5245 Dissertation

8/13/2019 5245 Dissertation

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Determinants of individualinvestors behavior in portfoliodecisions

Dmitry Salimov

Universite Paris 1 Pantheon-Sorbonne02 UFR EconomicsMaster 2 Economie Theorique et EmpiriqueSupervisor: Jean-Marc TallonJune 14, 2012


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Determinants of individual investors behavior in portfoliodecisions

Dmitry Salimov

Universite Paris 1 Pantheon-Sorbonne106 - 112 Boulevard de lHopital, 75013 Paris, France

Abstract

In my thesis I study aggregate aspects of individual investors behavior such aschoices of the share of risky assets and amount of investment, choice of invest-ment instruments and the duration of relationship with the investment company.I attempt to explain the variations in these parameters by using demographic, so-

cioeconomic and, most importantly, personality trait variables such as aversion torisk, cognitive skills and several others.I make a particular emphasis on the decisions related to the share of risky assetsin the overall portfolio of the investor. I eliminate standard risk and ambiguityaversion measures as possible explanatory variables for the share of risky assets butprovide an intermediary measure that is defined over actual behavior of the subjectsin situations involving risk.I find out that the choice of the aggregate level of risk by the investor is actuallyquite rational and relies mostly on the ability of the investor to quantify and controlthe risk meaning that the irrationality appears only on the specific level.

The University of Paris 1 Pantheon-Sorbonne does not intend to give any approvalor disapproval to the opinions expressed in this paper and must be considered theauthors own.


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CONTENTS 3

4 Models 174.1 Linear model for uc share . . . . . . . . . . . . . . . . . . . . . . . 17

4.2 Robustness check . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3 Hurdle model for uc share . . . . . . . . . . . . . . . . . . . . . . . 18

5 Conclusions 20

Appendix: Tables and figures 22

References 29


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Chapter 1

Introduction

The question of quantifying human behavior was always one of my favorite ones.

The methods for collecting data on human behavior have rapidly evolved in the pastdecade and nowadays we can perform empirical studies of actual human behaviorinstead on relying on the artificial experimental data. In my analysis I will attemptto provide explanation for some basic decisions that are made by individual investorsby using their demographic and socioeconomic characteristics and their personalitytraits.

1.1 Behavior of individual investors

Analyzing every small decision made by investors like the decision to invest a specificamount of money to buy stock of a specific company on a specific date is virtuallyimpossible. Small decisions almost always depend on the context: the investor mayhave seen in the news that this particular company had some major breakthroughor maybe he just discovered that he will not be able to go on a holiday and decidedto invest this money instead and this particular stock was recommended to him by

the agent.

Because of this uncertainty I do not attempt to study individual decisions butinstead construct aggregate measures that characterize the aggregate state of theinvestors portfolio reached as the final result of these small decisions made by theinvestor. Due to the specifics of the data and my interest the emphasis of theanalysis will be made on the measure of the share of risky assets (e.g. stocks, hedgefunds shares) in the overall portfolio of the investor.

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CHAPTER 1. INTRODUCTION 2

I would also like to note that when I study the share of risky assets I implicitlyuse the law of large numbers since investors characteristics do not influence theshare as is but instead make an impact on the separate small decisions made by theinvestor.

1.2 Goals of the study

The main goal of my research was to obtain some intuition behind the factors thatinfluence the decisions of an individual investors. There are a lot of studies that

focus on the impact of demographic or socioeconomic variables on the decision ofthe investors or the impact of performance-based indicators.

But I was more interested in the relationships between the decisions and the personalcharacteristics of the subject such as his cognitive abilities, his aversion to risk orhis self-control. This was my main reason for including a lot of measures relatedto the character of the investor into my analysis. I also include several measures offinancial risk perception to check whether it affects the choices related to the riskyassets in the portfolio.

The reason for my focus on explaining the choice of the share of risky assets isthe fact that this aspect of an investment decision is the one that is most prone

to be affected by factors that are hard to observe and not directly related to theinvestment problem. For example the decision about the amount of money to investwill mostly vary depending on the investors wealth and the studying the impactof other factors would require a large number of observations that would allow usto study the variability for different fixed levels of wealth. The choice of the shareof risky assets on the other hand does no have any extremely prominent factorsallowing us to study the relationships between the variables even in the cases ofrelatively small samples.

I would also like to articulate the fact that because of the lack of good data onboth sides of the equation (the data on actual behavior of investors and the data

concerning their personality) at the same time a general analysis of these relation-ships between the investment decisions and their possible factors was impossible.But the appearance of AXA dataset changed that and allowed me to study thebasic connections between the personality and the actual behavior of an individualinvestor.


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1.3 Other studies

There are several notable studies that focus on the behavior of individual investors,on the impact of personal traits on economic decisions or on the relationships be-tween the risk attitude measures:

Barber and Odean in [BO11] study the stock trading behavior of individualinvestors. They found that instead of behaving rationally individual investorsexhibit a lot of behavioral biases seriously affecting their financial well being.In my study I show that risk attitude is somewhat related to the personality

and behavioral traits of the individual which can explain the irrationality inchoices.

Burks, Carpenter, Goette, and Rustichini in [BCGR08] find that cognitiveskills significantly affect individual preferences. In particular they find thatwillingness to take risks and patience both increase with cognitive skills andin my study I also find some support for this statement.

