Date of Birth: 18.09.1989 (Bonn, Germany) Student number: 1889249

Name: Timo Meyring

Date of Birth: 18.09.1989 (Bonn, Germany) Student number: 1889249

Supervisor: Dr. V. Angelini

Project: Personality and financial investment decisions.

Keywords: Behavioral & Household Finance.

Acknowledgments: In this paper use was made data from the DNB Household Survey.

Abstract:

In this article we tackle the problem of differentiating between uncertainty and

expectations, with regards to income, life and housing price expectation. We are trying to divert away from using the approach of revenue realization by using subjective expectations in a panel setting during the years 2008- 2015. We are disentangling uncertainty from real expectation, as uncertainty should be regarded as a separate component when dealing with expectations. We do find significant results with regards to income and life expectations, as an example an increase in ones’ life expectations increases the probability of holding stocks by almost 12%, while an increase in life uncertainty reduces the likelihood by 8.34%. Basing our results on the DNB Household Survey, which uses around 2000 Dutch households, it is as such possible to use these results in a greater picture.

JEL – code: D01, D03, G01

Keywords: Income expectations, Life expectations, Risk

2 | P a g e

Introduction:

After the markets collapsed in 2008 many people have taken it on themselves to manage their capital. However managing your portfolio is no easy task and it can be very challenging for someone who is not well versed in financial numeracy or literacy (Gaudecker 2015). In this paper we are going to analyze how people invest and how expectations and

uncertainties potentially impact these investment decisions. However with the sheer amount of investment opportunities into different asset classes it is an impossible task to find a universal perfect portfolio. We hope, that disentangling expectations and uncertainty we can show how these influence portfolios held by private investors. We all have different expectations of our future and how we perceive external events, which may impact our income and everyday life. It is standard practice to use risk and uncertainty interchangeably, but in this paper we try to draw a precise line between the two and look at their impact on portfolios individually. Moreover expectations are not limited to life expectations and income, we furthermore include a measure of how individuals perceive housing prices, in this case whether they are overestimated or underestimated. This perception of home prices is closely related to the asset class of real estate, however based on our data every single particpants is required to answer this question, whether they own property or not. As such we run a different regression specifically for the case of real estate. To establish the first two types of expectations we are using linear spline interpolation to dissect expectations and uncertainty, namely the median and the inter quartile range (IQR) respectively. Moreover, we propose two methods of measuring risk aversion, both of them are detailed and

explained in the data section of this paper. Nonetheless, risk aversion or risk lovingness, both

have significant impacts on an individuals’ preference for asset classes. Bringing us to our

dependent variables, the asset classes, which are as follows, mutual funds, bonds, stocks and

real estate, and a combined measure of a risky asset class portfolio including mutual funds,

bonds and stocks at the same time. Moreover, it is possible for individual investors to seek

the help from exogenous sources, and there is a large variety of sources that can potentially

contribute to making financial decision. These exogenous sources can be for example hiring

a professional financial advisor, using professional grade commercial software, or presenting

us with vast information via the internet, magazines or perhaps talking to people in our

3 | P a g e proximity. All of these sources have the power to influence our investment decision. Finally leading us to the following:

“How do individual expectations and uncertainties influence investment decision in Dutch households”

The structure of this paper is follows. After this section we will introduce the literature that play a predominant role for our research, this will furthermore enable us to infer certain expectation and the influence of the variables we use will have on our dependent variables.

We will then continue with the data part and how we construct and generate our variables for our analysis, we will furthermore go into great detail here on how we made our risk indicators. Following then we will discuss the different models and techniques we apply to our data set to run our analysis. Afterwards we discuss the different results we obtain for each part of or regression. And finally we will put it all together in the conclusion section, in which we will also discuss certain limitations that we run into through the course of this paper.

Literature review:

This section will deal with the literature that we use for our research, we have to address several issues have when trying to include expectations in ones’ analysis. The first one is what kind of expectation to use, back in the day it was common practice to analyze income expectation in a panel setting focusing on revenue realization Hall and Mishkin (1982), or a more recent approach proposed by Dominitz and Manski (1994). Following this

determination, we have to select an appropriate model, whether to use a parametric model or a spline model Bellemare et al. (2012). The remainder of this section will deal with the different aspect of eliciting expectation and propose other articles that played a significant role for this research.

Dominitz and Manski (1994) were among the first in trying to elicitate subjective

expectation into a measurable variable. In a telephone survey conducted by the University of Wisconsin, survey of economic expectations (SEE), they attempted to estimate respondents’

subjective probability distributions for the next years’ household income. Asking each

participant specific questions about the minimum income they would attain in the next 12

months. From this value follow up thresholds were calculated on an individual bases, asking

4 | P a g e particpants about this thresholds and requiring them to assign a particular probability to these thresholds. These different income limits, enabled them to calculate and estimate a subjective probability distribution, about each respondents future income. Dominitz and Manski finds that the subjective interquartile range (IQR) tends to rise at a stagnated rate than the individual median. In this case the personal median represents the central tendency of the person and the subjective IQR represent the spread, or in our case the uncertainty.

Furthermore Dominitz and Manski conclude that contrary to previous research, settled in a panel setting, the subjective IQR is not constant across households and also not proportional to the subjective median. As such from this result we can conclude that if we can choose an appropriate distribution model we can disentangle expectations and uncertainty. Dominitz and Manski propose that one way of generating an analyzable variable is by using a

parametric distribution, for which we have to make sure that the reported probabilities are increasing. From this we can then continue to calculate the median and the 25 ^th and 75 ^th percentiles. And using the difference between those two namely highest minus lowest to calculate the IQR. Another important point posed by Dominitz and Manski is that the phrasing of the questions is crucial when dealing with subjective expectations.

This phrasing of questions also deals with the problem that individuals’ most of the time base decisions on incomplete or partial information, Manski (2004), and that it would be more relevant to measure expectations based on subjective probabilities. Manski (2004) pointed out the following advantages of using actual probabilities over verbal questions.

These benefits are as follows:

1. Probabilities provide a well-defined absolute numerical scale of responses. Responses may be interpersonally comparable.

2. Algebra of probabilities can be used to examine the internal consistency of a respondent's expectation about different events.

3. Compare elicited subjective probabilities with known event frequencies and reach conclusions about the correspondence between subjective beliefs and frequentist realities.

As uncertainty plays a significant role in estimations, using these kind of probabilities is

precisely the reason why we use them. As such from this paper and the previous we have to

5 | P a g e make sure that the participants of the survey answered with actual probabilities and that the expectations we are focusing on, are increasing or decreasing depending on the expectation.

Concluding the part on what kind of data is required to attain possible answers in our

research and the required properties, we are now going to discuss different literature on the type of model we are planning to use and results that other researchers have found who used a similar process.

The first question we have to answer now is what type of distribution we should use. As there are several models such as the above mentioned parametric model, however there are also spline models which include linear, quadratic or cubic distribution. The definition of a spline is as follows:

“A cubic spline is a piecewise polynominal function defined on a specific interval.”

In the paper from Bellemare et al. (2012), they found the following results, namely that “it is possible to learn about subjective expectations without imposing parametric restrictions on point- identify beliefs.” One other crucial finding was that there is hardly any difference in which splines to use, as such we will be using linear splines for our analysis. Bellemare et al.

furthermore highlight the disadvantages of using a parametric distribution when eliciting subjective expectation when using for example a logarithmic normal or a normal

distribution. One fatal problem is that if due to chance there is a misspecification in the distribution it may produce a bias for our forecasting variable and inferences.

