Department of Statistics and Actuarial Science

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https://scholar.sun.ac.za/handle/10019.1/73

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Browsing Department of Statistics and Actuarial Science by browse.metadata.advisor "Conradie, Willie"

Now showing 1 - 4 of 4
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    Analysing GARCH models across different sample sizes
    (Stellenbosch : Stellenbosch University, 2023-03) Purchase, Michael Andrew; Conradie, Willie; Viljoen, Helena; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: As initially constructed by Robert Engle and his student Tim Bollerslev, the GARCH model has the desired ability to model the changing variance (heteroskedasticity) of a time series. The primary goal of this study is to investigate changes in volatility, estimates of the parameters, forecasting error as well as excess kurtosis across different window lengths as this may indicate an appropriate sample size to use when fitting a GARCH model to a set of data. After examining the T = 6489 1-day logreturns on the FTSE/JSE-ALSI between 27 December 1995 and 15 December 2021, it was calculated that an average estimate for volatility of 0.193 670 should be expected. Given that a rolling window methodology was applied across 20 different window lengths under both the S-GARCH(1,1) and E-GARCH(1,1) models, a total of 180 000 GARCH models were fit with parameter and volatility estimates, information criteria and volatility forecasts being extracted. Given the construction of the asymmetric response function under the E-GARCH model, this model has greater ability to account for the `leverage effect' where negative market returns are greater drivers of higher volatility than positive returns of an equal magnitude. Among others, key results include volatility estimates across most window lengths taking longer to settle after the Global Financial Crisis (GFC) than after the COVID-19 pandemic. This was interesting because volatility reached higher levels during the latter, indicating that the South African market reacted more severely to the COVID-19 pandemic but also managed to adjust to new market conditions quicker than those after the Global Financial Crisis. In terms of parameter estimates under the S-GARCH(1,1) model, values for a and b under a window length of 100 trading days were often calculated infinitely close to zero and one respectively, indicating a strong possibility of the optimising algorithm arriving at local maxima of the likelihood function. With the exceptionally low p-values under the Jarque-Bera and Kolmogorov-Smirnov tests as well as all excess kurtosis values being greater than zero, substantial motivation was provided for the use of the Student's t-distribution when fitting GARCH models. Given the various results obtained around volatility, parameter estimates, RMSE and information criteria, it was concluded that a window length of 600 is perhaps the most appropriate when modelling GARCH volatility.
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    Analysis to indicate the impact Hindsight Bias have on the outcome when forecasting of stock in the South African equity market
    (Stellenbosch : Stellenbosch University, 2023-12) Heyneke, Anton Lafrass; Conradie, Willie; Alfeus, Mesias; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: A novel Artificial Neural Network (ANN) framework presented in this study has the ability to mimic the effect that cognitive biases, specifically hindsight bias has on the financial market. This study investigates how hindsight bias influences models and their outcomes. During this study the hindsight bias effect will be measured within a South African context. The decisions that people make when faced with uncertainty are characterized by heuristic judgments and cognitive biases. If these characteristics are systematic and confirmed through research and literature related to this topic, it would form a quintessential part to the explanation of the behaviour of financial markets. This research presents a methodology that could be used to model the impact of cognitive biases on the financial markets. In this study, an ANN will be used as a stand-in for the decision-making process of an investor. It is important to note that the selection of the companies, on which the ANN will be trained, validated and tested, demonstrated cognitive bias during the study's preparation. Though there are many cognitive biases that have been identified in the literature on behavioural finance, this study will concentrate solely on the impact of hindsight bias. On financial markets, hindsight bias manifests when outcomes seem more predictable after they have already happened. This study attempts and succeeds – to some degree - to replicate the return characteristics of the ten chosen companies for the assessment period from 2010 to 2021. The study described here may still be subject to various cognitive biases and systemic behavioural errors in addition to the hindsight bias. The further application of this technique will stimulate further research with respect to the influence of investor behaviour on financial markets.
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    A quantitative analysis of investor over-reaction and under-reaction in the South African Equity Market : a mathematical statistical approach
    (Stellenbosch : Stellenbosch University, 2022-04) Mbonda Tiekwe, Aude Ines; Conradie, Willie; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: One of the basic foundations of traditional finance is the theory underlying the efficient market hypothesis (EMH). The EMH states that stocks are fairly and accurately priced, making it impossible for investors to use stock selection, technical analysis, or market timing to out-perform the market by earning abnormal returns. Several schools of thought have challenged the EMH by presenting empirical evidence of market anomalies, which seems to contradict the EMH. One such school of thought is behavioural finance, which holds that investors over-react and/or under-react over time, driven by their behavioural biases. The Barberis et al. (1998) theory of conservatism and representativeness heuristics is used to explain investor over-reaction and under-reaction. Investors who exhibit conservatism are slow to update their beliefs in response to recent evidence, and thus under-react to information. Under the influence of the representativeness heuristics, investors tend to produce extreme predictions, and over-react, implying that stocks that under-performed in the past tend to out-perform in the future, and vice-versa (Aguiar et al., 2006). In this study, it is investigated whether South African investors tend to overreact and/or under-react over time, driven by their behavioural biases. The 100 shares with the largest market capitalisation at the end of every calendar year from 2006 to 2016 were considered for the study. These shares had sufficient liquidity and depth of coverage by analysts and investors to be considered for a study on behavioural finance. In total, a sample of 163 shares had sufficient financial statement data on the Iress and Bloomberg databases to be included in the study. Analyses were done using two mathematical statistical techniques i.e. the more mathematical Fuzzy C-Means model and the Bayesian model, together with formal statistical tests. The Fuzzy C-Means model is based on the technique of pattern recognition, and uses the well-known fuzzy c-means clustering algorithm. The Bayesian model is based on the classical Bayes’ theorem, which describes a relationship between the probability of an event conditional upon another event. The stocks in the financials-, industrial- and resources sectors were analysed separately. Over-reaction and under-reaction were both detected, and differed across the three sectors. No clear patterns of the two biases investigated were visible over time. The results of the Fuzzy C-Means model analysis revealed that the resources sector shows the most under-reaction. In the Bayesian model, underreaction was observed more than over-reaction in the resources and industrial sectors. In the financial sector, over-reaction was observed more often. The results of this study imply that a momentum and a contrarian investment strategy can lead to over-performance in the South African equity market, but can also generate under-performance in a poorly performing market. Therefore, no trading strategies can be advised based on the results of this study.
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    Twitter predicts Naspers share price
    (Stellenbosch : Stellenbosch University, 2022-04) Sebitlo, Kgomotso Julian; Conradie, Willie; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY: Naspers is a publicly listed South African company, and @Fin24 is the financial news Twitter account that belongs to Naspers. Using Natural Language Processing techniques, Twitter sentiment and emotional analysis is applied to extract emotions from @Fin24 and these emotions are used to predict the Naspers share price. Two Twitter emotion extraction methods are compared. The first method is a character-based recurrent neural network which was developed to specifically recognise emotions on Twitter, while the second method is lexicon-based and was developed to recognise emotions from any text. The first method emotion scores, particularly the two-day lag Anticipation score, is found to contain useful information that may assist in predicting the daily Naspers share price.