Discussion Papers In Economics
And Business

Disposition Effect and Diminishing Sensitivity:
An Analysis Based on a Simulated Experimental Stock Market
Youki Kohsaka
Grzegorz Mardyla
Shinji Takenaka
Yoshiro Tsutsui

Discussion Paper 13-02-Rev.2

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANDisposition Effect and Diminishing Sensitivity:
An Analysis Based on a Simulated Experimental Stock Market
Youki Kohsaka
Grzegorz Mardyla
Shinji Takenaka
Yoshiro Tsutsui

Discussion Paper 13-02-Rev.2
December 2013

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANDisposition Effect and Diminishing Sensitivity: An Analysis
Based on a Simulated Experimental Stock Market Youki Kohsaka†
Grzegorz Mardyla‡
Shinji Takenaka§
Yoshiro Tsutsui¶

Abstract
We experimentally investigate the existence of the disposition effect and diminishingsensitivity as its potential cause. Our approach includes three key characteristics: (i) An
environment closely resembling actual stock markets; (ii) Individual-specific reference
prices; (iii) A direct test of diminishing sensitivity as a cause of the disposition effect.
We find strong support for the existence of the disposition effect as an independent
hypothesis. This is an improvement over previous studies, which tested this hypothesis
only jointly with others. Our results also strongly point to diminishing sensitivity, of thetype postulated by prospect theory, being a source of the disposition effect.

JEL classification codes: G02
Keywords: disposition effect, diminishing sensitivity, investor behavior, experimental
economics



An earlier version of this paper was presented at the 6th annual meeting of Association of
Behavioral Economics and Finance, and at a conference held at Hosei University. We are grateful tothe participants of those events for their useful comments. We also express gratitude to Hiroshi
Izawa, Jie Qin and Shunichiro Sasaki for helpful comments and constructive collaboration during theearly stages of this project.
†
Waseda University Center for Finance Research, Email: kohsaka@aoni.waseda.jp‡
Kinki University Faculty of Economics, Email: greg@kindai.ac.jp§
Japan Center for Economic Research, Email: s.takenaka@jcer.or.jp¶
Osaka University Graduate School of Economics, Email: tsutsui@econ.osaka-u.ac.jp
11. Introduction
The purpose of this paper is to test the existence and causes of the disposition effect.
Empirical evidence indicates that individual investors exhibit a greater propensity torealize gains than to realize losses, thereby causing them to incur excessive losses.
Numerous informal “investing advice” books have been written on how to avoid thetrap of being unable to cut one’s losses early. Such informal publications are based
mostly on casual observations and often themselves suffer from representativenessbiases. In this paper we attempt to carefully examine the disposition effect in anexperimental setting, in order to discover how psychologically difficult it really is forhuman traders to sell stocks at a loss, and to shed some light on the underlying causes ofthat difficulty.
There are two basic strands of extant research on this topic. The first one involves
empirical investigations of real-world financial transaction data, while the second
consists of laboratory experiments. Papers in the first strand analyze data from various
securities markets around the world. Some representative empirical work, all of which
confirms the existence of the disposition effect in various markets, includes: Odean(1998) – U.S. stock market; Grinblatt and Keloharju (2001) – Finnish stock market;
Coval and Shumway (2005) – The Chicago Board of Trade; Shumway and Wu (2006) –Shanghai stock market; Fogel and Berry (2006) – 176 members of the American
Association of Individual Investors; Misumi at al. (2007) – Tokyo Stock Exchange; andChoe and Eom (2009) – South Korean futures index market.1 Concerning the second
1

Choe and Eom (2009) find in addition that individual investors are much more susceptible to thedisposition effect than institutional or foreign investors.
2strand of literature, the disposition effect has also been demonstrated in laboratory
experiments conducted mainly on a university students in various locations, including:Weber and Camerer (1998) – Germany; Chui (2001) – Macau; Kirchler et al. (2005) –Austria; Rubaltelli et al. (2005) – Italy; Vlcek and Wang (2007) – Switzerland; andShiroshita (2009) – Japan.
Empirical analyses of the disposition effect are valuable, since they directly test for
the existence of the effect in real-world financial markets. Experimental research, on theother hand, while it cannot guarantee external validity, has the undisputed merit ofallowing for a strict control over, and accurate design of, the environment in whichstocks are traded. On top of that, individual investor information, which is vitally
important yet difficult or impossible to obtain in empirical research, can be acquired
relatively easily in experimental studies. In our case, this information includes
individual-specific reference points, individual degrees of diminishing sensitivity, andthe personal and demographic attributes of subjects. Economic experiments, besides
offering another avenue to test for the existence of the disposition effect, thus also
permit an opportunity to investigate the effect’s potential causes.
In order to show why this is important, observe that there exist a multitude ofcandidate explanations for the apparent prevalence of the disposition effect. These
include:(1) The shape of the value function from Kahneman and Tversky’s (1979) prospect
theory, which implies that agents are risk averse in the domain of gains and risk
loving in the domain of losses. In this paper, we refer to this phenomenon simply3

as “diminishing sensitivity”.
(2) Belief in reversion to the mean: If investors believe that stocks trading at a loss
will rebound in the future with high enough probability, then holding on to suchstocks might be optimal.
(3) Portfolio rebalancing: Investors might wish to maintain a constant cash value ofcertain stocks in their portfolios. This would lead them to rationally hold on to,or perhaps buy still more of, losing stocks.
(4) Transaction costs: All else equal, selling losing stocks entails higher per-unit
transaction costs. This, in turn, implies that holding on to them is the smart thing
to do.
(5) Psychologically-motivated reasons, such as mental accounting, regret aversion,and self-control (Shefrin and Statman (1985)).
(6) Tax reasons: Although early research on the disposition effect (Shefrin andStatman (1985), Lakonishok and Smidt (1986), Odean (1998)), following
Constantinides’ (1984) exposition of a rational loss realization model, pointed to
tax-related issues as a possible cause, tax exemption rules associated with capital
losses would seem to preclude a tax-motivated disposition effect.
Odean (1998) conjectured that diminishing sensitivity might bring about thedisposition effect. While demonstrating the effect’s existence in a large data sample, he
excluded a number of other factors as its possible sources. In particular, Odean’s (1998)
results do not support the trading costs hypothesis, which is shown to be inconsistent
with the disposition effect; investors in his sample sell winners more frequently than4

they sell losers, regardless of transaction costs. Also, by eliminating from his analyses
trades that might have been motivated by a desire to rebalance, he effectively controlled
for portfolio rebalancing. Odean (1998), while initially reluctant to reject belief in mean
reversion as a potential cause of the disposition effect, refers later to his complementary
paper based on the same sample of investors (Odean (1999)). In that paper he finds thatthe investors tend to buy stocks that have outperformed the market in the past, whereasa belief in mean reversion would imply the exact opposite.
In a related study, an experiment by Weber and Camerer (1998) finds thatparticipants are significantly more inclined to buy stocks trading at a loss as opposed tothose trading at a gain. The authors attribute these findings to prospect theory, yet do not
exclude belief in mean reversion or, more generally, the misperception of stochastic
processes, as probable reasons for the effect.
It has long been suspected that the convexity of prospect theory’s value function in
the domain of losses might account for the disposition effect. This suspicion, however,has itself come to be questioned recently. Kaustia (2010) parameterizes cumulative
prospect theory’s S-shaped value function (Tversky and Kahneman (1992)) to show thatpropensity to sell is highest at the reference point (purchase price) and declines wheneither gains or losses inflate. Oddly enough, the model predicts that in most cases
holding any stock is more beneficial than selling. On the other hand, Kaustia (2010)
finds empirically, using Finnish transaction data, that the propensity to sell a stock does
not decline as paper gains or losses increase, but rather is increasing or constant in thedomain of gains and insensitive to returns in the domain of losses. In other words, there5

