Discussion Paper No. 664

EXPERIMENTS ON RISK ATTITUDE:
THE CASE OF CHINESE STUDENTS
Shunichiro Sasaki
Shiyu Xie
Fumio Ohtake
Jie Qinand
Yoshiro Tsutsui

June 2006

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Experiments on Risk Attitude:

The Case of Chinese Students

Shunichiro Sasaki a, Shiyu Xie b, Fumio Ohtake a,
Jie Qin c, Yoshiro Tsutsui a*aOsaka University, Institute of Social and Economic Research, 6-1 Mihogaoka, Ibaraki,
Osaka 567-0047, Japanb

Fudan University, Department of World Economics, 220 Handan Road,
Shanghai 200433, P. R. Chinac

Ritsumeikan University, Faculty of Economics, 1-1-1 Noji-higashi, Kusatsu,
Shiga 525-8577, Japan*Corresponding author: Phone: +81-6-6879-8560, Fax: +81-6-6878-2766

Email Addresses: ssasaki@iser.osaka-u.ac.jp (S. Sasaki), syxie@fudan.edu.cn (S.
Xie), ohtake@iser.osaka-u.ac.jp (F. Ohtake), jieqinjp@yahoo.co.jp (J. Qin),tsutsui@econ.osaka-u.ac.jp (Y. Tsutsui)Abstract
This paper examines Chinese students’ risk attitude using buying and selling
experiments with lotteries. We found that subjects were more risk averse in the buying
experiment than in the selling experiment, suggesting the endowment effect. In the
selling experiment, subjects were risk loving when there was a low win probability andrisk averse with a high win probability, whereas they were risk averse in the buying
experiment. Using the prize money won during the experiment as a measure of wealth,
we found decreasing absolute risk aversion. Subjects’ risk attitude as revealed in theexperiments explains their risky asset holding behavior.
JEL classification: C91, D81
Keywords: risk aversion, economic experiment, China

1. Introduction
This paper examines Chinese students’ risk attitude by using buying and selling
experiments with lotteries, based on the BDM method (Becker et al., 1964).
Experiments in China are especially interesting in that prizes won by subjects are
relatively large compared to those in developed countries because of the highpurchasing power of the Chinese yuan. It is often argued that economic experiments are
not reliable because prizes are too small to give subjects an adequate incentive.
Experiments in China might be immune to such a criticism.1 Indeed, the cost of livingin 2005 was 6.5 times lower for our Chinese subjects than for Japanese subjects after an
exchange rate conversion.2 Nevertheless, to our knowledge, there have been few such
experiments in China.3
Our experiment is unique in that we conducted both a buying and a selling
experiment with the same subjects. Previous studies conducted selling experiments(Kachelmeier and Shehata, 1992, Eichberger et al., 2003) and buying experiments(Cramer et al., 2002, Shavit et al., 2001, Hartog et al., 2002) separately. However, to ourknowledge, no studies have examined both selling and buying experiments

1

Another response to this criticism is to use the results of TV shows that pay huge prizes. Fullenkamp etal. (2003) and Beetsma and Schotman (2001) reported that people are risk averse, while Metrick (1995)
does not reject the proposition that they are risk neutral.
2

This figure is based on responses to our questionnaire from subjects of the experiment done in Shanghai

and Tokyo. We asked the cost of living per month.
3

Kachelmeier and Shehata (1992) were a notable exception. They conducted an experiment to measurerisk attitude and found that the risk attitude of Chinese subjects did not differ from that of subjects in the
US and Canada. They are risk loving for lotteries with a small win probability and risk neutral otherwise.

1

comprehensively. 4 Comparing the results of previous studies based on selling andbuying experiments, one could argue that subjects participating in buying experiments
were more risk averse than those in selling experiments. However, it is not convincing
to draw the conclusion that people are more risk averse when they sell lottery tickets
than when they buy them, as the difference may be due to a difference in subject
characteristics. Thus, it is important to conduct an experiment where the same subjects
participate in both buying and selling experiments.
Our study was also unique in that we asked the subjects to answer a detailed
questionnaire that included scenario questions on risk attitude. We analyzed how risk
attitude related to their demographic and economic attributes such as knowledge offinancial economics and wealth. Although Barsky et al. (1997), Donkers et al. (2001),
and Hartog et al. (2002) examined these relationships using questionnaire surveys, ourmethod has merit in that we measured risk attitude in a controlled experiment where
subjects had monetary incentives. We examined whether subjects’ risk attitudes can
explain their risky asset holdings. We also investigated whether subjects’ risk attitudes
as revealed in the experiments were consistent with those in the questionnaire. Finally,
we examined how subjects’ risk aversion correlated with their time discount rates,
which was measured in our experiment.
The rest of the paper is organized as follows. In the next section, we explain our
experimental method. In Section 3, we show the risk attitude according to probability of4

Knetsch and Sinden (1984) is a notable exception. Their TEST3 consists of buying and selling

experiments which ask similar questions to ours. However, they are different from ours in that different
subjects are used for buying and selling experiments.

2

winning a lottery and compare the results with those of Kachelmeier and Shehata (1992).
In Section 4, we investigate how risk attitude relates to the attributes of the subjects. In
Section 5, we analyze whether subjects’ risk attitudes can account for their actual
behaviors. In Section 6, we compare the risk attitude revealed in the experiment and in
the questionnaire. In Section 7, we examine the relationship between time discount rate
and risk aversion. Section 8 concludes.

2. Experimental method
The experiment was conducted on March 11, 2005, at Fudan University inShanghai. Subjects were 30 undergraduate students of the Department of World
Economics at Fudan University.5 Their attributes are summarized in Table 1. Out of 30
subjects, 26 (86%) were female. The subjects were 20 or 21 years old. Their income andwealth was widely dispersed; household income ranged from less than 20,000 yuan
(US$2,400) to over 220,000 yuan (US$26,400) and the mode was 20,000 (US$2,400) to
40,000 yuan (US$4,800).
[Table 1 about here]
The experiment on risk attitude started at 6 pm and ended around 8 pm. An
experiment on time discounting was then conducted until 9 pm. The subjects were thenrequested to complete a test on financial economics and fill in a questionnaire. As forthe test, refer to Appendix A. The session finished around 10 pm.6

5

One subject felt unwell and left after the selling experiment was completed, so that the number of thesubjects for the buying experiment was 29.
6

According to teachers and students at Fudan University, the students there study until around 10 pm