In his paper „ Probabilities in Household Surveys“, Hurd (2008) found that subjective probabilities have a high amount of predictive power, when considering the amount of private information that individuals’ have. Including for example life expectations and retirement expectations. He furthermore finds that in general stock market gains

significantly differ across individuals’ this can be explained by the access and processing of financial information, this is very useful with regards to our dependent variables that deal with financial advice. He furthermore stresses the importance of scale when modeling expectation and how important this is to be able to compare results across individuals.

Resulting in having to use actual probability questions, as proposed by Manski, because

statements that involve words such as “likely” or “unlikely” hold petite meaning if used in a

research framework as every individual perceives these differently. Following this criterion is

6 | P a g e important in choosing which expectation to use in our model. There are in fact four different types of expectations present in the DNB Household Survey that use actual probabilities and we will be dealing with these in the data section of this paper. Furthermore using said probabilities, results in the model having a considerable amount of predictive power of actual outcomes in the future. However the predictive power is not immune to biases, this may be due to the participants having misinformation about probabilities. Finally Hurd emphasizes how important it is to have indicators that measure the quality of chances, reported by the participants of a survey. Should we lack those indicators would result in a weak relationship on subjective probabilities and how individuals’ behave.

Hochguertel et al. (1997), found that there is a highly significant effect of the marginal tax rate on income, by using the same data set as we are going to use. As such households that have to pay a higher tax rate, have larger holdings in financial wealth. The reasons for this greater financial wealth is because returns from savings and dividends are tax exempted, and as such are more appealing to households, being one of the explanations as to why wealthier people appear to have more invested into stocks and bonds, when their income rises. Hochguertel et al. go as far as to call stocks and bonds luxurious goods. Based on this we would expect that an increase in net income will have a positive effect on holding a greater variety of asset classes such as mutual funds, bonds and stocks. Moreover the level of education seems to play a significant role with regards to financial wealth. As such we expect that a greater degree of education has a positive effect on whether individuals hold different asset classes. Furthermore with regards to Hochguertel et al. findings we assume that a medium to lower type of education in general has a negative effect on holding different financial assets. They also found that risk aversion decreases as wealth increases, which prompts investments into risky assets. From this we form the expectation that and decrease in risk aversion will have a positive effect on holding mutual funds and stocks.

Finally they found that age has a positive effect on holdings of different asset classes. Finally

from this paper we can make a fair amount of inference as to what kind of impact our

variables will have on our various asset classes. The next paper deals with a similar topic by

Hryshko, Luengo- Prado and Sørensen (2012). They deal with how education plays a role on

equity ownership, specifically they focus on stocks and mutual funds. This paper is of

tremendous help for us to form our expectation, not only do they deal with the education

7 | P a g e part and its role but also the position of the family member within in the household. They find similar evidence to Hochguertel et al. as in the higher educated appear to be more likely to own stocks, part of this observation may however is attributed to the higher educated having more wealth. In particular college education seems to play a crucial role with regards to stock and mutual fund investments. As financial decisions are also largely dependent on the risk aversion level of the individual, this is something we have to keep in mind. Kapteyn and Teppa (2011) deal with this exact problem in their paper “Subjective measure of risk aversion, fixed costs, and portfolio choice”. They analyze several different methods of eliciting risk aversion levels using the DNB Household Survey. This first on is grounded in economic theory and is a variable for risk tolerance, however Kapteyn and Teppa (2011) conclude that this variable has little ability to explain the relationship between portfolio allocation and risk aversion. The name two different reasons for this, the first is the complexity of the question, which as a result may be hard to comprehend by the

respondents. As the question has the basis of the particpants current situation, this can lead to a risk aver person being slightly more risk tolerable in his/her current situation. For

example a risk taking person, that is currently in a downward drift of portfolio returns can be more risk averse than he7 she usually is. The next variable is of particular interest for our analysis as this is based on factor analysis, these measures according to Kapteyn and Teppa (2011) seem to a lot more accurate with regards to explanatory power. As such from this we decided to use principal component analysis (PCA) to calculate our risk indicators. These kind of ad hoc questions seem to be a lot more comprehensible for participants. So from this we thought about a risk measurement for the individual questions, which spouted the idea of using two different risk indicators and compare their results.

To sum it all up based on the literature we expect the following signs for our variables. A

higher expected income may encourage people to invest more as such we assume a positive

effect of expected income on stocks, risky asset classes, and real estate. Income uncertainty

can have a somewhat ambiguous effect if uncertainty is high it may encourage investments

to attempt to reduce uncertainty. However if uncertainty is small it can help people to

invest, increasing returns. An increase in ones’ life expectancy can motivate people

undertake riskier investments to (or “intending to”) smoothen consumption after

retirement, as such a positive effect. Again the uncertainty component has ambiguous

8 | P a g e effects one can make an argument that life uncertainty has more of an upward trend as such risky investments may be required to maintain an appropriate standard of living. However a counter argument can be made, that one may be reluctant to invest into risky asset classes as one no longer earns any money, he/ she do not want to lose the money they already receive. We assume a positive effect of net income on holding stocks and riskier asset classes, this is because if a person earns more money, he/ she can invest the excess into these categories. And after a certain quality of life is met he/ she can potentially invest into asset classes to have a higher return than in for example a checking account. For our PCA risk indicator we expect for component one to have a positive effect, as this element measure risk taking/ loving behavior, and an adverse effect of the second factor, which measures risk aversion. We propose a similar reasoning for our risk indicator. High to medium risk aversion will hurt risky asset classes and stocks, and little risk aversion would have a positive effect on our dependent variables. Moving on to different levels of education, as we are using a fixed effects model, there may be a problem with regards to the within variation, nonetheless we assume that a higher level of education has a positive effect on holding stocks and riskier asset classes. Moreover, for medium and low education we expect the effect to be negative.

For our different types of advice, using a professional advisor and assuming that individuals follow advice, we expect this effect to be positive. For the other kinds of help coming from magazines, internet and word of mouth etc. we would expect ambiguous results, as these rely heavily on the interpretation of the information, being on an individual basis. We expect similar signs for real estate, however we would assume that if people are overestimating prices that they will sell property vice versa for underestimating prices.

The next section will put some of the points raised from the literature into practice, namely the ones regarding the data part of our analysis.

Data and Methodology:

In this section, we will discuss the data used in this paper. The data we use are from the DNB Household Survey (DHS). The DNB Household Survey is a data set that comprises

information about both psychological and economic aspects of participant financial

behavior. The data set, where the first wave launched in 1993, includes information on work,

pension, housing, mortgages, income possessions, loans, health, economic and psychological

9 | P a g e concepts, and personal characteristics (DHS 2016). Around 2000 households are

participating in this survey (CentERpanel) ¹ . While this database comprises a large variety of data, we are mainly interested in variables which asked the participants for their expectation of future outcomes. These expectations had to be based on probability questions, as this is paramount in eliciting expectations. We will be focusing on Dutch households as the DNB Household Survey is conducted in the Netherlands and we will include the years from 2008 to 2014. For our financial decision-making index we want to identify who is making the financial decision in the household as such we use the variable that asked the participant who is the most involved in financial decisions.

Dependent Variables:

We are using the following dependent variables in our analysis, which have the basis in the ownership of the individual classes:

1. Stocks

2. Risky asset classes*

3. Real estate (as physical property not as a stock option)**

*We combined the ownership of several different asset classes into one, in this case we combined mutual funds, bonds and stocks. The reason being that overall not many people owned them individually, especially for bonds.

**Real estate will include another form of expectation and will be an entirely different analysis based on the ownership of a property.

