Effects of risk aversion on securities portfolio performance in underdeveloped capital markets: the case of the capital market of Bosnia and Herzegovina

Abstract The main goal of this article is to examine risk aversion impact on securities portfolio performance in underdeveloped capital markets. For the purpose of this research, portfolio performance was taken as a dependent variable, whereas investors’ attitude towards risk was considered as an independent variable. The analysis results have revealed that, ceteris paribus, an increase in risk aversion leads to a decrease in expected return and the creation of more superior securities portfolio. The article is expected to produce useful pieces of information which might be helpful for investors in the process of creating their portfolios in underdeveloped capital markets.


Introduction
As well-known, the trade-off between risk and return is central to the theory of finance, where one of the central tenets is that investors expect higher return for taking risk. Lintner (1965) and Mossin (1966) are one of the first scholars who described a relationship between risk and expected return by developing the Capital Asset Pricing Model (CAPM) which outlines that it is only systematic risk that is rewarded by the market. Fama and MacBeth (1973) demonstrated that, on average, there seems to be a positive trade-off between return and risk, with risk measured from the portfolio viewpoint. They also pointed out that, in making a portfolio decision, an investor should assume linear relationship between a portfolio expected return and risk. Black, Jensen, and Scholes (1972), Fama and MacBath (1974), as well as Friend and Blume (1970) found out that, while there is a positive relationship between beta and average excess return, there are significant deviations from the predicted relationship. Many other scholars, e.g., Bollerslev, Engle, and Wooldridge (1988), Harvey (1989), Baillie and DeGennaro (1990), Campbell and Hentschel (1992), Ghysels, Santa-Clara, and Valkanov (2005), Ludvigson and Ng (2007), etc. have also reported a positive risk-return trade-off relation. In contrast, Breen, Glosten, and Jagannathan (1989), Nelson (1991), Glosten, Jakannatha and Runkle (1993), Brandt and Kang (2004), etc. suggested a ABSTRACT The main goal of this article is to examine risk aversion impact on securities portfolio performance in underdeveloped capital markets. For the purpose of this research, portfolio performance was taken as a dependent variable, whereas investors' attitude towards risk was considered as an independent variable. The analysis results have revealed that, ceteris paribus, an increase in risk aversion leads to a decrease in expected return and the creation of more superior securities portfolio. The article is expected to produce useful pieces of information which might be helpful for investors in the process of creating their portfolios in underdeveloped capital markets. KEYWORDS securities portfolio; investor's attitude towards risk; underdeveloped capital market strong negative trade-off. In short, estimating expected returns from time series of realised stock return data is very difficult, as summarised by Merton (1980, p. 326) 'to attempt to estimate the expected return on the market is to embark on a fool's errand. ' Expected return determines the risk premium which represents the compensation investors require for taking on the additional risk. As risk premium increases, so does the risk aversion. According to Tobin (1958) and Pratt (1964) the risk premium on the market portfolio was linked to investors' risk aversion. Risk premium has to remain positive because it rewards investors for taking the risk. However, the literature also confirms the evidence of negative risk premium, documented by Boudoukh, Richardson, and Smith (1993), Ostdiek (1998), Arnott and Bernstein (2002), Arnott and Ryan (2001), Bakshi and Kapadia (2003), etc. The literature dealing with the relationship between portfolio selection and risk aversion shows a variety of approaches. Although there has been extensive research into the empirical and theoretical aspects of tradeoff between risk and return, most of these studies usually focus on the well-developed capital markets. Taking into account the above-mentioned, the authors decided to select the topic for this article due to the fact that, according to the authors' best knowledge, very few publications dealing with the issue of the trade-off between risk and return in underdeveloped capital markets are found in the existing literature.
The main goal of this article is to examine effects of investor's attitude towards risk on securities portfolio performance in underdeveloped capital markets. But, why should this kind of research be important? First of all, the examination of the effects of investors' attitude towards risk on securities portfolio performance and structure could result in gathering some useful pieces of information which might be beneficial for investors in creating their portfolios in underdeveloped capital markets. Furthermore, due to many specific features of underdeveloped capital markets (such as: low market capitalisation, poor liquidity and turnover, weak legal protection for minority shareholders, low correlation with developed and emerging capital markets, etc.), the results of this research might be recognised as useful guidelines which could assist investors to improve their investment strategies. The starting point of this research study is related to addressing the following question: How does the investor's risk aversion impact portfolio performance in case of underdeveloped capital market? With regard to the research question, the central research hypothesis has been defined as follows: Hypothesis: Increase in risk aversion leads to decrease in expected return and to creation of more superior securities portfolio as well.
The main limitations of this study are related to the shorter available financial time series in newly formed capitalistic economy and missing data (due to the lack of collective records on levels of securities offerings issues).
The article is organised as follows. After introduction, the following section gives a brief outline of theoretical background that is relevant to the research. The article moves on describing methodology, after which follows the discussion of the results. In the end a brief summary of the main conclusions is given in accordance with the analysis findings.

