An econometric analysis of the equity returns-inflation relationship in South Africa.

Abstract

Previous empirical evidence regarding the nature and magnitude of the relationship between equity returns and inflation has proven to be conflicting and inconsistent. Although several papers have considered this issue, there is still a lack of consensus as to the nature of the relationship between equity returns and inflation. This represents a considerable point of concern as it is this relationship that acts as an indicator of the historical efficacy of equities as an inflationary hedge. While the classical theory dating back to the 1930’s dictates that equities should function as an effective hedge against inflation because they are based on underlying assets with a fixed real value, a substantial number of studies have obtained results that contradict this theory. Many attempts have been made to explain this phenomenon and to resolve the debate since the 1980’s, notably with the application of cointegration theory andmethods (which were developed in the 90’s). Despite advances in econometrics, the issue remains unresolved on an international scale, with conflicting results still occurring in recent studies (Chaves and Silva, 2018; Bhanja and Dar, 2018; Al-Nassar and Bhatti, 2018). The literature that focuses on the South African case is a typical example of the disparity: relatively modern studies using fairly similar statistical approaches find vastly differing results as to the capacity for equities to act as an inflationary hedge, including findings of positive and negative results (Alagidede and Panagiotidis, 2010; Khumalo, 2013), as well as approaches that failed to produce conclusive results (van Rooyen and Jones, 2018). This thesis aims to resolve the issue for the South African case in order to determine whether or not equities have acted as a historically effective inflationary hedge. The South African economy represents a perfect natural experiment for the study due to its high volatility, especially in terms of macroeconomic indicators such as inflation, over the past thirty-five years. The analysis makes use of the Consumer Price Index (CPI) as a proxy for inflation and the Johannesburg Stock Exchange’s All Share Index (ALSI) as a proxy for equity returns over the period 1980 to 2015. The study is undertaken as a collection of publications that each seek to address particular issues, mostly of an econometric nature, that arise when studying the relationship. The first of these papers deals with the disparity in the South African economy regarding the order of integration of the two variables and seeks to provide a comparative analysis with previous studies. Further, the research contained in paper one seeks to identify possible explanations for the conflicting results in previous studies. The study finds that a significant, positive cointegrating relationship between inflation and equity returns exists in South Africa, at least when using conventional cointegration techniques, implying that equities have exhibited the historical capacity to act as an effective historical hedge against inflation, in contrast to the findings of much of the literature. Further, it resolves previous issues with differing findings as to the orders of integration of the variables, which represents a particularly prevalent problem in studies using South African data. While these initial findings would appear to lend support to the conventional theory that equities are able to act as an effective inflationary hedge in South Africa, when examining the issue more deeply it becomes evident that this finding may potentially be impacted by the inherent assumptions of the models employed. Based on the results of previous studies and the results of the first paper, the second paper posits that the equity- inflation relationship is both time and country dependent, potentially contributing to the aforementioned disparities in the existing literature. The implication of potentially flawed model assumptions is that the results of the first paper may be inaccurate (the model risk of a poor model choice giving unreliable results). As a result of this potential limitations bias, the remaining papers of this doctoral dissertation delve into the assumptions behind the classic model, reflecting more deeply on the nature of the data employed and seeking to determine if this relationship holds when various, arguably more realistic, alternate assumptions are considered. The first of these assumptions that is critiqued is that the relationship is time-invariant, such that the equity-inflation relationship does not exhibit variance over time. In an economy such as South Africa, which has shown exceptional macroeconomic volatility, such an assumption may well be inaccurate and is likely to have reduced the integrity of the conventional tests. Relaxing the assumption of time-invariance allows one to consider that the relationship may have experienced shifts over time as a result of exogenous shocks. This idea is tested by investigating the possibility of structural breaks in the individual time series, as well as in the relationship itself. Structural breaks here refer to an unexpected shift in a time series that can lead to forecasting errors, compromising the reliability of the model. Should a model rely on the assumption of time-invariance it is unable to account for the existence of such structural breaks, leading to compromised results. In the second paper, significant evidence for the existence of structural breaks was found in the case of both variables as well as in the overall relationship. Using the most significant structural break as a breakpoint and investigating the relationship preceding and subsequent to the break pointed to clear evidence that the relationship