3

The experiment was based on the BDM method as follows.
Selling experiment: Subjects were given a lottery ticket by which they receive
1000 points if they win and nothing otherwise. The win probability was set
randomly by the computer in each round. After subjects put their selling priceinto the computer, the computer showed its buying price, which was
determined randomly. If the buying price exceeded the selling price, the lottery
ticket was traded at the buying price. Otherwise, subjects retained their tickets
and the computer determined the win or lose randomly following the win
probability. Subjects who won got 1000 points. Subjects who lost received
nothing. The subjects recorded their results in each round in order to check theresults and to have time to consider their strategies. This procedure wasrepeated for five rounds as practice and for 20 rounds as real sessions. At theend, the points obtained in the real sessions were summed and converted toyuan with 1000 points equal to 20 yuan (US$2.4); that amount was paid at theend of all the experiments on that day.
Buying experiment: The buying experiment was the same as the selling
experiment with the following exception. Subjects were given 10,000 points atthe outset.7 They input their buying price (the highest value that they could
offer) for a lottery ticket for which the win probability was shown on their own

every day, so the evening experiment was not a burden to them. We conducted the experiment in theevening because it was difficult to recruit students during for daytime experiments as they were expected
to attend classes.
7

This is necessary because in selling experiment subjects were given 20 lottery tickets with the expected

payoff of 10,000 points. Furthermore, subjects would have been too embarrassed to buy a lottery ticket if
they had no points at the outset.

4display. If this buying price exceeded the selling price offered by the computer,the ticket was traded to the subject at the selling price. In this case, if they won,
the payoff was the 1000 points minus the selling price; if they lost, they
suffered a loss equal to the selling price.
Points won by subjects and their converted payoffs in yuan are presented in Table 2.
The average payoff was 261 yuan (US$31, 13,033points) for the selling experiment and
260 yuan (US$31, 12,977 points) for the buying experiment.8[Table 2 about here]

3. Risk attitudes in the selling and buying experiment
We adopted the following measure of absolute risk aversion (ARA) developed in
Cramer et al. (2002):

ARA =aZ − p,1 / 2 × ( aZ 2 − 2apZ + p 2 )where Z is the lottery prize, p is the price evaluated by a subject, and a is the win
probability. We also present the result of the “transformed risk averse price (TP)”defined as:
TP = 1 −p.
aZ

To compare our results with those in Kachelmeier and Shehata (1992), we
calculated the average ARA and TP for each category of win probability, 0–10%, 10–20%, and so on. The results are presented in Figures 1–4, where the horizontal axis

8

In addition to payoffs, subjects received a 120 yuan (US$14) participation fee.

5

represents the win probability and the vertical axis represents ARA or TP.
[Figure 1 about here]
Figure 1 shows TP for the selling experiment, which corresponds to Figures 1 and
2 in Kachelmeier and Shehata (1992).9 These figures appear superficially similar. The
subjects were risk loving in lotteries with win probabilities of less than 20% and almost
risk neutral in the others. Close examination, however, reveals a difference. As Figure 1
in our paper shows, subjects were risk averse in the lotteries with win probabilities ofover 30%, at the 5% significance level, whereas Kachelmeier and Shehata (1992)
reported that the subjects were at most risk neutral.10 Kachelmeier and Shehata’s result
was important because subjects facing very high rewards in the experiment were risk
loving or neutral, implying that these characteristics did not appear just because they
were gambling for smaller amounts of money. Indeed, they show that the subjects wererisk loving in lotteries with small prizes, but risk neutral in lotteries with large prizes,
implying that the subjects became more risk averse as prizes became larger. If subjects’risk attitudes vary depending on the amount of prizes as they observed, it would bepossible to interpret our results as meaning that our subjects show a risk-averse attitude
because the prize was very large. The average prize won by the subjects was 632 yuan
(US$76) while they reported that their average monthly living expenses were 2048 yuan
(US$246); subjects therefore earned on average one third of their monthly living

9

Note that Kachelmeier and Shehata (1992) show the certainty-equivalent ratio, which is equivalent to 1-

TP.
10

They do not show the confidence interval, so that we cannot evaluate the significance of their results.

6

expenses in two hours.11 Our results cast a doubt on Kachelmeier and Shehata (1992)’s
finding: people may be risk averse in lotteries with a win probability greater than 30%.
If we adopt the other risk measure, ARA, the risk-averse attitudes become moreevident. In Figure 2, the subjects were risk loving only in lotteries with win probabilitiesof less than 10%. They were risk neutral in lotteries with win probabilities of 10–50%,
and risk averse in those of over 60%.12 Specifically, it seems that they became more risk
averse with higher win probabilities.
[Figure 2 about here]
Figures 3 and 4 show the results of the buying experiments.13 These results arequite different from those in Figures 1 and 2. Specifically, the subjects showed riskaverse attitudes in lotteries with any win probability, which is consistent with the usualassumptions of economic theory.
[Figures 3 and 4 about here]
To check whether the difference between risk attitudes in selling and buying
experiments is significant, we regressed the risk attitude variables (ARA and TP) over
the win probability (PROB) and the buying dummy variable (BUY), which is set at unity
for buying experiments and zero for selling experiments. We pooled all the data, 20
rounds for each of the selling and buying experiments multiplied by the number of11

According to a teacher at Fudan University, most Chinese students’ living expenses per month should

be under or around 1000 yuan (US$120). If this is true, our prize is tantamount to more than half theirmonthly living expenses.
12

These results are the same as those from Japanese experiments. See Tsutsui et al. (2005).

13

In the calculation of ARA data, we excluded one sample because the subject assigned 999 points to alottery with a win probability of 100%, leading to an extreme value of 2.

