Browsing by Author "Bradfield, David"

Now showing 1 - 6 of 6
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    Covariance matrix estimation methods for constrained portfolio optimization in a South African setting
    (2010) Madume, Jaison Pezisai; Bradfield, David; Munro, Brian
    One of the major topics of concern in Modern Portfolio Theory is portfolio optimization which is centred on the mean-variance framework. In order for this framework to be implemented, esti- mated parameters (covariance matrix for the constrained portfo- lio) are required. The problem with these estimated parameters is that they have to be extracted from historical data based on certain assumptions. Because of the di erent estimation methods that can be used the parameters thus obtained will su er either from estimation error or speci cation error. In order to obtain results that are realistic in the optimization, one needs then to establish covariance matrix estimators that are as good as possi- ble. This paper explores the various covariance matrix estimation methods in a South African setting focusing on the constrained portfolio. The empirical results show that the Ledoit shrinkage to a constant correlation method, the Principal Component Analy- sis method and the Portfolio of estimators method all perform as good as the Sample covariance matrix in the Ex-ante period but improve on it slightly in the Ex-post period. However, the im- provement is of a small magnitude, as a result the sample covari- ance matrix can be used in the constrained portfolio optimization in a South African setting.
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    Open Access
    Enhanced minimum variance optimisation: a pragmatic approach
    (2016) Lakhoo, Lala Bernisha Janti; Bradfield, David; Brandt, Tobias
    Since the establishment of Markowitz's theory, numerous studies have been carried out over the past six decades or so that cover the benefits, limitations, modifications and enhancements of Mean Variance (MV) optimisation. This study endeavours to extend on this, by means of adding factors to the minimum variance framework, which would increase the likelihood of outperforming both the market and the minimum variance portfolio (MVP). An analysis of the impact of these factor tilts on the MVP is carried out in the South African environment, represented by the FTSE-JSE Shareholder weighted Index as the benchmark portfolio. The main objective is to examine if the systematic and robust methods employed, which involve the incorporation of factor tilts into the multicriteria problem, together with covariance shrinkage – improve the performance of the MVP. The factor tilts examined include Active Distance, Concentration and Volume. Additionally, the constant correlation model is employed in the estimation of the shrinkage intensity, structured covariance target and shrinkage estimator. The results of this study showed that with specific levels of factor tilting, one can generally improve both absolute and risk-adjusted performance and lower concentration levels in comparison to both the MVP and benchmark. Additionally, lower turnover levels were observed across all tilted portfolios, relative to the MVP. Furthermore, covariance shrinkage enhanced all portfolio statistics examined, but significant improvement was noted on drawdown levels, capture ratios and risk. This is in contrast to the results obtained when the standard sample covariance matrix was employed.
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    A framework for regime identification and asset allocation
    (2016) Kondlo, Mpumelelo; Bradfield, David
    The purpose of this thesis is to examine a regime-based asset allocation strategy and evaluate whether accounting for regime-dependent risk and return of asset classes provides any significant improvement on portfolio performance. The South African market and economy are considered as a proxy for the analysis. Motivation of this thesis stems from the growing body of research by practitioners devoted to models that are reflective of the interdependency between financial assets and the real economy. The asset classes under consideration for the analysis are domestic and foreign cash, domestic and foreign bonds, domestic and foreign equity, inflation linked bonds, property, gold and commodities. In order to evaluate the performance of the regime-based strategy, this thesis proposes a framework based on Principal Component Analysis and Fuzzy Cluster Analysis for regime identification and asset allocation. The performance of the strategy is tested against two strategies that are not cognizant of regime changes. These are an equally weighted portfolio and a buy-and-hold strategy. Furthermore, relative performance analysis was performed by comparing the regime-based strategy proposed in this thesis against the Alexander Forbes Large Manager Watch Index. Due to data limitations, the analysis is done on an in-sample basis without an out-of-sample testing. The results from the analysis showed the extent of outperformance of the proposed regime-based strategy relative to an equally weighted strategy and a buy-and-hold strategy. These results were consistent with existing literature on regime-based strategies. Furthermore, the results provided strong motivation for the use of the regime identification framework together with tactical asset allocation proposed in this thesis.
