Thin trading, non-normality and the estimation of systematic risk on small stock markets - Bowie, David Colin (Department of Philosophy, 2024)
This thesis examines and extends research into two of the most important attributes of small stock markets, namely thin trading and non-normality, and how they impact on the estimation of systematic risk. Bearing these points in mind, the primary objective of the thesis is to offer concrete suggestions for selecting estimators of beta coefficients. In order to attain the objective outlined above, the first steps are to establish the extent and to model the characteristics of thin trading and non-normality. This is achieved in the thesis with the aid of empirical investigations using data from the Johannesburg Stock Exchange. The second step in providing concrete recommendations for beta estimation is to contrast beta estimators with a view to assessing their relative abilities to counteract the effects of thin trading and non-normality. In the thesis the comparison of both existing and modified versions of the estimators is performed both empirically and in simulation studies. In particular, the improved efficiency of robust estimators of beta coefficients is demonstrated using a comprehensive array of robust estimators (some of which incorporate the concept of bounding the influence of outlying market returns). Furthermore, the findings presented in the thesis confirm that further efficiency in the estimation of beta coefficients can be accomplished by implementing a well-known Bayesian adjustment in conjunction with the trade-totrade approach of avoiding the biases caused by thin trading. Using unbiasedness and efficiency as the necessary criteria of estimators of beta, the thesis concludes that a robust, bounded-influence version of the trade-to-trade beta estimator should be implemented on small mar~ets. A novel contribution in further modifying the proposed estimators is the consideration of flexible interval lengths over which to measure the security and market returns. The adaptive data selection procedure recommended in the thesis arises from the basic premise that there is more information in stock market prices in each month than is available at the month-end. Substantial increases in the efficiency of beta estimation are shown to emanate from the proposed procedure in an empirical evaluation using data from the JSE. A further aspect of thin trading is also considered in the thesis, namely the effect that it has on the estimation of covariances between securities. It is argued that the covariances between the return series of thinly trading securities cannot readily be estimated using a trade-to-trade approach because of the difficulties in matching the trading times of two thinly traded securities. Therefore, an aggregated coefficients estimator is more appropriate. In order to implement the aggregated coefficients estimator efficiently without sacrificing unbiasedness completely, a practical solution to the selection of the number of leading and lagged coefficients is proposed. A complication involved in using the· aggregated coefficients estimator is shown to exist when there is autocorrelation in the market returns ( over and above that induced by thin trading in the component securities). An analytical' expression is therefore derived to ascertain the extent to which the aggregated coefficients estimators of covariances are biased upwards by the serial correlation. The development of the analytical expression also enables a correction procedure for the upward bias to be proposed. An extension of the methodology using a continuous-time framework is developed to widen the applicability of the technique into the well traded markets where the durations of pricing delays are generally shorter than one day. In the light of the evidence regarding the stability of beta coefficients highlighted in the thesis and in other literature, a robust, multivariate, state-space approach to beta estimation is proposed. The new information to be gained from knowing the correlations between any movements in the beta coefficients of securities from different sectors facilitates the interpretation of why and how beta coefficients vary over time. For the practitioner, the results of an empirical study conducted on the JSE demonstrate that fresh insight into the management of systematic risk in portfolios can be gained from the multivariate approach.