7

subjects, and estimated fixed effects and random effects models.
The estimation results are presented in the first and second columns of Table 3.
Here, we show the results of a random effects model for the case of ARA; the random
effects model was not rejected against the fixed effects model on the basis of theHausman specification test. However, for the case of TP, the results of the fixed effects
model are shown because the random effects model was rejected at the 1% significancelevel. The estimated coefficients of PROB are always positive and significant, implyingthat the subjects show more risk-averse attitudes to lotteries with higher win
probabilities. This can be seen in Figure 2 (ARA; selling experiment), whereas Figure 4(ARA; buying experiment) does not show this tendency. Regression analysis ofcombined data from both experiments confirms the tendency. The coefficients of BUY
are significantly positive for both cases, indicating that the subjects are significantly
more risk averse in buying experiments than in selling.
[Table 3 about here]
Figures 1–4 reveal differently shaped graphs in many aspects between selling andbuying experiments; e.g., ARA and TP are decreasing in win probability in buying
experiments, while they are increasing in the selling experiments. To confirm thedifferences, we added PROB2, BUY*PROB, PROB2, and BUY*PROB2 into theregression equation. The estimation results are shown in the third and fourth columns ofTable 3. ARA and TP are increasing in PROB in the selling experiments, while ARA is
decreasing in the buying experiments. The tendency is not clear in the case of TP in thebuying experiments. ARA and TP are concave in the selling experiments, while ARA isconvex and TP is concave in the buying experiments. These results are also confirmed
8

by the estimation splitting the samples between the selling and buying experiments (seecolumns 5–8 in Table 3).
The finding that subjects are risk averse in buying experiments has been reported
in Shavit et al. (2001), Hartog et al. (2002), and Cramer et al. (2002). In addition, thefinding that subjects are risk loving or risk neutral in selling experiments has beenreported in Kachelmeier and Shehata (1992) and Eichberger et al. (2003). Our
experimental results confirm that subjects exhibit different risk attitudes in selling andbuying lotteries even when the same subjects participated in both experiments.
Why does risk attitude differ between selling and buying experiments? One
argument is that the subjects learned the structure of the experiments and the optimal
strategy during the selling experiment that was conducted before the buying experiment,so that they revealed their true attitude in the buying experiments. However, thisinterpretation is not very convincing because the amount of money won by the subjects
did not differ between experiments, leading us to reject the notion of a learning effect.
Another possible interpretation for higher risk aversion in the buying experiment is theendowment effect (Kahneman et al., 1990). Among other studies, Knetsch and Sinden(1984) observed that subjects’ willingness to accept (WTA) in a lottery was higher thantheir willingness to pay (WTP), which implies that they were more risk averse when
they bought a lottery ticket than when they sold one. Our finding is consistent with thisendowment effect.

4. How does the risk attitude relate to attributes of the subjects?
In this section, we examine how the risk attitude revealed in the experiments

9relates to the socioeconomic attributes of the subjects. Specifically, we focus on wealth,knowledge of financial economics, and gender.
How risk attitude depends on wealth has been an important topic. Arrow (1970)
argues decreasing absolute risk aversion and increasing relative risk aversion withrespect to wealth. As for absolute risk aversion, using the results of a questionnaire
survey, Hartog et al. (2002) find decreasing absolute risk aversion with respect torespondents’ annual income. Based on survey results, Donkers et al. (2001) also reportthat risk aversion decreases as income increases, although they do not use absolute risk
aversion as the risk measure. In an experiment in which subjects invest money into risky
projects, Levy (1994) found decreasing absolute risk aversion and decreasing (orconstant, at most) relative risk aversion with respect to wealth varying during theexperiment. As for relative risk aversion, most studies measure relative risk aversion
using the risky asset holding ratio, and decreasing relative risk aversion has beenreported instead (Cohn et al., 1975, Guiso et al., 1996, and Kessler and Wolf, 1991).
The effect of education on risk attitude has been also studied. Donkers et al. (2001)
and Hartog et al. (2002) report that subjects with higher education levels tend to be
more risk loving. In this paper, the subjects are all university students, and our aim was
to investigate the effect of knowledge of financial economics on their risk attitude. As
standard finance theory is based on the assumption that economic agents are risk averse,
students who study finance theory may believe that they must behave as if they are risk
averse. To test this hypothesis, after the experiments we requested the subjects tocomplete a test that consisted of seven economics problems including three on risk
aversion. We analyzed the relationship between the test score and risk attitude.

10

As in the previous section, we pooled all the data, 40 rounds multiplied by the
number of subjects, and estimated fixed and random effects models with them. Becausesome of the subjects did not answer questions about their income and assets, theirobservations were dropped from the estimation. Win probability (PROB) and thedummy variable representing the buying experiment (BUY) are considered in the
regression analysis, as risk attitude is systematically influenced by these, as shown in
the previous section.
For the gender variable, we adopted a dummy variable MALE, which takes thevalue of unity if the subject is a male, and zero otherwise. For the variable representing
knowledge on financial economics, we adopted TEST, which is the score of the subjects
on the test conducted immediately after the experiment. For the wealth data, weconsidered three different variables, INCOME, ASSETS, and POINTS, whose definitions
will be explained below.
The results of the random effects model are shown in Table 4 for the cases of ARA
and TP because the Hausman specification test does not reject random effects models
against fixed effects models. In the first and second columns, the results when ASSETS
is adopted as the wealth variable are shown, where ASSETS is the logarithm of theamount of financial and real assets owned by a subject’s household. PROB and BUY aresignificantly positive, confirming the results in Table 3. TEST is positive, but
insignificant. MALE is negative, but only significant in the TP case. ASSETS is positive,
but insignificant. This unexpected result might be because ASSETS includes assets
owned by the subjects’ parents. ASSETS probably does not represent most subjects’
personal wealth.

11

[Table 4 about here]
Considering the above problem, we adopted INCOME, which is defined as thelogarithm of subjects’ annual income including support from their parents. The results
are presented in the third and fourth columns. PROB, BUY, and MALE produce similar
results to the case of ASSETS. TEST is positive and significant at around the 10% level
here. INCOME is negative as expected, but insignificant.
A problem with INCOME may be that it is constant for all the rounds of theexperiments, whereas risk attitude measured as ARA or TP differed between rounds.
Meanwhile, actual wealth of the subjects was also changed by the prizes they won ineach round. We should not neglect this change in wealth during the experiment, which
the subjects confirmed on their PC monitors in each round; they also wrote the value on
their record sheets. According to the prospect theory (Kahneman and Tversky, 1979),
subjects may recognize the outset of the experiment as the “reference point” and focus
on the change in wealth resulting from wins and losses in each lottery.
In the fifth and sixth columns, we present the results with POINTS adopted as thewealth variable, where POINTS is the cumulative total of points that subjects had won
before each round of the experiment. The effect of INCOME, which varies only among
subjects, if at all, may be captured in individual constant terms. POINTS is significantly
negative as expected, implying decreasing absolute risk aversion. The coefficients of theother variables are similar to the results obtained when INCOME or ASSETS are used.
INCOME, which represents the level of wealth before the experiment, may have anadditional effect to POINTS on risk attitude. To examine this possibility, we included
both POINTS and INCOME as the wealth variables. The results, which also include
12