does change over time. As previous studies have generally assumed the series do not contain breaks, the assumption of time-invariance in previous work may have led to inherently flawed conclusions. However, what this second paper was able to demonstrate, was that even when accounting for breaks, equities maintained their capacity to act as a hedge against inflation in South Africa on either side of that structural break. Further, cointegration testing allowing for structural breaks indicated that the overall relationship was significant and positive and affirmed the prior conclusion that equities are an effective inflationary hedge in the long-run. That is, even when relaxing the assumption of time-invariance and accounting for structural breaks, the overall conclusion for the South African case – that equities are able to perform a hedging function against inflation – remains true. This thesis then continues by developing on this idea of addressing the previous assumptions that may affect this type of analysis, building towards a final, more robust, conclusion. Two additional assumptions remain which require consideration. In recent literature the question of asymmetric adjustment has arisen, including in the analysis of the relationship between equity returns and inflation. Such studies have aimed to deal with the idea that there is no compelling reason to assume that adjustments of the relationship between equity returns and inflation have necessarily been symmetric. Further, it is possible that the relationship may have been subject to a threshold effect, where it exhibits different characteristics depending on whether stocks are underpriced or overpriced relative to goods. It was shown that the adjustment coefficients differ substantially depending on whether they are above or below a certain threshold, and thus that the assumption of linear adjustment is flawed as the relationship exhibits asymmetric adjustment in reality. Further testing for asymmetric adjustment and allowing for such adjustments in the relationship led to the conclusion that the relationship has experienced asymmetric adjustment over the sample period and that the relationship between equity returns and inflation is more appropriately modelled using threshold cointegration techniques. Such findings drastically improve our understanding of the dynamics of the equity returns-inflation relationship and emphasize the importance of accounting for these factors in similar studies. The weakness in previous cointegration testing is somewhat exposed by the strength of the evidence of asymmetric adjustment and effectively questions the findings of the majority of the previous literature which has relied on these techniques. The model far more accurately estimates the relationship between equity returns and inflation and provides new evidence that it experiences a measure of variance around an endogenously determined threshold. Due to the relative power of the model as well as the fact that it has accounted for these factors it can be stated with far greater certainty that South African equities are able to provide an effective hedge against domestic inflation. The evidence of threshold effects is of importance to investors and policy makers, as it is at this point that the adjustment coefficients will vary in terms of their response to exogenous shocks. This is particularly important in the context of this thesis because of the evidence of multiple structural breaks in the cointegrating relationship (found in the second publication) indicating that the relationship has been affected by exogenous shocks at multiple points over the sample period. These factors, namely structural breaks, threshold effects and asymmetric adjustment, are a likely reason why previous studies, on an international scale, have exhibited such conflicting results. Should these studies be reconsidered to incorporate such effects, it would vastly improve the robustness of the results of these studies. It should be noted that the magnitude of the relationship is likely to differ across countries and time periods due to the variation in structural dynamics and macroeconomic conditions. It is therefore improbable that some standard measure of the relationship, such as the conventional theory by Fisher, would accurately estimate the relationship regardless of the sample country or sample period, given the findings in this thesis that the relationship is affected by exogenous factors. Due to the findings of asymmetric adjustment in the third research paper, it is not only the magnitude of the relationship that will cause varied responses, but also potentially the direction of the adjustment. This is investigated further in the fourth paper of this thesis, which aims to disaggregate the overall adjustment coefficient in order to better understand the effects of positive and negative adjustments when they differ substantially from the long-term aggregate relationship. Disaggregating the overall adjustment coefficient into its positive and negative components provided a novel understanding of the dynamics of the relationship. The results of the disaggregation were surprising due to the magnitude of the disparity between the positive and negative adjustments coefficients and indicated that it is important to consider the possibility of imminent fluctuations in inflation when best deciding how to hedge against it. Collectively however, this thesis has proven that equities are able to function as an effective long-run hedge against inflation in South Africa. Further this thesis demonstrates that the inherent assumptions in conventional cointegration techniques, especially those of time-invariance and symmetric adjustment are flawed and have likely contributed to the disparities in the previous literature.