What is the Relationship between an Individual’s
Attitude Towards Risk and their Propensity to hold an
Incomplete Portfolio?
This research project is submitted in part-fulfilment of the degree of
Bachelor of Arts (Honours) Economics, Finance and Banking
Nottingham Business School
Nottingham Trent University
Summer 2014
Journal of Financial Economics
Declaration:
I declare that I have personally prepared this article and that it has not, in whole or in part,
been submitted as an assessment for any other module, degree or qualification. The work
described here is my own, carried out personally unless otherwise stated. All sources of
information, including quotations, are acknowledged by means of appropriate referencing.
I declare that this project has been conducted in accordance with Nottingham Trent
University’s Regulations on Academic Irregularities, including those pertaining to research
ethics and Data Protection legislation.
1
Abstract
This paper evaluates the relationship between risk aversion and the propensity to hold an
incomplete portfolio of financial assets, along with socioeconomic and demographic
characteristics. Using two measures of risk aversion, it becomes apparent from the results,
that only one has an effect on an individual’s willingness to diversify. This measure being
the risk-return trade off an individual is willing to make, and the measure that does not
have a significant effect been how much emphases an individual puts on the safety of their
portfolio decisions.
Keywords: Diversification; Risk Aversion; Asset Allocation; Retirement Wealth Management;
Financial Sophistication; Private Households
Word Count: 7,843
2
What is the Relationship between an Individual’s Attitude Towards Risk and their
Propensity to hold and Incomplete Portfolio?
1. Introduction
Carone et al. (2005) present evidence suggesting that the EU countries have an increasingly
large proportion of old people, leading to an ageing population and predict it to worsen in
the coming decades. This is causing many concerns within economies, both for households
and governments. There are growing concerns within households over the management of
retirement wealth, and this has become apparent with the rise in popularity of directed
retirement accounts, and many individuals are finding it necessary to educate themselves in
this area (Shum and Faig, 2006).
Governments are finding it necessary to try and encourage people to contribute towards
savings plans and social security plans, in the hope that this will reduce the burden on their
expenditure (Benartzi and Thaler, 2001). In both environments, individuals are given some
responsibility to make their own asset-allocation decisions, raising concerns about how well
they do this task. There are concerns about the quality of the decisions individuals are
making in regard to the allocation of their financial assets, with the main concern being the
lack of financial sophistication in the general public. Therefore, it is essential that the
investment decisions of households are well documented and understood, this paper hopes
to add to the literature and understanding of household investment decisions.
Modern Portfolio Theory and The Capital Asset Pricing Model have usefully emphasized the
ability of diversification to reduce the risk of portfolios. The literature, however, suggests
that the majority of households hold under-diversified portfolios, holding only a subset of
available assets, with many not investing any of their wealth in equities. There are
numerous empirical studies that find various explanations for the prevalence of incomplete
portfolios; these include investor’s lack of financial sophistication (Goetzmann and Kumar,
2008); high transaction and search costs (King and Leape, 1987); incomplete information
about investment opportunities (King and Leape, 1987) and preferential tax treatment of
certain assets (King and Leape, 1998).
Despite these explanations, they do not fully explain why many households choose to hold
under-diversified portfolios. For example, transaction and search costs are unlikely to be a
deterrent for wealthier people from fully diversifying their portfolio, or lack of information
from affecting the portfolio choices of experienced and sophisticated investors.
Therefore, this paper is going to consider, in addition to the factors mentioned above, how
investors’ attitude towards risk may affect their propensity to hold an incomplete portfolio.
Risk aversion affects investors’ preference for specific portfolios because the level of
portfolio risk depends on its composition. For instance, if an incomplete portfolio contains
only a few very risky assets then it is likely that the investor has a very low tolerance
3
towards risk. Therefore, the relationship between risk aversion and the probability of
holding a fully diversified portfolio is positive because the investor can reduce the risk by
allocating their wealth among a larger number of asset types (Baraskinska et al., 2012).
Barasinka et al. (2012) also mention in their research that there is an inverse relationship
between risk aversion and willingness to fully diversify a portfolio if it contains only risk-free
assets, this is because investing in more assets implies investing in riskier assets, which in
turn will increase the risk of the portfolio. Therefore, the effect of risk aversion depends on
what assets types the portfolio is comprised of. This study takes a closer look at the
relationship between investors’ risk attitude and portfolio composition.
2. Review of Theory and Empirical Studies
As stated in DeMiguel, Garlappi and Uppal (2009) it is well documented within the finance
literature that diversification is a key technique in reducing portfolio risk. It dates back to at
least the fourth century when Rabbi Issac Aha gave the following advice on asset allocation:
“One should always divide his wealth into three parts: a third into land, a third in
merchandise, and a third ready to hand”. (Babylonian Talmud: Tractate Baba Mezi'a, Baba
Mezi'a 42a).
Ever since then there has never been any considerable advances in the literature up until
Markowitz (1952) pioneering work in portfolio theory. Markowitz’s mean-variance analysis
represents the benefits resulting from diversification, and explains how investors choose an
efficient combination of assets, given the mean and variance of portfolio returns. Barasinska
et al. (2012) declare that a major assumption with the model is that investors prefer
diversified portfolios with moderate expected returns if they have a high risk aversion, to
undiversified portfolios with high expected returns because diversification reduces the
portfolio risk associated with variance of returns on individual assets. Whereas, there is no
predicted relationship between an investor’s risk aversion and the level of diversification in
The Capital Asset Pricing Model, which is derived from the mean-variance analysis. This
model assumes that regardless of an investor’s risk aversion they should hold fully
diversified portfolios, and the determinant of an investor’s tolerance to risk is the portion of
risky assets in the portfolio.
2.1.Under-diversification within Households
According to Modern Portfolio Theory and The Capital Asset Pricing Model, investors should
allocate their financial wealth across all available assets leading to a fully diversified
portfolio. However, there are many empirical studies that provide evidence suggesting
portfolio composition varies significantly across investors and that many hold underdiversified portfolios.
4
Research by Campbell (2006) finds that households often make serious mistakes when it
comes to investing, and perhaps the greatest failure is to not hold fully diversified portfolios.
It is believed that the typical household portfolio only contains a subset of the available
assets (Hochguertel et al, 1997; King and Leape, 1998), with the majority keeping most of
their financial wealth in savings accounts with building societies and banks (Burton, 2001).
Although Haliassos and Hassapis (2002) find that the percentage of households holding
risky assets has increased over the last decade.