As such these variables have either a number of zero or one. All of these variables are present in the DNB Household Survey.

Income Expectation:

We end up using three different types of expectations, namely income expectancy, life expectancy and house price expectations. This next section will deal with the subjective income expectation part of our paper. In this section, we will describe again how the data was used to arrive at our variables. The following set of questions were asked, starting with a question of the lowest and highest net income that is due in the next 12 months. The

1

http://www.centerdata.nl/en/databank/dhs-data-access

10 | P a g e questions for each participant is individually constructed based on the lower and upper bound he or she had specified beforehand. These are the issues that particpants have to answer (DNB household survey, 2014):

1. What do you think is the probability (in percent) that the net yearly income of your household will be less than (1.1) in the next 12 months?

2. What do you think is the probability (in percent) that the net yearly income of your household will be less than (1.2) in the next 12 months?

3. What do you think is the probability (in percent) that the total net yearly income of your household will be less (1.3) in the next 12 months?

4. What do you think is the probability (in percent) that the total net yearly income of your household will be less than (1.4) in the next 12 months?

Following this are calculations of different thresholds for every individual and their

previously entered expectations. The survey included the formulas for each threshold and as such we directly incorporated those in our analysis. The formulas were as follows:

𝑃𝑟𝑜1 = 𝐿𝑜𝑤 + (𝐻𝑖𝑔ℎ−𝐿𝑜𝑤)∗2

10 1.1

𝑃𝑟𝑜2 = 𝐿𝑜𝑤 + (𝐻𝑖𝑔ℎ−𝐿𝑜𝑤)∗4

10 1.2

𝑃𝑟𝑜3 = 𝐿𝑜𝑤 + (𝐻𝑖𝑔ℎ−𝐿𝑜𝑤)∗6

10 1.3

𝑃𝑟𝑜4 = 𝐿𝑜𝑤 + (𝐻𝑖𝑔ℎ−𝐿𝑜𝑤)∗8

10 1.4

In the following part, we are going to talk about the Methodology eliciting expectations. As mentioned beforehand we are trying to disentangle life and income expectations. Capturing the uncertainty component of these expectations is done by the interquartile range (IQR) (Manski 2004) and having the center of the income calculated as the median of the expectation set, (Manski 2004). In order calculated these variables we employed linear interpolation using the following equations for income:

𝑀𝑒𝑑𝑖𝑎𝑛 𝑖𝑛𝑐𝑜𝑚𝑒 = 𝐼𝑛𝑐𝑜𝑚𝑒 ₁ + 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ^{𝐼𝑛𝑐𝑜𝑚𝑒}

^{−𝐼𝑛𝑐𝑜𝑚𝑒} −𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦

∗ (0.5 − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ) (2.1)

𝐼𝑛𝑐𝑜𝑚𝑒 _25𝑡ℎ = 𝐼𝑛𝑐𝑜𝑚𝑒 ₁ + 𝐼𝑛𝑐𝑜𝑚𝑒 ₂ − 𝐼𝑛𝑐𝑜𝑚𝑒 ₁

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₂ − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ∗ (0.25 − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ) (2.2)

11 | P a g e 𝐼𝑛𝑐𝑜𝑚𝑒 _75𝑡ℎ = 𝐼𝑛𝑐𝑜𝑚𝑒 ₁ + 𝐼𝑛𝑐𝑜𝑚𝑒 ₂ − 𝐼𝑛𝑐𝑜𝑚𝑒 ₁

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₂ − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ∗ (0.75 − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ) (2.3) 𝐼𝑛𝑐𝑜𝑚𝑒 ₁ = 𝑇ℎ𝑒 𝑙𝑜𝑤𝑒𝑟 𝑡ℎ𝑒𝑠ℎ𝑜𝑙𝑑 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒.

𝐼𝑛𝑐𝑜𝑚𝑒 ₂ = 𝑇ℎ𝑒 𝑢𝑝𝑝𝑒𝑟 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑎𝑏𝑜𝑣𝑒 𝑡ℎ𝑒 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒.

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ = 𝑡ℎ𝑒 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑡𝑜 𝑡ℎ𝑒 𝑙𝑜𝑤𝑒𝑟 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 (𝐼𝑛𝑐𝑜𝑚𝑒 ₁ ).

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₂ = 𝑡ℎ𝑒 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑡𝑜 𝑡ℎ𝑒 𝑢𝑝𝑝𝑒𝑟 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 (𝐼𝑛𝑐𝑜𝑚𝑒 ₂ ).

Now we will discuss where these equations originate. As we mention before we are using linear interpolation so the formula we are using has two assumptions:

1. We have two points given in the form of (𝐼𝑛𝑐𝑜𝑚𝑒 ₁ , 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ) for point one and point two (𝐼𝑛𝑐𝑜𝑚𝑒 ₂ , 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₂ ), point one has to be below the threshold or equal to the threshold and point two has to be equal or above the threshold.

2. We know the value of the “y” value we want to calculate, 0.5, 0.25 and 0.75.

Having income on the x- axis and probability on the y- axis the general formula of a value of x along the line between point one and point two is given by:

𝑦 − 𝑦 ₁

𝑥 − 𝑥 ₁ = 𝑦 ₂ − 𝑦 ₁

𝑥 ₂ − 𝑥 ₁ (3.1) Rearranging for “x” we get:

𝑦 − 𝑦 ₁

𝑥 − 𝑥 ₁ = 𝑦 ₂ − 𝑦 ₁

𝑥 ₂ − 𝑥 ₁ 𝑥 = 𝑥 ₁ + 𝑥 ₂ − 𝑥 ₁

𝑦 ₂ − 𝑦 ₁ ∗ (𝑦 − 𝑦 ₁ ) (3.2)

We also have to distinguish between several cases here when calculating both the Median

and the quartiles. The three cases are if we already have a 50% value (1 Fifty cases). The

second instance is when we have no 50% value. And the final case is when we have more

than one fifty value. This process repeats for the different quartiles. In the end, this gave us

the Median, the 25 ^th and the 75 ^th quartile, finally subtracting the 25 ^th percentile from the

75 ^th percentile to calculate our IQRs.

12 | P a g e Life Expectations:

For life expectancy, the participants have to answer questions on how likely it is that they would reach a certain age, for example, “How likely is it that you will attain (at least) the age of 65?” These questions repeat themselves for the following age level, 75, 80, 85, 90, 95 and 100 (the exact questions are in Appendix 1A). As one can see asking someone at the age of 65, if he or she would turn 65 would become redundant, as the participant had already reached that age. The participants were then sorted into age groups and were asked questions based on their age bracket. The first bracket namely (16-55), had to respond to the first question, reaching 65. The next group increased the bracket to include older participants, namely (16-65), which now included being asked a second question,

respectively that of reaching the age of 75. Furthermore, participants in the age bracket 16-

70 have to answer the question of reaching 80 year of age. Asking the people in the age

bracket 65-75, what the probability is for them to reach the age of 85. The next age bracket

now includes people age 70-80, asking how likely it is that they will reach age 90. Following

age group 75-85, and their expectation on reaching age 95. And finally the last group being

age 80-90, and the likelihood of reaching 100 years of age. Strictly speaking, these intervals

present us with a problem namely that there is no closed bound, which is a requirement

when eliciting subjective expectations. Furthermore, we have to be careful when calculating

our variables as obviously not everyone was asked the same question when it came to life

expectancy. We thus use the fact that the current age of a participant has already been

reached or will happen shortly, less than 12 months from the time of the survey. As such we

assume that this is a starting point, which is almost 100% guaranteed. Finally, the end points

we decided to take as such our zero percent value was set to be 110. The reason we choose

110 and not something higher, is based on research done by Bissonnette and de Bresser

(2014), who had investigated this exact problem and obtain results suggesting that there is

no real difference in choosing 100, 110 or 120. One reason for choosing 110 was due to the

fact that an age of 100 is present for some particpants. One additional thing to note here

again is the fact that probabilities should be monotonic, this means that for increasing

thresholds, our probabilities should be decreasing. We use a similar approach for calculating

the variables than what we used for income expectation.

