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.

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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 SchoolNottingham Trent University

Summer 2014

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

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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 towards risk. Therefore, the relationship between risk aversion and the probability of holding

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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 under-diversified portfolios.

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

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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 under-diversification is difficult to reconcile with conventional portfolio theory. They present evidence that transaction costs clearly go some way to explaining the incidence of under-diversification 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.

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

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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.

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.

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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 under-diversify 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)

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

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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 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

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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 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

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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 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 Methodology4.1.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 so-called set-top box with a built-in internet connection and, if necessary a television set as

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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.

Table 1: Statistics of Respondents

Age Income (€)

Mean 61.34 28295.94Standard Deviation -0.258 29761.445Minimum 26 -3136Maximum 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 Assets11

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 AccountsEmployer-sponsored saving accountsSavings/deposit accountsDeposit books

2 Insurance Policies Single-premium annuity insurance policiesSaving 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)

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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 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

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1 2 3 4 5 6 70

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0.00%

10.00%

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Total Number of Different Asset Types Held

Frequency Percentage

Number of Different Assets Held

Freq

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Perc

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Figure 1: Frequency of Different Asset Types HeldAccounts Policies Mutual Funds Bonds Shares Money lent out

Business Equity

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Frequency of Different Asset Types Held

Different Asset Types

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Figure 2: Total Number of Different Asset Types Held

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 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

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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:

DI=1−HI=1−∑i=1

N

W i2

DI=DiversificationindexHI=Herfindahl index

W i=the proportion of portfoliomarket valueinvested∈asset i (¿decimal form )

N=thenumber of assets∈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.

Table 3: Self-assessed questions on risk attitude

No. Label used in analysis

Question

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

this investment”

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

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(1)

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”

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.

Table 4: Components for Risk Aversion Statements

Component Risk Statements Description

Component 1 3 – Borrowing 5 – Financial Risk 6 – Chance to Gain Emphasis on Risk-return trade off

Component 2 1 – Guaranteed Returns

4 – Safe Investment Emphasis on Safety

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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.

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 807Mean -0.0039 0.0052Standard Deviation 0.9981 0.9911Variance 0.996 0.982Range 5.5407 4.9165Minimum -4.0455 -3.3298Maximum 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 807Mean 0.5095 0.5095Standard Deviation 0.2971 0.2978Variance 0.088 0.089Range 0.9988 0.9802Minimum 0.0012 0.0198Maximum 1.0000 1.0000

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.

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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 Selection4.6.1. 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 self-employed 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 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).

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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.

Table 8: Description of Independent Variables

Independent Variable Description

Gender Dummy Variable, =1 if respondent is male, =0 is respondent is femaleUniversity Dummy Variable, =1 is the respondent has completed a University education,

=0 if the respondent has not completed a university educationSelf-Employed Dummy Variable, =1 if the respondent is Self-Employed, =0 if the respondent is

not Self-EmployedRetired Dummy Variable, =1 if the respondent is Retired, =0 if the respondent is not

RetiredFRA1 Fractional Rank of RA1 - Component 1 from the factor analysisFRA2 Fractional Rank of RA2 – Component 2 from the factor analysisAge Age of the respondent in yearsIncome Net annual income of the respondent, divided by 1000, in Euros

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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 , FRA 2, Income , Age )=exp (β0+β1Gener+β2University+β3Self−Employed+β4 Retired+β5FRA 1+ β6 FRA 2+ 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.

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

DI=β0+ β1Gender+β2University+β3Self−Employed+β4 Retired+β5FRA 1+β6FRA 2+β7 Age+β8 Income

5. Findings and Results

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(5)

(4)

(3)

(2)

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 6DI .1894 .22998 0.00 .75Gender .64 .480 0 1University .17 .377 0 1Self-employed .05 .217 0 1Retired .35 .478 0 1FRA1 .509519 .2971372 .0012 1.0000FRA2 .509519 .2977964 .0198 1.0000Income 28.29596 29.761446 -3.136 689.704age 61.34 13.485 26 89

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)Gender 1.126* 0.032*

(0.053) (0.062)University 1.218*** 0.082***

(0.003) (0.000)Self-Employed 1.239* 0.093***

(0.051) (0.009)Retired 0.921 -0.028

(0.288) (0.215)FRA1 0.656*** -0.178***

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(0.000) (0.000)FRA2 0.904 -0.033

(0.272) (0.200)Income 1.001 0.001***

(0.182) (0.008)Age 1.003 0.001

(0.211) (0.198)

R2 0.137Adjusted R2 0.128Log-Likelihood -1130.323Observations 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 , FRA 1, FRA 2, Income , Age )=exp (1.665 (C )+1.126 (Gender )+1.218 (University )+1.239 (Self−Employed )+0.921 (Retired )+0.656 (FRA1 )+0.904 (FRA 2 )+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 (FRA 1 )−0.033(FRA 2)+0.001(Age)+0.001(Income )

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).

