We examine how investor preferences and beliefs affect trading in relation to past gains and losses. The probability of selling as a function of profit is V-shaped; at short holding periods, investors are more likely to sell big losers than small ones. There is little evidence of an upward jump in selling at zero profits. These findings provide no clear indication that realization preference explains trading. Furthermore, the disposition effect is not driven by a simple direct preference for selling a stock by virtue of having a gain versus loss. Trading based on belief revisions can potentially explain these findings. Paper available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1876594

1. Are Investors Really Reluctant to Realize their Losses?
Trading Responses to Past Returns
and the Disposition Effect
Itzhak (Zahi) Ben-David
The Ohio State University, Fisher College of Business
David Hirshleifer
Paul Merage School of Business, University of California, Irvine
April 2012

2. What makes individual investors trade?
• Several studies attack this question by testing
whether Pr(Sell|Gain) > Pr(Sell|Loss)
– Yes: the Disposition Effect
• DE has been interpreted as providing insight about
investor preferences:
– A disposition to realize winners more than losers.
• We explore here how individual investors trade in
relation to size as well as sign of gains or losses
– Try to understand how preferences, beliefs, and
constraints affect trading.
Trading in relation to
past gains and losses

3. • Beliefs differences
– Speculative behavior
• Preferences
– Risk attitudes (e.g., portfolio rebalancing)
– Realization Preference
• Burst of utility from realizing a gain/loss
• Constraints
– Taxes, Transactions costs, liquidity
• Which effects predominate in the data?
• What does the disposition effect tell us about these sources?
Factors that can affect the form of
trading in relation to gains and losses

4. • Disposition Effect: The empirical phenomenon that
investors have a higher probability of selling
conditional on a position being a winner than a loser
• Realization Preference: Preference of investors to
sell winners over losers
Disposition Effect ≠ Realization Preference
• Does DE provide any evidence for RP?
– No.
A Key Distinction!

5. Disposition Effect
• One of the most robust findings in behavioral finance
– E.g., Shefrin & Statman (1985), Odean (1998), Weber & Camerer (1998),
Genesove & Mayer 2001), Kaustia (2009), Jin & Scherbina (2011)
• Found over different
– Time periods
– Holding periods (intraday up to 3 years)
– Asset classes (stocks vs. real estate)
– Investor types (individual vs. institutional)
– Test settings (field vs. experimental)
• Many authors interpret as window into investor psychology
• Basis for theoretical modeling, explanation for return
anomalies
– E.g., Grinblatt & Han (2005), Shumway & Wu (2006), Frazzini (2006)

6. • Original motivation (Shefrin & Statman 1985):
– Avoid pain of losses, seek pleasure of gains
– “In our view, investors ride losers to postpone regret, and sell winners
‘too quickly’ to hasten the feeling of pride at having chosen correctly
in the past.”
• p. 782
– Title: “The disposition to sell winners too early and ride losers too
long: …”
• Other Hints of Realization Preference
– Title: “Are investors reluctant to realize their losses?” (Odean 1998)
– Abstract of review paper: disposition effect comes from the “the human desire
to avoid regret.” (Barber & Odean 1999)
– Media discussions of disposition effect research (e.g., instructing investors to
be ‘disciplined’ about realizing painful losses)
• However, these authors also highlight other interpretations…
Motivation for Disposition Effect Tests

7. Prospect theory explanation:
• After losses, investors hold risky
positions to gamble
• However:
Other Interpretations
of the Disposition Effect
• In model of Barberis & Xiong (2009), prospect
theory does not explain DE
Leaves RP as leading preference interpretation:
• Can explain DE
• Barberis & Xiong (2011)
Belief in mean reversion
• Also doesn’t work
• Literature note: Empirical papers sometimes use “loss aversion” ((from prospect theory) as loose equivalent for RP

8. • Situation where sign realization preference is only
influence on trading. Discontinuity at zero gains
One way to get the
disposition effect
Loss Gain Profits
Likelihood
of selling
Discontinuity in
the likelihood
of selling

9. • Magnitude realization preference: “Call option”
shape – probability of selling increases with gains
(Barberis and Xiong 2011)
Another Way
to Generate Disposition Effect
Loss Gain Profits
Likelihood
of selling
Asymmetric
likelihood
of selling