This is also demonstrated by Goetzmann and Kumar (2008) who present evidence that US
individual investors hold under-diversified portfolios, with the degree of under-diversification
greater among younger, low-income, less-educated, and less-sophisticated investors.
Polkovnichenko (2005) also provides evidence that on average individual investors hold
under-diversified portfolios in the US.
However, these studies do not take into account the effect of real estate and it is widely
acknowledged that most households like to keep the majority of their wealth in housing.
Flavin and Yamashita (2002) suggest that housing plays an important role in the asset
portfolio of the household, with it being the dominant asset. Their findings imply that
households optimize their portfolios subject to a constraint on housing, and this constraint
varies across households. The ratio of housing to net worth declines over the life cycle,
therefore the housing constraint generally induces a life-cycle pattern in the portfolio of
financial assets. For example, young households, which typically have large holdings of real
estate relative to their net worth, are highly leveraged and therefore forced into a situation
of high portfolio risk. As a result, these young households respond to the housing constraint
by using their net worth to either pay down their mortgage or buy bonds instead of buying
stocks. In comparison, ownership of stocks is more attractive to older households that have
accumulated greater wealth and therefore reduced their ratio of housing to net worth.
2.2.Reasons for Under-diversified Portfolios
A great deal of empirical work is aimed at understanding why so many households hold
incomplete portfolios. King and Leape (1987) explore the changing composition of the
household portfolio over the life cycle and their evidence suggests that a degree of underdiversification is difficult to reconcile with conventional portfolio theory. They present
evidence that transaction costs clearly go some way to explaining the incidence of underdiversification but are inadequate to explain the absence of diversification within the rich.
Therefore,
they
consider
that
incomplete
knowledge
about
available
investment
opportunities may play some role. Their findings provide empirical justification that it does
influence the degree in which households diversify. Information about investment
opportunities is necessary for the construction of the optimal portfolio, therefore if
households have insufficient informational then they are likely to construct a suboptimal
portfolio.
5
However, it is hard to believe that experienced and sophisticated investors will have
incomplete knowledge about investment opportunities so this does not fully explain why
many households hold incomplete portfolios.
Age is an important determinant of portfolio composition, because new information arrives
over time. In other words, it is believed that as an investor ages they acquire more
information about investment opportunities, so they should therefore be more efficient at
constructing an optimal portfolio. Kelly (1995) confirms this theory as he presents evidence
that diversification increases with age. Calvet, Campbell, and Sodini (2007) show findings
that also underpin this theory as they show that diversification increases with age, along
with wealth and financial sophistication, but this also leads to investors taking on more
aggressive positions.
Blume and Friend (1975), however, find evidence that contradicts this as they find that
the age of the investor has little effect on the degree of diversification. They also,
somewhat surprisingly, present evidence that suggests the self-employed generally hold
more diversified portfolios, whereas, the retired are less diversified. This is surprising
because it is believed that the self-employed often concentrate their wealth in their firms,
meaning they are unlikely to allocate much of their wealth across different asset types.
On the other hand, self-employed investors may actually acquire more wealth through
successful businesses along with more financial sophistication and experience, so have
better knowledge on how to invest their wealth efficiently.
There are many empirical studies that prove diversification increases as an investor’s
wealth increases (Calvet, Campbell and Sodini, 2007). There could be many explanations
for this, such as they have more wealth to allocate across available assets and are less
likely to be deterred by transaction costs. Also, they may be more willing to invest in
riskier assets as they have more money to lose, whereas an investor with not so much
wealth may be less willing to invest in the riskier assets because they need their wealth
to act as a ‘safety buffer’. Barasinska et al. (2012) states for households that are credit
constrained their financial wealth acts as a ‘safety buffer’ against periods of low income,
so adding risky assets to a portfolio can be seen as adding more risk and reducing the
safety buffer. Roche, Tompaidis and Yang (2013) confirm this as they find that investors
with little financial wealth rationally limit the number of assets they invest in, when faced
with credit and margin requirement constraints. Their results imply that younger
investors are more likely to be affected by financial constraints so are therefore more
likely to hold under-diversified portfolios than older investors.
Polkovnichenko (2005) supports that wealthier households hold more diversified
portfolios, but states that not all wealthy households are well diversified. He argues that
households are well aware of the higher risk associated with under-diversified portfolios
and believes preferences with rank dependency are a possible explanation.
6
Goetzmann and Kumar (2008) find several explanations for the incidence of incomplete
portfolios, such as: small portfolio size and transaction costs; search and learning costs;
investor demographics and financial sophistication; and behavioural biases such as illusion
of control, investor overconfidence, local bias, and trend-following behaviour.
King and Leape (1998) examine the impact of taxes on portfolio composition and present
evidence confirming that tax rates are a significant incentive for investors to under-diversify.
However, surprisingly, their results suggest that tax does not impact the share of net worth
invested in the asset.
Another fundamental explanation for the incidence of incomplete portfolios could be
explained by the availability heuristic, this is touched upon in Benartzi and Thaler (2001),
who find that the asset allocation decision made by investors is heavily dependent upon the
choices offered to them. Kapteyn and Teppa (2011) summarize it nicely when they say, “if
they are offered n choices they tend to allocate 1/n of their investment to each of the
choices offered, irrespective of the risk characteristics of the investment opportunities”.
2.3.Why do Many Households not Invest in Equities?
As the above literature suggests, there are many explanations for why households underdiversify their portfolios. It is also apparent in the literature that many households choose
not to invest in equities, and if they do it is likely to be in the company in which they are
employed.
Many empirical studies have been conducted to try and explain why many households hold
very little or no equities at all. Gomes and Michaelides (2005) investigate low stock market
participation within the population. When studying data for U.S. households they find that
only 52% hold stocks either directly or indirectly (for example, through pension schemes).
One explanation they provide for this empirical observation is that low risk-averse investors
accumulate little wealth over the life-cycle and therefore have less of an incentive to pay
the fixed costs associated with stock market participation. On the other hand, more risk
averse investors who are more prudent acquire more wealth so have more of an incentive
to pay the fixed entry costs. As a result, the marginal stockholders are more risk averse and
consequently are reluctant to invest much, if any, of their wealth in equities.
Research by Yunker & Melkumian (2010) support this theory as they suggest that wealthier
investors tend to hold a larger proportion of their assets in stocks, compared to less
wealthier investors. The reasoning behind this being that wealthier investors are more able
to afford the transaction costs involved. There is an abundance of empirical work suggesting
that small entry costs can be consistent with the observed low stock market participation
rates (Attanasio and Paiella, 2006; Degeorge et al., 2000; and Vissing-Jorgensen, 2002)
7
Kapteyn and Teppa (2011) state that there is a sub-optimal degree of international
diversification in equity markets and a potential explanation for this is ‘home asset bias’.
