Masters Degrees (Statistics and Actuarial Science)

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The application and testing of smart beta strategies in the South African market
(Stellenbosch : Stellenbosch University, 2018-03) Viljoen, Jacobus; Conradie, W. J.; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
ENGLISH SUMMARY: Smart Beta portfolios have recently prompted great interest both from academic researchers and market practitioners. Investors are attracted by the performances produced by these portfolios compared to the traditional market capitalisation weighted indices. The question that this thesis attempts to answer is: Do smart beta portfolios outperform the traditional cap-weighted indices in the South African market? According to BlackRock’s smart beta guide (Ang, 2015), the smart beta strategies aim to capture stock return drivers through rules-based, transparent strategies. They are generally long only and usually implemented within an asset class, in the case of this assignment, only equity. Smart beta is thus an investment strategy that positions itself between active and passive investing. Smart beta strategies are active in the sense that they invest in factors that drive return to improve risk-adjusted returns. In the same way, these strategies are closely related to passive strategies in that they are transparent, systematic and rules based. In this assignent five different fundamental factor portfolios (value, quality, momentum, volatility and a combination of the four, called multi-factor) were created based on the smart beta methodology. The factors that were used are well researched in the market and have been proven to provide investors with excess return over the market. Firstly, stock selection was done using two different techniques (time series comparison and cross-sectional comparison). The best stocks were selected based on their fundamental factor characteristics. Secondly, two different smart beta weighting strategies as well as a market-cap weighting strategy were applied to the selected stocks in order to create the various portfolios. The risk and return characteristics of the created portfolios were compared to those of the two benchmarks (JSE All Share Index and the JSE Shareholder Weighted All Share Index). The smart beta portfolios created in this thesis outperformed the benchmarks as well as the market-cap weighted portfolios. Lastly, the estimation of the macroeconomic exposure of the smart beta portfolios using a methodology outlined in a Citi Research paper is presented (Montagu, Krause, Burgess, Jalan, Murray, Chew and Yusuf., 2015).
Application of the moving block bootstrap method to resampled efficiency : the impact of the choice of block size
(Stellenbosch : Stellenbosch University, 2021-12) Retief, Jan; Conradie, W. J.; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
ENGLISH SUMMARY : Modern Portfolio theory was first developed in the 1950’s and revolutionised the way in which financial information is used to construct portfolios. Unfortunately, the theory is limited by the sensitivity of the constructed portfolio’s weights to uncertainty in the constituent’s risk and return estimates. Various advancements to the classical theory have been proposed to address this problem. One of these methods is called Resampled Efficiency (RE), which addresses the sensitivity problem by sampling expected return and risk estimates for each security included in the portfolio. Multiple portfolios are then built based on the sampled returns to construct a single averaged portfolio. The result is more robust portfolio’s that have been proven to have better out of sample performance. There are two methods available for sampling the security expected returns and risk: (1) generating random security returns (via Monte Carlo methods) or (2) using bootstrapping techniques based on observed security returns. For the second method, the moving block bootstrap (MBB) method can be used to construct bootstrapped samples for a non-stationary series of security returns. The MBB method works by ordering the historical series of observed returns into a pre-defined number of blocks (block sizes). As such, the choice of block size can have a significant effect on the sample that is obtained and used for portfolio construction. The goal of this study was to fully investigate what impact the choice of block size can have on the out of sample performance of resampled efficiency portfolios. After a literature review that assessed modern portfolio theory, resampled efficiency and the moving block bootstrap method, RE portfolios were hypothetically built based on actual security return observations. The constituents from the FTSE/JSE Top 40 index was used to construct RE portfolios for different choices of block sizes for the period between 2016 and 2017. The results indicate that the block size used can have a significant impact on the out of sample performance of the constructed portfolios, however no single block size or range of block sizes could be found that consistently result in the best performing RE portfolios. For different periods, and different levels of risk, the ideal block size differs.
