Portfolio Composition Strategy through a P-Spline Based Clustering Approach

Portfolio management and asset selection are important issues in the financial domain. Portfolio composition is concerned with the problem of making portfolio decisions by selecting the securities to include in the portfolio and the amount to invest in each security. Modern portfolio theory aims at building an optimized portfolio by selecting stocks with the highest expected return for a given level of risk, which is measured by the standard deviation of returns. Modern portfolio theory also suggests to consider assets in a diversified portfolio that have correlations of returns less than one with each other because in this way it can decrease portfolio the risk without sacrificing the return. The simplicity of portfolio composition by using modern portfolio theory have attracted significant attention both in academia and in practice. Over the last years, thanks to the recent interests in a financial context, both statistical and machine learning techniques have been used in order to both building and selecting portfolios. Amongst others, many proposals are based on clustering the financial series as preliminary steps for portfolio selection. Recently, a new clustering method for time series applications has been proposed by exploiting the properties of the P-splines approach. This semi-parametric tool has several advantages, i.e. it facilitates the removal of noise from time series and it allows for a reduction of the dimensionality of the clustering task ensuring a computational time saving. In this paper, we propose to use this clustering approach on financial data with the aim of providing a strategy to build a portfolio of stocks able to support the investment choices of the portfolio managers. Our proposal works directly on time series without any heavy pre-processing step, it does not require the well-known conditions of stationarity and invertibility of time series. In a few words, we propose to cluster the series of prices and then to build a portfolio on selected stocks coming from the achieved partitions. From the modern portfolio theory point of view, examples on real financial time series show that our strategy is useful to support the investment decisions of financial practitioners.