Planificación de costes

The Mean-Variance criterion (hereafter, M-V) introduced by Markowitz (1952) proposes a mathematical framework for investment allocation in financial markets. As a portfolio construction theory, the technique now remains the lingua franca in portfolio risk management. The theory is suitable for investors who care only about the expected returns

Author(s) Issue(s) Findings/Conclusion

Selden (1912) Psychology of the Movements of stock prices are dependen to a considerable degree on stock market the mental attitude of market participants.

Festinger, Riecken, and Social psychology A state of cognitive dissonance arises when two simutaneously held Schachter (1956) cognitions are inconsistent. Because the experience of dissonance is unpleasant, the person will strive to reduce it by changing beliefs. Pratt (1964) Utility and risk A consideration of utility functions, risk aversion and risk as a

proportion of total assets.

Tversky and Kahneman (1973) Judgemental heuristics Development of the availability heuristic postulating that a person evaluates the frequency of classes or the probability of events by availability and anchoring.

Kahneman and Tversky (1979) Prospect theory People underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty.

Thaler (1980) Prospect theory Advocating the use of prospect theory as an alternative descriptive theory.

Tversky and Kahneman (1981) Judgemental heuristics Introduction of the concept of framing.

Shiller (1981) Efficient market The efficient markets model is at best an "academic" model and does hypothesis not describe observed movements in financial prices.

De Bondt and Thaler (1985) Market inefficiency People overreact systematically to dramatic news events, which results in substantial weak-form inefficiencies in the stock market.

Yaari (1987) Expected utility theory Modification to expected utility theory to obtain the "dual theory of choice under risk".

Samuelson and Zechauser (1988) Status quo bias Decision making experiments confirm the presence of status quo bias. Kahneman et al. (1990) Loss aversion Loss aversion and endowment effect persist even in market settings

with opportunities to learn.

Tversky and Kahneman (1992) Cumulative prospect An updated version of prospect theory which addresses the key theory drawbacks in the initial model to accommodate true human

behaviour in the real world.

Shefrin and Statman (1994) Noise trading There is a heterogeneous capital market where noise traders tend to distort certain principles of finance. The behavioural efficient market hypothesis is presented.

Benartzi and Thaler (1995) Equity premium puzzle The puzzle is explained in terms of behavioural concepts: loss aversion combined with a prudent tendency to monitor wealth frequently. Odean (1998a) Disposition effect Investors have a tendency to sell winning investments too soon and

hold losing investments for too long.

Holt and Laury (2002) Risk aversion A simple lottery choice experiment shows differences in risk aversion between behaviour under hypothetical and real incentives.

Harrison and Rutstrom (2009) Prospect theory Expected utility theory and prospect theory can be reconciled by using a mixture model.

Frydman, Barberis, Camerer, Realisation utility Activity in two areas of the brain, which are important for economic Bossaerts, and Rangel (2014) decision making, exhibit activity consistent with the predictions of

realisation utility.

of their portfolios and their risks. Additionally, the M-V portfolio theory is prescriptive, prescribing optimal M-V portfolios to investors who accept its assumptions. As discussed earlier, the two key statistics under the MPT remain the mean and the standard deviation (variance). The standard deviation is a statistic that is related to the variance; both measure the dispersion of assets returns (historical). Statistically, the two measures depend on the first two moments of asset returns distribution.

When asset returns distribution deviates from the Gaussian distribution, the distribution exhibits skewness and kurtosis. However, the M-V criterion for portfolio selection does not take into consideration the skewness and the kurtosis statistics of the asset returns distribution. Thus, under the MPT, asset returns distribution is assumed to be normally distributed and hence best described by its mean and standard deviation. Additionally, the two statistics associated with non-Gaussian distribution depend respectively on the last two moments of asset returns distribution. While the skewness statistic measures the lop- sidedness or asymmetry of a distribution, on the other hand, the kurtosis statistic measures the heavy tails of a distribution.

In other words, the M-V criterion does not utilise the complete asset returns distribution characteristics, and hence the two classical measures do not give the complete description of market returns. Thus, practitioners in financial markets and investors alike primarily consider only the first two moments of asset returns distribution in their investment decision-making process. However, the mean and the standard deviation only describe Gaussian distributions. Nevertheless, asset returns distribution is generally non-Gaussian and may be characterised by its skewness and kurtosis. The mean and variance in the case of non-Gaussian distributions are not appropriate statistics in describing such distributions. Hence, the M-V criterion is suitable especially when asset returns distribution exhibit normality.