13 | P a g e 𝑀𝑒𝑑𝑖𝑎𝑛 𝐴𝑔𝑒 = 𝐴𝑔𝑒 ₁ + 𝐴𝑔𝑒 ₂ − 𝐴𝑔𝑒 ₁

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₂ − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ∗ (0.5 − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ) (4.1) 𝐴𝑔𝑒 _25𝑡ℎ = 𝐴𝑔𝑒 ₁ + 𝐴𝑔𝑒 ₂ − 𝐴𝑔𝑒 ₁

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₂ − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ∗ (0.25 − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ) (4.2) 𝐴𝑔𝑒 _75𝑡ℎ = 𝐴𝑔𝑒 ₁ + 𝐴𝑔𝑒 ₂ − 𝐴𝑔𝑒 ₁

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₂ − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ∗ (0.75 − 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ ) (4.3) 𝐴𝑔𝑒 ₁ = 𝑇ℎ𝑒 𝑙𝑜𝑤𝑒𝑟 𝑡ℎ𝑒𝑠ℎ𝑜𝑙𝑑 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒.

𝐴𝑔𝑒 ₂ = 𝑇ℎ𝑒 𝑢𝑝𝑝𝑒𝑟 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑎𝑏𝑜𝑣𝑒 𝑡ℎ𝑒 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑖𝑙𝑒.

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₁ = 𝑡ℎ𝑒 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑡𝑜 𝑡ℎ𝑒 𝑙𝑜𝑤𝑒𝑟 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 (𝐴𝑔𝑒 ₁ ).

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ₂ = 𝑡ℎ𝑒 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑡𝑜 𝑡ℎ𝑒 𝑢𝑝𝑝𝑒𝑟 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 (𝐴𝑔𝑒 ₂ ).

Housing price expectations:

For this variables we used two variables supplied to us by the survey the first one asked particpants whether house prices will be overestimated, underestimated or not change within one year. The DNB household survey phrases this in the following way:

“In your opinion, are the current prices on the housing market consistent with the value of houses? Are the prices too high, too low or equal to the real value?”

The second variable we use includes the percentage change.

“According to you, what is the percentage that houses are over/underestimated?”

As such we generate dummy variables that capture either of the three cases. Once we have our dummy variables we can now apply the percentage change to correspond to either the over or under estimated state from the second variable. In this case now the variable that captures no change will be omitted in our analysis.

Risk Indicators:

Risk preference is a measure on a scale of one to seven, where seven means totally agree

and one means totally disagree. The questions can be found in the appendix 2A at the end of

this paper, from these we calculated our risk aversion index. We furthermore used

14 | P a g e Cronbach’s alpha to measure the consistency of the answers, the details, results, as well as the implications will be discussed in the methodology and results section.

From these question, we generate our risk aversion index, which includes low, medium and high-risk aversion, afterward we replace the small, medium and high indices by numbers corresponding to the levels of agreement. One, two and three correspondent to low risk aversion for the first risk aversion question. Four and five for medium risk aversion and finally six and seven being highly risk averse. We use a similar approach for questions two and four. The remaining three issues were dealt with in the opposite way so high-risk aversion now corresponds to numbers, one, two and three, medium risk aversion is still the same at four and five and low-risk aversion now corresponds to six and seven.

As we now have six indices for each of the three levels of risk aversion, we can move onto the next step. This move includes calculating three new indices which involve adding all six indices for a particular degree of risk aversion together, namely low (Low_Riskaversion), medium (Medium_Riskaversion) and high (High_Riskaversion). For all three of the new variables, Low_, Medium and High_Riskaversion, the numbers are between zero and six. For our analysis, we prefer having values of either zero or one. As such in the last step, we generated our final indices (High_Risk_aver, Medium_Risk_aver, and Low_Risk_aver) by saying that if either of the previous three indices is bigger than two, for low, medium and high-risk aversion the index is equal to one otherwise it is zero. We will also be using one other method for measuring risk aversion namely Principle component analysis.

As mentioned before we check whether the answers for the risk aversion of the participants are reliable. To measure this reliability we use Cronbach’s alpha, which is defined as follows by the University of Virginia:

“Cronbach’s alpha is a measure used to assess the reliability, or internal consistency, of a set of scale or test items. In other words, the reliability of any given measurement refers to the extent to which it is a consistent measure of a concept, and Cronbach’s alpha is one way of measuring the strength of that consistency.”

There are two different formulas in computing Cronbach’s alpha (University of Virgina):

15 | P a g e 𝛼 = ( 𝑘

𝑘 − 1 )(1 − ∑ ^𝑘 _𝑖=1 𝜎 _𝑦 ²

𝜎 _𝑥 ² ) 𝛼 = 𝑘 ∗ 𝑐̅

𝑣̅ + (𝑘 − 1)𝑐̅

With:

𝑘 = # 𝑜𝑓 𝑠𝑐𝑎𝑙𝑒 𝑖𝑡𝑒𝑚𝑠

𝜎 _𝑦 ²

= 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑤𝑖𝑡ℎ 𝑖𝑡𝑒𝑚 𝑖 𝜎 _𝑥 ² = 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑡𝑜𝑡𝑎𝑙 𝑠𝑐𝑜𝑟𝑒

𝑐̅ = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑓 𝑎𝑙𝑙 𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝑠 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑖𝑡𝑒𝑚𝑠 𝑣̅ = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑖𝑡𝑒𝑚

The results we get have a closed and bounded interval between 0 ≤ 𝛼 ≤ 1. A high alpha means that the variables have a shared covariance and are thus measuring the same underlying concept ² . Usually coefficients that are under 0.5 are unacceptable for further data usage. The results for Cronbach’s alpha:

Table 4. Cronbach’s Alpha for Risk Aversion Variables.

Label Variable Correlation Covariance Alpha

Spaar 1 0.3175 0.738303 0.6404 I think it is more important to have safe investments and guaranteed returns, than to take a risk to have a chance to get the highest possible return.

Spaar 2 0.4465 0.586099 0.5899 I do not invest in shares, because I find this too risky.

Spaar 3 0.2887 0.818744 0.6439 If I think an investment will be profitable, I am prepared to borrow money to make this investment

Spaar 4 0.3906 0.722615 0.6122 I want to be certain that my investments are safe Spaar 5 0.3497 0.736695 0.6253 If I want to improve my financial position, I

should take financial risk

Spaar 6 0.547 0.614736 0.5598 I am prepare to take the risk to lose money, when there is also a chance to make money

Test Scale 0.702866 0.6557 → Cronbach’s Alpha

16 | P a g e One considers an alpha below 0.5 as inadequate, as such our analysis yielded a satisfactory answer, which we can use for our data.

The second method we employed was the earlier mentioned principal component analysis (PCA). To determine which method to use, Kaiser or Cattell, we performed the following steps. First, we will test the results for the Kaiser methodology, namely that we keep components that have an eigenvalue of bigger than one. Since we are furthermore

interested in the high correlation between the variables we are using a threshold of|0.3|. By using this threshold we now only receive results that have a value greater than the threshold and everything below that is a blank. The results are as follows, as we can see from Table 5.

