### Browsing by Author "Bosman, Petrus"

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- ItemOpen AccessBenefits of a Tree-Based model for stock selection in a South African context(2014) Giuricich, Mario Nicolo; Bosman, PetrusQuantitative investment practitioners typically model the performance of a stock relative to its benchmark and the stock's fundamental factors in a classical linear framework. However, these models have empirically been found to be unsuitable for capturing higher-order relationships between a stock's return relative to a benchmark and its fundamental factors. This dissertation studies the use of Classification and Regression Tree (CART) models for stock selection within the South African context, with the focus being on the period from when the Global Financial Crisis began in early 2007 until December 2012. By utilising four types of portfolios, a CART model is directly compared against two traditional linear models. It is seen that during the period focused upon, the portfolios based on the CART model deliver the best excess return and risk-adjusted return, albeit in most cases modestly above the returns delivered by the portfolios based upon the linear models. This is observed in the hedge-fund style and long-only portfolios constructed. Moreover, it is observed that the CART-based portfolios' returns are not correlated with those from the linear-model-based portfolios. This observation suggests that CART models offer an attractive option to diversify model risk within the South African context.
- ItemOpen AccessA comparative analysis of non-linear techniques in South African stock selection(2015) Hutheram, Nikhil Arnaidas; Bosman, PetrusForecasting stock performance has long been one of the primary objectives of financial practitioners. Literature has shown that the classical linear approach to modelling the interactions among company-specific factors and its stock market re- turns in time have become less suited for capturing the movements of the stock market. Hence, attempts to predict the performance of a stock have become associated with additional layers of complexity. This has led to the adoption of non-linear approaches to forecast stock performance. This dissertation explores the performance of some non-linear models in the South African market. These were classification and regression trees (CART), logistic regression and a random forest approach com- pared against a linear regression model. Moreover, a hybrid model between CART and logistic regression was considered. The models fell into two categories (i.e., static and dynamic models). Using a set of classification and portfolio performance metrics it was found that that a dynamic modelling approach outperformed a static approach. Overall, the logistic and linear regression models dominated in terms of performance against the tree-based models and hybrid approaches. The results also demonstrated that a hybrid approach offered an improvement over a stand-alone CART.
- ItemOpen AccessThe detection of phase transitions in the South African market(2016) Van Gysen, Michael; Mahomed, Obeid; Bosman, PetrusThis dissertation details the performance of two specific trading strategies which are based on the Johansen-Ledoit-Sornette (JLS) model. Both positive and negative bubbles are modelled as a log-periodic power law (LPPL) ending in a finite time singularity. The stock prices of the constituents of the FTSE/JSE Top40 index are taken as inputs to the JLS model from 3 June 2003 to 31 August 2015. It is shown that for certain time horizons into the past, the JLS based trading strategies significantly outperform random trading strategies. However this result is highly dependent on how far the model looks into the past, and if the model is calibrating to positive or negative bubbles. The lack of research with regards to the "stylized facts" of the JLS model, specifically relating to the time horizon and type of bubble, poses a significant hurdle in correctly identifying a LPPL structure in stock prices. These core features of the JLS model were developed from a number of positive bubbles that built up over many years. The results suggest that these features may not apply over all time horizons, and for both types of bubbles.
- ItemOpen AccessInvestigation of factor rotation routines in principal component analysis of stock returns(2014) Weimar, Nicole; Bosman, PetrusThis paper investigates rotation routines that will produce uncorrelated rotated principal components for a dataset of stock returns, in an attempt to identify the macroeconomic factors that best explain the variability among risk-adjusted stock returns on the Johannesburg Stock Exchange. An alternative to the more traditional rotation approaches is used, which creates subsets of principal components with similar variances that are rotated in turn. It is found that only one of the three normalisation constraints examined can retain uncorrelated principal components after rotation. The results also show that when subspaces of components are rotated that have close eigenvalues, the different rotation criteria used to rotate principal components will produce similar results. After rotating the suitable subsets using varimax rotation, it is found that the first rotated component can be explained by the African Industrials sector, the second rotated component is related to the African Consumer Services sector while the third rotated component shows a significant relationship to the African Finance factor.