is a discontinuity (a “jump”) in investors’ attitudes towards selling exactly at a point
where capital gains are zero. Given this evidence, he concludes that the S-shaped valuefunction cannot predict the pattern of realized returns found in the data and hence thatthe disposition effect is unlikely to be driven by prospect theory preferences.
Barberis and Xiong (2009) study theoretically the trading behavior of an investor
with prospect theory preferences and conclude (in the first part of their study) that for asignificant range of parameter values, prospect theory predicts investors will be more
inclined to sell stocks with losses than to sell stocks with gains – exactly opposite towhat the disposition effect leads to.2
Both Barberis and Xiong (2009) as well as Kaustia (2010) employ a carefully
calibrated prospect theory-type value function and show that it does NOT lead to thedisposition effect. This finding sent a shockwave throughout the behavioral financecommunity, spurring whole new streams of research in the area.
One alternative disposition effect explanation that has surfaced recently isrealization utility theory. The actions of selling and buying stocks result in changes in
the internal constitution of an investor’s wealth, NOT in changes in the investor’s
overall wealth level. Hence, it is problematic that the mere act of stock trading, in and of
itself, should be considered as an event capable of generating any extra utility.
Both of the two studies cited above make clear distinctions between the evaluation
period for changes in an investor’s wealth/utility levels and the stock trading timeintervals. Barberis and Xiong (2009), after first modeling a “traditional” wealth-level2

Hens and Vlcek (2011) derive an analogous result.
6

utility-maximizing investor and concluding that such an investor would not be prone tothe disposition effect, proceed with a simulation exercise based on the premise that any
act of buying or selling stocks generates a prospect theory-type “utility surge” andreport significant disposition effect incidence as a result. Barberis and Xiong (2012)
term this type of utility function “realization utility” and propose a linear specification,
on which they subsequently base their theoretical and computational modeling exercise.
In a related study, Henderson (2012) utilizes a Tversky-Kahneman (1992) S-shaped
value function to solve for an asset-liquidation optimization problem of a realization
utility investor. Her model predicts that disposition effect becomes more pronounced asconvexity of the value function in the loss domain increases.
Importantly, the prevalence of the disposition effect is not extreme in Henderson(2012) – investors do sell at a loss voluntarily. The predictions of her model are thus
closer to (nonetheless, still an order of magnitude higher than) observed empirical andexperimental results on the intensity of the disposition effect. And her predictions are
more accurate than those stemming from several competing theories, which are capableof producing only a very strong version of the disposition effect wherein investors nevervoluntarily realize losses.
The theory of realization utility has also been experimentally validated by Frydman
et al. (2012) with an fMRI study. They report that ventral striatum exhibits a positive
response when subjects realize capital gains.
The theory of realization utility is not the only recently debated candidate for
explaining the disposition effect. Meng (2012) focuses on the prospect theory reference

7point and shows with a simulation exercise similar to Barberis’ and Xiong’s (2009) thatthe disposition effect obtains readily once we redefine the reference point by a rationally
expected return rate (above the riskless interest rate) rather than by a status quo level.
On the other hand, Li and Yang (2013) build a general equilibrium model toendogenously solve for the risky asset return rate. Again, using a Tversky-Kahneman(1992) value function, they find that diminishing sensitivity does predict a disposition
effect.
Summarizing recent research efforts aimed at explaining the disposition effect withprospect theory-related arguments, we recognize two distinct lines of reasoning. The
first line focuses on the effects of the kink at the reference point of the value function,
associated with loss aversion. In this case, prospect theory is found to explain thedisposition effect in Meng (2012) (conditional on the reference point being sufficiently
high above the risk-free rate), as well as in Barberis and Xiong (2012) (in which theeffect is caused by the realization utility function). The second line of reasoning
emphasizes diminishing sensitivity – the convexity of the value function in the domainof losses. In this case as well, prospect theory is found to be a persuasive explanation
for the disposition effect, be it through the introduction of realization utility in
Henderson (2012), or in the stylized extension of a general equilibrium model in Li andYang (2013).
This paper attempts to examine whether diminishing sensitivity can explain thedisposition effect without resorting to any specific theory. Such an attempt has been alongstanding challenge ever since the seminal paper by Shefrin and Statman (1985).

8

Our approach has three key characteristics. First, we use data generated through anexperiment designed to mimic as closely as possible a real-world security market – ourdata is thus very similar to actual stock market data. The simulated market in our
experiment lasts for four weeks. It is open for four and a half hours each trading day –exactly like the Tokyo Stock Exchange (TSE). Our market is open in the evening hours
to facilitate frequent trading. We use real-world historical price data for 10 stocks fromthe TSE, edited from tick data so that the prices are updated every two minutes. 3
Participants in our experimental market may trade during any time the market remains
open. Remuneration for participating in the experiment is proportional to the earnings(or losses) they acquire through trading. Thus we may assert that any results obtained
through the experiment mimic closely those of a real world stock market.
Second, our method directly tests whether or not diminishing sensitivity leads to thedisposition effect. We do this by eliciting the degree to which subjects are prone todisplay diminishing sensitivity, and correlating this with the strength of the disposition
effect they exhibit in trading. To this end, we perform supplemental experiments tomeasure our subjects’ degrees of risk aversion in the domains of gains and losses. Thismethod allows a more general inquiry into the potential causal relation between
diminishing sensitivity and the disposition effect. Without the need to rely on aparticular theory, our method offers a direct test of the hypothesis that diminishingsensitivity causes the disposition effect.
The third characteristic of our study is related to Odean’s (1998) observation that

3This method guarantees that subjects will be able to trade at their desired price.
9

testing for the disposition effect is equivalent to testing a joint hypothesis about thedisposition effect’s existence and the location of the agents’ reference points. Assuming
a particular value for the reference price – e.g. first purchase price, last purchase price,
weighted average purchase price, etc. – has been the standard practice used in empiricalresearch on the disposition effect. This practice does constitute a type of robustness
check of the results obtained, but it ignores the possibility of heterogeneity in reference
points across investors. To address this problem, we solicit individual participants’reference points using a questionnaire survey, and use the obtained values when
computing gains and losses. In effect, our method constitutes an independent test for the
disposition effect, not merely a test of the joint hypothesis described by Odean.
In addition to the three features outlined above, our setup also allows us to exclude
both taxes and transaction costs as potential explanations for the disposition effect.
Our analyses, employing the techniques spelled out above, clearly confirm theexistence of the disposition effect, and point to diminishing sensitivity as being one ofits causes. We also examine the potential link between individual time preferences andthe incidence and strength of the disposition effect and find, contrary to expectations,that higher discount rates are associated with a weakening of the disposition effect.
The rest of this paper is arranged as follows. In the next section we describe theexperimental design and methods. In Section 3, we explain the techniques used toanalyze the data. In Section 4 we report our main results and robustness checks
involving subjects’ personal attributes; we also verify that our results remain unaffected
when alternative values are substituted for individual reference points. Our examination10

of the relationship between time discounting and the disposition effect is also containedin Section 4. We offer conclusions in Section 5.