Their research suggest that investors tend to over invest in domestic markets because of
the different transaction costs associated with invested in foreign countries, along with other
factors such as real exchange rate volatility, informational costs and asymmetries, and
transparency in international markets.
Kelly (1995) demonstrates evidence that the median stockholder owns a single publicly
traded stock, often in the company in which they work. When looking at a sample of
high-income households, who accounted for one third of all publicly traded stocks, the
median holding is only 10 stocks. Transaction costs do not seem an adequate
explanation for the lack of diversification because three quarters of the households in the
top quintile of stock ownership had fewer than ten different stocks.
Shum and Faig (2006) study the stock holdings of US households using data from the
Survey of Consumer Finances and find that stock ownership is positively correlated with
various measures of wealth, age, retirement savings and having sought financial advice.
It is negatively correlated with holdings of alternative risky investments, such as
investments in private businesses, and the willingness to undertake non-financial
investments in the future.
Ivkovic et al. (2008) suggest that, when looking at equities, investors take riskier positions
as the size of the account balance increases. When examining the same data set Kumar
(2007) finds that young investors have a strong preference for riskier stocks, which could
be explained by having a lower amount of wealth so take riskier positions to try and
increase their returns.
2.4.Investment Strategies
The investment strategy that a household adopts tells us how they compose their portfolio
and how they allocate their wealth among assets. Depending on the financial sophistication
of the individual they may decide to use a naïve investment strategy or a sophisticated
strategy.
According to Huberman and Jiang (2006) the majority of private investors use a naïve
investment strategy, such as the 1/n rule to allocate their money among n funds. This is
consistent with Benartzi and Thaler (2001) as they show that a large proportion of private
investors use the 1/n rule to allocate their wealth among available assets.
Dreu and Bikker (2012) state that the methods private investors use to invest their wealth
is hard to reconcile with standard theory and many of them make investment mistakes.
They often use simple allocation methods when composing their portfolios across asset
classes, resulting in suboptimal investment portfolios. This is as a result of private investors
8
having limited financial sophistication, meaning they have limited attention, memory,
education and processing capabilities.
Less sophisticated investors may underestimate risk and consequently take more risk by
investing in high risk, high expected return assets. Alternatively, less sophisticated investors
may be more risk averse, thus compensating for weaker risk management skills, e.g. the
ability to measure and control risk and implement diversification strategies. This is
confirmed by previous research, showing that risk tolerance in individuals is negatively
correlated with financial knowledge and education (Grable, 2000).
Whereas, Dreu and Bikker (2012) state that investors may have suboptimal portfolios due
to using naïve investment strategies, Pflug, Pichler and Wozabal (2012) present evidence
that naïve diversification is hard to outperform as an investment strategy in a portfolio
management context.
2.5.Relationship between Risk aversion and Diversification
Barasinska et al. (2012) study the relationship between individual risk attitudes and the
composition of financial portfolios. The researchers examine a relationship similar to what is
being studied in this paper, but whereas the data they use in their study does not provide
information on how much money is invested in each individual asset, the data used in this
study does. Therefore, this paper is able to get a better measure of diversification.
Their findings suggest that more risk averse investors are more likely to hold incomplete
portfolios, consisting of mainly risk-free assets. Their results clearly show there is a
negative relationship between risk aversion and the number of assets held in a portfolio.
One explanation for this inverse relationship could be because of the precautionary saving
motive. If this theory holds then most households decide to invest in safe assets, like saving
accounts, and once these precautionary saving needs have been met, they will then invest
in other riskier assets, like stocks.
It is plausible to expect that if a household holds only one asset then it will be a safe one.
Therefore, we would expect that an individual would be more willing to invest in riskier
assets once their safety needs were satisfied. Thus, they conclude that the propensity to
diversify, by including risky assets in their portfolio, is highly dependent on whether their
safety needs have being satisfied. They also find that even for the wealthiest of investors in
their study that risk aversion still has a negative relationship on the propensity to hold a
diversified portfolio.
They conclude that households do not fully diversify their portfolios because they are credit
constrained and prefer to hold safe and liquid assets to act as a ‘safety buffer’ against
periods of low income. The higher an individual’s risk aversion the less likely they are to
hold risky assets. Hence, more risk averse individuals are more likely to hold incomplete
9
portfolios. Kelly (1995) support this as they also present evidence that risk aversion has a
negative effect on the number of assets held in a portfolio.
Campbell, Chan and Viceira (2003) note that as an investors risk aversion increases then
their demand for stocks decrease and demand for cash rises, and vice versa. The most risk
averse of investors will hold the majority of their wealth in safe assets such as cash,
whereas the more risk seeking of investors will hold the majority of their wealth in riskier
assets, such as stocks. Hence, not surprisingly, there is a negative relationship between risk
aversion and the willingness to hold risky assets.
They demonstrate that the relationship between risk aversion and the probability of holding
a diversified portfolio is a hump shaped function. However, their analysis only looks at three
asset types: cash; bonds; and stocks, which is very simplistic but still provides a useful
indication on the relationship between risk aversion and diversification. They explain that
the most risk averse investors will be on the left hand slope of the hump because they are
only willing to hold safe assets, in this case cash. Whereas, the least risk averse investors
will make up the right hand slope of the hump as they comprise their portfolio of only stocks,
the risky assets. Finally, the investors with moderate risk aversion make up the middle of
the hump as they allocate their wealth across all three asset types, cash, bonds and stocks,
holding a fully diversified portfolio.
The literature on this topic is scarce and as the studies above suggest the results are not in
agreement. Whereas these studies have examined the relationship between risk aversion
and the composition of household portfolio, they have not taken into account the amounts
of money that investors have allocated to each of these assets, so their measures of
diversification are fairly simplistic. This paper contributes to the literature by examining the
relationship between risk aversion and diversification, taking into account the amounts that
are allocated to assets in order to provide a more efficient measure of diversification.
3. Hypothesis
The tests presented in this paper aim to give greater understanding on the relationship
between an investors risk aversion and the composition of their portfolio, along with other
socioeconomic and demographic factors. It aims to give a greater understanding on how
households determine their asset allocation and what effects their diversification.
