Browsing by Author "Bailey, Geraldine"

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    Robust portfolio construction controlling the alpha-weight angle
    (2013) Bailey, Geraldine; Bradfield, Dave
    Estimation risk is widely seen to have a significant impact on mean-variance portfolios and is one of the major reasons the standard Markowitz theory has been criticized in practice. While several attempts to incorporate estimation risk has been considered in the past, the approach by of Golts and Jones (2009) represents an innovative approach to incorporate estimation risk in the sample estimates of the input returns and covariance matrix. In this project we discuss the theory introduced by Golts and Jones (2009) which looks at the direction and the magnitude of the vector of optimal weight and investigates them separately, with focus on the former. We demystify the theory of the authors with focus on both mathematical reasoning and practical application. We show that the distortions of the mean-variance optimization process can be quantified by considering the angle between the vector of expected returns and the vector of optimized portfolio positions. Golts and Jones (2009) call this the alpha-weight angle. We show how to control this angle by employing robust optimization techniques, which we also explore as a main focus in this project. We apply this theory to the South African market and show that we can indeed obtain portfolios with lower risk statistics especially so in times of economic crisis.
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    Robust portfolio construction using sorting signatures
    (2014) Kasenene, Lillian; Bradfield, Dave; Bailey, Geraldine
    Mean-variance analysis introduced by Harry Markowitz has been criticised in the past mainly due to the counter-intuitive and unstable nature of the resultant portfolios from the optimisation. These disappointing results have been linked to the presence of estimation error in the estimates of the expected returns and covariances which serve as input to the optimisation. Several attempts have been made to produce more reliable estimates, with a significant amount of effort and resources placed in estimation of expected returns, which is generally a more difficult task than estimation of covariances. Almgren and Chriss (2006) provide a methodology for portfolio selection in which the order of expected returns replaces the numerical values of the returns. This framework allows full use of the covariance matrix, in a method analogous to mean-variance optimisation. We adopt this framework in our analysis together with the robust optimisation technique introduced by Golts and Jones (2009) which improves the estimate of the covariance matrix by direct modification in the optimisation process. Golts and Jones (2009) argue that a reduction of the angle between the input return forecasts and the output portfolio positions results in more investment relevant portfolios, inline with the investment manager's insights. They relate this angle to the condition number of the covariance matrix and use robust optimisation to improve the conditioning of this matrix. Assuming perfect alpha foresight of an investment manager, we apply a combination of the techniques of Almgren and Chriss (2006) and Golts and Jones (2009) to South African equity data and show that the resultant robust portfolios, though conservative in their risk-adjusted return statistics, are more diversified and exhibit lower leverage than mean-variance portfolios. We further show that independent of the optimisation method, there is a marginal difference in the performance of portfolios created using ordering information and actual returns.