2. Experimental Design and Procedures
The main experiment in our design is called the “Stock Trading” experiment, in which
participants buy and sell shares in a simulated stock market. We also conduct two
supplemental experiments: the “Insurance Buying” experiment and the “Lottery Selling”
experiment, which we use to measure participants’ risk aversion in the domains oflosses and gains.

2.1. Stock Trading Experiment2.1.1. Outline of the Experiment
The “Stock Trading” experiment required its participants to buy and sell shares of 10
companies in a simulated stock market accessed through the internet. Each participant
was given an initial endowment of virtual shares and virtual cash with which to trade.
The market lasted for four weeks, and was open for four hours and thirty minutes every
day from 18:00 through 22:36 (with a six minute break from 20:00 to 20:06).4
The stock price data we used is authentic mid-price tick data from the past, edited sothat it is updated every two minutes. 5 In this way, we avoid any possible negative
4

The six minute break replicates the lunchtime break from 11:00 through 12:30 instituted on theTokyo Stock Exchange.
5
Specifically, we randomly selected ten high-liquidity stocks traded on the Tokyo Stock Exchange
and for each extracted 33 days worth of tick data from “Nikkei Tick Data”. We subsequently createdfor each of the ten stocks a vector of mid-quotes corresponding to those observed at the mid-quotesof 2-minute intervals in the original data file, and used morning period mid-quote data for the 18:00
through 20:00 experiment trading period, and afternoon mid-quote data for the 20:06 through 22:36
11

auto-correlation issues resulting from the bid-ask spread, which we might haveencountered if we had used actual execution prices. Subjects in our experiment wereguaranteed that their trades are going to be carried out exactly at the prices shown on
their monitors, and that those prices are not in any way affected by their own, nor byother subjects’ quantities demanded or quantities supplied. 6 Short-selling and negative
cash positions were not allowed. We performed a simple linear transformation on theprice data to preclude the possibility of identification of actual stocks by theparticipants.
The initial endowment of each participant consisted of 10 shares of each of the ten
stocks and a cash allotment of 10,000,000p (“points”). Participants had access to atransaction panel (Figure 1), where they received information on the present
composition of their portfolios, stock prices and cash holdings. The panel also allowed
them to make buy and sell orders, which were immediately executed: for instance, bychanging the number of shares in the “After Transaction” column and clicking on the“Execute Trade” button, a corresponding order is completed. Traders in our experimentalso had access to graphs representing both past price paths (closing quotes) up to thepresent day, and the same-day price paths, starting from the opening bell until thepresent time.7 There were no dividends or transaction costs, nor were there any taxes.
This differs from real world markets but has the benefit of excluding from our analysis
the above-mentioned factors as possible explanations for the disposition effect.

trading period.
6Consequently, experiment participants emulate small individual investors facing a highly liquidmarket.
7
On the first day of the experiment, data from the preceding five trading days is made available.
122.1.2. Compensation Structure
Participants received three types of compensation. The first type depended on thenumber of days they logged on to the experiment homepage throughout its duration. In
addition to ¥30 (The exchange rate was around ¥90 per $1 as of the time thisexperiment was conducted.) for each day a subject logged on, a subject was entitled to abonus payment of a few thousand yen if they accessed the system on at least 18 days. 8
The second type of compensation was commensurate with the final portfolio return –for each percentage point of the return on a subject’s portfolio, ¥180 were awarded. Incase of negative returns, the resulting losses were subtracted from bonus payment
awarded for regular logging on to the experiment homepage described above. 9 The
third payment type was a ¥30,000 “winner prize” awarded to the participant whose final
holdings at the end of the experiment were the highest. This prize was instituted tofacilitate frequent trading activity and hence to generate enough experiment data.
Experiments such as ours suffer, due to the inherent funding limits, from the problem ofproviding monetary incentives high enough to mimic real world activities. A chief
characteristic of our experimental design is participants’ ability to engage in stock
trading anyplace where they have access to the internet, at the time of their choosing
during the one month duration of the experiment. This differs substantially frommajority of economic laboratory experiments. Participants in such experiments are

8

These bonus payments are: ¥1,800 for logging on between 18 and 22 days, ¥2,600 for logging on
between 23 and 27 days, and ¥3,600 for logging on 28 days (every day of the experiment).
9
Should the resulting yen amount turn out to be negative, relevant subjects were to receive ¥0.
However, there were no such cases.
13

confined in the laboratory environment and have no choice as to the time and place, inwhich to decide and act. Moreover, constant surveillance by experimenters makes
neglecting to participate in the experiment very difficult.

Since our experimentparticipants do not need to cope with such unusual and strenuous conditions, it isplausible to expect that they might be tempted to slack off on participation. The ¥30,000
winner prize, whilst being affordable in terms of experimenters’ budget constraints, islarge enough to serve as an effective trading incentivization device. 10 This type of
incentive scheme, though it might not be an exact imitation of real world conditions,does resemble actual stock trading in that it allows for a possibility of quite high returns.

2.1.3. Basic Experiment Data
Participants were recruited (with the assistance of an internet research company) fromamong individual investors with previous stock trading experience, defined as having
recent history of trading at least once per month on the stock market. The average age ofthe participants was 41.94 years (SD=10.74; For males 41.03, SD＝10.98, for females
44.38, SD=10.06). Detailed attributes of the experiment participants are summarized inTable 1. The most numerous age groups were people in their 30s, followed by 40s, witha few participants in their 60s and 70s. Employment income earners comprised about
half of the pool of subjects. Four of the male participants were self-employed.
Household income ranged from slightly below 3 million yen to 15 million yen. Finally,
10

As we report below in section 4.2, this incentive structure resulted in ample trading activity andhence, an adequate amount of valid experiment data.
14

the real-world trading frequency reported by subjects was most commonly “roughly
once a week” or “almost daily”, each of these accounting for over 30% of the total.
On January 24th 2010, all the subjects were gathered together at a computerlaboratory at the Osaka University campus, where the experiment was thoroughly
explained. On the same day, the supplemental risk aversion estimation experiments(detailed below) and the questionnaire survey (designed to elicit individual reference
points) were conducted. From Monday January 25 th 2010 through Sunday February 21 st2010, the simulated stock market was open for trading every evening between the hours
18:00 and 22:36.

2.2. Diminishing Sensitivity Measurement Experiment
Measurements of individual diminishing sensitivity levels were carried out by means of
two simple experiments. The “Insurance Buying Experiment” was implemented toestimate individual risk aversion levels in the loss domain. The “Lottery Selling
Experiment” was implemented to estimate risk aversion levels in the gain domain.

2.2.1. Insurance Buying Experiment
In this experiment, each subject was asked whether they were willing to purchaseinsurance at various prices displayed on the monitor. Given an initial endowment ofassets, the insurance – if purchased – guarantees a payment equivalent to the value of
assets in case these are lost or damaged. This design in effect allows the experimenters
to estimate the degree of a participants’ risk tolerance in the domain of losses.