ASSETS, are shown in the seventh and eighth columns of Table 4. POINTS is again
negative and significant. INCOME is still insignificant, but its P-value increases to 15%
for the ARA case. ASSETS is again positive but not significant. These results confirm theconclusion that absolute risk aversion is decreasing in wealth.
Arrow (1970) argued that relative risk aversion (RRA) may be increasing withwealth. However, the empirical evidence is not decisive. Although most of the studies
on relative risk aversion adopted the risky asset holding ratio as the measure of relativerisk aversion, our study is unique in that we used the more direct measure of relativerisk aversion derived from the pricing of lotteries. We constructed RRA by multiplying
ARA by POINTS, and regressed it against POINTS (representing wealth), PROB, and
BUY. 14 The results are presented in the ninth column of Table 4. POINTS is not
significant, implying constant relative risk aversion. We repeated the analysis using
RRA defined as ARA × exp(ASSETS) and ARA × exp(INCOME) to obtain similar results.
These results suggest that relative risk aversion is constant with respect to wealth,supporting the conventional use of the constant relative risk averse (CRRA) utility
function in macrofinance.
Let us summarize the results of the other variables. The coefficient of PROB isalways significantly positive, implying that the subjects are more risk averse in lotteries
with higher win probabilities. The coefficient of BUY is always significantly positive,
confirming the estimation results in the preceding section. The coefficient of MALE isalways negative but significant at the 5% level only when the dependent variable is TP.

14

As the fixed effects model is chosen by the Hausman specification test, MALE and TEST are dropped in

the estimation.

13

The observation that males are more risk loving than females is consistent with thefindings of Barsky et al. (1997), Donkers et al. (2001), and Hartog et al. (2002), all ofwhich were based on questionnaire surveys.
The coefficient of TEST is always positive but significant at the 10% level only
when the dependent variable is ARA and when INCOME was utilized as the wealthvariable. Although this result is not strong, it suggests that students who have more
knowledge of financial economics are likely to be more risk averse. Levy and Levy
(2001, 2002) measured risk attitudes of business school students and practitioners (fundmanagers and financial analysts) to find that practitioners were more risk averse thanstudents. As practitioners would have more knowledge about financial economics thanstudents, these results are consistent with ours. Meanwhile, Donkers et al. (2001) andHartog et al. (2002) reported that subjects with higher education levels tend to be morerisk loving. Thus, a consistent interpretation is that higher general education levels
make people more risk loving, but specific knowledge of financial economics makes
people more risk averse.

5. Subjects’ risky asset holdings and their risk attitudes
Can risk attitude revealed in the experiment explain subjects’ actual behavior? In
this section, we investigate the relationship between subjects’ risk attitudes and theirrisky asset holdings. We postulate that more risk-averse subjects have smaller
proportions of risky assets, and we test this hypothesis with our data.
As for the risky asset holdings, we asked the following question in thequestionnaire completed at the end of the experiment.

14

What percentage of the financial assets of your entire household are in
Investment Trusts, Stocks, Futures/Options, Corporate Bonds, Foreign
Currency Deposits, Government Bonds of Foreign Countries?
Let us define the variable RISK as the percentage that subjects reported in responseto this question. As the variable for risk attitude for each subject, we define AVARA andAVTP as the average ARA and average TP over the 40 rounds in the selling and buying
experiments.
We regressed RISK against AVARA (or AVTP), ASSETS (or INCOME), andMALE.15 The estimation results are shown in Table 5. Tobit was used for the estimation
because one subject answered that she had no risky assets.16 The estimated coefficientsof AVARA were significantly negative, supporting our hypothesis, while those of AVTP
were negative but insignificant.
[Table 5 about here]
This is somewhat surprising, considering that AVARA represents the subjects’ risk
attitude, while the risky asset holding ratio is usually determined by their parents. Thus,
to understand this result, we need to assume that risk attitudes of parents and children
correlate. Is this assumption reasonable? The answer is “yes.” Indeed, Hirata et al.
(2006) conducted a questionnaire survey of parents and their children and found that thecorrelation coefficient between the risk aversion of parents and their children was 0.18

15

We do not use POINTS as the wealth variable here because risky asset holding has nothing to do withthe change in wealth during the experiments.
16

The results by OLS are almost the same as those in Table 5.

15when lottery questions were used.17 Thus, the finding of negative correlation between
parents’ risky asset holding ratio and children’s absolute risk aversion may bereasonable.
ASSETS is significantly positive, whereas INCOME is positive but insignificant.
This result is reasonable because ASSETS comprises assets owned by the household,whereas INCOME is the income of the subjects (i.e., the children). The risky asset
holding ratio of a household may relate more strongly to the former than to the latter.
However, the positive correlation between RISK and ASSETS is not consistent withthe theoretical model of Friend and Blume (1975). They developed a model based on
the Capital Asset Pricing Model (CAPM) in which the proportion of risky assets to total
assets (RISK) is equal to the ratio of expected excess return (rm − r f ) and variance ofreturn on the market portfolio (σ m 2 ) divided by relative risk aversion (RRA). That is:

RISK =(rm − r f )σ m 2 RRA.

Most previous researchers, including Friend and Blume (1975) themselves, reliedon this relation to use risky asset share (RISK) as a proxy for risk tolerance (

1
) and
RRA

examined how RRA relates to the wealth. Thus, in their analyses, if relative risk
aversion is increasing with respect to wealth, risky asset share should negatively relate

17

The sample size was 260, so the correlation coefficients were significant (5% critical value is 0.12).

Hirata et al. (2006) report that the correlation coefficient between time discount rates of parents and theirchildren is around 0.2, while the correlation coefficient between random pairs who have no relationship is
zero.

16

to the wealth. However, in many cases, the opposite is detected, indicating that therelation does not describe reality (e.g. MacCarthy (2004))18
Our paper is unique in that we can test the relation between risky asset share and
RRA because we have data on absolute risk aversion as well as the wealth. As relativerisk aversion is absolute risk aversion multiplied by wealth, Friend and Blume’s (1975)
model predicts that the share of risky assets negatively correlates with ARA and ASSETS,
when both of them are included in regression equation to explain RISK. This is indeed
what we report in Table 5. Although our result is consistent with the model in that ARA
negatively correlates to the share, it does not support the model because the coefficientof ASSETS is significantly positive. Our results suggest that use of risky asset share as aproxy for RRA may be problematic. Moreover, we found that RRA is constant withrespect to the wealth in the preceding section, implying that RISK would have been
constant with respect to the wealth, if Friend and Blume’s (1975) model is true. The factthat RISK positively correlates to the wealth suggests the rejection of their model.
A problem of this estimation is that ASSETS consists of real asset and financial
asset, while RISK is defined as the ratio to financial asset only. Thus, it may beappropriate to estimate the equation adopting financial asset (FINASSETS) instead of
ASSETS. The results are shown in the far right columns of Table 5. The results generally
confirm the above conclusion: that AVARA is significantly negative at the 10% level and
FINASSETS is positive, even if it is not significant at the 10% level.