10. • V-shape in Pr(sell|profits)
– Pr(Sell|large loser) > Pr(Sell|small loser)
– In contrast with simple magnitude RP
• No sign-RP
• The disposition effect is generated by the extremes
A Third Way
to Generates Disposition Effect
Loss Gain Profits
Likelihood
of selling
Asymmetric
likelihood
of selling

11. • Possible mixture of sign RP, magnitude RP, many other possible
effects
• Barberis/Xiong (2009): not clear implication of prospect theory
• Literature recognizes various factors that affect Pr(Sell|Loss) vs.
Pr(Sell|Gain)
– Tax incentives, margin calls, belief in mean reversion
• However, more generally, speculative motive for trade in general
induces either DE or opposite
– Take position in hope of a gain is asymmetric
• Plan is to sell after reach gain region
• No general presumption that Pr(Sell|Loss) = Pr(Sell|Gain)
• Depends how investor updates beliefs about the promise of the position
• DE tests do not distinguish major plausible hypotheses
Disposition Effect Tests
Hard to Interpret

12. • Focus here (as in past empirical studies) on simple,
intuitive, static effects of RP
• Recent dynamic models suggest more complex
patterns of trading in relation to past returns
• Barberis & Xiong (2011)
– RP, don’t sell losers, do sell winners
• Ingersoll & Jin (2012)
– Prospect theory & RP
– Do sell losers
• We do not rule out that dynamic preference models
involving RP or combination of prospect theory & RP
might explain our findings
Dynamic Models

13. • Confirm disposition effect in data
• Explore probability of selling stocks
in relation to gains/losses.
– V-shape
• Test for discontinuity around zero:
Not much, not major source of DE
• V-shape & reverse DE effect for buying additional shares:
– Not about (simple static) realization
• X-sectional determinants of V-shape in selling and buying.
A possible explanation: Speculation
Road Map

14. • All trades of a set of 77,000 individual investors from a
large discount broker
• A sample of 10,000 investors is used in most tests
• 1991-1996
• Restrictions:
– Stocks only
– Long transactions only
– Use algorithm to remove positions that were opened pre-
1991
– Stocks covered in CRSP
• Unit of observation:
– Investor-stock-day
Data

15. • Disposition effect (DE) present, substantial magnitude
(21-67% of unconditional probability of selling)
Preliminary:
Verifying the Disposition Effect
1 to 20 21 to 250 >250 All
N 1,245,126 8,829,899 11,493,943 21,568,968
Unconditional probability (%) 0.72** 0.33** 0.12** 0.24**
(25.36) (45.33) (56.85) (46.26)
PSW (%) 1.00** 0.44** 0.13** 0.29**
(21.69) (43.83) (46.26) (41.70)
PSL (%) 0.51** 0.23** 0.10** 0.18**
(20.46) (33.57) (46.04) (39.61)
Disposition effect: PSW – PSL (%) 0.49** 0.21** 0.03** 0.11**
(11.20) (25.04) (8.61) (19.22)
(PSW – PSL) / Unconditional probability (%) 67.26 62.68 21.75 44.68
Prior holding period (days):

16. • Right branch steeper than left branch
• Flattens over time
• For holding periods > 10 days, left branch
basically flat
Asymmetric V-shape for Selling

17. Day 1 Holdings
• Pr(Sell|Large Loss) > Pr(Sell|Small Loss)
• Magnitude RP not the dominant force on left branch

18. Day 5 Holdings

19. Day 20 Holdings

20. Day 125 Holdings

21. Day 250 Holdings

22. Testing Sign Realization
Preference

23. • Key advantage:
– Control for other effects
– Tax incentives, belief-based trading
– Expect such effects to be correlated with
gains/losses
– No reason to expect interfering effects to be
discontinuous at zero
– Tax effect, or inference, from a tiny gain versus
loss, should be small
Test for Jump at Zero

24. • Discontinuity tests around the origin
• Restrict sample to ±0.5 standard deviations of holding period return
• Test 1: Single regression over all returns, compare LHS vs. RHS residuals
– Step 1: single continuous regression specification
I(sell) = f(ret, ret2, ret3, ret*sqrt(time), ret2*sqrt(time), ret3*sqrt(time), sqrt(time),
log(price)
– Step 2: Compare residuals around the origin
Testing Realization Preference
Compare mean
residuals when
returns positive vs.
negative