The reason for using PCA, is to lessen the number of variables, and to check furthermore if there is a connection between the variables, and if so if we can put those variables into categories (Abdi et al 2010). For PCA to be the most effective we need to have highly correlated variables, which we can then combine into one variable. In our case we are interested in receiving components that describe risk aversion. However to run this test we first have to determine how many parts we want to use, using two different ways. For both methods we however first have to determine the Eigenvalues and the total variance that each component explains. While one could consider picking some elements seems arbitrary, the two before mentioned methods can help us make a decision. The first introduced by Kaiser (1960) also known as the Kaiser criterion. Kaiser proposed that: “We can retain only factors with eigenvalues greater than one”.

Table 5 Principal component analysis using Eigenvalues above one.

Components using Eigenvalues above one.

Variables Component 1 Component 2 Unexplained*

Spaar 1 -0.3176 0.5594 0.3011

Spaar 2 -0.4505 0.1509 0.5074

Spaar 3 0.3529 0.3517 0.5326

Spaar 4 -0.3519 0.5469 0.2701

Spaar 5 0.4183 0.4071 0.3553

Spaar 6 0.5223 0.2752 0.2699

Note: * How much percent of the variance is still unexplained after using an additional

element.

17 | P a g e We can also infer from the table that there is still a large part of the variance unexplained when using two components, namely between 30 and 50 percent. Since we want a higher emphasis on a particular factor, it is standard practice to rotate the loadings matrix now.

There are two methods of rotation namely Orthogonal and Oblique. According to Katchova (2013), the orthogonal rotation preserves the perpendicularity of the axis and the oblique rotation allows for correlation between the factors. Because we do not want any

relationship between our factors we are using an orthogonal rotation. Kaiser (1960) proposes to use a varimax rotation to maximize the square loadings variance across the variables being the sum of all factors. Table 6 presents the two components after using the varimax rotation.

Table 6 Principal component analysis using Eigenvalues above one using orthogonal rotation.

Components using Eigenvalues above one.

Variables Component 1 Component 2 Unexplained*

Spaar 1 0.6408 0.3011

Spaar 2 0.3804 0.5074

Spaar 3 0.4903 0.5326

Spaar 4 0.6500 0.2701

Spaar 5 0.5756 0.3553

Spaar 6 0.5861 0.2699

Note: * How much percent of the variance is still unexplained after using an additional component.

Now from Table 6 above we can already see a pattern emerging from our initial questions of the survey. Namely question one, two and four represent issues dealing with a high level of risk aversion and three, five and six deal with low-risk aversion, potentially even risk-loving.

As such we found two potential components, component one is risk loving/ low risk aversion and component two deals with risk aversion, which we can use as our level of risk aversion.

The next method was proposed by Cattell (1966) and is known as the scree test. This

approach involves a graphical analysis of the eigenvalues in a line plot. Graph 1 presents the

screeplot for the eigenvalues of our PCA:

18 | P a g e Figure 1.1 Scree plot of eigenvalues after PCA.

We now apply Cattell’s idea by looking for the spot where the decrease in eigenvalues seems to be smoothing out.

Now the question that remains is which method are we using? Both approaches have been studied extensively by Browne, 1968; Cattell & Jaspers, 1967; Hakstian, Rogers, & Cattell, 1982; Linn, 1968; Tucker, Koopman & Linn, 1969. According to I. Dinov Assistant professor at UCLA, it seems that the Kaiser method can occasionally retain too many factors while the scree test potentially can keep to few. Moreover, Dinov concluded that they both do very well under normal conditions and that, one should check both to see which one makes more sense. From Graph 1 we can now check for the factorial scree, scree is a term from geology which refers to the part of a mountain where debris can collect. For this case, there would be one point where this can occur and that would be after the third eigenvalue. As such we can now rerun the process we implemented before to determine if we should use two or three components in our analysis. We get the same eigenvalues as we had before however now including an additional component we can explain more of the variation in our data (Table 7).

.5 1 1 .5 2 2 .5

Ei g e n va lu e s

1 2 3 4 5 6

Number

Scree plot of eigenvalues after pca

19 | P a g e Table 7 Principal component analysis using Eigenvalues according to the Screeplot**

(Graph 1).

Components using Eigenvalues above one.

Variables Component 1 Component 2 Component 3 Unexplained*

Spaar 1 -0.3176 0.5594 -0.2809 0.2396

Spaar 2 -0.4505 0.1509 0.6294 0.1986

Spaar 3 0.3529 0.3517 0.6643 0.1886

Spaar 4 -0.3519 0.5469 -0.2030 0.238

Spaar 5 0.4183 0.4071 -0.0093 0.3553

Spaar 6 0.5223 0.2752 -0.2060 0.2368

Note: * How much percent of the variance is still unexplained after using an additional component.

** The scree plot showed us that there is a smoothing of the eigenvalues after the third component as such we use three parts instead of two.

For the same reason as before we rotate the variable using varmix and applying our threshold of |0.3|.

Presenting the results in Table 8.

Table 8 Principal component analysis using Eigenvalues according to the Screeplot**

(Graph 1), using an orthogonal rotation

Components using Eigenvalues above one.

Variables Component 1 Component 2 Component 3 Unexplained*

Spaar 1 0.6995 0.2396

Spaar 2 -0.7262 0.1986

Spaar 3 0.8187 0.1886

Spaar 4 0.6772 0.238

Spaar 5 0.3730 0.4160 0.3553

Spaar 6 0.5616 0.2368

Note: * How much percent of the variance is still unexplained after using an additional component.

** The scree plot showed us that there is a smoothing of the eigenvalues after the third component as such we use three parts instead of two.

In this case, it becomes already harder to define the variables, which appeared to be a lot clearer cut when using two components. In this case, it becomes more difficult applying a particular description of the individual components. As such from this analysis we concluded that it is better to proceed with a two component risk aversion measure. We use an

additional test to verify whether it is sensible to conduct PCA, this test is called the “Kaiser-

Meyer-Olkin measure of sampling adequacy”. Again an overall score of less than 0.5 is

20 | P a g e undesirable, as the variables have little in common to warrant using PCA. From Table 9, we can see that we received an overall value of 0.6477. As such it is sensible to use PCA for our variables.

Table 9 Kaiser- Meyer- Olkin (K.M.O) measure of sampling adequacy for PCA*.

Variables K.M.O

Spaar 1 0.5949

Spaar 2 0.6998

Spaar 3 0.7537

Spaar 4 0.5919

Spaar 5 0.6677

Spaar 6 0.6338

Overall 0.6472

Note: * A measure to determine whether it is sensible to conduct PCA, to reduce factors.

With a score of over 0.5 we conclude that it is indeed reasonable to use PCA to reduce the number of factors involved.

During our analysis we found that very few people hold different kinds of asset classes, as such we are combining three of the asset classes together namely bonds, stocks and mutual funds. However, because stocks overall are considered the most risky we decided to run a separate regression for those.

Control Variables:

The next part will deal with the control variables we use:

1. Current income 2. Education

3. Position in the household 4. Gender

For the case of education, we divide the participants into different groups, which includes

small, medium and high education, for this paper, we are using the highest level of

21 | P a g e education completed. Showing below are the specific educational levels (DNB household survey):

1. (Voortgezet) speciaal onderwijs / (continued) special education 2. Kleuter-, lager- of basisonderwijs / kindergarten/primary education

3. Voorbereidend middelbaar beroepsonderwijs (VMBO) / pre-vocational education 4. HAVO/VWO / pre-university education

5. MBO of het leerlingwezen / senior vocational training or training through apprentice system

6. HBO (eerste of tweede fase) / vocational colleges 7. Wetenschappelijk onderwijs WO / university education 8. Did not have education (yet)

9. other sort of education/training

Before starting we decided, to not include eight and nine in our education levels, as these belong to an age group that most likely has no interested in financial asset holdings, yet. The first three points were combined with little education, then taking a number zero or one.