Butler, Guiso and Jappelli in [BGJ11] make a link between the decision style(intuition vs. reasoning) and both risk and ambiguity aversion when conduct-ing a study of a large sample of retail investors. Although I did not haveany data on the decision style in my study I observed a negative relationshipbetween risk and ambiguity aversion which by the results of the [BGJ11] canbe present among relatively wealthy individuals.

1.4 Aversion to Risk

Risk is the potential that a chosen action or activity (including the choice of inaction)will lead to a loss (an undesirable outcome). Risk aversion is the reluctance of aperson to accept a bargain with an uncertain payoffrather than another bargainwith a more certain (meaning lower potential losses), but possibly lower, expected

payoff. For example, a risk-averse investor might choose to put his or her moneyinto a bank account with a low but guaranteed interest rate, rather than into a stockthat may have high expected returns, but also involves a chance of losing value.

Example: A person is given the choice between two scenarios, one with a guaranteedpayoffand one without. In the guaranteed scenario, the person receives $50. In theuncertain scenario, a coin is flipped to decide whether the person receives $100 ornothing. The expected payofffor both scenarios is $50, meaning that an individual


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who was insensitive to risk would not care whether they took the guaranteed pay-ment or the gamble. However, individuals may have different risk attitudes. Theaverage payoffof the gamble, known as its expected value, is $50. A person is saidto be:

risk-averse (or risk-avoiding) - if he or she would accept a certain payment(certainty equivalent) of less than $50 (for example, $40), rather than takingthe gamble and possibly receiving nothing

risk-neutral - if he or she is indifferent between the bet and a certain $50payment

risk-loving (or risk-seeking) - if the guaranteed payment must be more than$50 (for example, $60) to induce him or her to take the guaranteed option,rather than taking the gamble and possibly winning $100

1.5 Aversion to Ambiguity

Ambiguity aversion (also known as uncertainty aversion) on the other hand describesan attitude of preference for known risks over unknown risks. People would rather

choose an option with fewer unknown elements than with many unknown elements.It is demonstrated in the Ellsberg paradox (i.e. that people prefer to bet on anurn with 50 red and 50 blue balls, than in one with 100 total balls but where thenumber of blue or red balls is unknown).

The distinction between ambiguity aversion and risk aversion is important but sub-tle. Risk aversion comes from a situation where a probability can be assigned toeach possible outcome of a situation. Ambiguity aversion applies to a situationwhen the probabilities of outcomes are unknown [Eps99]. The main idea behindambiguity aversion encompasses the idea of risk aversion. A real world consequenceof increased ambiguity aversion is the increased demand for insurance because thegeneral public are averse to the unknown events that will affect their lives andproperty.


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Chapter 2

Data

The data used in my thesis comes from two sources:

AXA panel: panel data on the portfolio actions of 618 AXA clients betweenyears 2002 and 2011. The data comes from the AXAs management systemand includes contract/support level data on all the actions that were preformedon the clients accounts.

Two waves of questionnaires conducted by phone via computer. They wereorganized by Institut dEtudes marketing by the request of Paris School ofEconomics. Subjects were not aware of the questionnaires relation to theAXA. The first questionnaire has a sample of 1000 participants, second - 807participants.

Note: the legend for all ambiguously named variables is given at the beginning ofappendix (see table 5.1 on page 22).

2.1 Data transformationInitially the data from the AXA panel was collected at two different networks: AA(external agents) and RCS (employees of AXA). Because of different data manage-ment protocols the information was presented in the following structures:

client id >contract id >support id >year >month for AA network

client id >contract id >year >month for RCS network

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CHAPTER 2. DATA 6

Since I was only interested in the effects on the client level I aggregated the twodatasets into one by taking sequential averages/sums over the variables of interest.For example uc share variable was obtained by calculating averages (over time) ofthe amounts of risky and total assets for every contract, summing up the contractaverages for every client and then dividing the amount of risky assets over the totalassets.

There is an implicit assumption of the fact that the riskiness of different risky assetsis more or less the same. I am backing up this assumption by the fact that unlike astand-alone investment opportunity the assets that we are talking about are offeredby an insurance company. Most of them are complex financial instruments and

off

ering any assets with exceptional risks&returns would likely be unprofitable forthe company.

Also, I would like to mention that although the preliminary analysis of the missingobservations was conducted before I received the data I did not use any variableswith a significant share of missing values. Because of this precaution I felt secureexcluding the missing observations when I performed the tests.

2.2 Bias in the data

From my point of view there are two main potential sources of bias in the sample:questionnaire data comes from people who accepted the request to participate inthe questionnaires and AXA data comes from people who have a assurance viecontract in AXA. I believe this biases to be of small significance because of thefollowing reasoning:

According to the organization conducting the questionnaires almost nobodyrejected the request to participate in the first questionnaire and almost 81%of of these people also participated in the second one. This means that therejection rate is small enough for our sample to be similar in distribution to

the general population. A majority of people in France hold assurance vie contracts because they

provide significant tax benefits to the holder. AXA is one of the biggest insur-ance companies in France, its clients are well distributed both geographicallyand socioeconomically. AXA Group ranks as the 9th largest company in theworld (based on revenue) on the 2010 Fortune Global 500 list.