Firstly, as has been mentioned in the literature, in Barasinska et al. (2012), there is thought
to be a negative relationship between an individual’s risk aversion and the probability of
them holding a fully diversified portfolio. For this reason, this paper’s main hypothesis is
that as risk aversion increases an investor’s willingness to diversify decreases.
Secondly, as many empirical studies have suggested, socioeconomic factors are important
in explaining portfolio composition. Therefore, this investigation aims to determine whether
10
factors such as income, having a university education, and being self-employed are
statistically significant on portfolio composition.
Thirdly, to establish whether demographic characteristics have an impact on an individual’s
willingness to diversify, then it is hypothesised that age and gender have a statistically
significance on portfolio composition.
4. Data Selection and Methodology
4.1.Data Selection
The data used in this paper have been collected from households by the DNB Household
Survey, which is conducted by CentERdata (2012) at Tilburg University. It is representative
of the Dutch population, comprising of some 2000 households in the Netherlands. The data
are collected through the Internetpanel of CentERdata (the CentERpanel). Participating
respondents do not necessarily have to have their own computer with an internet
connection. If a household does not have access to the internet, CentERdata provides a socalled set-top box with a built-in internet connection and, if necessary a television set as
well, so that the households can fill in questionnaires via the television set. This paper will
be using the 2011 wave of the DNB Household Survey (DHS), which was conducted over
the period April 2011 – December 2011.
Renneboog and Spaenjers (2009) summarise it nicely when discussing the data: “The data
are grouped in eight categories. Six basic categories cover these topics: (i) general
information on the household; (ii) household and work; (iii) accommodation and mortgages;
(iv) health and income; (v) assets and liabilities; (vi) economic and psychological concepts.
Two more aggregated categories comprise: (vii) information on income and (viii)
information on assets, liabilities, and mortgages of the households”.
As multiple people from any household can fill out the survey, it is ensured that only one
respondent from each household is included in the analysis and that they make the financial
decisions. This ensures that the data is as accurate as possible, and because the
respondents have to fill out statements to measure their risk attitude towards financial
decisions it is important that the respondents are the ones who make financial decisions, if
the respondents are not the ones who make the financial decisions it is likely their tolerance
to risk, regarding financial decisions, will be unreliable. This leaves a sample size of 807.
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Table 1: Statistics of Respondents
Age
Income (€)
Mean
61.34
28295.94
Standard Deviation
-0.258
29761.445
Minimum
26
-3136
Maximum
89
689704
Table 1 provides a statistical overview of the respondents, regarding their age and income.
As can be seen the mean age of 61 is relatively high which means the study over represents
the older population. In terms of income, which is measured in euros, then it seems there is
a good range of low income and high income earners.
The purpose of this study is to investigate the economic and psychological determinants of
the savings behaviour of households. One advantage of using DHS is that the database
contains information on portfolio composition and several self-assessed measures of risk
attitude.
4.2.The Ownership of Assets
In order to assess how an individual constructs their financial portfolio, the assets which
they hold must be analysed. The survey contains information on whether households hold
numerous different types of financial assets; these can be seen in Table A.1 in Appendix A.
Some of these assets are very similar, therefore they are sorted into seven different asset
types which can be seen in Table 2.
Table 2: Different Asset Types used in Data
1
Accounts
Checking Accounts
Employer-sponsored saving accounts
Savings/deposit accounts
Deposit books
2
Insurance Policies
Single-premium annuity insurance policies
Saving or endowment insurance policies
3
Mutual Funds
4
Bonds
5
Shares in companies
6
Money lent out to friends/family
7
Business equity
Business equity (professions)
Business equity (self-employed)
12
Figure 1 shows us the ownership rates of the different asset types used in the study.
Whereas, Figure 2 provides an overview of the total number of asset types the respondents
hold. It is evident that the majoirty of households are very under-diversifed, as 48.30%
hold only one asset types and none of the households hold all seven asset types. The most
any household holds is six asset types and only one household in the whole study holds this
many. This supports the empirical lierature, that many households hold under-diversified
Frequency of Different Asset Types Held
900
800
700
600
Frequency
500
400
300
200
100
0
Accounts
Policies
Mutual
Funds
Bonds
Shares
Money lent
out
Business
Equity
800
219
196
35
107
73
34
Frequency
Different Asset Types
Figure 1: Frequency of Different Asset Types Held
Total Number of Different Asset Types Held
450
60.00%
400
Frequency
300
40.00%
250
30.00%
200
150
20.00%
100
10.00%
50
0
1
2
3
4
5
6
7
Frequency
394
256
112
36
17
1
0
Percentage
48.30%
31.40%
13.70%
4.40%
2.10%
0.10%
0.00%
Number of Different Assets Held
Frequency
Figure 2: Total Number of Different Asset Types Held
13
Percentage
0.00%
Percentage
50.00%
350
portfolios, as was discussed in section 2.1.
4.3.Measures of Diversification
In order to measure how well diversified the portfolios in the study are we must analysis the
investment strategies used. There is no common approach to measuring the diversification
of household assets and empirical studies suggest various different methods. Barasinska et
al. (2012) breaks down portfolio composition into two types of decisions:

What kind of assets the investor owns

What proportion of wealth to allocate to each of these assets
As has been mentioned, their study was limited by the fact that they did not have
information on the amounts of money that were invested in each of the assets so they only
focused on the first aspect of portfolio composition, the ownership of the different assets.
Whereas, the data used in this study does have all the available information so will be
analysing both measures of portfolio composition.
Blume and Friend (1975) suggest using the method of considering the total number of
different assets held in a portfolio. As just discussed, this method will be used in this study.
On the one hand, it is useful in that it gives us a good indication on how well a portfolio is
diversified in terms of how many assets an investor chooses to divide their wealth across.
However, on the other hand, it is very simplistic as it does not take into account the
amounts that are invested in the different assets so in that sense it is a poor measure of
diversification. For instance, a household could hold all possible asset types meaning they
would seem very well diversified when using the first measure of portfolio composition, but
upon closer inspection when looking at the amounts invested in each asset they may keep
the majority of their money in just one or two of the assets and only have very small
amounts invested in the rest, meaning their portfolio is very unbalanced and not very well
diversified after all.
There is a significant problem in the literature in that when discussing the topic of portfolio
size and diversification they do not actually address the problem of whether a specific
portfolio is adequately diversified. Most of the empirical studies assume that portfolios are
evenly distributed when in reality it would be incredibly rare for an investor to have his
wealth evenly distributed among all available assets.