Theoretical framework
As well-known, investors' risk preferences reflected in asset allocation choices have been widely discussed in literature both theoretically and empirically. It is probably true to say that Friedman and Savage (1948) are one of the first scholars who tried to conceptualise investor's attitude towards risk, i.e., risk aversion by concluding that investors must be paid a premium to induce them to undertake moderate risk, instead of subjecting themselves to either small or larger risks. According to Friedman and Savage (1948), the main factor that gradually changes the investor's attitude towards risk is actually the size of their wealth.
Risk can be defined as a difference between realised and expected return. Therefore, the risk averse investor is the one who dislikes risk and requires a higher rate of return as a reward to buy riskier securities. On the other hand, risk neutral investor is indifferent between investing in risk-free and risky investment, under the presumption of the same expected return. Risk-lovers, however, acquire investments of higher risk with a lower expected return. The first notable efforts in understanding the factors that influence the degree of risk aversion were made by Pratt (1964) and Arrow (1965). They pointed out that, for the certain amount of risk, an investor with high risk aversion demands much larger risk premium compared to the one required by the risk-lovers. How will an investor behave depends on how he interprets a risk-return trade-off. This 'interpretation' is measured by investor's utility curve. Risk aversion, which has been defined by absolute risk aversion coefficient, is also known as Arrow-Pratt absolute risk aversion. This coefficient at point x is defined as: where U , (x) and U ,, (x) denotes the first and second derivative of utility function, respectively. Utility functions with constant absolute risk aversion coefficient are called CARA utility functions. However, it is often assumed that most investors have constant relative risk aversion. Utility functions with constant relative risk aversion coefficient are called CRRA utility functions. Arrow (1971) defines a measure of relative risk aversion which is invariant to positive linear transformations and involves only the first two derivatives of the utility function: Arrow (1971) hypothesises that R (x) is an increasing function of wealth (Graves 1979, p. 205) Basically, utility functions give us a way to measure investor's preferences for wealth, as well as the amount of risk they are willing to undertake in order to attain greater wealth. This makes it possible to develop a theory of portfolio optimisation, which implies that utility theory lies at the heart of modern portfolio theory (MPT). According to Markowitz (1959) rational risk averse investors expect either a maximum return for a given level of risk, or a given return for minimum risk. In line with it, 'the most important aspect of Markowitz's work was to show that it is not a security's own risk that is important to an investor, but rather the contribution the security makes to the variance on his entire portfolio' (Rubinstein 2002(Rubinstein , p. 1042.
Since this research deals with the effects of the investor's risk aversion on portfolio performance in case of underdeveloped capital market, the research is expected to show that an increase in risk aversion leads to decrease in expected return and to creation of more superior securities portfolio. Figure 1 illustrates this theoretical concept. (1) The main premise behind our theoretical concept is that there is a negative trade-off between risk aversion and expected portfolio return and risk. Canner, Mankiw, and Weil (1997) used similar approach in their attempt to describe the influence of an investor's attitude toward risk on the composition of his portfolio.