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CHAPTER 2. DATA 7

Based on the information above I make an assumption that that there is no signif-icant deviation in the distribution of my sample with respect to the general popu-lation.

2.3 AXA data

The information coming from AXA panel mainly concerns clients balance, actionson the contracts and some basic demographic data. Based on this information Icreated several variables that allow me to identify clients behavior using several

axis:

share of risky support in the portfolio;

the amount of investment;

usage of active/passive instruments;

prevalence of withdrawals.

In my thesis I will pay most attention to the share of risky support in the portfolio.For the other points of interest I will only provide some interesting findings obtainedduring the analysis of the data.

2.4 Questionnaire data

Among the data that was collected during the questionnaires I selected the demo-graphic data (education, employment, income) and data on personal traits (cog-nitive and mathematical abilities, financial literacy, character traits). One of thenovelties of my work is the fact that this is the first time when character traits suchas (self-confidence, thoughtfulness, negligence) and attitude to managing personalfinances are used in an attempt to explain the actual decisions of investors because

such data was not available before.

Also included in the questionnaires are some standard measures of risk and ambigu-ity aversion including the risk tolerance measure of Barsky [Bea97] that is prevalentin studies of decisions under risk. Here is an example of such measure:

You have a choice between two options:(a) Earn 400 euros for sure.(b) Have a 50% chance to win 1000 euros and a 50% chance of winning nothing.


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CHAPTER 2. DATA 8

If the respondent picked (a), the survey continues to ask:(c) Earn 300 euros for sure.(d) Have a 50% chance to win 1000 euros and a 50% chance of winning nothing.

If the respondent picked (b), the survey continues to ask:(e) Earn 500 euros for sure.(f) Have a 50% chance to win 1000 euros and a 50% chance of winning nothing.

From the answers to this question we obtain a categorical variable taking valuesfrom 1 to 4 that is increasing in the degree of relative risk aversion. In the mainsection of my thesis I will show that such measures have little explanatory power onthe agents decision about the share of risky assets in his portfolio. Similar result

but in a more theoretic framework were obtained by Kapteyn and Teppa in [KT02].

2.5 Riskav variable

As stated in the previous paragraph standard measures of risk aversion have almostno explanatory power on the share of risky assets in the portfolio. But I was able toconstruct an aggregate ad hoc measure of risk attitude named riskav that has asignificant relationship with the share of risky assets and an even closer relationshipwith standard risk aversion measures. This means that riskav can serve as an

intermediary variable connecting the standard measures and share of risky assets.

The components for riskav measure come from Questionnaire 1 and answer followingquestions:

Q7: If you have or if you would have children, do you or would you be willingto encourage them to take risks?

Q9: Did you have a health check over last 5 years?

Q12: How often do you take a raincoat / an umbrella when weather is uncer-tain?

Q16a: Did you ever happen to not pay your parking at the parking ticketmachine for less than one hour?

Q16b: Did you ever happen to park outside of authorized areas?

Q17: Did you play following in the past 12 months: a) PMU, b) lotto, c)scratch type lotteries, d) in casino, e) online poker?

S8a: Do you own any shares?


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CHAPTER 2. DATA 9

The principal component analysis (see table 5.3 on page 23) showed that all of theseven components account for at least 9% of variability (which is a very high valueconsidering the average of 14% per component) so all seven should be used in theaggregate. But correlational analysis of these components against the share of riskyassets in the portfolio shows that Q17 responses have a very surprising patternwhere part of the risky game activities correlates positively with the share whilethe other part correlates negatively. Due to this uncertainty Q17 component wasexcluded from the final version of riskav variable.

As we will see in sections 3&4 personality traits and risk perception measures willhave little direct impact on the value of uc share. However (same as with risk

aversion measures) they will have implicit relationship with uc share through riskav.Now I will list all notable effects of the aforementioned measures on riskav (seetable 5.4 on page 23):

Self-confident people are more likely to engage in risky activities.

Impulsive people are more likely to engage in risky activities ( 90% confi-dence).

Emotional people are less likely to engage in risky activities.

People who associate financial risks with enjoyment are more likely to engage

in risky activities. People who associate financial risks with gain are more likely to engage in

risky activities ( 90% confidence).

People who are decision-makers in their household are more likely to engagein risky activities ( 90% confidence).

People with higher cognitive abilities are more likely to engage in risky activ-ities.

Men are more likely to engage in risky activities.

From several of the statements above I could make a reasonable assumption that thepossibility of engaging in a risky activity is closely intertwined with the perceivedability of the individual to avoid or control losses that may occur as the result ofthe activity. Thus self-confidence, cognitive abilities, confidence in own financialmanagement skills greatly influences the chances of an individual to engage in anyrisky activity.

Also, speaking about the differences in the likelihood of participating in risky activ-ities between different employment categories (see figure 5.2 on page 25): ordinary


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CHAPTER 2. DATA 10

employees, laborers and students are less likely to engage in risky activities. On theother hand CEOs, senior staffand people of liberal professions are more likely toengage in risky activities.

In the end riskav measures the amount of risky activities that given individualparticipated in. For a risk averse individual we would expect the value of riskav tobe low and for risk loving one to be high.