18

Friend and Blume (1975) themselves reported that risky asset share positively correlates to financial

assets. However, when wealth is defined as the total of financial and real assets, they found the negative
correlation.

17

The risky asset holding of male subjects is higher than that of female subjects(32.6% vs. 22.2%), and males are less risk-averse than females (AVARA is 0.09 vs. 0.58).
However, MALE is positive but insignificant in Table 5, implying that the higher risky
asset holding of males is due to their lower risk aversion and nothing else.

6. Subjects’ risk attitude in experiments and in the questionnaire

In the questionnaire completed at the end of the experiment, we asked several
questions to elicit subjects’ attitudes toward various types of risk. Specifically, we
asked:
When you go out, how high does the probability of rain usually have to be
before you take an umbrella?
We define the variable RAIN as 100–x, where x(%) is the answer to this question. We
also asked:
One proverb, “Nothing ventured, nothing gained,” reveals a belief that it isnecessary to take risks if you expect excellent results. On the other hand,another proverb, “A wise man never courts danger,” reveals a belief that you
should avoid risks as much as possible. Which way of thinking is closest to
yours? On a scale of 0–10 with “10” being completely in agreement with theformer statement, and “0” being completely in agreement with the latterstatement, please rate your behavioral pattern.
We define VENTURE as 10–x, where x is the answer to this question.
Another question was:18

When you go out, are you usually careful about locking doors/windows andturning off appliances to prevent a fire? On a scale of 0–10 with “10” being the“least careful”, and “0” being the “most careful”, please rate your level ofcaution.
We define FIRE as 10–x, where x is the answer to this question.
Questions 13–16 asked the subjects their subjective price in various lotteries,
which are similar to the trials in the experiment. Specifically, in Q13 subjects wereasked what their buying price would be in a lottery with a prize of 160 yuan (US$19)
with a win probability of 50%. Question 14 asked their buying price in a lottery with theprize of 8000 yuan (US$960) with a win probability of 1%. Question 15 asked theselling price of the lottery in Q13. Question 16 asked about insurance against losses
instead of a lottery. Specifically, we asked:
Assume that you know there is a 1% chance of being robbed of 8000 yuan
(US$960). However, you can take out an insurance policy that covers losses
from a robbery. How much would you pay for this insurance?
For Q13–Q16, we calculated the ARA and TP for each subject. The correlation
coefficient between AVARA in the experiment and risk attitude in the questionnaire isshown in the first column in the top panel of Table 6.
[Table 6 about here]
AVARA revealed in the experiment significantly correlated with RAIN and
VENTURE, but it did not significantly correlate with FIRE. AVARA has a relatively highcorrelation with Q13ARA and Q15ARA, which are the most similar questions to that in
the experiment. These results imply that the risk attitudes revealed in the experiments
19and in the questionnaire are generally consistent.19
At the same time, however, the results in Table 6 suggest that risk attitude varies
substantially depending on the types of risk asked about. The correlation between
AVARA and Q14ARA is almost zero. These two questions ask about risk attitudes inquite different situations: the prize in Q14ARA was very large (8000 yuan (US$960)),
while the prize in the experiment was only 20 yuan (US$2.4). The correlation between
Q16ARA and AVARA is also close to zero. These two questions are also quite different.
In Q16ARA, subjects were asked their subjective price of insurance where the possible
loss was very large (8000 yuan (US$960)), while attitude towards an uncertain small
gain (20 yuan (US$960)) is asked in the experiment.
In sum, although one may expect all the variables in Table 6 to be highly correlated
because they all represent risk attitude, this is not the case at all. The risk attitude isquite different depending on the type of risk.
This finding is confirmed if we look at the correlations between items in thequestionnaire instead of looking at the correlations between those in the experiment andin the questionnaire. In the top panel of Table 6, a positive correlation is significant at
the 5% level in only three cases out of 2820. This result may be due to the following
reasons. One is that the measures based on psychological questions, RAIN, VENTURE,
and FIRE, ask about attitudes toward different types of risks. Rain risk is a small risk,

19

Therefore, the low correlation mentioned below is not due to the difference in methods (experiment andquestionnaire).
20

Only one case is significant out of 21 cases between items in the questionnaire, which is, the correlation

between the most similar questions (Q13 and Q15).

20

while fire risk is a large risk, and people may show different attitudes depending on therisk size. The second possible reason, already argued above, is that Q13 and Q14 havedifferent win probabilities and different prizes, which results in the different risk
attitudes demonstrated in Section 3. Question 16 is concerned with insurance against an
expected loss, while Q13–Q15 are concerned with the evaluation of an expected gain.
Thus, “loss aversion” proposed in Kahneman and Tversky (1979) produces a different
risk attitude. If the difference is not identical among the subjects, correlation will be
weak or even negative.
In the bottom panel of Table 6, we show the correlation between AVTP of theexperiment and several variables from the questionnaire. Here, AVTP in the experimenthas a positive correlation with all the measures in the questionnaire, although it isinsignificant. Most of the correlation coefficients are positive, but they are notsignificant, confirming the results of AVARA.

7. Risk aversion negatively correlates with time discount rate

In this section, we examine the relationship between time discounting and risk
aversion. The time discount rate is calculated from the results of an experimentconducted after the experiment on risk attitude. Let us briefly explain the experiment ontime discount rate.
Subjects were asked to choose whether they would prefer to (A) receive u yuan
after x months (or x’ days) or (B) receive v yuan after y months (or y’ days). We fix u, x,
and y, and change v from a small amount to a large amount for 32 pairs to find the point
at which the subjects switch from A to B. Let us call the interest rate corresponding to21this switching R (%). Higher R indicates a higher discount rate. We conducted theexperiments for 12 pairs of (u, x, y) including experiments with and without prizes, sothat there are 12 items of data on R for each subject21. We take the logarithm of these Rs
and average them (TD).
The correlation between the time discount rate TD and AVARA is –0.274, and thatbetween TD and AVTP is –0.114. They are negative, although insignificant, suggestingthat less patient people may tend to be less risk averse. The negative correlation
between the time discount rate and risk aversion is also reported in Hiruma and Tsutsui(2005) and Tsutsui et al. (2005), who based their findings on experiments with Japanese
subjects. Thus, the observation may be a robust fact, even if the correlation is not strong.
The reason for this observation is an interesting question for future investigation.

