Robust beta estimation and applications

Modern portfolio theory was developed by Harry Markowitz more than forty years ago and is now considered to be an indispensable tool in portfolio construction. Sharpe introduced the index models as a simplification of the original Markowitz formulation, as this required fewer parameters to be estimated. One of the premises underlying the Sharpe Index model was that the returns of shares and market proxies followed a normal distribution and under this assumption, model parameters could best be estimated using Ordinary Least Squares (OLS) regression. More recent empirical evidence has however cast doubt over the assumption of normality and has suggested that market returns tend to be non-normal. If the assumption of normality is no longer upheld then OLS or Maximum Likelihood Estimates may no longer produce the best estimates of parameters and hence may compromise optimal portfolio constructions. In addition to the parameter estimation problems, at the time of the initial formulation of the portfolio models, managers were not allowed to participate in short sales (selling a share one does not own). This practice is now quite common in most developed markets and any portfolio formulation model needs to be generalised to allow for this. Empirical studies have shown that share returns and the returns of market proxies do not follow a normal distribution but rather seem to follow a skew distribution and has long tails. It is the aim of this thesis to explore robust regression procedures which should be an improvement of OLS when the data does not come from a normal distribution. The robust regression procedures will then be used to estimate the parameters used in the Sharpe Index models and examine whether or not they aid in the portfolio construction process. The robust procedures will be applied to the classical portfolio formulations as well as the generalised models.

Grantor dc:publisher.institution

Department of Statistical Sciences

Year dc:date.issued

2003

Author dc:creator

• Khan, Mohamed Rezah

Advisor dc:contributor.advisor

• Troskie, Casper G

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/8593

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/8593