2.6 Other constructed variables

There are several other variables that did not come directly from AXA panel andquestionnaires but were constructed from raw data.

uc share is the share of risky assets in the portfolio of a given client obtainedas an average (over time) value of risky assets in the portfolio over the similaraverage value of total assets

d ifuc is the dummy for uc share >0

d uc is the dummy for uc share >mean(uc share)

PMA is the average value of total assets for a given client

nbacts is the total number of observed actions performed by the client

Q2 Q15 fin is the measure of financial literacy that counts the correct answersto financial questions in the Questionnaire 2 (e.g. about income tax in Franceor CAC 40 index)

Q2 beta describes the type of time discounting exhibited by the subject

cogn is the measure of cognitive abilities that counts the correct answers tocognitive questions in the Questionnaire 2 (e.g. coin toss results or complexinterest rates)

shAE and shAW are shares of active instruments used by the client for oper-

ations with the accounts (E stands for entries such as opening a new contractor making an additional installment, W stands for withdrawals)


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Chapter 3

Basic Analysis

The instruments that I use to analyze the data are all very common. I used standardPearsons correlation and rank correlation to perform the initial analysis of the rela-tionships between the variables. In some cases I also used boxplot (box-and-whiskerdiagram) graphs to perform the visual analysis of the relationships. Afterwards Iused linear and binary response regression models to study the explanatory powerof the investors characteristics on their decisions.

My reasons for using the Spearmans rank correlation test to study the variables are

following. First, the rank correlation assesses how well the relationship between twovariables can be described using a monotonic function (if there are no repeated datavalues, a perfect Spearman correlation of +1 or -1 occurs when each of the variablesis a perfect monotone function of the other) because of this it is often better suitedfor analyzing the categorical variables which constitute the majority of my dataset.Second, unlike the standard correlation coefficient Spearmans rank correlation testgives us not only the coefficient but also the p-value for the test which allows us toobjectively measure the significance of the relationships between variables.

I used boxplots to visually analyze the data in the cases when the statistical resultswere ambiguous. Unlike scatterplots boxplots dont work very well on the variables

with a large support but with the categorical variables boxplots provide a a moreinformative representation of the data because instead of just plotting the databoxplots allow to visually compare the differences in the main statistics of thedistribution (e.g. mean, spread, skewness) of one variable for different values of theother.

I use RA (AA) to identify standard risk (ambiguity) aversion measures from Ques-tionnaire 2, for Barsky risk aversion measure from Questionnaire 1 I will use thename barsky to identify it.

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CHAPTER 3. BASIC ANALYSIS 12

3.1 Risk

As we can see in the table below the relationship between uc share and standardrisk and ambiguity aversion measures (barsky, RA, AA) is insignificant. In fact ifwe try to build regression models for uc share with those measures as independentRHS variables the resulting p-values will be much higher that 0.05.

Note: the relationship relationship between risk and ambiguity aversion is negative(rank correlation also shows significance at 2% level). According to [BGJ11] thispattern can be present among relatively wealthy individuals but any conclusiveresults will require a separate study.

Table 3.1: Pairwise correlations for risk-related variables

uc share riskav barsky RA AAuc share 1.0000

riskav 0.1457 1.0000barsky -0.0590 -0.3441 1.0000

RA -0.0747 -0.2191 0.3038 1.0000AA 0.0696 0.0843 -0.0732 -0.1027 1.0000

The results above mean that standard risk attitude measures either do not reflect

the real risk attitude of the subject or, more likely, are too simplistic to explain sucha complex decision as the decision about the balance between the risky and risklessassets in the portfolio.

On the other hand our aggregate measure riskav has a more significant correlationwith uc share and can be used as an explanatory variable. At the same time it hasa very strong relationship with the standard risk aversion measures. This meansthat risk tolerance measures have some explanatory power on the actual behaviorrelated to risk (such as illegal parking and attending regular health checks) but arenot powerful enough to predict behavior in a complex financial framework.

Other notable effects (see table 5.5 on page 24):

People who are more confident in managing their finances are more likely toinvest in risky assets

People with higher level of education are more likely to invest in risky assets

People who are currently retired are less likely to invest in risky assets

People with higher monthly income are more likely to invest in risky assets(note that there is no similar effect from the total assets measure)


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People with higher level of financial literacy are more likely to invest in riskyassets

On the topic of differences in the share of risky assets between different employmentcategories (see figure 5.1 on page 24): ordinary employees, students and retirees aremore likely to have a lower share of risky assets in the portfolio. On the other handcraftsmen, shopkeepers, senior staffand people of liberal professions are more likelyto have a higher share.

I am would like to point out that the general conclusion from the results above wouldbe the fact that the choice of the share of risky assets in the portfolio relies on the

ability of the investor to account for (financial confidence and literacy, education)and control (employment, monthly income) the risk. This indicated that the choiceof aggregate risk is a very rational decision.

3.2 Amount of investment

In order to measure the PM (amount of investment) I created three variables:

PMA = average PM during the active time over all contracts (at least one

contract with PM>0) PMM = maximal level of PM reached during the active time

PMT = PMA*time measures the impact of investment more accurately thanjust the amount of PM (an investment that lasts 2 years has more impactthan the one that lasts only 1 year)

Table 3.2: Pairwise correlations for amount of investment variables

pma pmm pmtpma 1

pmm 0,9455 1pmt 0,9407 0,9177 1

Pairwise correlation analysis for different measures for amount of investment showthat all of these measures are similar to the point that all the conclusions made forone of them will most likely be valid for other ones too. In this case I will use PMAfor all further analysis.