8. Conclusion

In this paper, we present the results of an experiment on risk attitudes conducted at
Fudan University in Shanghai. First we investigated how risk attitude depends on win
probabilities of lotteries. The results of the selling experiment were similar to those ofKachelmeier and Shehata (1992) in that risk-loving attitudes with a win probability ofless than 20% were confirmed. However, subjects held risk-averse attitudes when win
probability exceeded 30%. Thus, Kachelmeier and Shehata’s results need to bereconsidered.
In buying experiments, subjects showed risk-averse attitudes for all win
probabilities. We found that subjects were more risk averse in buying experiments than21

12 pairs of (u, x, y) are shown in Appendix B.

22

in selling experiments, which is generally consistent with previous literature. Our
results are unique in that this tendency is confirmed even when the same subjects
participated in both the selling and the buying experiments. The higher risk aversion inbuying experiments can be interpreted as an endowment effect, as proposed in Knetschand Sinden (1984) and Kahneman et al. (1990).
Using the data from the questionnaire completed after the experiment, we observedthat (1) males may be more risk loving than females, (2) those who have more
knowledge of financial economics are more risk averse, and (3) absolute risk aversion isdecreasing and relative risk aversion is constant with respect to change in wealth.
Subjects’ risk attitudes revealed in the experiments can account for their risky asset
holding. The risk attitudes revealed in the experiment are generally consistent withthose revealed in the questionnaire, but risk attitudes are different depending on various
types of risks. Finally, we find a negative correlation between risk aversion and time
discount rate.

Acknowledgments

This research was supported by the 21st Century COE program at Osaka
University and Grant-in-Aid for Scientific Research 17203025 of the Ministry of
Education, Culture, Sports, Science and Technology in Japan.

23

References

Arrow, K. J., 1970. Essays in the theory of risk-bearing. North-Holland: Amsterdam.
Barsky, R. B., Juster, F. T., Kimball, M. S., Shapiro, M. D., 1997. Preference parameters
and behavioral heterogeneity: an experimental approach in the health and retirement
study. Quarterly Journal of Economics 112(2), 537–579.
Becker, G. M., Degroot, J., Marschak, J., 1964. Measuring utility by a single responsesequential method. Behavioral Science 9, 226–232.
Beetsma, R. M. W.-J., Schotman, P. C., 2001. Measuring risk attitudes in a naturalexperiment: data from the television game show Lingo. Economic Journal 111, 821–848.
Cohn, R. A., Lewellen, W. G., Lease, R. C., Schlarbaum, G. G., 1975. Individual investor
risk aversion and investment portfolio composition. Journal of Finance 30, 605–620.
Cramer, J. S., Hartog, J., Jonker, N., Van Praag, C. M., 2002. Low risk aversion
encourages the choice for entrepreneurship: an empirical test of a truism. Journal of
Economic Behavior and Organization 48, 29–36.
Donkers, B., Melenberg, B., Van Soest, A., 2001. Estimating risk attitudes using
lotteries: a large sample approach. Journal of Risk and Uncertainty 22(2), 165–195.
Eichberger, J., Guth, W., Muller, W., 2003. Attitudes towards risk: an experiment.
Metroeconomica 54(1), 89–124.
Friend, I., Blume, M. E., 1975. The demand for risky assets. American Economic
Review 65(5), 900–922.
Fullenkamp, C., Tenorio, R., Battalio, R., 2003. Assessing individual risk attitudes using
field data from lottery games. Review of Economics and Statistics 85(1), 218–226.
Guiso, L., Jappelli, T., Terlizzese, D., 1996. Income risk, borrowing constraints, andportfolio choice. American Economic Review 86, 158–172.
Hartog, J., Carbonell, F. I., Jonker, N., 2002. Linking measured risk aversion toindividual characteristics. Kyklos 55 (1), 3–26.
Hirata, K., Ohtake, F., Tsutsui, Y., 2006. Is time preference inherited? mimeo.
Hiruma, F., Tsutsui, Y., 2005. Are people really risk-averse?: an experimental study.
Osaka Economic Papers 55 (2), 43–68 (in Japanese).
Kachelmeier, S. J., Shehata, M., 1992. Examining risk preference under high monetary
incentives: experimental evidence from the People’s Republic of China. American
24Economic Review 82(5), 1120–1141.
Kahneman, D., Tversky, A., 1979. Prospect theory: an analysis of decision under risk.
Econometrica 47, 263–291.
Kahneman, D., Knetsch, J. L., Thaler, R., 1990. Experimental tests of the endowment
effects and the Coase theorem. Journal of Political Economy 98, 1325–1348.
Kessler, D., Wolf, E. N., 1991. A comparative analysis of household wealth patterns inFrance and the United States. Review of Income and Wealth 37, 249–266.
Knetsch, J. L., Sinden, J. A., 1984. Willingness to pay and compensation demanded:
experimental evidence of an unexpected disparity in measures of value. Quarterly
Journal of Economics 99, 507–521.
Levy, H., 1994. Absolute and relative risk aversion: an experimental study. Journal of
Risk and Uncertainty 8(3), 289–307.
Levy, M., Levy, H., 2001. Testing for risk aversion: a stochastic dominance approach.
Economic Letters 71, 233–240.
Levy, M., Levy, H., 2002. Experimental test of the prospect theory value function: astochastic dominance approach. Organizational Behavior and Human Decision
Processes 89, 1058–1081.
McCarthy, D., 2004. Household portfolio allocation: a review of the literature. mimeo.
Metrick, A., 1995. A natural experiment in “Jeopardy!” American Economic Review 85,
240–253.
Shavit, S., Sonsino, D., Benzion, U., 2001. A comparative study of lotteries-evaluationin class and on the web. Journal of Economic Psychology 22, 483–491.
Tsutsui, Y., Ohtake, F., Ikeda, S., 2005. Estimation of degree of risk aversion: an
experiment at Osaka University. mimeo (in Japanese).