This is discussed in Woerheide and Persson (1993) and they address this problem by
evaluating five different measures of diversification. As can be seen from above the most
common measure of diversification is simply to count the number of assets in the portfolios.
However, this naïve measure has meaning only when the portfolio is evenly distributed
across all holdings, and the point of their research is to define a more effective measure
when asset holdings are not evenly distributed. They find that the Herfindahl index is the
14
most effective and is a good indicator of the degree of diversification of an unevenly
distributed portfolio. It is perhaps the most widely used measure of economic concentration.
This measure not only takes into account the number of different assets they have invested
in but also the amounts they have invested into each asset.
Therefore, in order to measure the proportion of wealth that investors have allocated across
assets, the second measure of diversification this study will be using is a complement of the
Herfindahl index. This is calculated by squaring the weightings invested in each asset and
then summing them together. Using Woerheide and Persson’s (1993) method, they minus
the index value from the Herfindahl from 1. The value can be anywhere between zero and
one. A value of one representing ultimate diversification, an investor who has allocated their
wealth across all available asset types, and a value of zero representing no diversification,
have invested 100% of their wealth in one asset. This gives a better indication on how well
diversified a portfolio is.
The formula for the diversification index is as follows:
𝑁
𝐷𝐼 = 1 − 𝐻𝐼 = 1 − ∑ 𝑊𝑖2
𝑖=1
𝐷𝐼 = 𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑖𝑛𝑑𝑒𝑥
𝐻𝐼 = 𝐻𝑒𝑟𝑓𝑖𝑛𝑑𝑎ℎ𝑙 𝑖𝑛𝑑𝑒𝑥
𝑊𝑖 = 𝑡ℎ𝑒 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 𝑜𝑓 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝑖𝑛 𝑎𝑠𝑠𝑒𝑡 𝑖 (𝑖𝑛 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑓𝑜𝑟𝑚)
𝑁 = 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑠𝑠𝑒𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜
4.4.Measures of Risk Aversion
One of the main advantages of using the DHS is that it asks respondents six statements to
determine their attitude towards risk. These statements can be seen in Table 3. They are
asked to respond to each statement indicating to what extent they agree or disagree on a
scale from 1 to 7, where 1 indicates ‘totally disagree’ and 7 indicates ‘totally agree’.
As can be seen in Bucciol and Miniace (2012) it was necessary to reverse the values for risk
questions 3, 5 and 6. Therefore, a value of 7 now declared a value of 1, a value of 6 now
declared a value of 2, a value of 5 now declared a value 3, and vice versa. This was to
ensure that all the questions are framed in such a way to seek agreement with risk aversion
sentences. Whereas, before questions 3, 5 and 6 were stated in such a way that they
instead seemed agreement with risk tolerance sentences.
15
(1)
Table 3: Self-assessed questions on risk attitude
No.
Label used in
Question
analysis
1
Guaranteed returns
“I think it is more important to have safe investments and guaranteed returns, than
to take risk to have a chance to get the higher return”
2
No investment
“I would never consider investments in shares because I find this too risky”
3
Borrowing
“if I think an investment will be profitable I am prepared to borrow money to make
4
Safe investment
“I want to be certain that my investments are safe”
5
Financial risk
“I get more and more convinced that I should take greater financial risks to
this investment”
improve my financial position”
6
Chance to gain
“I am prepared to take the risk to lose money, when there is also a chance to gain
money”
Table 3: Source: Bucciol and Miniaci (2012). Note: Answers are provided on a scale of 1 (“totally disagree”) and 7 (“totally agree”).
In the analysis, the answers to questions 3, 5, and 6 are transformed to ensure that the higher values now indicate more risk
aversion. This ensures that all the answers are now on the same scale, so that an answer of 1 indicates a risk seeking attitude,
whereas an answer of 7 indicates a risk averse attitude.
In order to reduce the 6 statements and produce a factor score for each respondent this
paper adopts the method used in Kapteyn and Teppa (2011). As stated in their paper “We
apply a factor analysis to our sample in order to determine the factor structure of these six
indicators of risk aversion. The factor analysis is a principal components analysis (PCA), with
varimax rotation, where the extraction method is based on eigenvalues greater than 1.” The
factor loadings, from the rotated component matrix, can be seen in Table A.2 in the
Appendix.
The largest factor loadings in each column are highlighted in bold face. As can be seen, in
the results for PCA1 in Table A.2, the second statement, risk question 2, has multiple
loadings (it doesn’t have a large loading on either side). This is cause for concern as it
means that the statement is neither suited for Component 1 or Component 2. Therefore,
the PCA analysis is run again, this time omitting risk statement 2. These results, PCA2, can
be seen in Table A.3 in the Appendix, and now produce clear loadings on each side.
However, this outcome is not optimal because now there are only two factors for
Component 2 but still three for Component 1. Nonetheless, this does not make much
difference when conducting the regression analysis. The regression results for PCA1 are not
included in this paper but are available upon request.
The fact that the PCA produces two factor scores is useful because they both tell us different
things. Component 1 is made up of risk statements three, five and six. These all have an
emphasis on the risk-return trade off the individual is willing to make. Whereas, Component
2 is made up of risk statements one and four which put more of an emphasis on safety. This
is made clear in Table 4.
16
Table 4: Components for Risk Aversion Statements
Component
Component 1
Risk Statements
3 – Borrowing
5 – Financial Risk
Description
6 – Chance to Gain
Emphasis on
Risk-return trade
off
Component 2
1 – Guaranteed
4 – Safe Investment
Emphasis on
Returns
Safety
This gives us an explanation for why risk statement 2 did not produce a high loading for
either component, because of the fact is does not quite fit into either of these categories, it
is has neither an emphasis on safety or the risk and return trade-off.
Component 1 will be known as RA1 and component 2 will be known as RA2.
Table 5: Statistics for Risk Aversion Components
RA1
RA2
Observations
807
807
Mean
-0.0039
0.0052
Standard Deviation
0.9981
0.9911
Variance
0.996
0.982
Range
5.5407
4.9165
Minimum
-4.0455
-3.3298
Maximum
1.4952
1.5867
As can be seen from Table 5, the scale on which the factor scores lie is hard to interpret. To
combat this problem, the cases were ranked in order of each of their component scores,
using the fractional rank method. This produced a fraction rank for each component and
generated a value between 0 and 1, which gives us a better indication of the risk aversion
for each respondent. The higher the figure for either of these values the higher the degree
of risk aversion. A value of 1 represents the highest degree of risk aversion and a value of 0
represents the lowest degree of risk aversion.. The fractional rank for Component 1 will be
known as FRA1 and the fractional rank for Component 2 will be known as FRA2.