Notable effects (see table 5.6 on page 25):


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People with higher level of education are likely to have invested more People who are decision makers in their household education are likely to have

invested more

People who have children are more likely to have invested less

People with higher amount of total assets are likely to have invested more (notethat effect from higher monthly income is much smaller, a reverse situationw.r.t. uc share)

People with higher level of financial literacy are likely to invest more

People who are older / retired are more likely to have invested more

People who like to gamble are less likely to have invested more

Here I would like to point out the difference in the two financial measures: incomeand wealth. The total wealth measures the level of financial situation of theinvestor and influences the amount of money that is invested. Monthly incomeon the other hand measures the stability of financial situation and while it alsoslightly influences the amount of investment its impact on the choice of risk level ismuch more important.

Note also the fact that education level and financial literacy have a positive influenceon both the amount of investment and the level of risk while the correlation between

the latter two is actually negative. This implies a very strong connection betweeneducation / financial literacy and the choice of the level of risk.

Interestingly, Q2 beta (time discounting factor) has no influence on the amount ofinvestment even though we would expect people with high factor to invest moresince they are more patient in terms of their intertemporal consumption.

3.3 Active / passive instruments

When managing their portfolios AXA clients can use different instruments which I

separated into four categories according to the sign (entries/withdrawals) and type(active/passive). Active instruments are the ones that should be initiated by clientevery instance (e.g. opening a new contract, making a custom installment), passiveare the ones that are programmed to be executed at certain times (e.g. a fixedmonthly payment from a bank account).

As I suspected there are some differences in the use of instruments depending on theclients personal traits but most of the variability comes from the fact that differentinstruments are convenient in different situations.


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Notable effects for entries (see table 5.7 on page 26):

Older / retired people are more likely to use active investment instruments.

Methodical people are more likely to use passive investment instruments.

Men are more likely to use active investment instruments.

The higher use of passive investment mechanisms also corresponds to a largeramount of actions on the contract.

Notable effects for withdrawals (see table 5.8 on page 26):

Retired people are more likely to use passive withdrawal mechanisms.

People who participate in risky activities more actively are more likely to useactive withdrawal mechanisms.

Men are more likely to use active withdrawal mechanisms.

The use of passive withdrawal mechanisms almost doesnt change at all withthe increase of the amount of actions on the contract.

Note that negligent people are more likely to use active investment instruments

which means that there is no self-correction mechanism. Sophisticated negligentagents would prefer to use passive instruments in order to behave more rationallyand avoid possible losses coming from their negligence.

The fact that people who engage in risky activities more often are more likely touse active withdrawal instruments is quite expected. When people engage in riskyactivities the outcomes of their actions become less predictable implying a higherlevel of irregularity.

Lastly I would like to point out the fact that men are more likely to use activeinstruments of both types. This is a peculiar gender difference which I have noexplanation for.

3.4 Duration of relationship with AXA

The variable dur axa from the AXA panel gives us the duration of the clientsrelationship with AXA in years that reaches values from 0 (= less than one year)to 42 years. I also studied the effects on time - active time over all contracts (atleast one contract with PM>0).


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Apart from the obvious results such as the fact that older / retired people andwealthy people are more likely to have a longer relationship with AXA there arealso some more interesting relationships.

Notable effects for time and dur axa (see table 5.9 on page 26):

People with good mathematical abilities are more likely to have longer con-tracts.

Ambiguity-averse people are more likely to have longer contracts.

Risk-averse people are more likely to have longer relationship with a life in-

surance company. People with a high share of risky support in their portfolio are less likely to

have long relationship with a life insurance company.

People who like to gamble are less likely to have long relationship with a lifeinsurance company.


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Chapter 4

Models

In this section I will present some of the regression models that i used to analyzethe data. Most of the focus will be on the uc share variable. The results attained inthis study are not very rich (the most complex model for uc share explains only 12%of the variability in the data) but nevertheless allow us to make some interestingconclusions.

4.1 Linear model for uc share

The first model I used was the standard linear regression model (see table 5.10 onpage 27). It can explain 9% of the variability in the uc share. I consider this adecent result given the complexity of uc share measure and the decisions that formits value.

The variables that have significant impact in the linear regression model are: riskav,Q1 S20 (monthly income), dur axa (length of relationship with AXA), d aa (ex-ternal agents) and time. Sadly none of the character type and risk perceptionvariables show direct impact on uc share. But as I have shown in section 2.5 they

are implicitly in this equation since they influence riskav.

The fact that this model is not very informative can be primarily attributed to tworeasons: non-linear data generating process and the complexity of uc share. Tobattle the complexity we could either use more variables and a larger sample orconstruct an experiment that would simulate the choice of the share of risky assetsin the portfolio in a simpler setting. To battle the fitness of the model we couldstudy the data generating process and propose a non-linear model that would betterfit the way that the investors use to make their decisions.