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    Low volatility alternative equity indices
    (2015) Oladele, Oluwatosin Seun; Bradfield, David
    In recent years, there has been an increasing interest in constructing low volatility portfolios. These portfolios have shown significant outperformance when compared with the market capitalization-weighted portfolios. This study analyses the low volatility portfolios in South Africa using sectors instead of individual stocks as building blocks for portfolio construction. The empirical results from back-testing these portfolios show significant outperformance when compared with their market capitalization weighted equity benchmark counterpart (ALSI). In addition, a further analysis of this study delves into the construction of the low volatility portfolios using the Top 40 and Top 100 stocks. The results also show significant outperformance over the market-capitalization portfolio (ALSI), with the portfolios constructed using the Top 100 stocks having a better performance than portfolio constructed using the Top 40 stocks. Finally, the low volatility portfolios are also blended with typical portfolios (ALSI and the SWIX indices) in order to establish their usefulness as effective portfolio strategies. The results show that the Low volatility Single Index Model (SIM) and the Equally Weight low-beta portfolio (Lowbeta) were the superior performers based on their Sharpe ratios.
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    Robust portfolio construction: using resampled efficiency in combination with covariance shrinkage
    (2017) Combrink, James; Bradfield, David
    The thesis considers the general area of robust portfolio construction. In particular the thesis considers two techniques in this area that aim to improve portfolio construction, and consequently portfolio performance. The first technique focusses on estimation error in the sample covariance (one of portfolio optimisation inputs). In particular shrinkage techniques applied to the sample covariance matrix are considered and the merits thereof are assessed. The second technique considered in the thesis focusses on the portfolio construction/optimisation process itself. Here the thesis adopted the 'resampled efficiency' proposal of Michaud (1989) which utilises Monte Carlo simulation from the sampled distribution to generate a range of resampled efficient frontiers. Thereafter the thesis assesses the merits of combining these two techniques in the portfolio construction process. Portfolios are constructed using a quadratic programming algorithm requiring two inputs: (i) expected returns; and (ii) cross-sectional behaviour and individual risk (the covariance matrix). The output is a set of 'optimal' investment weights, one per each share who's returns were fed into the algorithm. This thesis looks at identifying and removing avoidable risk through a statistical robustification of the algorithms and attempting to improve upon the 'optimal' weights provided by the algorithms. The assessment of performance is done by comparing the out-of-period results with standard optimisation results, which highly sensitive and prone to sampling-error and extreme weightings. The methodology looks at applying various shrinkage techniques onto the historical covariance matrix; and then taking a resampling portfolio optimisation approach using the shrunken matrix. We use Monte-Carlo simulation techniques to replicate sets of statistically equivalent portfolios, find optimal weightings for each; and then through aggregation of these reduce the sensitivity to the historical time-series anomalies. We also consider the trade-off between sampling-error and specification-error of models.
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    The optimal asset allocation for South African real return investors
    (2019) Van Zyl, Barry; Bradfield, David
    This research aims to establish the optimal asset allocations for targeting specific real returns over short, medium and long-term investment horizons. The joint returns are modelled with data-centric methods that are empirical and non-parametric in nature, and are able to capture the dependencies of returns over time. The asset classes that are considered are South African (SA) equities, SA bonds, SA cash, SA property, global equities, global bonds, global cash, and global property. The returns of each asset class are modelled, each class with its own empirical distribution based on monthly returns from 1972 to 2017. The monthly returns are grouped in a block of rolling periods of varying block lengths in order to attempt to capture dependencies across time. These blocks of data are resampled in order to simulate the distributions of returns of portfolios with their own unique empirical distribution. The optimal portfolios are derived using a genetic algorithm, showcasing how these extremely versatile optimisation tools can be used in combination with resampling methods to find the optimal portfolio for virtually any criterion. A comparison is also made to the traditional mean-variance optimal portfolios, yielding an estimate of the bias in mean-variance optimisation’s (MVO) optimal weights. It is investigated how these optimal portfolios are influenced by the choice of risk criterion and investment horizon. The effect of the most important and consequential nuisance parameter in this research’s model, the block length, is discussed. The relationships established between the characteristics of optimal portfolios and investment horizon and risk criterion and the comparisons with classic MVO should be of interest to investors and investment professionals alike. Economic and market regimes are “identified” on the basis of economic and market data, consequently the resampling probabilities will be unequal. The optimal weights conditional on regimes are derived. Both static and changing regimes are considered. Lastly, an out-of-sample backtest of the performance of the optimal portfolios conditional on the regime across time at six month intervals is conducted from 1983 to 2017. It shows that out of the three block lengths tested for a single investment horizon of 36 months, a block length of 24 months yielded the best overall risk-adjusted performance, on average. Conditioning for regimes is shown to generally outperform the unconditional approach. The improvements are marginal and further research is recommended to investigate the performance for longer investment horizons and other values of the two tuning parameters, block length and tactical pressure. The higher level aim of this work is to present a broad sense of how data-driven nonparametric methods can be used in conjunction with metaheuristic procedures. The objective of combining these techniques is to find optimal portfolios under very general conditions and with very few assumptions regarding the underlying distributions.