Table 6: Statistics for Fractional Ranks of Risk Aversion Components
FRA1
FRA2
Observations
807
807
Mean
0.5095
0.5095
Standard Deviation
0.2971
0.2978
Variance
0.088
0.089
Range
0.9988
0.9802
Minimum
0.0012
0.0198
Maximum
1.0000
1.0000
17
However, care must be taken when interpreting these values. Whereas, a value of 1 may
represent the highest degree of risk aversion in our sample, it does not represent the
population as a whole, this figure is just based on the respondents in the sample.
4.5.Model Specification
Only once the measures of diversification and risk aversion have been established can the
process of building a model begin. As discussed in section 4.3 this paper will use two
different measures of diversification, Asset Types and DI. These measures will be used as
dependent variables in the model, therefore it is necessary to use two different regressions,
because both of these measures differ in their measurements.
Asset Types is a count variable, meaning a linear model would be inappropriate as it breaks
the assumption of a normal distribution, and has a Poisson distribution, as can be seen in
Figure A.1 in Appendix A. Therefore, when using Asset types as a dependent variable, a
Poisson regression is adopted. This is not applicable when using DI as the dependent
variable, as this is continuous and has a normal distribution, therefore a Multiple Linear
regression is suitable.
4.6.Variable Selection
4.6.1. The Dependent Variables
As has already been discussed, this paper will be using the two different measures of
diversification as the two dependent variables within the model and these can be seen in
Table 7, along with a brief description.
Table 7: Description of Dependent Variables
Measure
Description
Asset Types
Simply the number of different asset types that the individual holds in their portfolio.
DI
Calculated by subtracting the Herfindahl Index from 1. Gives a better indication of how
well an individual has diversified their wealth across asset types.
4.6.2. The Independent Variables
Table 8 provides an overview of the independent variables that will be used in this paper.
There are two measures of risk aversion, which were discussed in section 4.4, FRA1 and
FRA2. It also includes socioeconomic factors, four of which are dummy variables, such as
whether the respondent has completed a university education, is the respondent selfemployed and are they retired, it also includes the income of the respondents. Furthermore,
it includes demographic characteristics such as age and gender.
The predicted relationship between gender and diversification is thought to be positive. As it
is a dummy variable, were it equals 1 if the respondent is male, this means that it is
expected males will hold a more diversified portfolio than females. The reason for this being
18
that it is well documented in the literature that males are more risk tolerant than females so
are more likely to be willing to invest in riskier assets, such as stocks, and in turn hold more
diversified portfolios.
University is predicted to have a positive relationship with diversification because as
individuals gain higher education they are more likely to acquire more financial knowledge
and make smarter financial decisions. This can be seen in the literature, in particular Tin
(1998).
For individuals who are self-employed, it is predicted that the slope coefficient will be
positive because it is thought that they will have better knowledge of financial markets and
investment opportunities, this is expressed in Blume and Friend (1975).
Retired individuals are thought to be more risk averse than other investors, as they are no
longer earning disposable income, their only income is through pensions, so are predicted to
be more prudent with their asset allocation decisions, therefore only invested in a few, safe,
asset types. Thus, it is reasonable to predict that retirement will negatively affect
diversification.
The first measure of FRA1, which has an emphases on the risk and return trade off
individuals are willing to make, is predicted to have a negative slope coefficient. This is
because more risk averse investors are less likely to be prepared to take on the additional
risk of riskier assets such as stocks, so are unwilling to make the trade-off regardless of the
return, therefore are willing to hold incomplete portfolios.
The same relationship is predicted for FRA2, the second measure of risk aversion, which has
an emphasis on safety. It is believed individuals are more likely to want to invest in safer
assets that have guaranteed returns than more volatile, riskier assets, and have a
preference for safe investments.
As discussed in section 2.2, as an investor ages they are more likely to acquire financial
knowledge and better understanding of investment decisions. Therefore, the variable is
expected to have a positive coefficient.
Income is also thought to have a positive coefficient because as income rises an investor is
less likely to be deterred by factors that influence under-diversification, like transactions
costs, and have more disposable income to spread across more asset types.
19
Table 8: Description of Independent Variables
Independent Variable
Description
Gender
Dummy Variable, =1 if respondent is male, =0 is respondent is female
University
Dummy Variable, =1 is the respondent has completed a University education, =0
if the respondent has not completed a university education
Self-Employed
Dummy Variable, =1 if the respondent is Self-Employed, =0 if the respondent is
not Self-Employed
Retired
Dummy Variable, =1 if the respondent is Retired, =0 if the respondent is not
Retired
FRA1
Fractional Rank of RA1 - Component 1 from the factor analysis
FRA2
Fractional Rank of RA2 – Component 2 from the factor analysis
Age
Age of the respondent in years
Income
Net annual income of the respondent, divided by 1000, in Euros
4.6.3. The Poisson Regression Model
A Poisson regression is a class of Generalized linear models. It is applicable when the
dependent is a count variable, which can take on nonnegative integer values: {0,1,2,…}.
Especially interested in this model when y takes on relatively few values, including zero. For
our study, the dependent variable is the number of asset types held in the portfolio, which
can take a value of Y = (1,2,3,4,5,6,7). Exp(.) is always positive, this ensures that
predicted values for y will also be positive.
𝐸(𝑦|𝓍1 , 𝓍2 , … , 𝓍𝑘 ) = exp(𝛽0 + 𝛽1 𝓍1 + ⋯ + 𝛽𝑘 𝓍𝑘 ).
𝐸(𝑦|𝐺𝑒𝑛𝑑𝑒𝑟, 𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦. 𝑆𝑒𝑙𝑓 − 𝐸𝑚𝑝𝑙𝑜𝑦𝑒𝑑, 𝑅𝑒𝑡𝑖𝑟𝑒𝑑, 𝐹𝑅𝐴1, 𝐹𝑅𝐴2, 𝐼𝑛𝑐𝑜𝑚𝑒, 𝐴𝑔𝑒)
= exp(𝛽0 + 𝛽1 𝐺𝑒𝑛𝑒𝑟 + 𝛽2 𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦 + 𝛽3 𝑆𝑒𝑙𝑓 − 𝐸𝑚𝑝𝑙𝑜𝑦𝑒𝑑 + 𝛽4 𝑅𝑒𝑡𝑖𝑟𝑒𝑑 + 𝛽5 𝐹𝑅𝐴1
+ 𝛽6 𝐹𝑅𝐴2 + 𝛽7 𝐼𝑛𝑐𝑜𝑚𝑒 + 𝛽8 𝐴𝑔𝑒).