Aspects of some exotic options
(Stellenbosch : University of Stellenbosch, 2007-12) Theron, Nadia; Conradie, W. J.; University of Stellenbosch. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
The use of options on various stock markets over the world has introduced a unique opportunity for investors to hedge, speculate, create synthetic financial instruments and reduce funding and other costs in their trading strategies. The power of options lies in their versatility. They enable an investor to adapt or adjust her position according to any situation that arises. Another benefit of using options is that they provide leverage. Since options cost less than stock, they provide a high-leverage approach to trading that can significantly limit the overall risk of a trade, or provide additional income. This versatility and leverage, however, come at a price. Options are complex securities and can be extremely risky. In this document several aspects of trading and valuing some exotic options are investigated. The aim is to give insight into their uses and the risks involved in their trading. Two volatility-dependent derivatives, namely compound and chooser options; two path-dependent derivatives, namely barrier and Asian options; and lastly binary options, are discussed in detail. The purpose of this study is to provide a reference that contains both the mathematical derivations and detail in valuating these exotic options, as well as an overview of their applicability and use for students and other interested parties.
Calculation aspects of the European Rebalanced Basket Option using Monte Carlo methods
(Stellenbosch : University of Stellenbosch, 2010-12) Van der Merwe, Carel Johannes; Conradie, W. J.; University of Stellenbosch. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
ENGLISH ABSTRACT: Life insurance and pension funds offer a wide range of products that are invested in a mix of assets. These portfolios (II), underlying the products, are rebalanced back to predetermined fixed proportions on a regular basis. This is done by selling the better performing assets and buying the worse performing assets. Life insurance or pension fund contracts can offer the client a minimum payout guarantee on the contract by charging them an extra premium (a). This problem can be changed to that of the pricing of a put option with underlying . It forms a liability for the insurance firm, and therefore needs to be managed in terms of risks as well. This can be done by studying the option’s sensitivities. In this thesis the premium and sensitivities of this put option are calculated, using different Monte Carlo methods, in order to find the most efficient method. Using general Monte Carlo methods, a simplistic pricing method is found which is refined by applying mathematical techniques so that the computational time is reduced significantly. After considering Antithetic Variables, Control Variates and Latin Hypercube Sampling as variance reduction techniques, option prices as Control Variates prove to reduce the error of the refined method most efficiently. This is improved by considering different Quasi-Monte Carlo techniques, namely Halton, Faure, normal Sobol’ and other randomised Sobol’ sequences. Owen and Faure-Tezuke type randomised Sobol’ sequences improved the convergence of the estimator the most efficiently. Furthermore, the best methods between Pathwise Derivatives Estimates and Finite Difference Approximations for estimating sensitivities of this option are found. Therefore by using the refined pricing method with option prices as Control Variates together with Owen and Faure-Tezuke type randomised Sobol’ sequences as a Quasi-Monte Carlo method, more efficient methods to price this option (compared to simplistic Monte Carlo methods) are obtained. In addition, more efficient sensitivity estimators are obtained to help manage risks.
Interest rate model theory with reference to the South African market
(Stellenbosch : University of Stellenbosch, 2006-03) Van Wijck, Tjaart; Conradie, W. J.; University of Stellenbosch. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
An overview of modern and historical interest rate model theory is given with the specific aim of derivative pricing. A variety of stochastic interest rate models are discussed within a South African market context. The various models are compared with respect to characteristics such as mean reversion, positivity of interest rates, the volatility structures they can represent, the yield curve shapes they can represent and weather analytical bond and derivative prices can be found. The distribution of the interest rates implied by some of these models is also found under various measures. The calibration of these models also receives attention with respect to instruments available in the South African market. Problems associated with the calibration of the modern models are also discussed.
Modelling market risk with SAS Risk Dimensions : a step by step implementation
(Stellenbosch : University of Stellenbosch, 2005-03) Du Toit, Carl; Conradie, W. J.; University of Stellenbosch. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
Financial institutions invest in financial securities like equities, options and government bonds. Two measures, namely return and risk, are associated with each investment position. Return is a measure of the profit or loss of the investment, whilst risk is defined as the uncertainty about return. A financial institution that holds a portfolio of securities is exposed to different types of risk. The most well-known types are market, credit, liquidity, operational and legal risk. An institution has the need to quantify for each type of risk, the extent of its exposure. Currently, standard risk measures that aim to quantify risk only exist for market and credit risk. Extensive calculations are usually required to obtain values for risk measures. The investments positions that form the portfolio, as well as the market information that are used in the risk measure calculations, change during each trading day. Hence, the financial institution needs a business tool that has the ability to calculate various standard risk measures for dynamic market and position data at the end of each trading day. SAS Risk Dimensions is a software package that provides a solution to the calculation problem. A risk management system is created with this package and is used to calculate all the relevant risk measures on a daily basis. The purpose of this document is to explain and illustrate all the steps that should be followed to create a suitable risk management system with SAS Risk Dimensions.