Research site
This research is conducted focusing on the analysis of the capital market of Bosnia and Herzegovina. This capital market is characterised by territorial division, the incompatibility of entity institutions and legal regulations which negatively affect the investment climate and the liquidity of securities. MSCI Inc. (2013) provides an evaluation of the four market accessibility criteria, as follows: (1) openness to foreign ownership; (2) ease of capital inflows/ outflows; (3) efficiency of the operational framework; and (4) stability of the institutional framework. In case of capital market of Bosnia and Herzegovina, improvements are needed especially in case of the third criteria, i.e., information flow, clearing and settlement, trading, transferability 1 and short selling (see Appendix A). According to these criteria, the capital market of Bosnia and Herzegovina is characterised as the so called standalone market, which 'includes potential candidates for the MSCI Frontier Markets Indices that currently do not meet the minimum liquidity requirements as well as markets that are currently partially or fully closed to foreign investor. Furthermore, stocks lending and short selling are activities that are either not developed or completely prohibited in all standalone market countries and the summary does not highlight these issues on a country -by country basis' (MSCI Inc. 2013, p. 36). The capital market of Bosnia and Herzegovina consists of two independent territorial regions that have separate stock exchanges, i.e., the Sarajevo Stock Exchange (SASE) which operates in the Federation of Bosnia and Herzegovina and the Banja Luka Stock Exchange (BLSE) which operates in the Republika Srpska.

Variables
The investor's attitude towards risk measured by previously explained relative risk aversion coefficient R (x) is considered as an independent variable. A dependent variable is portfolio performance measured by: (1)  Excess Mu and expected excess growth rate are used as an indicator for an average return measures. Excess Mu ( e p ) is defined as: where μ p refers to portfolio Mu, r f denotes risk-free rate and d p is called portfolio dividend yield. Expected excess growth rate ( e p ) is defined as: where 2 p refers to portfolio volatility. Information ratio (I) is taken as an indicator of portfolio performance, and is defined by the following expression: where R e min is minimum acceptance excess rate. Sharpe ratio is a particular case of information ratio corresponding to R e min = 0. Volatility, value at risk (VaR) and conditional value at risk (CVaR) are used as risk indicators. Portfolio VaR is defined as a maximum portfolio loss over a given time interval at a given level of statistical confidence. This measure of portfolio risk is defined by following expression (Modern Investment Technologies 2006-2008: where r e [0,T] is portfolio excess simple return over [0,T] period. On the other hand, portfolio CVaR is conditional expectation of losses beyond VaR. Therefore, it is basically an average value of (1 − )100% of highest losses.

Sample
Given the large number of available but not actively traded securities, a subset of the most actively and highest capitalised stocks traded on SASE and BLSE 2 was used for the purpose of this research. These securities must have sufficiently large daily trading volumes to qualify for inclusion in a portfolio.

Risk free rate of return
Due to overall complex political and economic situation 5 , the government of Bosnia and Herzegovina still hasn't issued treasury bills. There have been some more or less successful attempts of treasury bills issue on SASE and BLSE separately, but the 'real' risk-free securities are still missing. As Mossin (1966) pointed out, to identify riskless asset as cash may be quite suggestive. Lintner (1965, p. 15) also assumed that 'each individual investor can invest any part of his capital in certain risk free asset, i.e., deposits in insured savings accounts all of which pay interest at a common positive rate' . In his reflections on the meaning of risk free Fisher (2013, p. 68) claims that 'returns on cash and cash equivalents are quite a handsome rate of return for something that is our best proxy for risk free' . This is also in accordance with the Society of Actuaries Committee on Finance Research (2009, p. 78) where 'the only safe harbour for assets in periods of crisis may be cash, short-term government bonds, and gold' . For the purpose of this study, and due to lack of treasury bills issue, fixed term deposit interest rate has been equalled with a proxy of risk-free rate of return. Based on the passive deposit money banks interest rate, given at the annual level i y , this rate at the monthly level i m is recalculated as follows:

Models for portfolio optimisation
If we assume that utility function of the investor belongs to the CRRA class and that the relative risk aversion coefficient value is known and equal to R (x), then the portfolio, that is optimal relative to a CRRA utility function, is obtained by the maximisation (over the set of all admissible portfolios) of one of the following utility function (Modern Investment  Technologies 2006-2008, p. 21): where ⃗ e denotes excess Mu vector, Ω stands for covariance matrix and ⃗ denotes the vector of constant portfolio weights, corresponding to risky securities. Upper asterisk ( * ) denotes trasposition operation. According to our optimality criterion and different portfolio structure, where i , i = 1, n and π 0 denotes weights in risky and riskless asset, respectively, the following four models have been defined and presented in Table 1. M 1 and M 2 models imply that the investor doesn't want to invest in riskless asset, whereas models M 3 and M 4 illustrate the possibility for investing in riskless asset. Although the original model given by Markowitz (1952) excludes short sales, in this article all the models were analysed with a possibility of short selling included (models M 2 and M 4 ).

