Advances in Risk Based Investing by means of Quantile Regression

PhD (Science with Business Mathematics), North-West University, Potchefstroom CampusThis thesis advances the relatively open-field of risk-based investing using methods available through quantile regression. To explain the complex relationship between different assets, practitioners and academics alike, rely on linear models and simplifying assumptions about the joint asset return distribution. These assumptions are made even though parametric distributions are often poor approximations for the full empirical distribution. Unlike other investment strategies which use multiple inputs in the portfolio construction process, risk-based strategies rely solely on the covariance matrix. In this context, the covariance matrix is the summary of joint asset return distribution for risk modelling purposes. It follows that any discrepancies between the actual and modelled asset relationships will have a direct impact on portfolio construction of risk-based investment strategies. These discrepancies usually exist in the tails since asset returns often exhibit fat tails that are difficult to approximate with parametric distributions. Quantile regression is a method that can give a fuller picture of an empirical sample, without making any distributional assumptions. The method is flexible and can readily be applied with linear, quadratic, or other models. For this reason, quantile regression is a natural choice to address problems involving the tails of distributions. As a result, this thesis uses quantile regression and methods derived from it, such as quantile simulation, to address a range of problems in the field of risk-based investing. Specifically, the portfolio construction framework, the measurement of portfolio risk, and the management of portfolio risk in the construction process.Doctora