Non-parametric volatility measurements and volatility forecasting models
(Stellenbosch : Stellenbosch University, 2005-03) Du Toit, Cornel; Conradie, W. J.; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
ENGLISH ABSTRACT: Volatilty was originally seen to be constant and deterministic, but it was later realised that return series are non-stationary. Owing to this non-stationarity nature of returns, there were no reliable ex-post volatility measurements. Subsequently, researchers focussed on ex-ante volatility models. It was only then realised that before good volatility models can be created, reliable ex-post volatility measuremetns need to be defined. In this study we examine non-parametric ex-post volatility measurements in order to obtain approximations of the variances of non-stationary return series. A detailed mathematical derivation and discussion of the already developed volatility measurements, in particular the realised volatility- and DST measurements, are given In theory, the higher the sample frequency of returns is, the more accurate the measurements are. These volatility measurements referred to above, however, all have short-comings in that the realised volatility fails if the sample frequency becomes to high owing to microstructure effects. On the other hand, the DST measurement cannot handle changing instantaneous volatility. In this study we introduce a new volatility measurement, termed microstructure realised volatility, that overcomes these shortcomings. This measurement, as with realised volatility, is based on quadratic variation theory, but the underlying return model is more realistic.
Probability of default calibration for low default portfolios: revisiting the Bayesian approach
(Stellenbosch : Stellenbosch University, 2016-03) Venter, Edward Stevens; Conradie, W. J.; Stellenbosch University. Economic and Management Sciences. Dept. of Statistics and Actuarial Science
ENGLISH ABSTRACT : The Probability of Default is one of the fundamental parameters used in the quantification of credit risk. When estimating the Probability of Default for portfolios with a low default nature the Probability of Default will always be underestimated. Therefore, a need exists for calibrating the Probability of Default for Low Default Portfolios. Various approaches have been considered in the literature review, with the main approaches being the Confidence Based Approach and Bayesian Approach. In this study the Bayesian Approach for calibrating the Probability of Default for portfolios of high grade credit is reconsidered. Two alternative prior distributions that can be used in the Bayesian Approach are proposed; these are an informative, Strict Pareto distribution and a non-informative Jeffreys prior. The performance of these proposals are then compared to existing calibration techniques by using real data.
Value at risk and expected shortfall : traditional measures and extreme value theory enhancements with a South African market application
(Stellenbosch : Stellenbosch University, 2013-12) Dicks, Anelda; Conradie, W. J.; De Wet, Tertius; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
ENGLISH ABSTRACT: Accurate estimation of Value at Risk (VaR) and Expected Shortfall (ES) is critical in the management of extreme market risks. These risks occur with small probability, but the financial impacts could be large. Traditional models to estimate VaR and ES are investigated. Following usual practice, 99% 10 day VaR and ES measures are calculated. A comprehensive theoretical background is first provided and then the models are applied to the Africa Financials Index from 29/01/1996 to 30/04/2013. The models considered include independent, identically distributed (i.i.d.) models and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) stochastic volatility models. Extreme Value Theory (EVT) models that focus especially on extreme market returns are also investigated. For this, the Peaks Over Threshold (POT) approach to EVT is followed. For the calculation of VaR, various scaling methods from one day to ten days are considered and their performance evaluated. The GARCH models fail to converge during periods of extreme returns. During these periods, EVT forecast results may be used. As a novel approach, this study considers the augmentation of the GARCH models with EVT forecasts. The two-step procedure of pre-filtering with a GARCH model and then applying EVT, as suggested by McNeil (1999), is also investigated. This study identifies some of the practical issues in model fitting. It is shown that no single forecasting model is universally optimal and the choice will depend on the nature of the data. For this data series, the best approach was to augment the GARCH stochastic volatility models with EVT forecasts during periods where the first do not converge. Model performance is judged by the actual number of VaR and ES violations compared to the expected number. The expected number is taken as the number of return observations over the entire sample period, multiplied by 0.01 for 99% VaR and ES calculations.

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Browsing Masters Degrees (Statistics and Actuarial Science) by browse.metadata.advisor "Conradie, W. J."

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