that includes returns of -2% to 2%. The tendency to sell a stock

increases dramatically as returns increase. For example, the hazard rate for selling stocks

up between 18-22% since purchased is 2.65 times greater than the hazard rate for selling

stocks that have experienced returns between -2% and 2%. Negative returns since a

stock was purchased also increase the hazard rate of selling, but not as dramatically as

positive returns. For example, the hazard rate for selling stocks up 18-22% since

purchased is 1.77 times greater than the hazard rate for selling stocks down 18-22% since

purchased. The results are qualitatively similar for the Finnish data.

A number of studies—both experimental and empirical—confirm the presence of

the disposition effect. Weber and Camerer (1998) provide early experimental support for

the disposition effect. In their experiment, subjects observe price changes on six stocks

(stocks A to G) over 14 periods. The probability that a stock will increase in value varies

across stocks, but not rounds. Subjects know the distribution of these probabilities, but do

not know which stock has the highest probability of increasing in price. A rational

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 4 Since the Cox models are computationally intense with time-varying covariates (i.e., returns since

purchase) and many households, estimating one model for the full 1995 to 2008 sample period is

computationally challenging.

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Bayesian would conclude that the stock with the most price increases has the greatest

chance of being the stock with a high probability of further increasing in value, so the

disposition effect (selling winners, holding losers) is clearly counterproductive in this

setting. Nonetheless, subjects sell winners at 50% higher rate than losers; 60% of sales

are winners, while 40% of sales are losers.

Odean (1998) examines trading records for 10,000 accounts at a large U.S.

discount brokerage for the period 1987 through 1993. In brief, Odean compares the rate

at which investors sell winners (realized gains) and losers (realized losses) and compares

the realization of gains and losses to the opportunities to sell winners and losers. He

finds that, relative to opportunities, investors realize their gains at about a 50% higher

rate than their losses and that this difference is not explained by informed trading, a

rational belief in mean-reversion, transactions costs, or rebalancing. (See Calvet,

Campbell, and Sodini (2009) for a comprehensive analysis of the rebalancing of

household portfolios.)

Grinblatt and Keloharju (2001a) examine the disposition effect using the trading

records for virtually all Finnish investors during 1995 and 1996. Controlling for a wide

variety of factors, they find that investors have a tendency to hold onto losers. Relative to

a stock with a capital gain, a stock with a capital loss of up to 30% is 21% less likely to

be sold; a stock with a capital loss in excess of 30% is 32% less likely to be sold.

Furthermore, stocks with high past returns or trading near their monthly high are more

likely to be sold.

Heath, Huddart, and Lang (1999) find that employee stock options are more likely

to be exercised when the stock is trading above its previous year’s high and that exercise

is positively related to stock returns during the previous month and negatively related to

returns over longer horizons.

Kaustia (2004) tracks trading volume following IPOs and finds that IPOs that

opened below their offer price experience significantly more trading volume when they

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trade above rather than below the offer price. Brown, Chappel, da Silva Rosa, and Walter

(2006) analyze records for Australian investors who subscribed to IPOs between 1995

and 2000 and find that the disposition effect “… is pervasive across investor classes.”

The disposition effect has been documented for individual investors in several

countries, for some groups of professional investors, and for different types of assets.

Shapira and Venezia (2001) analyze the trading of 4,330 investors with accounts at an

Israeli brokerage in 1994. About 60% of these accounts are professionally managed,

while for other accounts, investors make independent decisions. They measure the

duration of round-trip trades conditional on whether the stock was sold for a gain or loss.

A tendency to sell winners and hold losers would, ceteris paribus, yield shorter holding

periods for winners v. losers. Both professionally managed accounts and independent

accounts exhibit the disposition effect (the holding periods for winners is roughly half

that of losers), though the effect is somewhat stronger for independent accounts.

Feng and Seasholes (2005) use hazard rate models to estimate the magnitude of

the disposition effect for 1,511 Chinese investors using trades data from a Chinese broker

in 2000. These Chinese investors are 32% less likely to realize a loss. Chen, Kim,

Nofsinger, and Rui (2007) analyze almost 50,000 Chinese investors using data from a

Chinese brokerage firm over the period 1998 to 2002. Using methods similar to those in

Odean (1998), Chen et al. document that Chinese investors are 67% more likely to sell a

winner than a loser. For a small subsample of 212 institutional investors who trade

through this broker, Chen et al. document a much weaker disposition effect as institutions

are only 15% more likely to see a winner. Choe and Eom (2009) find a disposition effect

for investors in Korean stock index futures; the effect is strongest for individual investors.

Compelling evidence beyond Chen et al. (2007) and Choe and Eom (2009) suggests

that institutions suffer from the disposition effect, albeit to a lesser extent than individual

investors. Frazzini (2006) estimates, from 1980 through 2002, the rates at which U.S.

mutual funds realize gains and losses in their equity holdings relative to how many

positions they hold for a gain or a loss. For all funds, gains are realized at a rate 21%

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higher than losses; for funds in the previous year’s bottom performance quintile, gains are

realized at a rate 72% higher than losses. Barber, Lee, Liu, and Odean (2007) analyze

trading records for all investors at the Taiwan Stock Exchange from 1995 to 1999 to

compare the disposition effect of individual and various categories of institutional

investors. They find a strong disposition effect for individual investors, who are nearly

four times as likely to sell a winner rather than a loser. Corporate investors and dealers

also are disposed to selling winners (though the effect is much weaker than that observed

for individuals), but neither Taiwan mutual funds nor foreign investors in Taiwan are

disposed to selling winners.