Medium education was constructed using number four and five from the above list. High education included six and seven from the list. Both of the later were built to have either zero or one as well.

Limitations we encounter, are not- responses within the questionnaire, this non-

respondents, and participants who took the survey potentially creates a bias. As mentioned

before for several other variables, survey question could be possibly understood differently

depending on the reader. In several cases, during the various waves of the survey questions

are occasionally changed to make them more comprehensible. An example of this, is for one

of the risk aversion variables in 2012, one of the questions was rephrased but essentially had

the same core idea. In our opinion one of the more prevalent problems as some participants

showed inconsistency within their answers, be it with regards to probabilities, in this case,

the condition of them being monotonic. Or having a difference in the risk aversion portion of

the survey. Last but not least as we are interested in the person who makes the financial

decision we have to aggregate some of the household information, in this case, this would

be total net income.

22 | P a g e As mentioned before we are interested in the financial activities of the household as such individuals who are not part of that process are outside the scope of this paper, as such we decided to drop everyone who is not a spouse, so we removed all possible children from our data set. Constituting in a deletion of 12261 observations. Moreover, it implies that we will have to drop observations that are related to none financial decision maker. This condition reduced our dataset from 20452 to 12214 (a drop of 8238). Based on our risk aversion indicator we spotted that some participants answered the survey inconsistently which meant that for example, they experienced both high and low-risk aversion at the same time.

Dropping those 930 observations we ended up with 11284 for the period of 2008-2015,

(however since these observations only interfered with our index they will be kept for the

other risk indices). The descriptive statistics for the entire data set are below, as well as the

descriptive statistics when differentiating between homeowners and none homeowners:

23 | P a g e Table 1 Descriptive statistic example of the risky asset bundle.

Descriptive Statistics

Variables Mean Std.- Dev. Minimum Maximum N

Ln (Median Income) 10.265 0.813 -0.223 16.59 4,308

Ln (IQR Income) 6.753 1.511 -1.609 15.21 4,308

Ln (Median Age) 4.432 0.091 4.013 4.642 4,308

Ln (IQR Age) 2.913 0.375 1.427 3.818 4,308

Ln (Total Net Income) 10.012 0.816 2.485 12.18 4,308

High Riskaversion 0.739 0.439 0 1 4,308

Medium Riskaversion 0.279 0.449 0 1 4,308

Low Riskaversion 0.058 0.233 0 1 4,308

Advice 0.235 0.424 0 1 4,308

Financial Magazine 0.085 0.280 0 1 4,308

Financial Program 0.007 0.086 0 1 4,308

Internet 0.235 0.424 0 1 4,308

Word of Mouth 0.205 0.403 0 1 4,308

High Education 0.477 0.5 0 1 4,308

Medium Education 0.279 0.449 0 1 4,308

Low Education 0.236 0.424 0 1 4,308

Gender 0.633 0.482 0 1 4,308

Position in the Household 1.180 0.385 0 1 4,308

24 | P a g e Empirical Model:

Now that we have all our variables we can set up our regression model. To determine

whether to use random or fixed effects we run a Hausman test and reject the null hypothesis of using random effects. The reason for using a fixed effect model is the nature of our data, as we are dealing with individuals, and there are differences among people that do not change over time, for example, gender. As such there is the possibility that personal effects can have a correlation with the regressor. Furthermore, we do not wish for our error terms of one participant and the regressor to have any relationship with other members. Finally because we are using a linear probability distribution model there is heteroskedasticity present, for which we have to use robust standard errors to counter this problem. Using the newly calculated variables and variables already shown in the data part of this paper we are now able to set up our regression model for our risk aversion index:

𝑂 _{𝑐,𝑖,𝑗} = 𝛼 + 𝛽 ₁ (𝐼𝑄𝑅 _𝑖,𝑗 ^𝐼𝑛𝑐 ) + 𝛽 ₂ (𝑀𝑒𝑑𝑖𝑎𝑛 _𝑖,𝑗 ^𝐼𝑛𝑐 ) + 𝛽 ₃ (𝐼𝑄𝑅 _𝑖,𝑗 ^𝐴𝑔𝑒 ) + 𝛽 ₄ (𝑀𝑒𝑑𝑖𝑎𝑛 _𝑖,𝑗 ^𝐴𝑔𝑒 ) + 𝛽 ₅ (𝐻𝑖𝑔ℎ_𝑟𝑖𝑠𝑘_𝑎𝑣𝑒𝑟𝑠𝑖𝑜𝑛 _𝑖,𝑗 ) + 𝛽 ₆ (𝑀𝑒𝑑𝑖𝑢𝑚_𝑟𝑖𝑠𝑘_𝑎𝑣𝑒𝑟𝑠𝑖𝑜𝑛 _𝑖,𝑗 ) + 𝛽 ₇ (𝐿𝑜𝑤_𝑟𝑖𝑠𝑘_𝑎𝑣𝑒𝑟𝑠𝑖𝑜𝑛 _𝑖,𝑗 ) + 𝛽 ₈ (𝑁𝐼 _𝑖,𝑗 ) + 𝛽 ₉ (𝐸𝑑𝐻 _𝑖,𝑗 )+ 𝛽 ₁₀ (𝐸𝑑𝑀 _𝑖,𝑗 ) + 𝛽 ₁₁ (𝐸𝑑𝐿 _𝑖,𝑗 ) + 𝛽 ₁₂ (𝑃𝑜𝑠 _𝑖,𝑗 ) + 𝛽 ₁₃ (𝐴𝑑𝑣𝑖𝑐𝑒 _𝑖,𝑗 ) + 𝛽 ₁₄ (𝑀𝑎𝑔𝑎𝑧𝑖𝑛𝑒 _𝑖,𝑗 ) + 𝛽 ₁₅ (𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑃𝑟𝑜𝑔𝑟𝑎𝑚 _𝑖,𝑗 ) + 𝛽 ₁₆ (𝐼𝑛𝑡𝑒𝑟𝑛𝑒𝑡 _𝑖,𝑗 )

+ 𝛽 ₁₇ (𝑊𝑜𝑟𝑑 𝑜𝑓 𝑀𝑜𝑢𝑡ℎ _𝑖,𝑗 ) + 𝛽 ₁₈ (𝐺𝑒𝑛𝑑𝑒𝑟 _𝑖,𝑗 ) + 𝜇 _𝑖,𝑗 + 𝜀 _𝑖,𝑗 And for the principal component risk indicators we use a similar regression term:

𝑂 _{𝑐,𝑖,𝑗} = 𝛼 + 𝛽 ₁ (𝐼𝑄𝑅 _𝑖,𝑗 ^𝐼𝑛𝑐 ) + 𝛽 ₂ (𝑀𝑒𝑑𝑖𝑎𝑛 _𝑖,𝑗 ^𝐼𝑛𝑐 ) + 𝛽 ₃ (𝐼𝑄𝑅 _𝑖,𝑗 ^𝐴𝑔𝑒 ) + 𝛽 ₄ (𝑀𝑒𝑑𝑖𝑎𝑛 _𝑖,𝑗 ^𝐴𝑔𝑒 ) + 𝛽 ₅ (𝑅𝑖𝑠𝑘 𝑇𝑎𝑘𝑖𝑛𝑔 _𝑖,𝑗 ) + 𝛽 ₆ (𝑅𝑖𝑠𝑘 𝐴𝑣𝑒𝑟𝑠𝑖𝑜𝑛 _𝑖,𝑗 ) + 𝛽 ₇ (𝑁𝐼 _𝑖,𝑗 )