25. Residuals Test
Prior holding period (days): 1 to 20 21 to 250 >250 All
N 4,368,415 29,924,997 36,404,390 70,697,802
3rd degree (PSW residual – PSL residual) (%) 0.003 0.007** 0.003** 0.013**
(0.22) (2.73) (2.72) (8.15)
(PSW res – PSL res) / Uncond. probability (%) 0.4 2.2 3.2 5.7
(PSW res – PSL res) / Disposition effect (%) 0.6 3.6 14.5 12.8
4th degree (PSW residual – PSL residual) (%) 0.005 0.007** 0.002 0.010**
(0.33) (2.90) (1.72) (6.05)
(PSW res – PSL res) / Uncond. probability (%) 0.6 2.4 2.0 4.2
(PSW res – PSL res) / Disposition effect (%) 1.0 3.8 9.2 9.5
5th degree (PSW residual – PSL residual) (%) 0.000 0.005 0.002 0.009**
(-0.03) (1.84) (1.68) (5.86)
(PSW res – PSL res) / Uncond. probability (%) -0.1 1.5 2.0 4.1
(PSW res – PSL res) / Disposition effect (%) -0.1 2.4 9.0 9.2
Variable: Residuals of I(Sell stock)
• Weakening statistical significance of discontinuity
• Focus especially on short holding periods
• Economic magnitudes small
• Further tests: no important jumps in subsamples by trade size, trade
frequency, gender

26. • Discontinuity tests around the origin
• Restrict sample to ±0.5 standard deviations of holding period returns
• Test 2: Regression discontinuity
– Estimate two separate polynomials in the positive and the negative regions.
Measure the gap between the two around the origin
– Caveat: Test may be sensitive to the level of prices
• Due to tick size, stocks with high prices more likely to have returns near zero
Tests of Realization Preference

27. Regression Discontinuity Tests
Prior holding period (days):
Degree of polynomial: 3rd 4th 5th 3rd 4th 5th 3rd 4th 5th
I(ret > 0) (%) -0.038 0.016 0.022 0.012 -0.006 -0.001 0.007 -0.001 -0.001
(-1.28) (0.40) (0.44) (1.65) (-0.58) (-0.07) (1.75) (-0.12) (-0.21)
Include polynomials
and interactions with sqrt(Time owned) Yes Yes Yes Yes Yes Yes Yes Yes Yes
Observations
Pseudo R2 0.015 0.016 0.016 0.010 0.010 0.010 0.010 0.010 0.010
β(I(ret > 0)) / Uncond. probability (%) -5.2 2.2 3.0 3.7 -1.7 -0.3 6.4 -0.5 -1.1
β(I(ret > 0)) / Disposition effect (%) -7.7 3.3 4.4 5.9 -2.7 -0.4 29.4 -2.5 -5.2
Dependent variable: I(Sell stock) × 100
1 to 20 21 to 250 >250
4,368,415 29,924,997 36,404,390
• No significant discontinuity
• With polynomial degree of 4th or higher, economic
magnitudes small

28. The V-Shapes for Trading
as Function of
Returns since Purchase

29. • Flattens over time
• Stronger on right branch (for the short holding periods that
matter the most)
• Also include controls (e.g., volatility, price, square root time, gain indicator)
V-Shape in Probability of Selling
Prior holding period (days): 1 to 20 21 to 250 >250
Ret
–
-3.60** -0.20** -0.00
(-17.65) (-7.18) (-0.62)
Ret
+
3.79** 0.17** -0.01*
(23.49) (11.88) (-2.33)
Controls Yes Yes Yes
Observations 1,242,021 8,795,180 11,421,064
Pseudo R
2
0.036 0.019 0.012
Dependent variable: I(Sell stock) × 100

30. • Flattens over time
• Stronger on left branch (for the short holding periods that matter the
most)
• Strahilevitz, Odean & Barber (2011): V-shape in hazard rate of purchases of stocks formerly
owned by the investor
V-Shape in Probability
of Buying Additional Shares
Prior holding period (days): 1 to 20 21 to 250 >250
Ret
–
-2.77** -0.10** 0.00
(-19.59) (-13.06) (0.69)
Ret+
1.83** 0.10** 0.00
(12.55) (11.08) (1.74)
Controls Yes Yes Yes
Observations 1,242,021 8,795,180 11,421,064
Pseudo R
2
0.037 0.019 0.009
Dependent variable: I(Buy additional shares) × 100