Consistent with this investment behavior being a mistake that has its origins in

cognitive ability or financial literacy, the disposition effect is most pronounced for

financially unsophisticated investors. For example, the disposition effect tends to be

stronger for individual rather than institutional investors (Brown et al. (2006), Chen et al.

(2007), Choe and Eom (2009), and Barber et al. (2007)). Dhar and Zhu (2006) use the

LDB dataset to document that wealthier and professionally-occupied investors are less

likely to sell winners and more likely to sell losers. Calvet, Campbell and Sodini (2009)

document a similar result among Swedish investors. Finally, in the LDB data, investors

who place more trades on the same day are less likely to exhibit the disposition effect

(Kumar and Lim (2008)) and the disposition effect is greatest for hard-to-value stocks

(Kumar (2009a)).

There is also intriguing evidence that investors learn to avoid the disposition

effect over time. Among the Chinese individual investors they study, Feng and Seasholes

(2005) document that the disposition effect dissipates with trading experience (time since

first trade) and various measures of financial sophistication measured early in a trader’s

history. Seru, Shumway, and Stoffman (2010) examine trading records for individual

investors in Finland from 1995-2003. They find that the disposition effect declines with

experience when experience is measured in number of trades. The drop in the disposition

effect is much less when trading experience is measured in years.

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The research discussed above presents a remarkably clear portrait of a

prototypical individual investor who sells his winners and holds his losers. This behavior

is broadly categorized as an investment mistake because it is tax inefficient.5 Thus, while

taxes clearly affect the trading of individual investors, they cannot explain the disposition

effect. Investors' 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 long-term tax rates, investors should increase their tax-loss selling

gradually from January to December. 6 Australia has a June tax year end, so the

Constantinides model would predict accelerated selling in June for Australia, a prediction

confirmed by Brown et al. (2006).

Barber and Odean (2004) document the disposition effect for taxable and taxdeferred

accounts for the LDB dataset and for a dataset of trading and position records

from January 1998 through June 1999 for 418,332 households with accounts at a large

U.S. full-service brokerage. They find that at both the discount and full-service brokers,

the disposition effect is reversed in December in taxable, but not tax-deferred, accounts.

Using a Cox proportional hazard rate model and the U.S. discount brokerage data,

Ivkovich, Poterba, and Weisbenner (2005) document that “Investors are more likely to

realize losses in taxable accounts than in tax-deferred accounts, not just in December, but

throughout the year.”

3.2. Why do investors prefer to sell winners?

While the tendency of investors to sell winners more readily than losers is

empirically robust, recent research focuses on why investors behave this way. Shefrin and

Statman (1985) attribute the disposition effect to a combination of prospect theory, regret

aversion, mental accounting, and self-control issues. Prospect theory was developed from

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 5 In addition, selling winners rather losers arguably leaves individual investors missing out on some returns

that might be earned because of momentum effects (Jegadeesh and Titman (1991)).

6 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.

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a series of experiments in which Kahneman and Tversky (1979) ask students to choose

between hypothetical outcomes such as: “Which of the following would you prefer? A:

50% chance to win 1,000, 50% chance to win nothing; B: 450 for sure.” It is not obvious

exactly how such choices translate into the realm of investing. Shefrin and Statman

assume that, due to mental accounting (Thaler, 1985), most investors will segregate

gambles and thus tend to evaluate performance at the level of individual securities (e.g.,

stocks) rather portfolios.

What is less clear is what happens when investors apply prospect theory

preferences to stock investments. Barberis and Xiong (2009) model the trading behavior

of an investor with prospect theory preferences. They find that, if performance is

evaluated annually, prospect theory preferences do not necessarily lead to a tendency to

realize gains more readily than losses and can even have the opposite effect. Hens and

Vlcek’s (2011) model questions whether investors with prospect theory preferences

would even buy stocks in the first place. Henderson (2009) develops an optimal stopping

model based on prospect theory preferences and finds investors are more likely to realize

gains than losses. Kaustia (2010b) finds that prospect theory can lead to holding onto

both losers and winners. Yao and Li (2011) model a market in which investors with

prospect theory preferences interact with investors with constant relative risk aversion

(CRRA) and find that this interaction commonly generates a negative-feedback trading

tendency, which favors the disposition effect and contrarian behavior, for prospect-theory

investors.

Barberis and Xiong (2009, 2011) argue that investors gain utility from realizing

gains and dub this behavior "realization utility." They show that, if gains and losses are

evaluated when they are realized, a disposition effect obtains. In ongoing work using

brain-imaging (fMRI) while subjects are making buying and selling decisions in an

experimental market, Frydman, Bossaerts, Camerer, Barberis, and Rangel (2011) present

intriguing results that are consistent with the notion that investors get a burst of utility

when they sell a winner.

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Summers and Duxbury (2007) examine the role of emotions in creating the

disposition effect. They find no disposition effect in experimental markets when subjects

do not actively choose the stocks in their portfolios; if subjects do not feel responsible for

decisions leading to gains and losses, they no longer sell winners more readily than losers.

This suggests that the emotions of regret and its positive counterpart—referred to by

some authors as rejoicing and by others as pride—contribute to the disposition effect.

Muermann and Volkman (2006) develop a model of the disposition effect in which

investors respond to anticipated regret and pride. Strahilevitz, Odean, and Barber (2011)

document that individual investors are more likely to repurchase a stock that they have

previously sold if the price has dropped since the previous transaction. They attribute this

behavior to the emotions of regret when one repurchases at a higher price than one sold at

and rejoicing when one repurchases at a lower price. Consistent with this emotional story,

Weber and Welfens (2011) confirm in experiments that subjects exhibit this behavior

only when they were responsible for the original sale, suggesting that investors refrain

from repurchasing stocks at a higher price than their previous sale price to avoid regret.