15

The details of the experiment are as follows. A subject is first presented with an initialendowment of ¥2,000. Then, an amount of potential damage and the probability of its
occurrence are displayed along with a proposed insurance premium. The subject
chooses whether to purchase the insurance or to decline it. There are four categories ofpotential damage (¥100, ¥400, ¥1200, ¥2000) while the probabilities of their occurrence
are set constant at 50%. The insurance premiums (along with corresponding premium
rates, equal to the premium sum divided by the damage total) are displayed in random
order. An example screenshot is shown in Figure 2. This procedure is repeated 30 times
in a row for each category corresponding to the four potential damage totals, startingfrom the lowest ¥100.
Thus, each subject goes through 120 yes-or-no queries. After that, the computer
randomly chooses one of the 120 queries, which is then used to determine the actual
payment.11

2.2.2. Lottery Selling Experiment
Individual levels of risk aversion in the domain of gains were estimated via the “Lottery
Selling Experiment”. In this experiment the subjects were asked whether they werewilling to sell a lottery ticket at a proposed price. Each ticket has a 50% chance of
winning a prize. The prize falls into one of four categories: ¥100, ¥400, ¥1200, ¥2000. A

11

If a subject had in fact purchased insurance for the randomly chosen query, they were given theoption to avert any potential damage by actually paying the premium. In the case when they had notpurchased the insurance, the subject had to pay the amount of damage (in case it occurred), which
was subtracted from their initial endowment. The endowment was left intact whenever no damage
actually occurred. Whether the damage in fact occurred or not was selected randomly by thecomputer with independent probability of 50%.
16

participant’s task is to answer “yes” or “no” to 30 choice problems for each of the four
categories. The procedures as well as settlement of payments are analogous to those
employed in the “Insurance Buying Experiment”. 12

2.3. Questionnaire Survey
The survey was conducted mainly to elicit reference prices, but we also included
questions pertaining to subjects’ preferences and demographic attributes. Here, weconstrain ourselves to the description of our main purpose – identification of individualreference points.
In the questionnaire, hypothetical stock prices paths for two cases – a rising pricepath and a declining one – spanning 6 discrete time periods are presented. For eachpoint in time, hypothetical buy and sell transactions along with resulting positions in thestock in question are shown. Furthermore, a 7th period price is shown along with 8
different ways to calculate paper gains and paper losses for the relevant stock. Subjects
are then requested to choose a method of calculation closest to their own.13 The choices
available for a reference point are: (1) the first purchase price; (2) FIFO: first-in,
first-out; (3) the last purchase price; (4) LIFO: last-in, first-out; (5) the highest purchaseprice; (6) the lowest purchase price; (7) weighted average purchase price; (8) weighted
average purchase price minus average profit/loss for the portion of shares sold in the12

Out of 120 choice sub-tasks, one was selected randomly by the computer. If the subject chose to
sell the lottery ticket in that sub-task, they received an amount of money specified therein. In the
opposite case – when the subject had chosen to not sell – the computer drew the lottery andpayments were decided depending upon whether a winning ticket or a losing ticket was drawn. In
the former case the subject was paid the prize, while in the latter they received nothing.
13
There was also an additional item corresponding to a “none of the above” option, where a subject
was asked to describe in detail their method of calculation.
17

interim time.

3. Method of Analysis
3.1. Degree of Risk Aversion
We restrict our explanation here to the case of Insurance Buying Experiment, wherein
we used computational methods exactly analogous to those used in the Lottery Selling
Experiment.
First, we compute for all experiment participants their individual insurance values.
When specific insurance policies are ordered starting from the cheapest policy andgoing up in value to the most expensive one, we would expect to observe any given
subject first choosing “buy” a few times, at some point switching to “not buy”, and thencontinuing to choose “not buy” for the remaining cases. We define “individual insurance
value” as the average of the two values between which the switch occurs. It is howeverconceivable, and indeed turns out to be the case that, some subjects switch multiple
times. In these cases, we estimate a LOGIT regression model for the 30 proposed
insurance prices where we assign a “1” to each “buy” decision and a “0” to each “notbuy” decision. The individual insurance value is then defined as the one corresponding
to 0.5 in the regression.
The absolute risk aversion (ARA) coefficient for the ith subject is defined andcalculated according to the following formula due to Cramer et al. (2002).
ARAi 

az  pi1 (az 2  2api z  pi 2 )2(1)Here, a is the probability of winning equal to 0.5, z is the damage amount, and pi is the18

“individual insurance value”. As there are four different z values, we take an arithmetic
average of those to get the final ARA coefficient values. 14

3.2. The Estimation Model
Estimation of the disposition effect and its potential relationship with diminishingsensitivity is performed with a LOGIT analysis. The dependent variable 𝑆𝐸𝐿𝐿𝑖,𝑗,𝑡 isdefined as follows. For each subject i we first look for all instances (measured in
two-minute units) in which any trades were recorded. The subscript t then corresponds
to the ordinal location of a trade, when trades are ordered chronologically. 𝑆𝐸𝐿𝐿𝑖,𝑗,𝑡 is
set to 1 whenever a subject i sells a stock j at a time t and to 0 otherwise. The
independent variable 𝐿𝑂𝑆𝑆𝑖,𝑗,𝑡 is set to 1 whenever a stock j in a subject i’s portfolio istrading at a loss at a time t, and to 0 otherwise. The regression model is thus
Model 1：

𝑆𝐸𝐿𝐿𝑖,𝑗,𝑡 = 𝛼 + 𝛽1 ∙ 𝐿𝑂𝑆𝑆𝑖,𝑗,𝑡 + 𝜀𝑖,𝑗,𝑡 ,(2)where 𝛼 and 𝛽1 are the regression coefficients and 𝜀𝑖,𝑗,𝑡 is the error term. 𝛽1 will be
negative if the disposition effect obtains; that is, if the tendency to sell is stronger in thedomain of gains than it is in the domain of losses.
Next, we test for diminishing sensitivity as a potential cause of the disposition effect.
It is plausible that as the degree of diminishing sensitivity increases, the disposition
effect becomes stronger. The absolute value of the coefficient 𝛽1 from equation (2)would in this case increase with the degree of diminishing sensitivity. The regression
model in this case is14

Four subjects in total appeared to either answer Yes/No randomly, or reverse the “Yes’s” and the“No’s”. We exclude these subjects from all regressions.
19Model 2：𝑆𝐸𝐿𝐿𝑖,𝑗,𝑡 = 𝛼 + (𝛽11 + 𝛽12 ∙ 𝐷𝑆𝑖 ) ∙ 𝐿𝑂𝑆𝑆𝑖,𝑗,𝑡 + 𝜀𝑖,𝑗,𝑡= 𝛼 + 𝛽11 ∙ 𝐿𝑂𝑆𝑆𝑖,𝑗,𝑡 + 𝛽12 ∙ 𝐷𝑆𝑖 ∙ 𝐿𝑂𝑆𝑆𝑖,𝑗,𝑡 + 𝜀𝑖,𝑗,𝑡 .

(3)

We expect 𝛽12 to be negative if diminishing sensitivity is indeed a cause of thedisposition effect. We use here two alternative variables to represent diminishingsensitivity. The first one, DS1, is the degree of risk tolerance (the negative of risk
aversion) in the domain of losses, which corresponds to a measure of convexity of thevalue function. The second one, DS2, is the risk tolerance degree in the domain of losses
relative to its counterpart in the domain of gains, defined as risk aversion coefficient in
the domain of gains minus risk aversion coefficient in the domain of losses. This second
relative measure of diminishing sensitivity might be a more appropriate one, given thatthe disposition effect itself is essentially a relative measure of the extent to which
winners are more likely to be sold than losers.

4. Results
4.1. Reference Points
We use each experiment participant’s individual reference point, estimated from thequestionnaire survey data outlined above. Table 2 summarizes our findings on thereference points: reference points for the domain of gains are in rows, while those forthe domain of losses are in columns. For instance, the “1” in the left-uppermost cell of
the table indicates that one person chose the first purchase price as their reference point
for both the gain and the loss domains. Thus we find most subjects choosing a weighted
average of purchase prices for their reference points, noting that many of them take into20

account profits for the portion of shares sold in the interim. We also note that most
respondents selected the same reference points for both the loss and the gain domains.