The first two moments of asset return distribution under the M-V criterion are primarily described by the expected return and the risk of any given investments. In this case, investors are seen to be boxed in a financial world where their investment decisions are based strictly on two statistics (i.e. expected return and risk). Such an investment environment prescribed by the M-V criterion is rigid and consequently restrict investors from resorting to alternative statistics such as the third and fourth moments especially when asset return distribution is non-Gaussian. This makes the M-V criterion a normative theory.

According to the MPT, rational investors in financial markets always seek to maximise their utility by striking a balance between portfolios expected mean and variance. Thus, they select portfolios with minimum variance for given expected return or maximum expected return for given variance. However, the underlying factors that affect asset returns surpass what the M-V criterion dictates. On the other front, the M-V criterion does not take into account the influence of investors‟ psychology in their investment decision- making process. For many, if not most studies in the behavioural economics paradigm

have documented several cognitive biases and heuristics that influence investors and cause them to depart from the doctrines of the M-V criterion.

To ensure better forecast and understand many real-world phenomena in the financial environment, many researchers working in the field of behavioural economics recommend an in-depth review and an update of rational based expectations models to accommodation investors‟ decision-making mental biases. The M-V criterion has been severely criticised in many studies regarding its underlying assumptions and over-reliance on the mean and the standard deviation as the only important statistics of interest to investors. More so, the standard model was originally proposed and solved in a single-period setting under a discrete time specification.

In addition, the standard measure of dependence known as the Pearson correlation coefficient as documented, for example, by Jondeau & Rockinger (2006), Junker et al. (2006) and McNeil et al. (2015) fails to completely describe the type of dependence between assets returns. Consequently, the standard measure of dependence could lead to spurious results since it measures only linear dependence and fails to capture non-linear dependence. The use of the standard correlation coefficient as a measure of non-linear dependence undermines the M-V criterion in solving real-life problems. While there is considerable amount of literature exploring dependence using the standard Pearson correlation coefficient, the choice is much restricted to linear dependence. The M-V criterion has been questioned since assets returns also exhibit non-linear dependence. In an attempt to improve the standard M-V criterion for portfolio selection, several improvements have been suggested specifically to relax its fundamental assumptions and to extend the standard specification in relation to some identified weaknesses. In the past half-century, the M-V framework has been revised extensively by many authors. For example, portfolio theory in the dynamic setting in continuous-time setting (Zhou & Li, 2000) and in multi-period setting (Chen et al., 1971; Hakansson, 1971; Östermark, 1991; Pliska, 1997; Li & Ng, 2000) has been established primarily revolving around the standard M-V frameworks.

On the other front, to overcome the weaknesses of the M-V criterion in relation to its standard measure of dependence between stocks, a very promising methodology named the Copula has been recommended in the literature. Copula is a multivariate modelling tool which primarily offers a method of separating the description of the dependence structure of random variables from the joint distribution function. In other words, Copula simply offers a flexible alternative means of decoupling the distributions of individual random variables from the relationships between random variables.

Copula was first introduced by Sklar in 1957 as a measure non-linear inter-dependence between random variables. The concept has been widely accepted and applied in many fields especially where multivariate dependence is of essence. It has been applied in many areas such as actuarial science (Frees et al., 1996), biomedical studies (Wang & Wells, 2000), engineering (Genest & Favre, 2007), and finance (Embrechts & Lindskog, 2003).

Over the years, the M-V criterion has undergone drastic revision. Incorporating the proposed modifications to the conventional M-V framework, the standard criterion for portfolio selection and optimisation are solved by employing the quadratic optimisation technique.

Quadratic optimisation is employed in many fields. Optimisation problems primarily are solved subject to equality constraints by turning initial problems into quadratic optimisation problems. Thus, the M-V criterion in selecting portfolios is first formulated into a linear quadratic optimisation problem with series of defined constraints to reflect the investor risk-reward appetite. From the mathematical and practical viewpoints, the quadratic optimisation technique has great importance in solving many problems in the real world.