Research design
The research is organised in three phases. The first phase brings an analysis of some basic parameters of descriptive statistics and coefficients of correlation. These results have been considered of immense importance in terms of proper understanding of specificities of the observed financial time series. In the second phase, previously defined mathematical models were used for the purpose of conducting a comparative analysis of the portfolio performance and developing structure for each model respectively at a certain value of relative risk aversion coefficient. In the last phase, the empirical results of the research have been presented.
By applying Augmented Dickey-Fuller test of unit roots, and taking into account that statistics of the test in its absolute form is lower than theoretically critical values for all three significance levels (1%, 5% and 10%), null hypothesis H 0 : the series contains a unit root has also been rejected.
According to Grigoletto and Lisi (2009), and from a financial perspective, skewness is crucial since it may be considered as a measure of risk. Positive skewness means that the distribution has a long right tail, whilst negative skewness implies that the distribution has a long left tail.
In line with it, Kim and White (2004) highlight that, if investors prefer right-skewed portfolios then, for equal variance, one should expect a 'skew premium' to reward investors willing to invest in left-skewed portfolios. In a large number of analysed variables (BIGFRK3, BSNFRK2, ELGJR, FDSSR, JHKP-R-A, MIGFRK2, NOVB-R-E, TLKM-R-A) negative skewness indicates that there was a substantial probability of a big negative return.
On the other hand, kurtosis measures the degree to which extreme outcomes in the 'tails' of a distribution are likely. The normal distribution has a kurtosis of 3 (mesokurtic). Kurtosis, except for JHKP-R-A and TLKM-R-A, points out leptokurtosis for all selected variables. Furthermore, excess kurtosis is a measure of the fatness of the tails of kurtosis where there is higher likelihood of large gains or large losses on an investment. Excess kurtosis indicates that the volatility of the investment is highly volatile. Excess kurtosis has been in particular detected in case of ELGJR and FDSSR, meaning that investors may face higher likelihood of large gains or large losses when in investing in these stocks (See Appendix C).
Knowing the correlations between the returns of securities is important for the process of allocating investments among them. Therefore, the examination between selected securities seems to be the next logical step. Correlation between two variables indicates the level to which those variables move together. The sample correlation coefficient r is an estimate of the population correlation coefficient ρ.