4.2. Results of the Stock Trading ExperimentThroughout 28 days of the experiment and across 49 participants, we recorded a total of
3,527 sell transactions and 4,005 buy transactions – roughly 153 trades per subject, 5.5
trades per subject per day. Out of the 10 stocks traded, the most frequently traded stock
was traded 1,639 times, and the least popular one 430 times, while the corresponding
figures for remaining eights stocks were between 527 and 839. We observe thus an
overall abundance of trading activity, with one stock topping all the others in popularity.
Out of all sell orders, 1,620 (45.9%) were profitable while 1,357 (38.5%) wereaccompanied by losses. The remaining 550 (15.6%) trades were zero-profit transactions.
For the case of buy orders, 622 (15.58%) additional purchases were recorded in the gain
domain, and 1,108 (27.7%) additional purchases in the loss domain, while 2,275(56.8%) additional purchases were recorded on zero-profit accounts.
Final asset value scores, when compared with the initial benchmark of 10,000,000
points, averaged an approximate 70,000 point loss (SD=34,000), with the highest
scoring subject winning a profit of some 80,000 points and the biggest loser incurringsome 88,000 points in losses.

4.3. Results of the Risk Attitudes Measurement Experiment
The average absolute risk aversion coefficient across all subjects was –0.0014 in the21Lottery Selling Experiment and –0.0031 in the Insurance Buying Experiment. Subjects
thus exhibit apparently risk loving attitudes, on average. This outcome most likely
originates from small stakes used in the simple lottery tasks employed to estimate risk
attitudes.
When we subtract the risk tolerance coefficient measured in the Lottery Selling
Experiment from the one measured in the Insurance Buying Experiment, we obtain
0.00168, which is significant at a 5% level. We conclude therefore that our subjects
exhibit more risk-loving behavior in the domain of losses as opposed to the domain ofgains.

4.4. Incidence of the Disposition Effect – LOGIT Regressions
In Table 3 we present a summary of the LOGIT analysis using the individual-specificreference points from the questionnaire survey. The first panel reports pooled results for
all ten stocks. The “Model 1” section reports estimation results for formula (2). The
coefficient for the losing-stocks variable LOSS is significantly negative at 1%, revealinga tendency to avoid the realization of losses. The “Model 2 (1)” section adds the𝐷𝑆1 ∙ 𝐿𝑂𝑆𝑆 as an explanatory variable in the regression. Again, the LOSS coefficient isnegative at a 1% significance level. Together with the results of “Model 1”, this implies
reluctance on the part of subjects to get rid of losing stocks, and thereby the existence ofdisposition effect. Furthermore, the coefficient for the 𝐷𝑆1 ∙ 𝐿𝑂𝑆𝑆 variable is also
negative and statistically significant at a 1% level. For the alternative measure ofdiminishing sensitivity used in “Model 2 (2)”, the coefficient of interest is again

22

negative and statistically significant at the 1% level. These results support the
hypothesis that diminishing sensitivity is a cause of the disposition effect; the higher the
degree of diminishing sensitivity, the more reluctant investors are to sell losing stocks.
With the exception of stock #8, we obtain analogous statistically significant results
for the LOSS coefficients when we perform the regressions for individual stocks (notreported here). Regarding the interaction term with the diminishing sensitivity variable
DS1, the coefficients are all negative except for stock #8, and significantly negative
except for stocks #8, #1 and #5. When DS2 is substituted for the diminishing sensitivity
variable, the interaction term coefficients are negative except for stock #9, andsignificantly negative except for stocks #3 and #9. Hence we conclude that for mostcases our results are consistent with the disposition effect hypothesis, and thatdiminishing sensitivity is one source of the effect. In other words, these outcomes are
not driven by the special characteristics of any one stock in subjects’ portfolios, but area prevalent tendency evident throughout the entire stock spectrum.

4.5. Accounting for Participants’ Demographic and Personal Attributes
We next check whether results reported in the previous section are replicated when we
take into account participants’ individual demographic and personal traits. The
particular attributes we include in our analyses are gender, age, household income, andstock trading experience.
Table 4 summarizes the results. In a nutshell: (1) The disposition effect obtains evenwhen individual attributes are accounted for; (2) Cross-term coefficients for the losing

23

stocks term LOSS and both diminishing sensitivity terms DS1 and DS2 are negative andstatistically significant. Clearly, higher diminishing sensitivity produces a more
pronounced disposition effect.
A look at the control variables tells us that women are less prone to selling losing
stocks. Also, propensity to sell grows stronger with both age and income, albeit in adiminishing manner. Finally, those with more real world trading experience tend to sell
stocks more frequently.

4.6. Alternative Reference Points
In the analyses reported thus far we have used the individual-specific reference points
elicited from the participants through a carefully tailored questionnaire survey. It isprudent to verify whether the results thus obtained are changed when other, arbitrarily
chosen reference prices are employed. For completeness, we performed this verification
exercise for all subjects for each of the eight reference points specified above in Section
2.3, for both “Model 1” and “Model 2”. The findings do not differ much from the main
results reported above. In Table 5 we show the estimation results for two out of eight
possible reference prices – weighted average purchase price (WA1), and first-bought
first-sold (FIFO). These findings corroborate previous empirical studies that reportrobustness of the disposition effect with respect to a variety of assumptions on reference
points.

4.7. Time Discounting and the Disposition Effect24

The ongoing debate about the relationship between prospect theory and thedisposition effect needs to address the potential effects of time preferences on investors’
reluctance to realize losses. Time preferences – in particular, individual discount rates –are likely to influence the timing of trades. Although many intertemporal decision
making models assume, for tractability and simplicity, no discounting at all, it isplausible that individual discount rates could interact with the disposition effect.
Henderson (2012) conjectures that “the inclusion of time discounting would be likely togive an incentive to delay losses further, contributing to an even more pronounced
disposition effect”. In fact, Barberis and Xiong (2012), show in their model that for astrong disposition effect to obtain, sufficiently high time discount rates are required, in
combination with realization utility. In this section we attempt to supplement these
theories with an empirical test of the hypothesis that investors with higher time discountrates exhibit stronger disposition effects.
We elicited participants’ time discount rates using a questionnaire accompanying theexperiment. In the questionnaire, a subject is presented with a series of binary choicetasks, in which they must choose between receiving a payment of ¥10,000 in 90 days
(option “A”), or a payment of ¥X in 97 days (option “B”). The latter amount X is varied
from the minimum of ¥9,981 through eight values, increasing gradually to the
maximum of ¥10,574; these correspond to effective annual rates of return of –10% to+300%. Usually, the respondents choose the ¥10,000 option at low interest rates, but as
the imputed interest rate rises, they ultimately switch to the increasingly attractive “X”