CHAPTER THREE:

Testing Evidence of Herding Behaviour: A Frequentist

Approach

This chapter has been published in the Journal of Economic and Financial Sciences (2017), Vol. 10 (3), pp. 458-475. Under the title: “Test of Herding Behaviour in the Johannesburg Stock Exchange: Application of Quantile Regression Model”.

The abstract of the published version reads as follows:

Abstract:

The current study searches for evidence of herding behaviour in South Africa‟s financial industry using an alternative approach. As a departure from the conventional test methodologies, the current study adopts the quantile regression model in estimating the empirical data on daily stock returns from January 2010 to September 2015. Employing the median as an alternative measure of average market portfolio returns, the study finds evidence of herding behaviour in the banking and real estate sectors during the sample period. Herding behaviour shows asymmetry and investors in the banking sector exhibit the herding behaviour when the market is falling (bear phase), whereas in the real estate sector, investors exhibited the herding behaviour when the market is rising (bull phase). However, in the entire financial industry, the empirical results show evidence of herding behaviour only during the extreme market period (bull phase).

JEL Classification: G02, G11, G14, G15.

Keywords: Asymmetry, Herding Behaviour, Quantile Regression Model, Financial

Industry, Johannesburg Stock Exchange (JSE).

3.1 Introduction

A substantial number of studies in behavioural economics have primarily focused on one key concept, namely, herding behaviour. Herding behaviour has been extensively studied in many developed and emerging markets and has become an important subject in the economics literature, especially in the context of the recent financial crunches. Empirical evidence of investor herding behaviour has been proven in both developed and emerging markets. It has been shown that under severe market conditions herding behaviour is more prevalent in emerging markets than in developed markets (see, for example, Chang et al., 2000; Lobao & Serra, 2007; Tan et al., 2008; Lao & Singh, 2011; Economou et al., 2011; Vieira & Pereira, 2015). This according to the authors is as a result of deficiencies in information quality and thus creates anxiety in the minds of investors and uncertainty in the emerging market.

Firstly, following Chang et al. (2000) there is evidence of higher herding levels in emerging markets compared to developed ones. Vieira & Pereira (2015) confirm this idea and indicate that almost all studies designed to detect herding behaviour in developing stock markets and in relatively small illiquid capital markets found evidence of its existence. Therefore, it seems that herding is more likely to occur in less developed markets.

Herding behaviour has been identified among individual and institutional investors by critics of traditional economics. The phenomenon is described in the behavioural economics literature as an irrational behaviour contrary to what a rational model of expectations dictates. Indeed, the phenomenon is consistent and supports the findings of Asch (1952), who studied the impact of an individual‟s social environment on his decision behaviour and observed that within groups, individuals often set-aside their private information and rely predominantly on group opinion.

Herding behaviour is a popular phenomenon in the financial markets and stock markets of both developed and emerging markets. Herding is one such behavioural anomaly which defies the efficient market hypothesis (hereafter, EMH). According to EMH, investors make rational and informed decisions and determine their expected returns based on equilibrium models like the Capital Asset Pricing Model (hereafter, CAPM). Thus, equity dispersion continually increases with the market return.

The herding of participants in financial markets is defined as “the tendency to accumulate on the same side of the market”, which poses significant threat to stability and efficiency of financial markets (Kremer & Nautz, 2013). Likewise, Avery & Zemsky (1998) define herding in financial markets as a change in the investment opinion (subjective) of investors to the direction of the crowd. Theoretically, numerous studies have concentrated on the concepts and the classifications of herding behaviour in financial markets (Bikhchandani et al., 2001; Spyrou, 2013). Also, several papers have focused on its impact on financial system as well as factors that drive the market phenomenon.

Several empirical studies argue that the presence of herding in financial markets drives stock prices further from their fundamental economic levels and values and possibly causing destabilisation, inefficiencies and speculative bubbles causes (see, Scharfstein & Stein, 1990; Bikhchandani & Sharma, 2000; Shiller, 2003; Hsieh, 2013; Spyrou, 2013). Also, other studies argue that herding actually makes the market more efficient because prices are adjusted faster to new information (Hirshleifer et al., 1994; Hirshleifer & Hong Teoh, 2003). According to Christie & Huang (1995), herding becomes more pronounced, particularly during extreme market periods. Thus, investors mimic the actions of the crowd by reneging on their private information during extreme market condition.

