Abstract
A central issue in estimation techniques of asset pricing and risk management is the structure of asset return distributions. The predominant asset returns distribution assumption employed in financial economics is the Gaussian distribution. The wide use of the Gaussian distribution in empirical research can be attributed to the seminal portfolio selection work of Markowitz (1952), which gave birth to the mean-variance based Modern Portfolio Theory (MPT), the foundation upon which the field of finance is built. Consequently, the Gaussian assumption has been the workhorse of mainstream finance, not based on the belief that the assumption has superior capabilities of modelling financial data, but because of tractable characteristics (e.g., the convex objective function) which yield simple mathematical and numerical considerations such as quadratic optimisation (Benoit & Van den Poel, 2017; Lassance, 2021). Spurred by simple and tractable models based on the assumption that financial asset returns have normal (or conditional normal) distributions, the majority of empirical analysis in finance incorporates only a subset of the distribution characteristics of data. However, in many empirical applications, specification of the entire distribution of outcomes is more desirable (Arellano & Bonhomme, 2017). This assertion is supported by: (i) asset returns being predominantly fat tailed and negatively skewed, implying that the Gaussian distribution tends to underweight tail risk, (ii) variance not being an adequate risk measure in a portfolio perspective and (iii) investors deviating from the prediction of expected utility when evaluating risk or opportunity.
Thus, the overarching aim of this thesis is grounded in the idea of going beyond mean analysis and exploiting distributional properties of asset returns in asset pricing and risk modelling. The thesis makes use of quantile regression (QR) and QR-based methods particularly suited to full distributional analysis. To achieve the overall aim, the thesis explores the following three objectives. Firstly, the thesis reinvestigates the predictive ability of various predictor variables in predicting the full conditional South African equity risk premium (ERP) distribution out-of-sample (OOS). Whilst predictor variables proposed in literature are known to fail to predict the conditional mean of the ERP, a quantile approach is employed to determine predictive ability beyond the centre of the ERP distribution. The second objective involves exploring the nature of the United States of America (USA) equity and bond return dependence across the full range of conditional quantiles and to assess whether the direction of predictability between quantile returns is influenced by the source of market shocks. The third objective focuses on investigating the volatility process of South African equity returns, with a special focus on the asymmetric volatility response of headline and sectoral equity index returns to negative and
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positive return shocks. This relates considering whether there are different equity index responses due to market size and industry effects. To achieve these objectives, the core of this thesis is made up of three empirical chapters (Chapters 5-7).
The first empirical chapter (Chapter 5) shows that, beyond central quantiles, several predictor variables do indeed exhibit statistically and economically significant predictive ability, reinforcing evidence against the location shift hypothesis, which proposes that predictor variables affect only the location of the ERP conditional distribution. Consequently, it is hypothesised that around its median quantile, the South African ERP represents a random walk and that information contained in the 15 predictor variables considered individually is generally insufficient to forecast the future conditional ERP mean. Conversely, when the ERP is above or below its conditional median, certain predictor variables carry relevant information to forecast conditional ERP quantiles beyond the median. Exploiting the predictive ability of predictor variables selected by the ℓ1-penalised least absolute shrinkage and selection operator (LASSO) method of Belloni and Chernozhukov (2011) and the Lima and Meng (2017) predictor variable classification method across the ERP distribution, the chapter proposes a five-quantile post-LASSO quantile forecast combination specification based on a time-invariant weighting scheme as a robust estimator of the South African ERP mean.
Using the cross-quantilogram approach of Han, Linton, Oka and Whang (2016), the second empirical chapter (Chapter 6) results show that: (i) considering a shock emanates from either the bond or equity market, the lower and upper tail quantiles of equity (the S&P 500 Index) and bond return (the 10-Year Treasury Bond Index) distributions have heterogeneous dependence, i.e., the lower bond return quantile has positive dependence with lower equity quantiles and negative dependence with upper equity quantiles, whilst the upper bond quantile has negative dependence with the lower equity quantiles and positive dependence with the upper equity quantiles and vice versa, and (ii) there is bi-directional predictability in the cross-upper/lower quantiles of equities and bonds, implying that market shock source is immaterial in influencing the direction of predictability when both market returns are in their tails. However, absence of directional predictability (i.e., from the bond market to the median quantile of the S&P 500 Index and vice versa) is detected, in line with the empirical work (e.g., Goyal & Welch, 2008; Neely, Rapach & Zhou 2014; Pedersen, 2015), which documents that central quantiles of financial return distributions are difficult to predict. Considering time-varying diversification benefits for a portfolio composed of equal-weighted equities and bonds,
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the conditional diversification benefit (CDB) measure of Christoffersen, Errunza, Jacobs and Langlois (2012) shows that diversification benefits vary significantly, with no discernable structural shift.
Employing return variability response estimates which exploit the extreme lower and upper quantile autoregression (QAR) parameter estimates, the last empirical chapter (Chapter 7) shows that, based on disaggregating the equity market by market capitalisation, it is only the main headline index (JSE/FTSE All Share Index) and the Top 40 Index, representing the 40 largest companies by market capitalisation, which exhibit asymmetric volatility response. This result is consistent with the predictions of the ‘leverage effect’ hypothesis and shows that negative shocks are significant drivers of subsequent large company share price volatility dynamics. Thus, based on considering the ‘size effect’, asymmetric volatility response at the aggregate level is mainly driven by large companies and hence it might be misleading to generalise the asymmetric response phenomenon across the full market. Whilst the seminal studies of Christie (1982) and Cheung and Ng (1992) theorise that a negative relationship of lagged returns and current volatility is stronger for small firms due to small firms having higher financial leverage, Chapter 7 provides contrary evidence, which shows that it is actually larger firms with a stronger negative relationship. Given that the Top 40 Index largely drives the main South African market, the size effect results are in line with the covariance asymmetry hypothesis, which postulates that volatility asymmetry is likely to be strong if the conditional covariance between the Top 40 Index and the aggregate market index is asymmetric. From a ‘sector effect’ perspective (based on sector classification), Chapter 7 shows that sector indices generally exhibit asymmetric response to return shocks characteristics, similarly to the main market aggregate index, and in line with the covariance asymmetry hypothesis, thus suggesting that large co-movement of the sector and aggregate equity market returns negatively affects diversification opportunities for investors.
Varying dynamics in underlying economic conditions and the influence of extreme events significantly influence the non-normality characteristic of financial returns widely observed in financial markets. The findings of this thesis provide supporting empirical evidence for the appropriateness of QR and QR-based methods in capturing distributional information contained in quantiles of financial time series, thus allowing deeper insight into the stylised characteristics of financial time series.