A0872
Title: Projection pursuit and portfolio selection
Authors: Chris Adcock - Sheffield University Management School (United Kingdom) [presenting]
Abstract: Projection pursuit is a data analysis technique that generates one-dimensional sum-maries of complex multivariate data sets. The methods operate on estimates of themultivariate moments of the original n-dimensional data. For variance projection pursuit based on a covariance matrix $\Sigma$, the method computes the values of an n-vector w that maximizes the quadratic form $w^{T}{\Sigma}w$ subject to the normalization $w^{T}w = 1$. In portfolio theory, the data set comprises returns on a set of risky financial assets, and the elements of the vector w denote investment proportions. The minimum variance portfolio is computed by minimizing the same quadratic form. In this case, the normalization employed is that the weights sum to unity. It is usually also the case that the weight is required to be non-negative. The use of the same quadratic form suggests that the normalization used in portfolio theory could also be employed as an alternative method of data reduction in projection pursuit. In addition, the pursuit of skewness projection suggests variations in portfolio theory methods. Standard mean-variance portfolio selection could be replaced by skewness-variance or other combinations of higher moments. The aim is to investigate differences as well as similarities between projection pursuit and portfolio selection. Both potential synergies and aspects are reported, where the two methods are distinct.