The field of behavioural economics arose out of the criticism of classical economics by various researchers (see, for example, Kahneman & Tversky, 1979; Shefrin & Statman, 1984; Shefrin & Statman, 1985; Bondt & Thaler, 1985; Shleifer & Summers, 1990; Tversky & Kahneman, 1992; Shefrin & Statman, 1994; Shleifer & Vishny,1997; Shiller, 1999; Shefrin & Statman, 2000; Shefrin, 2001; Shiller, 2003). Behavioural economics has focused primarily on the study of the rationality of investors and the cognitive processes involved in the financial decisions made by investors, specifically, in their capital market investment decisions (Fromlet, 2001). Studies that seek to analyse investors‟ herding behaviour in financial markets have primarily adopted four main conventional methods proposed by Lakonishok et al. (1992), Christie & Huang (1995), Chang et al. (2000) and Hwang & Salmon (2001).

Predominantly, the two models proposed by Christie & Huang (1995) and Chang et al. (2000) have been widely used in testing for the presence of herding behaviour in financial markets. Thus, the two models; namely, the Cross-Sectional Standard Deviation (CSSD) and Cross-Sectional Absolute Deviation (CSAD) remains the lingua franca in analysing herding behaviour in financial markets. On the other hand, limited studies have employed the other two conventional models introduced respectively by Lakonishok et al. (1992) and Hwang & Salmon (2001) due to data requirements and its sensitivity.

For example, the availability of data on investors‟ portfolios and transactions is scarce. Thus, empirical evidence presented so far for emerging markets is limited especially employing the model proposed by Lakonishok et al. (1992). In statistical terms, the model measures the degree of herding behaviour in financial markets. The nature of data required to implement the Lakonishok et al. (1992) methodology is very detailed on investors‟ transactions. When available, it makes it possible to focus on empirical research on regional or country-specific and importantly to differentiate between different classes of investors.

Recently, other alternative models have been proposed specifically to improve upon the identified weaknesses of the conventional models. These models include but not limited to quantile regression, state space model, Bayesian regression, rolling regression method, non-parametric kernel regression, autoregressive distributed lag (ARDL) cointegration technique. Many of these methods are performed under the frequentist setting which

obviously has its challenges as well. Interestingly, several models used in testing evidence of herding behaviour are predominantly under the frequentist setting.

Application of many of these models in testing market data for evidence of herding behaviour has been conducted mostly in developed financial markets than emerging markets. Results of these studies using the advanced methodologies on many occasions contradict the findings of some conventional approaches. Likewise, results of studies employing only alternative but advance methods sometimes reach different conclusions. Consequently, this poses a real problem as stakeholders in the financial markets find it difficult to accept or disregard these findings. Several reasons have been put forward as the cause of these inconsistencies in the empirical results of these studies. Key findings among the documented causes of mix findings of evidence of herding behaviour in financial markets include, for example, the length of the study period and the frequency of data.

On the other front, the use of the mean as a measure of central tendency or more specifically market portfolio average return is also problematic. The standard CSSD and CSAD methodologies adapt the mean as market return proxy. Thus, the presence of outliers in the market portfolio may lead to spurious results which may as well contradict findings of other methodologies. It is a known fact that outliers greatly affect the mean as a measure of central tendency. An alternative measure of central tendency, the median is a suitable measure that is not sensitive to the presence of outliers. Thus, the median is a robust measure which could be employed as an ideal proxy of market return.

Again, many studies that seek to test the presence of herding behaviour in both developed and emerging markets primarily do so only at the composite market level ignoring the underlying constituents of the market such as the industries and the sectors. Thus, these studies fail to test for evidence of the market anomaly at the disaggregate levels. Ordinarily, the behavioural dynamics and investors‟ psychological profile in different industries, as well as its constituent sectors, may not exhibit the same behavioural trait. Hence, empirical studies on herding behaviour in financial markets could conceal the true investor mentality and psychology at the various levels of the entire market.

In validating the existence or absence of herding behaviour in specific stock markets, limited number of studies have focused on emerging countries. For example, in the context of the South Africa stock market, specifically the JSE, there is a dearth of literature on herding behaviour in the South African stock market using newly proposed methodologies. This chapter fills this void and offers two key contributions to the literature on herding behaviour.