25

option.15 The individual respondents’ discount rates can be inferred by estimating theinterest rate at which respondents are indifferent between the delayed receipt of ¥X andthe more immediate receipt of ¥10,000. The present study employed procedures ofmeasurement and analysis of time-discount rates similar to those outlined in Kimball,
Sahm, and Shapiro (2008). We estimated the gross discount rate for each respondentaccording to a lognormal distribution function. This estimation method enabled us toobtain the interest rates between which a subject switched his choice from option “A” to“B” for each respondent, including those who stuck either to option “A” or to “B” forall given choices. We term the time discount rates estimated using this method “TD1.”
Similarly, in another series of eight binary choices, participants chose between receiving¥10,000 in one month, or an amount ¥X ranging from ¥9,500 (for an annual rate of –5%) through ¥14,000 (for an annual rate of +40%) in 13 months. The discount rates
corresponding to this task are termed “TD2.”
Estimation results for equation (3) with added TD1*LOSS (TD2*LOSS) cross-term
coefficients are presented in Table 6. Subjects’ individual attributes, such as gender, age
and income, are added to the regression equations here as control variables. The results
remain unchanged if we omit these variables.
The LOSS coefficients are negative and significant in all cases, confirming theincidence of the disposition effect. The coefficients for DS1*LOSS and DS2*LOSS are
again negative and significant. However, both the TD1 and TD2 cross-term LOSS
coefficients are significantly positive, denying the intuition that higher time-discount15

We excluded from this analysis 3 cases wherein respondents switched multiple times between¥10,000 and ¥X.
26

rates lead to fewer instances of selling losers. The fact that the signs of the control
variables’ coefficients are identical to those in the diminishing sensitivity DS estimatesreported in Table 4 provides additional credibility to our findings.
In Table 7, we report estimation results for the cases in which the DS1*LOSS andDS2*LOSS cross-term coefficients are omitted from the estimated formula reported inTable 6. In other words, Table 7 presents results for estimation of equation (3) in which
the DS1 and DS2 data have been replaced with TD1 and TD2. Again, the findings wereport here include the control variables on the right hand side of the equation, but theyremain unchanged if we omit them.
Our basic results concerning time discounting and the disposition effect remainunchanged in this new regression. The LOSS coefficients are significantly negative(confirming the existence of the disposition effect), while the cross-term coefficients for
all combinations of TD1, TD2 and LOSS are significantly positive. The impact ofcontrol variables remains practically unaltered as well.
These findings contradict both Henderson’s (2012) conjecture and Barberis’ andXiong’s (2012) theoretical result that higher individual time-discount rates lead tostronger disposition effects.

5. Conclusions
The economic experiment reported in this paper adds to a substantial body of workon the existence of the disposition effect and its potential causes. While numerous
experimental studies exist on the topic, the distinguishing feature of our approach is the27close similarity of our experimental environment with real-world stock markets. For aspan of 28 days, participants of our simulated stock market bought and sold shares in 10
stocks, the prices of which were taken from actual past market data. Participants’
remuneration was commensurate with profits and losses incurred from buying andselling stocks. On top of that, a winner’s prize was awarded to the most successful
trader. As a result, we acquired ample trading data, with a total of 7,532 transactions.
Our experimental environment has the additional merit of allowing us to control for arange of conditions. For instance, the absence of taxation and transaction costs
eliminates the need to consider those effects.16
The greatest merit of our experiment lies in the fact that we were able to extract two
additional types of information from our participants. First, we pinpointed eachparticipant’s individual reference point using a questionnaire survey we conducted
before the experiment. This information is impossible to acquire in empirical studies,and to the best of our knowledge, no previous experimental studies even attempted toacquire it. Accordingly, we succeeded in testing an independent hypothesis about theexistence of the disposition effect, not merely a joint hypothesis of the disposition effectand a particular reference point.
Our second finding regards the source of the disposition effect, which we were able
to assess by measuring participants’ risk aversion in both domains (gains and losses) in
our two supplementary experiments. We find that diminishing sensitivity is a cause of
the disposition effect, as the latter becomes stronger whenever either (i) behavior in the
16

However, we can eliminate neither the “portfolio rebalancing” nor the “regression to the mean”
arguments as potential causes of the disposition effect, as we were unable to control for these.
28domain of losses becomes more risk-loving, or (ii) behavior in the domain of losses
compared to behavior in the domain of gains becomes more risk-loving.
Our approach, in contrast to previous studies, also has the merit of being a direct
examination of diminishing sensitivity as a potential cause of the disposition effect.
Odean (1998) deduces that diminishing sensitivity brings about the disposition effect in
an indirect manner. He shows by elimination that alternative explanations do not fully
account for the disposition effect, which persists even after these factors are taken into
account.
We demonstrate directly with our LOGIT analyses that the disposition effect exists
and that diminishing sensitivity is one of its causes. This result remains valid even when
we use a variety of alternative reference points for prices.
The debate over whether prospect theory can explain the disposition effect has heatedup recently. It has been convincingly argued by both Barberis and Xiong (2009) and
Kaustia (2010) that the traditional economic interpretation of a Tversky and Kahneman(1992) value function, wherein the sheer act of stock trading does not lead to changes inutility levels as long as consumption remains unchanged, will not generate thedisposition effect. In contrast, arguments based on prospect theory readily produce thedisposition effect in a series of recent studies. In Barberis and Xiong (2012) and in
Henderson (2012), the effect is generated by realization utility. In Li and Yang (2013), a
prospect theory-based extended general equilibrium model with endogenous returns
generates the effect. A modification of the value function reference point, which uses
the expected excess return rate as the reference point, yields the disposition effect in29

Meng (2012).
The two theoretical studies most closely related to ours, Henderson (2012) and Li andYang (2013), point to diminishing sensitivity as the vital link between prospect theory
and the disposition effect. In both papers, the larger the degree of diminishing sensitivity,
the more prominent the disposition effect. This is consistent with our empirical findings,
though we admit that it was not our intent in this project to verify the validity of eitherof the theories mentioned above. In order to fully validate those theories, it is necessary
to design experiments based on hypotheses aimed at clearly distinguishing between thevarious theories. This task remains a challenge for further research.
We also find, interestingly, that higher individual discount rates do not lead tostronger disposition effects; in fact, the opposite appears to be true, a result that negatesthe conjectures of both Henderson (2012) and Barberis and Xiong (2012). However, ourtime discounting analysis is a tentative one, and as such should be regarded with caution.
In contrast to our elicitation of risk attitudes through a rigorous economic experiment,
the time discount rates were estimated from participants’ responses to a simple
questionnaire. On top of that, the discount rates were estimated in the gains domain only.
Appelt et al. (2011) provide evidence for a lack of consistency in discount rates acrossthe gain/loss domains. A more thorough examination of the potential links between time
preferences and the disposition effect is another avenue for future research.

30

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33

Table 1: Summary of Experiment Participants’ Attributes
Participants were recruited (with the assistance of an internet research company) from among individual investors
with previous stock trading experience, defined as having recent history of trading on the stock market at least once
per month.
Malenage_group
20-29
30-39
40-49
50-59
60-69
70TotalJOB
civil servant
business executive
administrative staff
office staff
technical staff
sales/customer service
other salaried worker
teacher
medical expert
self-employedother part-time
homemaker
working homemaker
unemployed
other
Total
INCOME_GROUP (unit: 10,000yen)<100
100-200
200-300
300-400
400-500
500-600
600-700
700-800
800-900
900-1000
1000-1500
1500unknown
Total
FREQ_TRADE (about once in ~)a monthhalf a montha week
daily
Total

%

Female
%

n

Total
%

n

3
16
9
5
0
2
35

8.60%
45.70%
25.70%
14.30%
0.00%
5.70%
100.00%

1
4
5
1
2
0
13

7.70%
30.80%
38.50%
7.70%
15.40%
0.00%
100.00%

4
20
14
6
2
2
48

8.30%
41.70%
29.20%
12.50%
4.20%
4.20%
100.00%

1
2
1
2
10
4
2
1
1
4
2
1
0
1
3
35

2.90%
5.70%
2.90%
5.70%
28.60%
11.40%
5.70%
2.90%
2.90%
11.40%
5.70%
2.90%
0.00%
2.90%
8.60%
100.00%