31. • Independent work
– Barber & Odean (2011) report a V-shape in the hazard rate
of selling as a function of the profit using both U.S. and
Finnish data.
– Plots of selling probabilities in relation to profits also
appear in the contemporaneous study of Seru, Shumway,
& Stoffman (2010)
– Using Finnish data, Kaustia (2009) and a prepublication
version of Grinblatt, Keloharju, Linnainmaa (2011) report
patterns somewhat akin to a V for selling.
• None of these studies consider the implication of it for
understanding the disposition effect, or test for
discontinuities.
Other Work on V-Shape in Selling

32. V-Shape in Buying Additional Shares
Day 60 Day 125 Day 250
Day 1 Day 5 Day 20

33. • Speculation (beliefs)
– E.g., individual investors trade aggressively,
presumably in hope of profit
• Odean (1998, 1999); Barber & Odean (2000)
• Tax loss selling
• Margin calls
Possible Sources of the V-Shapes

34. • A good explanation will explain both selling patterns as well as buying
additional shares
• Speculator buys stock at P0, based on personal signal
• After a few days:
– Stock price unchanged P1 = P0  No/little information updating
– Stock price increases P1 > P0  Conclude target valuation reached?
– Stock price decreases P1 < P0  Concede defeat?
• Updating about:
– Whether market has now impounded one’s perceived information
– Whether one’s original viewpoint was correct
• Such updating can generate either buying or selling
– Least trading when no change
• Due to overconfidence and biased self-attribution, after losses investors
may be reluctant to ‘give up’ on their hypotheses  shallow tilt of left
branch of V-shape
• Attention/reexamination offers another possible reason for V-shape
V-Shape and Speculation

35. • Barber & Odean (2000, 2001) gender, aggressiveness
• V-shape of selling steepens with trading frequency, and for
male investors
• Holding period is days 1-20
Speculation: Steepness of V-shape for Selling
and Gender, Trade Frequency
Q1 Q2 Q3 Q4 Male Female
N 310,011 310,629 310,853 310,528 628,776 77,063
Selling:
Ret–
-0.88** -2.01** -4.24** -7.01** -3.84** -3.75**
(-8.18) (-8.93) (-12.55) (-9.35) (-12.73) (-5.97)
Ret+
0.98** 2.41** 4.48** 6.58** 3.95** 2.69**
(12.97) (16.25) (16.06) (10.61) (17.12) (4.37)
β+
– β–
1.86 4.41 8.72 13.59 7.79 6.45
Trading Frequency Gender

36. Pr(Sell|Return):
Frequent vs. Infrequent Traders
Day 5

37. • V-shape for buying additional shares steepens with
trading frequency, and for male investors
Speculation: Steepness of V-shape for Buying
and Gender, Trade Frequency
Q1 Q2 Q3 Q4 Male Female
N 310,011 310,629 310,853 310,528 628,776 77,063
Buying additional shares:
Ret–
-0.83** -1.71** -3.01** -5.42** -3.02** -2.62**
(-6.60) (-11.50) (-13.01) (-10.07) (-13.23) (-5.48)
Ret+
0.58** 1.40** 1.96** 3.17** 1.86** 1.96**
(4.47) (8.38) (8.62) (6.25) (8.58) (4.44)
β+
– β–
1.42 3.11 4.97 8.59 4.89 4.58
Trading Frequency Gender

38. • No material change in the left branch of the V in 4th quarter
• Right branch of V is less steep in the 4th quarter, resulting in
weaker disposition effect
Tax Loss Selling?
Month
Q1 Q2 Q3 Q4 December
N 350,886 321,646 282,376 287,113 96,345
Selling:
Ret–
-4.11** -3.12** -3.48** -3.76** -2.78**
(-11.40) (-10.92) (-8.35) (-10.47) (-4.91)
Ret+
4.05** 3.52** 4.15** 3.34** 2.56**
(16.54) (15.53) (14.56) (11.70) (6.10)
β+
– β–
8.16 6.64 7.63 7.10 5.34
Quarter of the Year

39. • Implication of margin calls: Higher value weight of position
in portfolio should result in steeper left branch
• Results are opposite: V steepest for the minor stocks (‘mad
money’ ?)
Margin Calls
Q1 Q2 Q3 Q4
N 310,263 296,123 309,915 309,465
Selling:
Ret–
-8.49** -0.15 -0.08 -0.30
(-13.07) (-1.48) (-0.77) (-1.77)
Ret+
10.94** 0.27** 0.19* 0.42**
(17.49) (3.72) (2.11) (3.32)
β+
– β–
19.43 0.42 0.27 0.72
Position ($) / Portfolio ($)

40. • If so, suggests a speculative story rather than
RP
• Instead of looking at sale of current holding,
look at mirror image, additional purchase of
current holding
– Could still be indirect realization effects going on,
e.g., selling another stock to finance the purchase
Do We See Behavior Reminiscent of
Disposition Effect without Realization?