25

Table 1. Attributes of the subjects

GenderOwn annual
incomeFrequency

Ratio

Male

4

0.13

Female

26

0.86

Age

Frequency

Ratio

20

14

0.47

21

13

0.43

NA

3

0.1

None

2

0.07

<100,000

30.1< 1,000

1

0.03

100,000–
200,000

4

0.13

1,000–
2,000

3

0.1

200,000–
400,000

3

0.1

2,000–
4,000

1

0.03

400,000–
600,000

5

0.17

4,000–
6,000

3

0.1

600,000–
800,000

2

0.07

6,000–
8,000

3

0.1

800,000–
1,000,000

2

0.07

8,000–
10,0002

0.07

1,000,000–
1,200,000

3

0.1

10,000–12,0002

0.07

1,200,000–
1,400,000

1

0.03

12,000–14,0003

0.1

1,400,000–
1,600,000

00

14,000–16,0003

0.1> 1,600,000

1

0.03

> 16,000

1

0.03

NA

6

0.2

NA

6

0.2

Household’s
real estate26

Household’s
annual income< 20,000

2

0.07< 20,000

4

0.13

20,000–40,0008

0.27

20,000–40,0002

0.07

40,000–60,0003

0.1

40,000–60,0002

0.07

60,000–80,0003

0.1

60,000–80,0000080,000–100,000

2

0.07

80,000–100,00000

100,000–
120,00000

100,000–
120,000

8

0.27

120,000–
140,00000

120,000–
140,00000

140,000–
160,000

1

0.03

140,000–
160,000

1

0.03

160,000–
180,00000

160,000–
180,00000

180,000–
200,00000

180,000–
200,00000

200,000–
220,000

1

0.03

200,000–
220,000

2

0.07> 220,000

30.1> 220,000

0

0

NA

7

0.23

NA

11

0.37

Household’s
financial assets

Note: Income and assets are in yuan. Own annual income includes spouse’s income and support byparents. Household income/assets include own income/assets and those of parents.

27

Table 2. Points and payoffs won by the subjects
Number ofStandard
Averagesubjects

PointsMinimum

Maximum

deviation

30

13033

1564

10183

16699

30

261

31

204

334

29

12997

1148

10804

15786

29

260

23

217

316

30

25597

2983

12812

29282

30

512

60

257

586

Sellingexperiment

Payoffs
in yuanPoints
Buyingexperiment

Payoffs
in yuanPointsTotal
Payoffs
in yuanNote: Points won in the buying experiment include 10,000 points given to the subjects at the outset ofthe buying experiment. In addition to payoffs above each subject is given 120 yuan as the participation
fee.

28

Table 3. Risk attitude, win probability, and endowment effectExperimentSell and buy

Sell and buy

Dependent

ARA

ARA

*1000

Buy

ARA

TP
variable

Sell

ARA

TP
*1000

TP
*1000

TP
*1000

Model of
RE

FE

RE

RE

FE

FE

RE

FE

0.292

0.295

1.4352

1.7671(0.000)(0.002)(0.000)(0.000)

0.845

0.416

2.8677

6.25301.79535.4547–1.3995

0.0945(0.000)(0.009)(0.000)(0.000)(0.010)(0.000)(0.094)(0.705)–4.3646–6.1079(0.000)(0.000)–1.4341–5.0875–0.5133–4.5084

1.5289–0.3976(0.068)(0.000)(0.440)(0.000)(0.054)(0.094)3.13124.6847(0.005)(0.000)estimation

BUY

PROB

BUY*PROBPROB2

BUY*PROB2–0.051–0.305–0.5795–1.4981–0.3538–1.29400.85130.2807(0.729)(0.003)(0.006)(0.000)(0.018)(0.000)(0.000)(0.000)Constant

Number of
1179

1179

600

579

30

30

30

29

observations
Number of
subjects
R2

0.03560.01430.05440.06010.08540.05360.00600.0393

Note: P-values are in parentheses. RE represents random effects model; FE represents fixed effects
model.

29

Table 4. Risk attitude and subjects’ attributes
Dependent

ARA

ARA

ARA

TP
variable

*1000

ARA

TP
*1000

RRA

TP
*1000

TP
*1000

(ARA*POINTS*1000)

Model of the
RE

RE

RE

RE

RE

RE

RE

RE

FE

0.747

0.592

1.015

0.687

0.910

0.458

0.982

0.854

0.5432(0.000)(0.002)(0.000)(0.001)(0.000)(0.004)(0.000)(0.000)(0.000)

0.397

0.377

0.380

0.357

0.543

0.511

0.632

0.677

0.5469(0.000)(0.001)(0.000)(0.004)(0.000)(0.000)(0.000)(0.000)(0.000)–0.388–0.681–0.412–0.629–0.545–0.704–0.114–0.504(0.329)(0.014)(0.298)(0.016)(0.116)(0.003)(0.776)(0.115)

0.102

0.046

–0.276–0.153(0.458)(0.633)(0.150)(0.316)

estimation

PROB

BUY

MALE

DroppedASSETS–0.158–0.114

0.070

0.072

(0.405)(0.363)(0.675)(0.550)

INCOME–0.481–0.419–0.318–0.4600.0053(0.001)(0.010)(0.075)(0.054)(0.970)

POINTS/10000

0.085

0.050

0.289

0.168

0.148

0.073

0.293

0.176

(0.532)(0.600)(0.077)(0.118)(0.207)(0.356)(0.060)(0.156)–1.730–1.1340.066–0.084–0.268–0.2450.162–0.596–0.1149(0.337)(0.368)(0.964)(0.930)(0.556)(0.448)(0.937)(0.717)(0.367)

Dropped

TEST

Constant

Number of
959

879

1159

759

1159

24

22

29

19

29

observations
Number of
subjects
R2

0.05370.04240.08760.04720.07100.04400.09880.0580Note: P-values are in parentheses. RE represents random effects model; FE represents fixed effects
model. Number of observations varies due to the lack of data for RISK and/or ASSETS.