0
1
0
3
0
2
0
0
0
0
0
4
2
1
0
13

0.00%
7.70%
0.00%
23.10%
0.00%
15.40%
0.00%
0.00%
0.00%
0.00%
0.00%
30.80%
15.40%
7.70%
0.00%
100.00%

1
3
1
5
10
6
2
1
1
4
2
5
2
2
3
48

2.10%
6.30%
2.10%
10.40%
20.80%
12.50%
4.20%
2.10%
2.10%
8.30%
4.20%
10.40%
4.20%
4.20%
6.30%
100.00%

1
0
1
3
5
5
5
2
6
4
1
1
1
35

2.90%
0.00%
2.90%
8.60%
14.30%
14.30%
14.30%
5.70%
17.10%
11.40%
2.90%
2.90%
2.90%
100.00%

0
1
0
2
1
3
0
2
0
1
0
3
0
13

0.00%
7.70%
0.00%
15.40%
7.70%
23.10%
0.00%
15.40%
0.00%
7.70%
0.00%
23.10%
0.00%
100.00%

1
1
1
5
6
8
5
4
6
5
1
4
1
48

2.10%
2.10%
2.10%
10.40%
12.50%
16.70%
10.40%
8.30%
12.50%
10.40%
2.10%
8.30%
2.10%
100.00%

9
2
11
13
35

25.70%
5.70%
31.40%
37.10%
100.00%

0
6
5
2
13

0.00%
46.20%
38.50%
15.40%
100.00%

9
8
16
15
48

18.80%
16.70%
33.30%
31.30%
100.00%34

Table 2: Questionnaire Survey of Reference Points – Summary of Results
This table summarizes the results of a questionnaire survey conducted to elicit individual reference points. It reports
the number of subjects corresponding to each combination of reference points. Each row represents a reference point
for the domain of gains and each column represents a corresponding reference point for the domain of losses. The
labels for each reference point are as follows. FIRST: first purchase price; FIFO: first-in first-out; LAST: lastpurchase price; LIFO: last-in first-out; HIGH: highest purchase price; LOW: lowest purchase price; WA1: weighted
average purchase price; WA2: weighted average purchase price minus average profit/loss for the portion of shares
sold in the interim time NULL: no response.

FIRST
FIFO
G
LAST
A
LOW
I
WA1
N
WA2
OTHER
TOTAL

FIRST FIFO
1
2
2

LAST

LIFO

LOSS
LOW WA1

1
1

1

4

1

1

2

1

15

1

35

1
16

WA2 OTHER NULL TOTAL
1
1
3
3
1
1
1
19
21
21
1
22
1
1
49

Table 3: Summary of LOGIT Regressions Using Individual-Specific Reference Points
This table shows regression results for two models – “Model 1” and “Model 2”. Data for this analysis consists oftrade records for all the stocks in subjects’ portfolios. The dependent variable SELL takes a value of 1 whenever a selltransaction occurs, and 0 otherwise. The variable LOSS is set equal to 1 whenever a stock is trading at a loss and 0
otherwise. Whether the stock in question is actually trading at a loss is determined via a subject-specific reference
point elicited through a questionnaire survey. Whenever such determination was not possible, the corresponding data
was excluded from the analysis. Diminishing sensitivity coefficients DS1 and DS2 used for Model 2 (1) and Model 2(2) are defined as DS1 = (–1) * (Degree of Risk Aversion in the Insurance Buying Experiment) and DS2 = (–1) *(Degree of Risk Aversion in the Insurance Buying Experiment) – (–1) * (Degree of Risk Aversion in the Lottery
Selling Experiment), respectively. *** indicates coefficients which are significant at the 1% significance level.

Model 1Model 2
(1)

coef.
LOSS

-0.748z-19.64 ***DS1･LOSS

coef.

z-0.528-10.39 ***-58.274-6.23 ***

DS2･LOSS
Constant-1.151-46.07 ***-1.151-46.07 ***

(2)
coef.

z

-0.555-13.10 ***-46.192-9.13 ***

-1.151-46.07 ***Pseudo R2

0.02

0.02

0.03

Number of
Observations

19451

19451

19451

Marginal
Effects
LOSS
DS1-0.110-19.91 ***-0.106-19.60 ***-3.609-6.23 ***

DS2

36

-0.106-19.53 ***-2.846-9.11 ***

Table 4: Summary of LOGIT Regressions Including Individual Attributes
This table reports results of regressions for “Model 1” and “Model 2” with experiment subjects’ personal attributes
added as independent variables. The dependent variable SELL takes a value of 1 whenever a sell transaction occurs,and 0 otherwise. The variable LOSS is set equal to 1 whenever a stock is trading at a loss and 0 otherwise. Whether
the stock in question is actually trading at a loss is determined via a subject-specific reference point elicited through aquestionnaire survey. Whenever such determination was not possible, the corresponding data was excluded from theanalysis. FEMALE is a dummy variable equal to 1 for females and 0 for males, AGE is the age variable and INCOME
is the income variable. FREQ_TRADE_dummy is the dummy variable with values assigned according to subjects’
real-world market trading experience. Diminishing sensitivity coefficients DS1 and DS2 used for Model 2 (1) andModel 2 (2) are defined as DS1 = (–1) * (Degree of Risk Aversion in the Insurance Buying Experiment) and DS2 = (–1) * (Degree of Risk Aversion in the Insurance Buying Experiment) – (–1) * (Degree of Risk Aversion in the Lottery
Selling Experiment), respectively. **, *** indicate coefficients that are significant at the 5% and 1% significancelevel, respectively.

Model 1Model 2
(1)

LOSS
DS1･LOSS
DS2･LOSS

coef.
-0.719z-18.30 ***coef.
-0.608-31.804(2)

z-11.28 ***-2.95 ***

coef.
-0.604z-13.68 ***-29.091-5.36 ***FEMALE-0.726-13.64***-0.660-11.44***-0.672-12.55***AGE(x0.01)

5.164

3.66

***

4.459

3.12

***

0.045

3.21

***

AGE (x0.0001)-6.851-4.81***-6.155-4.27***-5.975-4.21***

INCOME(x0.01)-0.127-10.77***-0.124-10.46***-0.115-9.66***

INCOME2(x0.0001)

0.001

11.10

***

0.001

10.84

***

0.001

10.14

***

2

(against “once/month”)

FREQ_TRADE_dummy(against “once/month”)(against “once/month”)

once in half a month-0.804-8.15***-0.827-8.34***-0.833-8.44***

once a week

-0.454-6.01***-0.487-6.39***-0.456

-6.09

***

daily

-0.011-0.16-0.013

-0.20

0.018

0.28

Constant-0.842-2.59-0.693-2.11-0.813

-2.53

***

**

2

Pseudo R

0.063

0.064

0.065

Number of Observations

19345

19345

19345

Model 1Model 2
(1)

Marginal Effects
LOSS

coef.

z

-0.099-18.61

***

***

DS1

(2)

coef.

z

-0.099-18.55***-1.880

-2.96

***

DS2

coef.

z

-0.098-18.46***-1.714-5.37***

FEMALE-0.100-13.74***-0.091-11.50***-0.092-12.62***AGE(x0.01)-0.148-5.58***-0.157-5.89***-0.130-4.89***-0.016-10.72***-0.015-10.39***-0.014-9.58***

INCOME(x0.01)
FREQ_TRADE_dummy(against “once/month”)(against “once/month”)(against “once/month”)

once in half a month-0.111-8.17***-0.114-8.36***-0.115-8.46***

once a week

-0.062-6.02***-0.067-6.41***-0.063

-6.10

***

daily

-0.001-0.16-0.002

-0.20

0.003

0.28

37

Table 5: LOGIT Regressions Results Summary under Weighted Average Purchase Price
WA1 and under the First-Bought First-Sold FIFO Rule as Reference Points
Panels A and B report regression results for “Model 1” and “Model 2” for the case when individual-specific reference
points are replaced with the weighted average purchase price and the first-bought first-sold FIFO rule (i.e. shares
which are purchased first are also sold first) as a reference point, respectively. The distinction between the domain ofgains and the domain of losses is accordingly revised to reflect this change in the reference point. For details, pleaserefer back to Table 3.

