Optimal Allocation of a Futures Portfolio Utilizing Numerical Market Phase Detection

Abstract

Abstract. 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][2006][2007][2008] 1. Introduction. In today's financial industry, computational finance is used for a wide field of applications. Throughout this paper, we will concentrate on the portfolio optimization problem, where, for return maximization and risk minimization problems, the evolution of security returns is estimated with a variety of different methods, in order to find an allocation that optimizes a suitable performance criterion, while limiting the risk [27,31]. For practical reasons, computational methods have to address the following points:1. Time series analysis. Market dynamics are most likely not reflected by a stationary process, but involve (hidden) market phases, such as economic cycles, harvest cycles (for grain, fruits, and other kinds of plants), and yearly holidays, and many more aspects influence the markets. This poses fundamental problems for estimation: To obtain sensible estimates for mean returns even in stationary linear models, hundreds of years of data would be needed. In shorter intervals, estimation risk becomes significant.

Metaheuristic multi-objective optimization of constrained futures portfolios for effective risk management

“…(5), (6) and (13)-(15) representing the diversification and risk budget aspects of the portfolio as its multiobjective functions and Eqs. (3), (4) and (10)- (12) representing the asset class, bounding and basic constraints of the portfolio, had to be solved to obtain metaheuristic Pareto-optimal solutions.…”

“…Putzig, Becherer and Horenko [6] discussed a futures portfolio optimization problem that dealt with a long-short portfolio for commodities with basic constraints and which employed a numerical optimization strategy based on the Tykhonov-type regularization for its solution. You and Daigler [7] examined the diversification benefits of using individual futures contracts instead of simply a commodity index.…”

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“…For instance, the approach in [63] is based on the following observation. The increase of the number of clusters leads to an increase of uncertainty of the estimated model parameters for each cluster as less data is assigned.…”

Statistical learning of nonlinear stochastic differential equations from non-stationary time series using variational clustering

“…In a series of works Horenko (2010a); Metzner et al (2012); Pospisil et al (2018) introduced and developed an efficient non-parametric model-based clustering framework which proved to be a successful analysis tool in atmospheric sciences (Horenko, 2010b;O'Kane et al, 2013;Vercauteren and Klein, 2015;Franzke et al, 2015;Risbey et al, 2015;O'Kane et al, 2016;Vercauteren et al, 2019;Boyko and Vercauteren, 2020) molecular dynamics (Gerber and Horenko, 2014) and computational finance (Putzig et al, 2010). The paradigm of the approach is based on two assumptions.…”