30

0.0460Table 5. Risky asset holdings and risk attitudes
Dependent variable

RISK

RISK

RISK

RISK

RISK

–11.8035–22.0727-10.9523(0.061)(0.004)(0.088)RISK

AVARA*1000–5.3120–8.5712-8.4272(0.519)(0.349)(0.221)AVTP

8.10347.2039(0.030)(0.066)ASSETS

5.75233.4924(0.151)(0.359)FINASSETS

1.45123.3515(0.718)(0.508)

INCOME

13.49028.689514.2525

8.5020(0.164)(0.346)(0.216)(0.501)–81.2837

12.2248–74.7764–12.1098-39.7429-19.9415(0.081)(0.727)(0.133)(0.780)(0.348)(0.631)

Number of observations

21

17

21

17

18

18

Pseudo R2

0.05180.08150.03290.02470.02670.0159MALE

Constant

Note: P-values are in parentheses. Estimation method is Tobit.

31

Table 6. Correlation coefficient between risk attitude in the experiment and risk
attitude in the questionnaire

ARA
AVARA

RAIN

VENTURE

FIRE

Q13ARA

Q14ARA

Q15ARA

AVARA

1.0000RAIN

0.3880**1.0000VENTURE

0.5469***0.23891.0000FIRE–0.05630.0643–0.0024

1.0000

Q13ARA

0.1899–0.2246

0.24240.10071.0000

Q14ARA–0.0171

0.14370.10580.30800.09821.0000

Q15ARA

0.16600.01970.13230.1054

0.5387***0.01141.0000

Q16ARA

0.04090.0797–0.1360

0.1073–0.2953–0.4129**0.1680Note: Q13ARA–Q16ARA are ARA of each subject derived from Q13–Q16 in the questionnaire. ***stands for significance at 1%, ** stands for significance at 5%, and * stands for significance at 10%.

TP
AVTP

RAIN

VENTURE

FIRE

Q13TP

Q14TP

Q15TP

AVTP

1.0000RAIN

0.18821.0000VENTURE

0.13240.23891.0000FIRE

0.20770.0643–0.0024

1.0000Q13TP

0.1948–0.3590*0.21170.10851.0000Q14TP

0.19050.14270.10560.3076

0.19491.0000Q15TP

0.2374–0.02930.19250.07460.4586**–0.0433

1.0000Q16TP

0.22470.0861–0.02850.0697–0.2809–0.4087**

0.2531

Q16TP

1.0000Note: Q13ARA–Q16TP are TP of each subject derived from Q13–Q16 in the questionnaire. *** stands
for significance at 1%, ** stands for significance at 5% level, and * stands for significance at 10% level.

32

Q16ARA

1.0000

33

34

35

36

Appendix A

Questions in the Test

Instruction
To examine whether your knowledge about economics is related to the results inexperiments, we ask you to answer the following questions. Your answers to the test
DO NOT affect the reward you earned in the experiment. That is, your reward is not
reduced if you submit incorrect answers.

37

Question 1(Quoted from Tversky, A., Kahneman, D., 1982. Judgment of and byrepresentativeness. in Kahneman, D., P. Slovic, Tversky, A., (eds). Judgment under
Uncertainty: Heuristics and Biases, Cambridge University Press, Cambridge.)
Linda is 31 years old, single, outspoken, and very bright. She majored inphilosophy. As a student, she was deeply concerned with issues of
discrimination and social justice, and also participated in antinuclear
demonstrations.
Please rank the following statements by their probability, using 1 for most probableand 8 for least probable.
(a) Linda is a teacher in elementary school. _____(b) Linda works in a bookstore and takes yoga classes. _____(c) Linda is active in the feminist movement. _____(d) Linda is a psychiatric social worker. _____(e) Linda is a member of the League of Woman Voters. _____(f) Linda is a bank teller. _____(g) Linda is an insurance salesperson. _____(h) Linda is a bank teller and is active in the feminist movement. _____

Question 2
Figure 1 depicts indifference curves for Good 1 and Good 2. Budget constraint isrepresented as the line AE. Under this budget constraint, at which point A, B, C, D, or
E is utility maximized? Circle the correct number from the following choices. If you
do not understand, circle “(1) I don’t know”. Do not guess.

38

Figure 1
Good 2A
B

C
D
E

Good 1(1) I don’t know.
(2) A
(3) B
(4) C
(5) D
(6) E

Question 3
Why do people purchase insurance? Circle the correct number from the following
choices. If you do not understand, circle “(1) I don’t know”. Do not guess.
(1) I don’t know.
(2) Because they are risk averse.
(3) Because they are risk neutral.
(4) Because they are risk loving.

39

Question 4
Suppose a lottery offering 80 yuan with a 50% probability of winning and a 50%
probability of losing. What is the expected payoff and variance of this lottery?
Calculate the answers and fill them in the following blanks. If you do not understand,leave them in blank. Do not guess.
Expected payoff ________
Variance ________

Question 5
If a person purchases a ticket in the lottery in Question 4 at a price above the expected
payoff, is this person risk averse, risk neutral, or risk loving? Circle the correct
number from the following choices. If you do not understand, circle “(1) I don’tknow”. Do not guess.
(1) I don’t know.
(2) Risk averse.
(3) Risk neutral.
(4) Risk loving.

40Question 6
Figures 2 and 3 depict the utility function for two different types. Circle the number ofcorrect combinations from the following choices. If you do not understand, circle “(1)I don’t know”. Do not guess.

Figure 2
Utility

80

160

240

Figure 3

Utility

320

400

Wealth

80

160

240

320

(1000 yuan)(1) I don’t know.
(2) A person who has the utility function in Figure 2 is risk averse; andA person who has the utility function in Figure 3 is risk neutral.
(3) A person who has the utility function in Figure 2 is risk averse; andA person who has the utility function in Figure 3 is risk loving.
(4) A person who has the utility function in Figure 2 is risk loving; andA person who has the utility function in Figure 3 is risk averse.
(5) A person who has the utility function in Figure 2 is risk loving; andA person who has the utility function in Figure 3 is risk neutral.

41

400

Wealth(1000 yuan)

Results of Test
Summary statistics of score

Observation

Mean Score

Std Dev.

Min

Max

29

3.690

1.039

2

6

Full score is 7.

Histogram of test score
12
10

Frequency

8
6
4
2
0
0

1

2

3

4
Score

42

5

6

7

Appendix B

12 pairs of (u, x, y)u (yuan)

x

y

prize

1

2800

one monthfour months

no pay2

240

one monthfour months

pay

3

240

one month

13 months

pay

4

240

ten months

13 months

pay

5

2800

two daysnine days

pay

6

2800

90 days

97 days

pay

7

2800

one monthfour months

pay

8

2800

one month

13 months

pay

9

2800

ten months

four months

pay

10

800000one monthfour months

no pay11800000one month

13 months

no pay12

800000ten months

13 months

no pay43