Panel A: Weighted Average Purchase Price WA1
Model 1LOSS
DS1･LOSS
DS2･LOSS
Constant
Pseudo R2
Number of
Observations
Marginal Effects
LOSS
DS1
DS2

coef.
-0.792z-21.01 ***-1.133-45.68 ***0.02

Model 2
(1)
(2)
coef.
z
coef.
z
-0.550 -10.87 ***-0.594 -14.20 ***-63.230-6.83 ***
-47.883-9.51 ***
-1.133 -45.68 ***-1.133 -45.68 ***
0.03
0.03

19992
coef.
-0.11419992

z-21.34 ***coef.
-0.111-3.908z-20.93 ***-6.82 ***

Panel B: The First-Bought First-Sold FIFO
Model 1LOSS
DS1･LOSS
DS2･LOSS
Constant
Pseudo R2
Number of
Observations
Marginal Effects
LOSS
DS1
DS2

coef.
-0.794-1.147coef.
-0.112z-20.94 ***-2.948-9.48 ***

Model 2z
-20.93 ***coef.
-0.511-74.417-46.96 ***0.02-1.14719992
coef.
-0.114

19992

(1)
z
-10.10 ***-7.94 ***
-46.96 ***
0.03

coef.
-0.582-53.295-1.14719992

z-21.25 ***coef.
-0.111-4.40038z-20.79 ***-7.92 ***

(2)z
-13.94 ***-10.28 ***-46.96 ***
0.03
19992

coef.
-0.113z-20.99 ***-3.138-10.23 ***Table 6: Summary of LOGIT Regressions Including the Time Discount Rates TD1 and TD2
Cross-Terms with LOSS besides the Diminishing Sensitivity and LOSS Cross-Terms.
This table reports regression results for “Model 2” (equation (3)) with TD1*LOSS and TD2*LOSS cross-term
coefficients added to the equation.

Model 2
coef.

(1)
z

-0.733-12.94 ***-0.696-12.43 ***DS1･LOSS -53.751-4.68 ***

-54.319-4.80 ***

LOSS

coef.

(2)
z

DS2･LOSS
TD1･LOSS(x0.01)

0.193

7.56 ***

TD2･LOSS(x0.01)

1.306

6.42 ***

coef.

(3)
z

coef.

(4)
z

-0.787-16.50 ***-0.758-15.93 ***-58.260-9.17 ***

-64.167-9.78 ***

0.292

10.41 ***
2.307

9.76 ***FEMALE-0.561-9.51 ***

-0.607-10.42 ***-0.555-10.12 ***-0.601-11.18 ***AGE(x0.01)

2.251

1.55

5.090

3.52 ***

2.069

1.46

5.597

3.96 ***AGE (x0.0001)-3.882-2.65 ***

-6.691-4.59 ***

-3.313-2.31 **

-6.720-4.72 ***

INCOME(x0.01)-0.169-13.63 ***-0.135-11.24 ***-0.161-13.08 ***-0.125-10.51 ***INCOME2(x0.0001)

0.002

14.03 ***

0.001

11.68 ***

0.002

13.68 ***

0.001

11.17 ***

2

FREQ_TRADE_dummy (against “once/month”) (against “once/month”) (against “once/month”) (against “once/month”)
once in half a month-0.924-9.21 ***

-0.837-8.41 ***

-0.943-9.47 ***

-0.842-8.51 ***

once a week

-0.708-9.06 ***

-0.515-6.76 ***

-0.673-8.84 ***

-0.451-6.04 ***

daily

-0.136-1.98 **

-0.053-0.80-0.114-1.67 *

-64.167

0.16

Constant

0.127

0.38

-0.794-2.38 **

0.015

0.04

-1.129-3.45 ***

2

Pseudo R

0.071

0.066

0.074

0.070

Number of Observations

19277

19345

19277

19345

39

Table 7: Summary of LOGIT Regressions Including the Time Discount Rates TD1 and TD2
Cross-Terms with LOSS instead of the Diminishing Sensitivity and LOSS
Cross-Terms.
This table reports regression results for “Model 2” (equation (3)) with TD1*LOSS and TD2*LOSS cross-term
coefficients replacing the DS1*LOSS and DS2*LOSS coefficients.

Model 2
coef.

(1)
z

-0.986-21.81 ***TD1･LOSS(x0.01) 0.0023

10.28 ***

LOSS
TD2･LOSS(x0.01)

coef.

(2)
z

-0.988-21.26 ***0.01809

coef.

(3)
z

coef.

(4)
z

-0.889-18.88 ***-0.849-17.99 ***0.156

6.44 ***
1.010

5.22 ***

9.44 ***FEMALE-0.670-12.32 ***-0.719-13.45 ***AGE(x0.01)

339.530

2.37 **

6.047

4.22 ***AGE (x0.0001)-5.027-3.48 ***

-7.656-5.31 ***

INCOME(x0.01)-0.171-13.77 ***-0.138-11.50 ***INCOME2(x0.0001)

0.002

14.09 ***

0.001

11.84 ***

2(against “once/month”) (against “once/month”)

FREQ_TRADE_dummy
once in half a month-0.877-8.83 ***

-0.800-8.09 ***

once a week

-0.643-8.34 ***

-0.460-6.09 ***

daily

-0.111-1.63-0.042-0.63-0.142-0.43-1.000-3.03 ***

Constant-1.167-46.36 ***-1.153-46.06 ***2

Pseudo R

0.029

0.027

0.069

0.065

Number of Observations

19290

19358

19277

19345

40

OsakaUniversity Graduate School of Economics Tsutsui Lab –Stock Trading Experiment
Cash

Next Update

Stocks

TOTAL

103 sec

COMPANY

STOCK PRICE

BEFORE

AFTER

MARKETVALUE

Trade History

RULES*Login Days

1
TIME
13:48
LOGOUT

Present Cash Assets (P)Transaction Amount (P)Balance (P)TRADEFigure 1: Screenshot of the Transaction Panel (translated from Japanese)
The screenshot in the figure above provides information on the present composition of the subjects’ portfolios, stock
prices and cash holdings. Subjects use it also to order their buy and sell transactions, which are immediately executed.
For instance, by changing the number of shares in the “AFTER” transaction column and clicking on “TRADE”, acorresponding order is completed.

41

Figure 2: Screenshot from the “Insurance Buying Experiment” (edited from Japanese)
The display for this experiment shows an amount of potential damage with the probability of its occurrence as well as
an insurance premium offer. The subject chooses either to purchase the insurance (”yes”) or to decline it (”no”).

42