Although, this model may not be the best fit for the data because a Poisson regression
requires the data’s mean and variance to be equal, whereas this is not true for the data
used in this paper. This could have limitations for the study and mean that the outcome is
not optimal for our results. Perhaps a more suitable method to use would be a multinomial
logit regression. This is scope for future research. A negative binomial regression was used
to see if this provided a better goodness of fit but these results concluded that a Poisson
would be a better fit.
20
(2)
(3)
4.6.4. The Multiple Linear Regression Model
When using DI as a measure of diversification then a multiple regression would be suitable,
as this variable is not a count variable, and can take on any value from 0 to 1.
𝑦 = 𝛽0 + 𝛽1 𝑥1 + 𝛽2 𝑥2 + 𝛽3 𝑥3 + ⋯ + 𝛽𝑘 𝑥𝑘
(4)
𝐷𝐼 = 𝛽0 + 𝛽1 𝐺𝑒𝑛𝑑𝑒𝑟 + 𝛽2 𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦 + 𝛽3 𝑆𝑒𝑙𝑓 − 𝐸𝑚𝑝𝑙𝑜𝑦𝑒𝑑 + 𝛽4 𝑅𝑒𝑡𝑖𝑟𝑒𝑑 + 𝛽5 𝐹𝑅𝐴1 + 𝛽6 𝐹𝑅𝐴2
(5)
+ 𝛽7 𝐴𝑔𝑒 + 𝛽8 𝐼𝑛𝑐𝑜𝑚𝑒
5. Findings and Results
This section presents the regression results. Table 9 presents a summary of the statistics for
the variables used in the regressions. The results to the two regressions are presented in
Table 10, Model 1 is the Poisson regression were the dependent variable is Asset Types and
Model 2 is the Multiple Linear regression were the dependent variable is DI.
Table 9: Descriptive Statistics of Variables
Mean
Std. Deviation
Minimum
Maximum
Asset Types
1.80
.983
1
6
DI
.1894
.22998
0.00
.75
Gender
.64
.480
0
1
University
.17
.377
0
1
Self-employed
.05
.217
0
1
Retired
.35
.478
0
1
FRA1
.509519
.2971372
.0012
1.0000
FRA2
.509519
.2977964
.0198
1.0000
Income
28.29596
29.761446
-3.136
689.704
age
61.34
13.485
26
89
21
Table 10: Results from regressions
Variable
Model 1 - Asset Types (Poisson)
Model 2 - DI (Multiple Linear)
Intercept
1.665***
0.185***
(0.002)
(0.000)
1.126*
0.032*
(0.053)
(0.062)
1.218***
0.082***
(0.003)
(0.000)
1.239*
0.093***
(0.051)
(0.009)
0.921
-0.028
(0.288)
(0.215)
0.656***
-0.178***
(0.000)
(0.000)
0.904
-0.033
(0.272)
(0.200)
1.001
0.001***
(0.182)
(0.008)
1.003
0.001
(0.211)
(0.198)
Gender
University
Self-Employed
Retired
FRA1
FRA2
Income
Age
R2
0.137
Adjusted R
0.128
2
Log-Likelihood
-1130.323
Observations
805
805
Table 10: Model 1 is the Poisson regression model, when the dependent variable is the number of different asset types held in
the portfolio. Model 2 is the Multiple Linear regression model, when the dependent variable is DI. The coefficients presented for
Model 1 are the exponential parameter estimates, where a β<1 is an inverse relationship, β=1 no relationship and β>1 is a
positive relationship. Standard errors presented in parenthesis. * Level of significance: p-value <0.10. ** Level of significance:
p-value <0.05. *** Level of significance: p-value <0.01.
Model 1:
𝐸(𝑦|𝐺𝑒𝑛𝑑𝑒𝑟, 𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦, 𝑆𝑒𝑙𝑓 − 𝐸𝑚𝑝𝑙𝑜𝑦𝑒𝑑, 𝑅𝑒𝑡𝑖𝑟𝑒𝑑, 𝐹𝑅𝐴1, 𝐹𝑅𝐴2, 𝐼𝑛𝑐𝑜𝑚𝑒, 𝐴𝑔𝑒)
(6)
= exp(1.665(𝐶) + 1.126(𝐺𝑒𝑛𝑑𝑒𝑟) + 1.218(𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦) + 1.239(𝑆𝑒𝑙𝑓 − 𝐸𝑚𝑝𝑙𝑜𝑦𝑒𝑑)
+ 0.921(𝑅𝑒𝑡𝑖𝑟𝑒𝑑) + 0.656(𝐹𝑅𝐴1) + 0.904(𝐹𝑅𝐴2) + 1.001(𝐼𝑛𝑐𝑜𝑚𝑒) + 1.003(𝐴𝑔𝑒)).
Model 2:
𝐷𝐼 = 0.185(𝐶) + 0.032(𝐺𝑒𝑛𝑑𝑒𝑟) + 0.082(𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦) + 0.093(𝑆𝑒𝑙𝑓 − 𝐸𝑚𝑝𝑙𝑜𝑦𝑒𝑑) − 0.028(𝑅𝑒𝑡𝑖𝑟𝑒𝑑)
− 0.178(𝐹𝑅𝐴1) − 0.033(𝐹𝑅𝐴2) + 0.001(𝐴𝑔𝑒) + 0.001(𝐼𝑛𝑐𝑜𝑚𝑒)
22
(7)
5.1.Empirical Results
The coefficient for Gender was found to be positive and significant in both models at the 1%
level. This is in line with the prediction made that males are more likely to hold better
diversified portfolios than females. This is consistent with Tin (1998) who find that gender is
statistically significant in portfolio decisions
University was found to be significant at 1% level in both models. The positive relationship
indicates that respondents who have a university education are likely to hold more asset
types and have a more diversified portfolio. This supports the prediction made and is
consistent with the findings of Barasinska et al. (2012).
Self-employed provided a positive coefficient and was significant at 10% level in Model 1
and 1% in Model 2. This positive relationship supports the expectations and is consistent
with the findings of Barasinska et al. (2012) and Blume and Friend (1975) who also find
that self-employed individuals tend to hold more diversified portfolios.
Retired was found to have a negative effect on both measures of diversification, but is not
significant in either model.