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CHAPTER 4. MODELS 18

In section 4.3 I construct a model that improves the results above by analyzing thedata generating process for uc share.

4.2 Robustness check

In order to verify the results obtained by the regression in section 4.1 I extractedyearly average values of uc share (from 2002 to 2011). First I calculated the corre-lation between uc share and its yearly values (see table 5.11 on page 27) and foundout that all of the yearly values are closely related to the average uc share (the

lowest correlation coefficient is 0.85).Then I ran same linear regression model on every yearly value and extracted thep-values to look at the significance of different explanatory variables at differenttime frames (see table 5.12 on page 27). I found out that Q1 S20 (monthly income)and dur axa (length of relationship with AXA) perform extremely well at all timeframes, riskav & d aa (external agents) are significant in majority of time framesand time is the least robust variable (significant in only 30% of yearly regressions).

4.3 Hurdle model for uc share

A hurdle model is a modified count model in which there are two processes, onegenerating the zeros and one generating the positive values. In our case the variableof interest in uc share. Hurdle model assumes that investors make two decisions:first they decide whether to invest any money into risky assets or not, then theydecide exactly how much to invest into risky assets.

Figure 4.1: The hurdle model for uc share


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CHAPTER 4. MODELS 19

This model makes sense in the context of decisions on purchasing risky assets be-cause before the investor chooses what amount of risky assets to buy he first decideswhether he wants to have any risky assets or not. The results of separate correlationanalysis (see tables 5.13 and 5.14 on page 28) show us that the two separate deci-sion are influence by two separate sets of variables. This means that hurdle modelis indeed better fitted to describe the decision process in our case.

The decision to buy risky assets is influenced by mostly behavioral traits such asQ1 Q1e (impulsiveness), financial literacy, cognitive abilities and education level.The choice of the amount of risky assets to purchase on the other hand in influencedby mostly socioeconomic and demographic factors such as Q1 S20 (monthly income)

and age. It is also heavily influenced by the clients relationship with AXA: dur axa(duration of the relationship), d aa (use of external agents) and the amount ofinvestment.

We can see that the hurdle model is a definite improvement. Personality traitslike impulsiveness affect the initial choice to purchase risky assets introducing somelevel of irrationality at this stage. At the second stage investors choose the amountof risky assets that they want to purchase by relying on socioeconomic and demo-graphic factors making this decision quite rational.

For the results of applying hurdle model to uc share via regression analysis seetables 5.15 and 5.16 on page 29. Here I would like to note that using the two-step

model increased the explanatory power of the linear model by more than 30%. Thenew linear model (uc share>0) explains 12% of the variability in the uc share.


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Chapter 5

Conclusions

Comments on the results:

In the end I believe that the most important result of my study was finding theconnection between the aversion to risk / personality traits and the choice of theshare of risky assets in the portfolio by introducing an intermediary measure ofdegree of engagement in risky activities. This measure is quite simple and easy toimplement. It is based on questions that are easy for the participants to understandas opposed for example to the risk tolerance measure. Plus the fact that this measure

is closely connected with the personality traits makes us more certain in its practicalapplicability.

The fact that the choice of aggregate level of risk in the portfolio is a mostly rationaldecision is also quite important. As evident in the section 4.3 only irrationalitycomes from the influence of personality trait factors at the first stage of the decisionprocess when the investors decide whether to purchase any risky assets or not. Thismeans that in the absence of the influence of behavioral biases in the decisionsrelated to certain risky assets the choice of risky assets would be quite rationalin general. It also means that by consciously forcing themselves to maintain adiversified portfolio of many different risky assets investors could get rid of the

irrationality.

Remarks for further research:

With regards to the direction of future studies and possible improvements I wouldlike to pay attention to the fact that in this study I only count the risk comingfrom having risky support in the portfolio. This does not take into account the factthat a person with steady income can allow himself to have a riskier portfolio anda person with an unsteady income will likely choose to make only safe investments.

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CHAPTER 5. CONCLUSIONS 21

There can also be other factors of financial risk that can affect the decision. Soin further studies I would propose to include the measure for overall safety of theinvestors own financial situation as an explanatory variable for the share of riskyassets in the portfolio.

Also one of the possible space for improvements would be using more objectivemeasures for the personality trait variables instead of self-reported ones. There area lot of psychological tests that contain questions used to identify the character ofthe subject and using such questions could bring us better data. The problem hereis the fact that collecting good psychological data requires the use of long and quitetiresome questionnaires making it harder to connect this data with the information

on actual investment decisions.In my opinion it would be interesting to conduct an experiment where the decisionprocess for the participant would be a simplified variant of uc share decision process.The participants would fill in the questionnaires and then participate in a dynamicgame where they would have as information their financial situation (wealth, income,employment stability) and would be required to choose their investment strategiesusing the pool of different investment opportunities and the information on thereturns in the previous period. If the game would be run for 36-60 steps (3-5 yearsof monthly decisions) I believe it would be able to closely simulate the actual decisionprocess of individual investors.


