Optimal Allocation of a Futures Portfolio Utilizing Numerical Market Phase Detection

This paper presents an application of the recently developed method for simultaneous dimension reduction and metastability analysis of high-dimensional time series in the context of computational finance. Further extensions are included to combine state-specific principal component analysis (PCA) and state-specific regressive trend models to handle the high-dimensional, nonstationary data. The identification of market phases allows one to control the involved phase-specific risk for futures portfolios. The numerical optimization strategy for futures portfolios based on Tikhonovtype regularization is presented. The application of proposed strategies to online detection of the market phases is exemplified first on the simulated data and then on historical futures prices for oil and wheat from 2005–2008. Numerical tests demonstrate the comparison of the presented methods with existing approaches.