Can a Statistical Understanding of Markowitz Mean Variance Efficiency Improve Portfolio Optimisation for U.K. Equities? - Pugh, Charles J. (2009)
This paper seeks to develop a better statistical understanding of the paradigm of Markowitz mean variance optimisation by investigating the inherent variability and limitations of the process. Then testing some of the proposed techniques to improve the performance of the optimiser in selecting portfolios which not only have investment value, but also make prude investment sense to the user. After a brief introduction where the origins of mean variance efficiency are discussed within the context of Markowitz’s own ideas of the development of mean variance efficiency and the reaction from some of his immediate peers, the aims of the paper are outlined. As noted above - an investigation into the statistical understanding of the process. Next an extensive overview of the existing literature on the subject is performed. The review starts at the very beginning of attempts to comprehend portfolio selection (‘portfolio optimisation’ as we now consider it is hardly an appropriate term for this early work), and notes the landmark introduction of mathematical technique that Markowitz (1952) brought to the area. The review moves on to look at the most serious limitations of mean variance efficiency as a practical tool of investment management, most notably instability and ambiguity. Finally a lengthy look at the research done on proposed alternative frameworks and improvements to classic mean variance optimisation for it to yield more investment intuitive optimised portfolios. In light of this a hypothesis is put forward in order to test the strengths of some of the improvements suggested. The methodology as outlined in this paper consists of initially specifying the data set used in the analysis. Then the computational algorithm of classic mean variance optimisation is outlined. It proceeds by describing the methods of implementation of the statistical procedures which are proposed to enhance the performance of the optimisation, including a basic institutionally constrained short selling example. The results demonstrate the variability and over reliance of the mean variance process on the estimated inputs. If the inputs do not give an accurate impression of future returns the results are “error maximised” portfolios, which even the statistical techniques can do little to improve. When the inputs give a fair reflection of future returns the statistical techniques perform very well at improving portfolio composition to give more investor intuitive results.