+ 𝛽 ₈ (𝐸𝑑𝐻 _𝑖,𝑗 )+ 𝛽 ₉ (𝐸𝑑𝑀 _𝑖,𝑗 ) + 𝛽 ₁₀ (𝐸𝑑𝐿 _𝑖,𝑗 ) + 𝛽 ₁₁ (𝑃𝑜𝑠 _𝑖,𝑗 ) + 𝛽 ₁₂ (𝐴𝑑𝑣𝑖𝑐𝑒 _𝑖,𝑗 ) + 𝛽 ₁₃ (𝑀𝑎𝑔𝑎𝑧𝑖𝑛𝑒 _𝑖,𝑗 ) + 𝛽 ₁₄ (𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑃𝑟𝑜𝑔𝑟𝑎𝑚 _𝑖,𝑗 ) + 𝛽 ₁₅ (𝐼𝑛𝑡𝑒𝑟𝑛𝑒𝑡 _𝑖,𝑗 ) + 𝛽 ₁₆ (𝑊𝑜𝑟𝑑 𝑜𝑓 𝑀𝑜𝑢𝑡ℎ _𝑖,𝑗 ) + 𝛽 ₁₇ (𝐺𝑒𝑛𝑑𝑒𝑟 _𝑖,𝑗 ) + 𝜇 _𝑖,𝑗 + 𝜀 _𝑖,𝑗

And finally for the particular case of real estate owned as a property and not as an option

(own risk indicator):

25 | P a g e 𝑅𝑒𝑎𝑙 𝐸𝑠𝑡𝑎𝑡𝑒 _𝑖,𝑗 = 𝛼 + 𝛽 ₁ (𝐼𝑄𝑅 _𝑖,𝑗 ^𝐼𝑛𝑐 ) + 𝛽 ₂ (𝑀𝑒𝑑𝑖𝑎𝑛 _𝑖,𝑗 ^𝐼𝑛𝑐 ) + 𝛽 ₃ (𝐼𝑄𝑅 _𝑖,𝑗 ^𝐴𝑔𝑒 ) + 𝛽 ₄ (𝑀𝑒𝑑𝑖𝑎𝑛 _𝑖,𝑗 ^𝐴𝑔𝑒 )

+ 𝛽 ₅ (𝐻𝑖𝑔ℎ_𝑟𝑖𝑠𝑘_𝑎𝑣𝑒𝑟𝑠𝑖𝑜𝑛 _𝑖,𝑗 ) + 𝛽 ₆ (𝑀𝑒𝑑𝑖𝑢𝑚_𝑟𝑖𝑠𝑘_𝑎𝑣𝑒𝑟𝑠𝑖𝑜𝑛 _𝑖,𝑗 ) + 𝛽 ₇ (𝐿𝑜𝑤_𝑟𝑖𝑠𝑘_𝑎𝑣𝑒𝑟𝑠𝑖𝑜𝑛 _𝑖,𝑗 ) + 𝛽 ₈ (𝑁𝐼 _𝑖,𝑗 ) + 𝛽 ₉ (𝐸𝑑𝐻 _𝑖,𝑗 )+ 𝛽 ₁₀ (𝐸𝑑𝑀 _𝑖,𝑗 ) + 𝛽 ₁₁ (𝐸𝑑𝐿 _𝑖,𝑗 ) + 𝛽 ₁₂ (𝑃𝑜𝑠 _𝑖,𝑗 ) + 𝛽 ₁₃ (𝐴𝑑𝑣𝑖𝑐𝑒 _𝑖,𝑗 ) + 𝛽 ₁₄ (𝑀𝑎𝑔𝑎𝑧𝑖𝑛𝑒 _𝑖,𝑗 ) + 𝛽 ₁₅ (𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑃𝑟𝑜𝑔𝑟𝑎𝑚 _𝑖,𝑗 ) + 𝛽 ₁₆ (𝐼𝑛𝑡𝑒𝑟𝑛𝑒𝑡 _𝑖,𝑗 )

+ 𝛽 ₁₇ (𝑊𝑜𝑟𝑑 𝑜𝑓 𝑀𝑜𝑢𝑡ℎ _𝑖,𝑗 ) + 𝛽 ₁₈ (𝑂𝑣𝑒𝑟𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝐻𝑜𝑢𝑠𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒𝑠 _𝑖,𝑗 ) + 𝛽 ₁₉ (𝑈𝑛𝑑𝑒𝑟𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝐻𝑜𝑢𝑠𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒𝑠 _𝐼,𝑗 )

+ 𝛽 ₂₀ (𝑛𝑜 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 ℎ𝑜𝑢𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒𝑠 _𝑖,𝑗 ) + 𝛽 ₂₁ (𝐺𝑒𝑛𝑑𝑒𝑟 _𝑖,𝑗 ) + 𝜇 _𝑖,𝑗 + 𝜀 _𝑖,𝑗 And for Principal component analysis:

𝑂 _{𝑐,𝑖,𝑗} = 𝛼 + 𝛽 ₁ (𝐼𝑄𝑅 _𝑖,𝑗 ^𝐼𝑛𝑐 ) + 𝛽 ₂ (𝑀𝑒𝑑𝑖𝑎𝑛 _𝑖,𝑗 ^𝐼𝑛𝑐 ) + 𝛽 ₃ (𝐼𝑄𝑅 _𝑖,𝑗 ^𝐴𝑔𝑒 ) + 𝛽 ₄ (𝑀𝑒𝑑𝑖𝑎𝑛 _𝑖,𝑗 ^𝐴𝑔𝑒 ) + 𝛽 ₅ (𝑅𝑖𝑠𝑘 𝑇𝑎𝑘𝑖𝑛𝑔 _𝑖,𝑗 ) + 𝛽 ₆ (𝑅𝑖𝑠𝑘 𝐴𝑣𝑒𝑟𝑠𝑖𝑜𝑛 _𝑖,𝑗 ) + 𝛽 ₇ (𝑁𝐼 _𝑖,𝑗 )

+ 𝛽 ₈ (𝐸𝑑𝐻 _𝑖,𝑗 )+ 𝛽 ₉ (𝐸𝑑𝑀 _𝑖,𝑗 ) + 𝛽 ₁₀ (𝐸𝑑𝐿 _𝑖,𝑗 ) + 𝛽 ₁₁ (𝑃𝑜𝑠 _𝑖,𝑗 ) + 𝛽 ₁₂ (𝐴𝑑𝑣𝑖𝑐𝑒 _𝑖,𝑗 ) + 𝛽 ₁₃ (𝑀𝑎𝑔𝑎𝑧𝑖𝑛𝑒 _𝑖,𝑗 ) + 𝛽 ₁₄ (𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑃𝑟𝑜𝑔𝑟𝑎𝑚 _𝑖,𝑗 ) + 𝛽 ₁₅ (𝐼𝑛𝑡𝑒𝑟𝑛𝑒𝑡 _𝑖,𝑗 ) + 𝛽 ₁₆ (𝑊𝑜𝑟𝑑 𝑜𝑓 𝑀𝑜𝑢𝑡ℎ _𝑖,𝑗 ) + 𝛽 ₁₇ (𝑂𝑣𝑒𝑟𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝐻𝑜𝑢𝑠𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒𝑠 _𝑖,𝑗 ) + 𝛽 ₁₈ (𝑈𝑛𝑑𝑒𝑟𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝐻𝑜𝑢𝑠𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒𝑠 _𝐼,𝑗 )

+ 𝛽 ₁₉ (𝑛𝑜 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 ℎ𝑜𝑢𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒𝑠 _𝑖,𝑗 ) + 𝛽 ₂₀ (𝐺𝑒𝑛𝑑𝑒𝑟 _𝑖,𝑗 ) + 𝜇 _𝑖,𝑗 + 𝜀 _𝑖,𝑗 Where the subscripts have the below-listed definitions:

𝑂 = 𝑂𝑤𝑛𝑒𝑟𝑠ℎ𝑖𝑝 𝑐 = 𝑎𝑠𝑠𝑒𝑡 𝑐𝑙𝑎𝑠𝑠 𝑖 = 𝑦𝑒𝑎𝑟

𝑗 = 𝐼𝐷 And finally we propose the following hypothesis:

𝐻 _0.1 : There will be no effect of life expectation, income expectations and control variables on stock ownership.