- ItemOpen AccessThe LIBOR market model in the South African setting(2009) Engelbrecht, Stephanus Francois; Bosman, Petrus
- ItemOpen AccessPairs trading: a copula approach(2014) Augustine, Cecilia; Bosman, PetrusPairs trading is an arbitrage strategy that involves identifying a pair of stocks known to move together historically and trading on them when relative mispricing occurs. The strategy involves shorting the overvalued stock and simultaneously going long on the undervalued stock and closing the positions once the prices have returned to fair values. The cointegration method and the distance method are the most common techniques used in pairs trading strategy. However under these methods, the measure of divergence between the stocks or the spread is assumed to be symmetrically distributed about the mean zero. In addition, the spread is assumed to be a stationary time series (cointegration method) or mean-reverting (distance method). These assumptions are the main drawbacks of these methods and may lead to missed and/or inaccurate trading signals. The purpose of this dissertation is to explore an alternative approach to pairs trading by use of copulas. This dissertation aims to investigate if copulas can improve the profitability of pairs trading. To achieve this aim, results of pairs trading by use of copulas are compared against those of cointegration and distance methods.
- ItemOpen AccessPortfolio selection using Random Matrix theory and L-Moments(2015) Ushan, Wardah; Bosman, Petrus; Taylor, DavidMarkowitz's (1952) seminal work on Modern Portfolio Theory (MPT) describes a methodology to construct an optimal portfolio of risky stocks. The constructed portfolio is based on a trade-off between risk and reward, and will depend on the risk- return preferences of the investor. Implementation of MPT requires estimation of the expected returns and variances of each of the stocks, and the associated covariances between them. Historically, the sample mean vector and variance-covariance matrix have been used for this purpose. However, estimation errors result in the optimised portfolios performing poorly out-of-sample. This dissertation considers two approaches to obtaining a more robust estimate of the variance-covariance matrix. The first is Random Matrix Theory (RMT), which compares the eigenvalues of an empirical correlation matrix to those generated from a correlation matrix of purely random returns. Eigenvalues of the random correlation matrix follow the Marcenko-Pastur density, and lie within an upper and lower bound. This range is referred to as the "noise band". Eigenvalues of the empirical correlation matrix falling within the "noise band" are considered to provide no useful information. Thus, RMT proposes that they be filtered out to obtain a cleaned, robust estimate of the correlation and covariance matrices. The second approach uses L-moments, rather than conventional sample moments, to estimate the covariance and correlation matrices. L-moment estimates are more robust to outliers than conventional sample moments, in particular, when sample sizes are small. We use L-moments in conjunction with Random Matrix Theory to construct the minimum variance portfolio. In particular, we consider four strategies corresponding to the four different estimates of the covariance matrix: the L-moments estimate and sample moments estimate, each with and without the incorporation of RMT. We then analyse the performance of each of these strategies in terms of their risk-return characteristics, their performance and their diversification.
- ItemOpen AccessPricing equity options on multiple underlyings in the South African context(2008) Preston, Bradley; Bosman, PetrusIt is well documented that financial asset prices returns are not normally distributed. Historical return distributions exhibit fatter tails and positive skewness that is not explained by a normal distribution. Moreover, the standard Black-Scholes option pricing framework that assumes that asset prices follow geometric Brownian Motion does not explain option prices observed in the market. In particular much work has been done trying to explain the volatility skew.
- ItemOpen AccessStatic hedging of barrier options : a review of four methods(2003) Bosman, Petrus; Ouwehand, PeterThis paper examines the static hedging of a European up-and-out call option. Four different static hedging models are examined in detail and are implemented. Their hedging performance is examined in a framework that aims to simulate real market conditions. This is done to determine the practical usefulness of the static hedging schemes in comparison with dynamic delta hedging. Only one of the four models, by Derman, Ergener and Kani (1995) seems to show promise when transaction costs and stochastic volatility are taken into account.
- ItemOpen AccessTwo approaches to modelling the volatility skew(2008) Masawi, Chipo; Bosman, PetrusThis study examines two approaches to modelling the volatility skew that is used to price options on the Johannesburg Stock Exchange (JSE) TOP40 index. The first approach involves using historical prices of the underlying index to obtain a model of the skew. Two models that use this approach, namely the Edgeworth and Normal Mixture AGARCH models were implemented.