The coefficient for Income was positive, which is in line with the predictions made, and
highly significant in Model 2, the 1% level, but not significant in Model 2. This may suggest
that income has a significant effect on diversification when measuring it in terms of how
well an individual as distributed their income across asset types but not when simply looking
at the number of asset types held. This supports the finding of Kapteyn and Teppa (2011)
who find that diversification increases with income.
Age provided a positive relationship but was not significant. This is somewhat surprising as
there was a lot of empirical literature suggesting that age has a big effect on the
composition of portfolios. An explanation for this could be that this study over represents
the older population as the mean age 61, so is therefore not representative of the
population as a whole.
The coefficients for FRA1 are significant at the 1% level in both models. The negative
relationship supports the hypothesis that as risk aversion increases the willingness to hold a
fully diversified portfolio decreases. FRA1 is for Component 1 of the risk aversion questions,
which has an emphasis on the risk-return trade off an individual is willing to make.
Therefore, this indicates to us that as risks increases individuals are not willing to sacrifice
their wealth and make the risk-return trade-off for higher returns, in order to diversify their
portfolio. This is consistent with the literature, such as Barasinska et al. (2012).
FRA2 was also found to have a negative coefficient but was not significant in either model.
This is interesting because it seems that in terms of safety, Component 2, this does not
have an impact on diversification, whereas Component 1 does.
23
6. Conclusion
The results of this analysis suggest that all three factors, socioeconomic, demographic and
risk attitudes, play some part in portfolio allocation decisions. The two measures of
diversification show similar results indicating that even when using simple measures, such
as simply counting the number of assets an individual holds, is just as adequate at
measuring diversification compared to when using the more sophisticated measure, the
complement of the Herfindahl index.
The main hypothesis of this investigation was to determine the relationship between an
individual’s risk aversion and their willingness to hold more asset types. Consistent with
previous studies (Barasinska et al., 2012; Kelly, 1995) the model finds that the relationship
is negative, when studying risk aversion in terms of how willing an individual is to make the
risk-return trade off, in regard to financial assets. This is in line with the hypothesis.
However, it is interesting how the second measure of risk aversion does not have any
significance on an investor’s willingness to diversify. This measure focuses on an individual’s
attitude towards safety, whether they prefer safe investments with guaranteed returns. It
seems that individuals put more emphasis on the increased gain they are likely to receive
from the increase in risk, then they do on the safety aspect, such as whether an investment
is safe and has guaranteed returns.
The results support the hypothesis that socioeconomic factors are statistically significant in
portfolio decisions. However, the coefficient for Retired was the only outlier, as it was not
significant. The reason for this could be because the sample over represented the older
population, with a mean age of approximately 61, so was therefore bias in that respect. This
could explain why Age also produced an insignificant coefficient. The other demographic
variable included in the models was Gender, which provided a significant result for both
results. These results support the literature in that socioeconomic and demographic
characteristics have a significant influence on portfolio decisions (Barasinska et al., 2012;
Uhler and Cragg, 1971; Tin, 1998).
This paper focuses on the determinants of what affects an individual’s willingness to
diversify. Thus providing further understanding on the relationship between risk aversion
and the composition of household portfolios, along with other socioeconomic and
demographic factors. A broader sample of respondents, which is more representative of the
population as a whole, would provide further insight into the relationships associated with
diversification.
The Model could be adapted to adopt a multinomial logit model, instead of Poisson
regression model, when using Asset Types as the dependent variable, as this may be a
better fit for the data, because of the reasons mentioned in section 4.6.3, therefore
producing a better overall goodness of fit. When using DI as the dependent variable, a Tobit
24
model could be used, as this may also be a better fit to the data and improve the goodness
of fit. It would also be interesting to add wealth into the model, in particular real estate, to
see the impact this has an the composition of household portfolios. This is scope for future
research to examine how and if the relationships differ once the model is changed.
This paper highlights the role of risk aversion on the composition of household portfolios,
but it is evident that it should be considered complementary to other factors such as
socioeconomic and demographic characteristics. It gives greater understanding to how
individuals make their investment decisions and can demonstrate to Governments how they
can influence individuals to make better asset allocation decisions and utilise their
retirement wealth more efficiently. It becomes apparent from the data that the majority of
households hold very under-diversified portfolios, containing only one or two assets, so are
therefore unwilling to fully diversify their portfolio. Policy makers should look at educating
individuals about the benefits of diversification and how to be more efficient at managing
their retirement wealth. Furthermore, policy makers ought to consider the impacts of
various
socioeconomic
and
demographic
variables
on
formulating policies on issues regarding portfolio decisions.
25
the
financial
markets
when
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Appendix A
Table A.1: Assets in the Dataset
Checking Accounts
Employer-sponsored saving accounts
Savings/deposit accounts
Deposit books
Single-premium insurance policies
Savings or endowment insurance policies
Mutual funds
Bonds
Shares in companies
Money lent out to friends/family
Business equity (professions)
Business equity (self-employed)
Table A.2: PCA1: Rotated Component Matrixa
Component
1
2
.050
.838
I would never consider investments in shares because I find this too risky
.501
.482
if I think an investment will be profitable, I am prepared to borrow money to make this
.685
.042
I want to be certain that my investments are safe
.076
.842
I get more and more convinced that I should take greater financial risks to improve my
.797
.074
.785
.249
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 returns
investment
financial position
I am prepared to take the risk to lose money, when there is also a chance to gain money
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization.a
a. Rotation converged in 3 iterations.
29
Table A.3: PCA2: Rotated Component Matrixa
Component
1
I think it is more important to have safe investments and
2
.087
.866
.720
-.006
I want to be certain that my investments are safe
.104
.859
I get more and more convinced that I should take greater
.822
.089
.769
.210
guaranteed returns, than to take a risk to have a chance to
get the highest possible returns
if I think an investment will be profitable, I am prepared to
borrow money to make this investment
financial risks to improve my financial position
I am prepared to take the risk to lose money, when there is
also a chance to gain money
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization.a
a. Rotation converged in 3 iterations.
Figure A.1
30
Appendix B
Article structure: Journal of Financial Economics
Subdivision - numbered sections
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31
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Hermalin, B., Weisbach, M., 1995. Endogenously chosen boards and their monitoring of the CEO.
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Williamson, O., 1986. Economic Organization: Firms, Markets and Policy Control. New York
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Smith, C., 1979. Application of option pricing analysis. In: Bicksler, J. (Ed.), Handbook of Financial
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32