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(7)

(6)

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.

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

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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 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

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their retirement wealth. Furthermore, policy makers ought to consider the impacts of various socioeconomic and demographic variables on the financial markets when formulating policies on issues regarding portfolio decisions.

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Appendix A

Table A.1: Assets in the Dataset

Checking AccountsEmployer-sponsored saving accountsSavings/deposit accountsDeposit booksSingle-premium insurance policiesSavings or endowment insurance policiesMutual fundsBondsShares in companiesMoney lent out to friends/familyBusiness equity (professions)Business equity (self-employed)

Table A.2: PCA1: Rotated Component Matrix a

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Component1 2

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

.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 investment

.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 financial position

.797 .074

I am prepared to take the risk to lose money, when there is also a chance to gain money .785 .249

Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization.a

a. Rotation converged in 3 iterations.

Table A.3: PCA2: Rotated Component Matrix a

Component1 2

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

.087 .866

if I think an investment will be profitable, I am prepared to borrow money to make this investment

.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 financial risks to improve my financial position

.822 .089

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I am prepared to take the risk to lose money, when there is also a chance to gain money

.769 .210

Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization.a

a. Rotation converged in 3 iterations.

Figure A.1

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Appendix BArticle structure: Journal of Financial Economics

Subdivision - numbered sections Divide your article into clearly defined and numbered sections. Subsections should be numbered 1.1 (then 1.1.1, 1.1.2, ...), 1.2, etc. (the abstract is not included in section numbering). Use this numbering also for internal cross-referencing: do not just refer to 'the text'. Any subsection may be given a brief heading. Each heading should appear on its own separate line.

Introduction State the objectives of the work and provide an adequate background, avoiding a detailed literature survey or a summary of the results.

Appendices If there is more than one appendix, they should be identified as A, B, etc. Formulae and equations in appendices should be given separate numbering: Eq. (A.1), Eq. (A.2), etc.; in a subsequent appendix, Eq. (B.1) and so on. Similarly for tables and figures: Table A.1; Fig. A.1, etc.

Abstract A concise and factual abstract is required. The abstract should state briefly the purpose of the research, the principal results and major conclusions. An abstract is often presented separately from the article, so it must be able to stand alone. For this reason, References should be avoided, but if essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself.

Keywords Immediately after the abstract, provide a maximum of 6 keywords, using American spelling and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field may be eligible. These keywords will be used for indexing purposes.

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Footnotes Footnotes should be used sparingly. Number them consecutively throughout the article, using superscript Arabic numbers. Many wordprocessors build footnotes into the text, and this feature may be used. Should this not be the case, indicate the position of footnotes in the text and present the footnotes themselves separately at the end of the article. Do not include footnotes in the Reference list. Table footnotes Indicate each footnote in a table with a superscript lowercase letter.

References

Citation in text Please ensure that every reference cited in the text is also present in the reference list (and vice versa). Any references cited in the abstract must be given in full. Unpublished results and personal communications are not recommended in the reference list, but may be mentioned in the text. If these references are included in the reference list they should follow the standard reference style of the

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journal and should include a substitution of the publication date with either 'Unpublished results' or 'Personal communication'. Citation of a reference as 'in press' implies that the item has been accepted for publication.

Reference Style Citations appear in the text as follows. Note that more than two authors are separated by commas, and multiple parenthetical citations are separated by semicolons:

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The procedure in French, Schwert, and Stambaugh (1987) ...

... as discussed in other studies (see, e.g., Smith and Watts, 1992; Lewellen, Loderer, and Martin, 1987) ...

Studies such as Coughlan and Schmidt (1985), Warner, Watts, and Wruck (1988), Weisbach (1988), Jensen and Murphy (1990a), and Murphy and Zimmerman (1991) have found ...

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The reference list follows any appendices to the paper. Everything in the list of references should be cited in the text, with no discrepancies in the spelling of the authors' names or in the date of publication. In the reference list, there are no quotation marks, no underlines, and no italics. The authors' last names and first initials are used. Only the first word of an article title is capitalized. Book and journal titles take normal initial capitals. The reference list is in alphabetical order by author, and multiple works by the same author are in chronological order. A standard reference is formatted as follows:

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Hermalin, B., Weisbach, M., 1995. Endogenously chosen boards and their monitoring of the CEO. Unpublished working paper. University of California, Berkeley.

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Williamson, O., 1986. Economic Organization: Firms, Markets and Policy Control. New York University Press, New York.

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Smith, C., 1979. Application of option pricing analysis. In: Bicksler, J. (Ed.), Handbook of Financial Economics. North Holland, Amsterdam, pp. 80-121.

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