Model performance analysis
Prior to discussing the analysis of the optimisation models results, it is important to outline that, taking into account previously-mentioned complex characteristics of the capital market of Bosnia and Herzegovina fixed term deposit interest rate were used as a proxy of risk-free rate of return.
Passive deposit money banks interest rate, on an annual basis, for December 2012, was 2.97% (CBBH Governing Board, 2012). Accordingly, equivalent monthly interest rate is: i m = 100 12 √ 1 + 2.97 100 − 1 = 0.244193481%. In line with the main goal of this research we analysed the sensitivity of the model to the various values of R (x). Among many others factors, Schooley and Drecnik (1996) have shown that investment in risky assets is significantly related to attitude toward risk taking. Since larger R (x) implies more risk aversion, we arbitrarily chose its values (2, 4, 6, 8 and 10) and incorporated it into the CRRA utility function that was our optimality criteria.
By applying previously defined mathematical models, 20 portfolios have been detected as a result of the optimisation process. Moreover, in the further process of portfolio optimisation and performance analysis, the sample was downsized only to those issuers that had positive average return (see Appendix B). General model performance analysis for all 20 portfolios is given in Table 2. Estimations were carried out by using Smartfolio (Version 3.0.88) software.
The results presented in Table 2 clearly lent some support to our hypothesis that, ceteris paribus, an increase in risk aversion leads to decrease in expected return and the creation of more superior securities portfolio. In case of all analysed models, average return measured by excess Mu and expected excess growth rate decreases as investor becomes more averse. In examining investor attitudes towards risk uncertainty as well as their reactions to market turmoil, Corter (2010) came up with the similar conclusion, i.e., higher levels of risk tolerance lead to riskier portfolios, and thus to higher exposure to losses. Liu and Xu (2010) have also revealed that in the absence of complicated constraints or objective terms, the return, risk, and utility of the optimal mean-variance portfolio decrease as the risk aversion increases.
Also, as Canner et al. (1997) pointed out, since the set of investment opportunities is not constant over time, investors should attempt to hedge their portfolios against adverse shifts in the asset-return distribution. Although the goal of this article was to examine the effects of investor's attitude towards risk on securities portfolio performance, it would also be necessary to shed some light on these 'abnormal' expected average returns (in case of models M 2 and M 4 ) presented in Table 2. Put simply, these returns may be explained by the fact that the securities listed on the SASE and BLSE are basically very risky and, consequently, generate high expected return. Under the assumptions of M 2 and M 4 models, short selling is not prohibited, but in reality, capital market of Bosnia and Herzegovina still doesn't have sufficiently developed infrastructure for short selling in the first place (see Appendix A). That is why it is probably wise not to include short selling in models when analysing portfolio performance on underdeveloped markets. However, this question of 'abnormal' expected average returns still remains open for some other research.
Also, based on the Sharpe ratio for each portfolio, it can be concluded that, ceteris paribus, an increase in risk aversion leads to creation of more superior securities portfolios. Range  (Table 2). Furthermore, if all issuers are ranked based on the excess kurtosis, it can be concluded that, as relative risk aversion increases proportion of highly risky investments in portfolio decreases (see Appendix C). Portfolio structure definitely supports this statement (see Appendix E). For example, excess kurtosis is particularly noticed in case of BSNLR, JPESR and TCMKR (see Appendix C), meaning that investors may face higher likelihood of large gains or large losses when in investing in these stocks. In addition, the portfolio structure also confirms that as relative risk aversion increases proportion of these highly risky securities decreases.
This conclusion is valid in case of all models analysed. On the assumption of the M 2 model, as risk aversion increases, the proportion of BSNLR goes from -62.68 for R (x) = 2 to -12.37 for R (x) = 10. JPESR and TCMKR are also classified as a highly risky investment. On the assumption of the same model (M 2 ), their portfolio proportion changes from 6.42 for R (x) = 2 to 2.74 for R (x) = 10 (JPESR) and from 1.15 for R (x) = 2 to 0.22 for R (x) = 10 (TCMKR) (see Appendix E).
The analysis results have also confirmed that the more risk averse investor is, the proportion of highly risked securities in its portfolio is smaller. In general, and as mentioned by Ameur and Prigent (2010), the optimal solution depends on the risk aversion of the investor. The main practical consequence of these results is that risk averse investors should rebalance their portfolios more frequently than risk-loving investors. This is in accordance with some previous research, such as that conducted by Jones and Stine (2005). Similarly, we also suggest that more risk-averse individuals should lower their allocation to risky assets. Dorn and Huberman (2010) have also concluded that the more risk averse investors will buy less volatile securities. Although further work is required to gain a more complete understanding of the effects of investor's attitude towards risk on securities portfolio performance, the results presented in this article may be a solid platform for creating portfolios especially on underdeveloped capital markets.

Conclusion
To sum up, the analysis results have revealed that an increase in risk aversion leads to a decrease in expected return and the creation of more superior securities portfolio. The main practical consequence of the obtained results is that risk averse investors should rebalance their portfolios more frequently than risk-loving investors. The main limitations of this study are related to the shorter available financial time series in newly formed capitalistic economy and missing data due to the lack of collective records on levels of securities offerings issues. The real implications of this research can be seen in the shaping of investment strategies of potential investors looking to diversify their portfolios. Further research should shed more light on measuring investor 'risk appetite' in the underdeveloped capital markets.
Source: Created by the authors. Table E1. Portfolio structure.