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Appendix: Tables and figures

Table 5.1: Legend for variables with ambiguous naming

Q1 Q14 Level of mathematical abilitiesQ1 Q18a Attitude to managing your finances: 1 Confident - Suspicious 7

Q1 Q1c Character type: 1 Methodical/orderly - Negligent 7Q1 Q1d Character type: 1 Shy - Self-confident 7Q1 Q1e Character type: 1 Thoughtful - Impulsive 7Q1 Q1f Character type: 1 Very emotional - Not emotional 7

Q1 Q25m Barsky risk aversionQ1 Q4a Financial risks perception: 1 Uncontrollable - Controllable 7Q1 Q4c Financial risks perception: 1 Anxiety - Enjoyment 7Q1 Q4e Financial risks perception: 1 Loss - Gain 7Q1 Q17 Amount of risky games (poker, lotto, etc.) playedQ1 S12 Educational levelQ1 S13 Are you the decision-maker in your household?Q1 S18 How many children do you have?

Q1 S1A Are you retired?Q1 S1R Employment typeQ1 S20 What is the level of the net monthly income of your household?

Q1 S6 What is the range of your total assets?Q2 Q1 Risk aversion on gains

Q2 Q15 fin Financial literacyQ2 Q2 Risk premiumQ2 Q5 Ambiguity aversion on gainsQ2 Q6 Ambiguity aversion on lossesQ2 Q9 Risk aversion on losses

Q2 beta Time discounting factorcogn cognitive abilitiesd aa dummy for reseau AA (contracts sold by external agents)

dur axa duration of relationship with AXA

qual axa quality of the client (by AXA)time observed duration of relationships with AXA


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Table 5.2: Q1 S1R: Employment types

1 farmers2 craftsmen, shopkeepers3 heads of businesses4 liberal professions5 senior management (senior professionals)6 middle management (intermediate professionals)7 employees8 laborers

9 retired10 students

Table 5.3: Principal component analysis for riskav components

Component Eigenvalue Difference Proportion CumulativeComp1 1,58707 0,477907 0,2267 0,2267Comp2 1,10916 0,0930667 0,1585 0,3852Comp3 1,0161 0,0770343 0,1452 0,5303

Comp4 0,939062 0,00238717 0,1342 0,6645Comp5 0,936674 0,153219 0,1338 0,7983Comp6 0,783456 0,154976 0,1119 0,9102Comp7 0,628479 0 0,0898 1

Table 5.4: Correlation analysis for riskav vs. personality variables

Variable Correlation Rank correlationQ1 Q1d 0,1709 0.1540 (p = 0.0007)

Q1 Q1e 0,0744 0.0760 (p = 0.0978)Q1 Q1f 0,1726 0.1813 (p = 0.0001)Q1 Q4c 0,1334 0.1244 (p = 0.0066)Q1 Q4e 0,0950 0.0846 (p = 0.0648)Q1 S13 0,0765 0.0772 (p = 0.0921)

cogn 0,1508 0.1614 (p = 0.0004)sex -0,1770 -0.1770 (p = 0.0002)


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Table 5.5: Correlation table for uc share

Variable Correlation Rank correlationQ1 Q18a -0,0924 -0.0805 (p = 0.0795)Q1 S12 0,1079 0.1183 (p = 0.0111)Q1 S1a -0,1183 -0.1241 (p = 0.0066)Q1 S20 0,1783 0.1445 (p = 0.0019)Q2 Q1 -0,0747 -0.0783 (p = 0.0877)

Q2 Q15 fin 0,0665 0.0834 (p = 0.0688)d aa 0,1661 0.1297 (p = 0.0046)

dur axa -0,1599 -0.1558 (p = 0.0006)

nbacts -0,0169 0.1052 (p = 0.0215)PMA -0,0993 -0.1539 (p = 0.0007)riskav 0,1258 0.1298 (p = 0.0045)

Figure 5.1: Boxplot of uc share over the employment type


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Table 5.6: Correlation table for PMA

Variable Correlation Rank correlationQ1 S12 0,1665 0.2050 (p = 0.0000)Q1 S13 0,1089 0.1252 (p = 0.0062)Q1 S18 -0,0977 -0.0921 (p = 0.0446)Q1 S1A 0,1604 0.2161 (p = 0.0000)Q1 S20 0,0748 0.1516 (p = 0.0011)Q1 S6 0,2385 0.3377 (p = 0.0000)Q2 Q9 -0,0764 -0.0996 (p = 0.0296)

Q2 Q15 fin 0,1007 0.1486 (p = 0.0011)

age 0,2014 0.2834 (p = 0.0000)cogn 0,0382 0.1175 (p = 0.0102)d aa -0,0887 -0.1671 (p = 0.0002)

dur axa 0,228 0.3870 (p = 0.0000)qual axa 0,3471 0.3956 (p = 0.0000)

time 0,1956 0.3687 (p = 0.0000)uc share -0,0993 -0.1539 ( p = 0.0007)Q1 Q17 -0,1399 -0.1362 (p = 0.0029)

Figure 5.2: Boxplot of riskav over the employment type


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Table 5.7: Correlation table for shAE

Variable Correlation Rank correlationQ1 S1A 0,1126 0.0833 (p = 0.0725)Q1 Q1C 0,0736 0.0890 (p = 0.0549)

age 0,1135 0.0918 (p = 0.0477)nbacts -0,3085 -0.5703 (p = 0.0000)

pma 0,2741 0.1370 (p = 0.0030)sex -0,0933 -0.0820 (p = 0.0769)