𝐻 _𝑎.1 : There is an effect of life expectation, income expectation and control variables on stock

ownership.

26 | P a g e 𝐻 _0.2 : There will be no effect of life expectation, income expectations and control variables on risky asset classes with regards to ownership.

𝐻 _𝑎.2 : There is an effect of life expectation, income expectation and control variables on risky asset classes with regards ownership.

𝐻 _0.3 : There will be no effect life, income, prices expectation and control variables on owning real estate.

𝐻 _𝑎.3 : There is an effect of life, income, prices expectation and control variables on owning real estate.

Results:

In this section we are going to discuss our regression results, Table 10 presents the results with stocks as our dependent variable. Starting with the regression using PCA risk indicator, we find that an increase in life expectancy has a positive effect on owning shares, an

increase of 11.9 percent. We furthermore find a decrease in the ownership of assets with

regards to uncertainties in life, it reduces the ownership of shares by roughly 8%, and is

highly significant. Looking at the risk indicators we received as a result of our PCA, we can

infer that being risk loving has a positive (0.0555) and statistically strong relationship with

owning stocks. Being completely in line with what one would expect as stocks have no upper

limit with regards to return, however people can only get a higher return when the amount

of risk they are willing to take increases as well. We receive the opposite results for our risk

aversion component, with the relationship being negative (-0.0432), individuals who prefer

to have a lower risk are willing to compensate by not investing into risky shares. Using

further inference with regards to a higher aggregated net income, which leads to an increase

in the ownership of stocks by roughly 3.22 percent, this is in line with our expectations as the

more money we have after all the necessities of life have been covered it seems that people

look for alternative investment vehicles rather then leaving their money in a bank. Moreover

we can see that word of mouth financial advice with individual in ones’ proximity has an

adverse effect of 0.0622 (p- value< 0.01). A reason for this could be that especially after the

financial crisis in 2008 the markets are taking a long time to recover, and that if news get out

about individual stocks they would appear to be negative as such prompting people not to

27 | P a g e invest in risky asset classes. Now we get strange results for higher education, which seems to hurt holdings of equity (-0.151), this is contradictory to what we anticipated.

Table 10 Panel Regression results (Fixed Effects) for Stocks using different risk indicators.

Coefficients

Variables Stocks PCA Stocks RI

Ln (Median Income) 0.0109 0.00825

(0.00726) (0.00812)

Ln (IQR Income) -0.00221 0.000494

(0.00432) (0.00355)

Ln (Median Age) 0.119* 0.145**

(0.0544) (0.0534)

Ln (IQR Age) -0.0834*** -0.0760***

(0.0132) (0.0107) Ln (Total Net Income) 0.0322*** 0.0342***

(0.00236) (0.00445)

High Riskaversion -0.227***

(0.0486)

Medium Riskaversion -0.0651

(0.0389)

Low Riskaversion 0.130

(0.0983) Prof. Financial Advice ¹ -0.0161 -0.0129

(0.0198) (0.0219) Financial Magazine ¹ 0.0494 0.0462

(0.0262) (0.0247) Financial Program ¹ -0.0152 0.0245

(0.0477) (0.0435)

Internet ¹ -0.0179 -0.0187

(0.0183) (0.0232) Word of Mouth ¹ -0.0622*** -0.0649***

(0.0143) (0.0157)

High Education -0.151*** -0.152**

(0.0354) (0.0431) Medium Education -0.169*** -0.172***

(0.0309) (0.0387)

Low Education -0.205*** -0.210***

(0.0378) (0.0419)

Gender 0.0210** 0.0375***

(0.00817) (0.00801) Position in the Household² 0.0277** 0.0302**

(0.00817) (0.00872) High Risk aversion PCA 0.0555***

(0.00217) Low Risk aversion PCA -0.0432***

(0.00289)

28 | P a g e But the results for medium and low education are negative and again highly significant, and reducing the chance of holding equity -16.9 and -20.5 percent respectively, being in line with our expectations. The gender of the person making the financial decisions has a positive effect on stock ownership increasing it by roughly 0.021 and a p- value< 0.05. It also appears that the position in the household has some influence on whether the family owns equity (0.0277). We found similar effects when using our risk indicator, with high risk aversion having a negative relationship, -0.227, on the ownership of shares and little risk aversion again having the opposite effect. Concluding our results with regards to stock ownership.

N 4,308 3,907

R² 0.151 0.131

Note: ¹ For these variables we use one variable from the dataset which asks the participants if and when what kind of financial advice they are using. So advice in this case includes financial advice form a professional. Also including information taken from financial magazines all the way down to talking to ones’ neighbors. The exact question can be found in appendix 3A.

² The position in the household differentiates between the head of the household and his/ her spouse. Kids were dropped from the regression as mentioned earlier.

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

29 | P a g e Table 11 Panel Regression results (Fixed Effects) for Risky

asset classes using different risk indicators.

Coefficients

Variables 𝑅𝑖𝑠𝑘𝑦 ¹ PCA 𝑅𝑖𝑠𝑘𝑦 ¹ RI

Ln (Median Income) 0.0131 0.00726

(0.0125) (0.0121)

Ln (IQR Income) -0.00329 -0.000245

(0.00404) (0.00467)

Ln (Median Age) 0.113 0.126*

(0.0669) (0.0625)

Ln (IQR Age) -0.105*** -0.0977***

(0.0128) (0.0130) Ln (Total Net Income) 0.0499*** 0.0556***

(0.00397) (0.00874)

High Riskaversion -0.343***

(0.0501)

Medium Riskaversion -0.107**

(0.0328)

Low Riskaversion 0.0552

(0.0489) Prof. Financial Advice² 0.000950 0.00434 (0.0102) (0.0132) Financial Magazine² 0.0891** 0.0767*

(0.0331) (0.0340) Financial Program² -0.157** -0.156***

(0.0577) (0.0331)

Internet² -0.0300 -0.0331

(0.0199) (0.0227)

Word of Mouth² -0.114*** -0.123***

(0.0122) (0.0132)

High Education -0.0755 -0.0785

(0.0390) (0.0533)

Medium Education -0.140** -0.145*

(0.0453) (0.0598)

Low Education -0.164*** -0.170**

(0.0438) (0.0560)

Gender 0.0531*** 0.0767***

(0.0101) (0.0111) Position in the household³ 0.0343 0.0421*

(0.0179) (0.0201) High Risk aversion PCA 0.0809***

(0.00384) Low Risk aversion PCA -0.0429***

(0.00454)

N 4,308 3,907

R² 0.177 0.1597

Note:

1 “Risky” is comprised of Stocks, Bonds and Mutual Funds

² For these variables we use one variable from the dataset