Bases teóricas

In Chapter 4, Bayesian methods were adopted as alternative statistical models to search evidence of herding behaviour and to re-examine the findings of the Frequentist approaches for two main reasons. First, the intuition in employing the Bayesian techniques is that the distribution of the residuals could be described sufficiently other than restricting it to the normal distribution as the case in the methods adopted in the conventional Frequentist framework. Secondly, Bayesian approaches also take into account other economic factors that affect variables under investigation and the timely manner they are updated. Thus, the behaviour of economic variables is not considered as static as the case in the Frequentist framework but fluctuates from time to time to consistently update these variables.

Major Findings

The Bayesian regression model was adopted in Chapter 4 to serve a similar purpose with regard to testing evidence of herding behaviour among investors. The Bayesian model analysis was conducted on the cross-sectional return data under two separate assumptions about the model‟s residuals. In the first Bayesian model, the model‟s residuals were assumed to be normally distributed while the residuals of the second Bayesian model were t-distributed. Under each of these models, the two market returns proxies, the mean and the median were employed as market return proxies to investigate herding behaviour. At the industry level, adopting the first Bayesian model, and using the mean proxy, we found evidence of herding behaviour when the market return exceeded the 90% threshold. Thus, investors in the financial industry compromised their personal beliefs to follow the crowd when the market condition switched to the bull phase. No other evidential trace of herding behaviour was found in the financial industry during the extreme and the normal market days using the mean and the median proxies.

On the other front, employing the second Bayesian models and using the mean proxy, we found evidence of herding behaviour in the financial industry when the market return fell below (above) the 5% (95%) and 10% (90%) thresholds. Also, during normal market days, the results showed evidence of herding behaviour which is inconsistent with the literature which suggests that herding behaviour is mostly evident in financial markets especially during extreme market periods than normal market periods. On the other hand, using the median proxy, the results showed no evidence of herding behaviour in the entire financial industry during both extreme and normal market days.

Likewise, a similar analysis was conducted using cross-sectional market data from the four categorised sectors under the financial industry. Using the two market return proxies, we found no evidence of herding behaviour in all the sectors during both extreme and normal

market periods adopting the two Bayesian models. Thus, the assumptions governing the behaviour of the residuals had virtually less or no influence on the sectoral analysis and results.

In the same chapter, we further used two additional conventional approaches of testing evidence of herding behaviour. The two methods; namely, the Cross-Sectional Standard Deviation (CSSD) and the Cross-Sectional Absolute Deviation (CSAD) are classical examples of a Frequentist approach. While the CSSD methodology adopts the dummy regression model approach, the CSAD, on the other hand, employs the Ordinary Least Squares (OLS) approach to search for evidence of herding behaviour. These models have been severely criticised in the literature because of its statistical flaws relating to key assumptions underpinning their implementations.

At the industry level, we found no evidence of herding behaviour employing the CSSD model during both extreme and normal market periods using both market return proxies. In relation to the alternative approach, CSAD, we found proof of herding behaviour during both extreme and normal market days. The results further showed that investors in the financial industry resorted to the herding behaviour when the market return either fell below the 5% (bear market phase) or exceeded the 90% (bull market phase) thresholds using the mean proxy only. However, we found no evidence of herding behaviour using the median proxy.

At the sectoral level, we found no evidence of herding behaviour using the CSSD approach in all the sectors except the general financials sector. Investors in the general financials sector exhibited the herding behaviour during normal market days using the mean and the median proxies. This finding is somehow unsual as investors have consistently shown to exhibit the market behaviour predominantly during the extreme market phase than the normal market phase (see, for example, Tan et al., 2008; Chiang et al., 2010; Qiao et al., 2014). The CSSD findings so far has re-affirmed the assertion in literature which seeks to suggest the difficulty in detecting herding behaviour in financial markets adopting the CSSD methodology.

On the other hand, adopting the CSAD approach, apart from the insurance sector, the results showed evidence of herding behaviour in all the remaining sectors during both the normal and the extreme market days. In the banking sector, we found evidence of herding behaviour only when market returns fell below the 10% threshold using the mean and the median proxies. Similarly, we found evidence of herding behaviour in the general financials and real estate sectors during normal market days using the median proxy only. The entire results so far point to the existence of herding behaviour in some sectors and the entire financial industry. Using all methodologies under the Frequentist (i.e. CSSD and CSAD) and the Bayesian statistical frameworks in testing evidence of herding behaviour, the results point to the presence of herding behaviour in some sectors and the entire financial industry of the Johannesburg Stock Exchange. At the industry level, the empirical evidence of herding behaviour during extreme market days was mixed. With the

exception of the insurance sector, we found evidence of herding behaviour under the Frequentist framework. These inconsistencies could be as a result of the statistical approach adopted. These empirical findings form the two foundational and empirical chapters of the thesis.

Generally, the entire results in this chapter have shown that there are inconsistencies relating to the methodologies adopted in testing evidence of herding behaviour in the financial industry of the Johannesburg Stock Exchange. The mix findings are evident across the sectors and the entire industry considering all market conditions. The discrepancies in the results especially considering the conventional approaches of testing evidence of herding behaviour and the proposed methodologies (i.e. quantile regression and Bayesian regression) were largely because of the respective assumptions underpinning these statistical approaches. While under the Bayesian framework, the state of nature is treated as a random variable, under the Frequentist framework it is treated as a fixed but unknown number. Theoretically, the Bayesian inferences are largely intuitive, coherent and consistent with the state of nature.

Comparing the Bayesian results to the quantile regression results, the results are evidently at variance with each other. The quantile regression results showed evidence of herding behaviour during extreme market days in two (i.e. the banking and real estate) out of the four sectors. Certainly, these results suggest that the methodological approach used in analysing the financial market data for evidence of herding behaviour matters.

The existence of herding behaviour in the financial industry as evident in Chapter 3 and Four justifies to some degree the adoption of behavioural approaches to portfolio selection and optimisation in this thesis since portfolio optimisation is mostly driven by rational assumptions. There are many other cognitive biases and inconsistencies (see, for example, overconfidence (Fischhoff & Slovic, 1980; Barber & Odean, 2001; Gervais & Odean, 2001), overreaction (DeBondt & Thaler, 1986), loss aversion (Kahneman & Tversky, 1979; Shefrin & Statman, 1985; Odean, 1998), mental/psychological accounting (Tversky & Kahneman, 1981), miscalibration of probabilities (Lichtenstein et al., 1982), hyperbolic discounting (Laibson, 1997), and regret (Bell, 1982; Clarke et al., 1994) in the trading behaviour of investors other than herding behaviour which undermines the rational hypothesis as projected in classical economics.

Indeed the findings so far contradict the rational assumption hypothesis both at the industry and the sectoral levels adopting all the methodological approaches. The existence hypothesis of herding behaviour in the financial industry of the JSE could therefore not be rejected.

For further insights, we investigated if investors could add value to their investment portfolios considering the behaviour of the investors in the financial industry. Chapter 5, the last empirical chapter of this thesis builds on the findings of the initial two empirical chapters (Chapter 3 and Chapter 4). Results of Chapter 5 were sub-divided into two parts.

The first part reported the behavioural stock selection and classification processes, and the second part was devoted to the M-V portfolio optimisation analysis.

Limitation(s)

As described and documented in Chapter Three, the same limitations apply to Chapter 4 as well. All methods used in this chapter namely the CSSD, CSAD and the Bayesian approaches suffer from the lack of high-frequency data (i.e intra day) coupled with insufficient data observation especially with the median proxy in comparison with the mean proxy at the extreme market phases (<1%; > 99%).