Table 5.8: Correlation table for shAW

Variable Correlation Rank correlationQ1 S1A -0,081 -0.1291 (p = 0.0259)nbacts -0,0563 -0.1290 (p = 0.0260)

pma -0,2156 -0.2856 (p = 0.0000)

riskav 0,0993 0.1205 (p = 0.0375)sex -0,0702 -0.1141 (p = 0.0490)

Q1 Q12 0,0909 0.1341 (p = 0.0205)

Table 5.9: Correlation tables for time and dur axa

time Correlation Rank correlationQ1 Q14 0,0841 0.0949 (p = 0.0383)Q2 Q5 0,0943 0.1065 (p = 0.0200)

dur axa Correlation Rank correlationQ1 Q25m 0,0939 0.1160 (p = 0.0113)uc share -0,1599 -0.1558 (p = 0.0006)Q1 Q17 -0,1139 -0.1063 (p = 0.0202)


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Table 5.10: Estimation results for linear regression of uc share

Variable Coefficient (Std. Err.)q1 s20 0.023 (0.007)d aa 0.059 (0.025)dur axa -0.007 (0.002)time 0.016 (0.006)riskav 0.009 (0.004)Intercept 0.075 (0.050)

Table 5.11: Correlation table for yearly uc share values

Variable Correlationuc share 2002 0,8782uc share 2003 0,8797uc share 2004 0,9129uc share 2005 0,9258uc share 2006 0,9272uc share 2007 0,9152uc share 2008 0,9083uc share 2009 0,9094uc share 2010 0,8692

uc share 2011 0,8518

Table 5.12: Table of p-values for original model and all yearly models

# obs q1 s20 d aa dur axa time riskav constuc share 477 0.001 0.017 0.000 0.008 0.031 0.128

uc share 2002 93 0.178 0.017 0.751 0.751 0.639 0.876uc share 2003 276 0.048 0.027 0.002 0.922 0.956 0.628uc share 2004 310 0.275 0.002 0.002 0.143 0.439 0.009uc share 2005 332 0.113 0.023 0.001 0.126 0.146 0.002

uc share 2006 361 0.060 0.040 0.001 0.331 0.045 0.003uc share 2007 385 0.014 0.185 0.002 0.564 0.020 0.004uc share 2008 417 0.001 0.288 0.000 0.097 0.065 0.261uc share 2009 458 0.001 0.186 0.000 0.002 0.014 0.614uc share 2010 473 0.001 0.525 0.000 0.004 0.003 0.250uc share 2011 465 0.001 0.295 0.000 0.008 0.006 0.258


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Table 5.13: Correlation table for d ifuc

Variable Correlation Rank correlationQ1 Q1e 0,1158 0.1243 (p = 0.0066)Q1 S12 0,1115 0.1126 (p = 0.0157)Q1 S13 0,1007 0.1030 (p = 0.0245)

Q1 S1A -0,1063 -0.1063 (p = 0.0203)Q1 S20 0,0976 0.0913 (p = 0.0500)

Q2 Q15 fin 0,0835 0.0948 (p = 0.0385)cogn 0,0854 0.0940 (p = 0.0406)

nbacts 0,1495 0.2159 (p = 0.0000)

qual axa 0,1195 0.1153 (p = 0.0183)riskav 0,088 0.0925 (p = 0.0436)

Table 5.14: Correlation table for uc share>0

Variable Correlation Rank correlationQ1 Q18a -0,1116 -0.1100 (p = 0.0386)Q1 S20 0,1624 0.1379 (p = 0.0093)

age -0,0981 -0.1033 (p = 0.0518)

d aa 0,2325 0.2171 (p = 0.0000)dur axa -0,2175 -0.2529 (p = 0.0000)nbacts -0,1485 -0.1071 (p = 0.0437)

pma -0,2050 -0.3516 (p = 0.0000)riskav 0,1340 0.1208 (p = 0.0228)

Note: marks the variables that have significant correlations with uc share inoriginal correlation analysis.


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Table 5.15: Estimation results for probit regression of d ifuc

Variable Coefficient (Std. Err.)q1 q1e 0.129 (0.043)q1 s13 0.310 (0.107)q1 s1a -0.354 (0.152)q1 s20 0.120 (0.039)qual axa 0.106 (0.040)Intercept -0.581 (0.270)

Table 5.16: Estimation results for linear regression of uc share (uc share>0)

Variable Coefficient (Std. Err.)q1 s20 0.018 (0.007)cogn -0.032 (0.012)d aa 0.089 (0.026)dur axa -0.005 (0.001)riskav 0.008 (0.005)Intercept 0.334 (0.053)


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chini. Cognitive skills explain economic preferences, strategic behavior,and job attachment. IZA Discussion Papers 3609, Institute for the Studyof Labor (IZA), July 2008.

[Bea97] Robert B. Barsky et al. Preference parameters and behavioral hetero-geneity: An experimental approach in the health and retirement study.The Quarterly Journal of Economics, 112(2):53779, May 1997.

[BGJ11] Jeffrey V. Butler, Luigi Guiso, and Tullio Jappelli. The role of intu-ition and reasoning in driving aversion to risk and ambiguity. CEPRDiscussion Papers 8334, C.E.P.R. Discussion Papers, April 2011.

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