41. • Something akin to disposition effect arises even when not
testing for realizations
• Highlights that DE (or opposite) could easily arise without RP
Reverse Disposition Effect
for Buying Additional Shares…
1 to 20 21 to 250 >250 All
N 1,245,126 8,829,899 11,493,943 21,568,968
Unconditional probability (%) 0.41 0.11 0.03 0.09
(24.03) (30.80) (24.99) (30.67)
PBW (%) 0.34** 0.09** 0.03** 0.07**
(17.73) (23.73) (19.02) (25.23)
PBL (%) 0.46** 0.13** 0.04** 0.11**
(19.24) (26.31) (22.35) (25.74)
PBW – PBL (%) -0.13** -0.05** -0.01** -0.04**
(-4.92) (-8.98) (-4.41) (-9.89)
(PSW – PSL) / Unconditional probability (%) -31.18 -42.27 -24.86 -45.01
Prior holding period (days):

42. • Reverse disposition effect for buying
previously documented by Odean (1998)
• However, Odean (1998) obtained inverted V
for buying, opposite of the shape we find

43. • Investor trading:
– Retail investors are more likely to sell stocks
as returns increase: V-shape
– Similar pattern for buying additional shares
– A possible explanation: speculation
• The disposition effect:
– Results from different slopes of the branches of the V
– Does not result from discontinuity at the origin
– Does not substantially reflect sign realization preference
– Seems potentially consistent with investors trading based upon beliefs
• Disposition effect in itself says little about investor preferences
– Says little about whether investors ‘disciplined’ in realizing painful losses
Conclusion

45. • No particular pattern of discontinuity around zero with
respect to position amount, trading frequency, and gender
Cross-section of the Discontinuity
Q1 Q2 Q3 Q4
N 1,113,152 1,113,115 1,115,169 1,115,986
PSW residual – PSL residual (%) 0.0918 0.0018 0.0008 0.0049
(1.60) (0.56) (0.19) (0.39)
(PSW res – PSL res) / Uncond. probability (%) 3.5 4.7 1.5 2.7
(PSW res – PSLres ) / Disposition effect (%) 3.6 12.9 3.5 6.4
Q1 Q2 Q3 Q4 Male Female
N 1,114,394 1,114,522 1,114,455 1,114,401 313,589 39,064
PSW residual – PSL residual (%) 0.0025 0.0127 0.0162 0.0481 0.0227 0.0171
(0.56) (1.43) (1.05) (0.79) (0.49) (0.19)
(PSW res – PSL res) / Uncond. probability (%) 1.9 3.5 2.0 3.0 3.0 2.4
(PSW res – PSLres ) / Disposition effect (%) 2.9 4.2 2.6 5.2 4.9 3.5
Position Amount ($)
Trading Frequency Gender

46. • V-shape of buying additional shares is steepest for small
trades
Speculation: probability of Buying
Additional Shares
Q1 Q2 Q3 Q4
Buying additional shares:
Ret–
-0.43** -1.18** -2.57** -7.08**
(-6.42) (-12.23) (-14.58) (-13.97)
Ret+
0.33** 0.53** 1.26** 4.01**
(4.84) (4.85) (6.92) (8.17)
β+
– β–
0.76 1.71 3.83 11.09
Position Amount ($)

47. • Source: Odean
(1998)
• Disposition effect
is weaker towards
the end of the
year
 Conclusion:
(“Rational”) Tax
loss selling
mitigates the
behavioral bias
Tax Loss Selling

48. • Source: Grinblatt and Keloharju, What makes investors trade (JF
2001)
Disposition Effect in the Literature

49. • In our sample
Replication: 1% buckets (Days 1 to 20)

50. • In our sample
Replication: 0.5% buckets (Days 1 to 20)

51. • In our sample
Replication: 0.25% buckets (Days 1 to 20)

52. • In our sample
Replication: by ticks
(Days 1 to 20, price ≤ $20)

53. • In our sample
Replication: by ticks
(Days 1 to 20, $20 < price ≤ $50)

54. • In our sample
Replication: by ticks (Days 1 to 20,
price ≤ $20)