Theory and Methodology
Massively parallel processing of recursive multi-period portfolio models

https://doi.org/10.1016/j.ejor.2016.10.009Get rights and content

Highlights

  • Recursive multi-period portfolio modeling.

  • Massively parallel processing.

  • Real-world evidence on portfolio efficiency.

Abstract

A recursive portfolio decision system is extended with parallel processing capability monitored by the Genetic Hybrid Algorithm (GHA). Massively parallel portfolio efficiency testing is conducted using stochastic simulation. Genuine out-of-sample forecasts are generated for all titles in the universe using fast cutting-edge time series algorithms. The computation of dynamic optimal portfolio weights is done within an affine multi-period setting. The terminal wealth within the planning horizon forms a moving target as the system evolves through time and only current transactions are carried out. Fixed and variable transaction costs are recognized without increasing computational complexity. We show using a recursive multi-period portfolio framework (RMP) that robust grid search and stochastic simulation with thousands of parallel processors can be conducted to provide evidence on portfolio efficiency. The downside risk of the RMP-strategy is significantly lower than that of the corresponding buy-and-hold strategy. The upside potential of RMP is much better than that of buy-and-hold. The non-parametric test procedure is independent of the underlying model and hence completely general. The modular structure of the system allows new forecasting techniques and optimization formulations to be introduced and tested in future development efforts.

Section snippets

Background

The basis for modern portfolio theory was laid by Markowitz (1952). In the Markowitz paper, portfolio selection is considered as the problem to choose an optimal composition of financial assets such that the portfolio variance is minimized for any level of expected return. Equivalently, expected return is maximized at any level of portfolio variance in the mean–variance formulation: maxw{E[rT]wλwTΣw|wTe=1},where w ∈ ℜn, E[rT] ∈ ℜn are the asset weight and expected return vectors, Σ ∈ ℜn × n

The recursive portfolio model

As stated by Mossin (1968), “any sequence of portfolio decisions must be contingent upon the outcomes of previous periods and at the same time take into account information on future probability distributions”. Robust multi-period problem formulations recognizing both fixed and variable transaction costs require simplifications for mathematical tractability (cf. Lobo et al., 2007, Palczewski et al., 2015, Zakamouline, 2005). In a recursive setting with a fixed horizon of reasonable length, the

Numerical experiments

The numerical testing reported in this section is conducted on a database comprising the weekly closing indexes for each Wednesday of a sample of 50 STOXX titles. The naïve equally-weighted buy-and-hold portfolio containing the same 50 titles or a subset of them is used as a benchmark in the below tests. The idea to use fixed mix buy-and-hold strategies as benchmarks for predictive models is not new per se (see e.g. DeMiguel et al., 2009, Fleten et al., 2002; Ҫanakoǧlu & Özekici, 2010, Bianchi

Conclusion

We have extended a recursive portfolio decision system (RMP) with parallel processing capability monitored by GHA. The search for the superior parameterization of the optimization model and portfolio efficiency testing are conducted by massively parallel processing. The computational exercise is a small experiment in a huge combinatorial problem involving both continuous and discrete parameters for the time series algorithms and the portfolio optimization model. A small subset of the dimensions

Acknowledgment

We are grateful for the continuous and tireless support provided by the experts at CSC IT Center for Science. The comments of two anonymous reviewers are gratefully acknowledged.

References (67)

  • R. Östermark

    A fuzzy vector valued KNN-algorithm for automatic outlier detection

    Applied Soft Computing

    (2009)
  • R. Östermark

    Incorporating asset growth potential and bear market safety switches in international portfolio decisions

    Applied Soft Computing

    (2012)
  • R. Östermark

    Solving difficult mixed integer and disjunctive non-linear problems on single and parallel processors

    Applied Soft Computing

    (2014)
  • J. Palczewski et al.

    Dynamic portfolio optimization with transaction costs and state-dependent drift

    European Journal of Operational Research

    (2015)
  • A.J. Patton

    A review of copula models in economic time series

    Journal of Multivariate Analysis

    (2012)
  • G.H. Pflug et al.

    Selected parallel optimization methods for financial management under uncertainty

    Parallel Computing

    (2000)
  • A. Shapiro

    On complexity of multistage stochastic programs

    Operations Research Letters

    (2006)
  • H. Akaike

    Information theory and an extension of the maximum likelihood principle

  • H. Akaike

    A new look at the statistical model identification

    IEEE Transactions on Automatic Control

    (1974)
  • A. Beltratti et al.

    Scenario modeling for the management of international bond portfolios

    Annals of Operations Research

    (1999)
  • A. Ben-Tal et al.

    Robust convex optimization

    Mathematics of Operations Research

    (1998)
  • M. Brandt et al.

    Parametric portfolio policies: Exploiting characteristics in cross-section of equity returns

    (2004)
  • D. Brown et al.

    Dynamic portfolio optimization with transaction costs: Heuristics and dual bounds

    Management Science

    (2011)
  • T. Bodnar et al.

    A test for the weights of the global minimum variance portfolio in an elliptical model

    Metrika

    (2008)
  • E. Ҫanakoǧlu et al.

    Portfolio selection in stochastic markets with HARA utility functions

    European Journal of Operational Research

    (2010)
  • E. Ҫanakoǧlu et al.

    HARA Frontiers of Optimal Portfolios in Stochastic Markets

    European Journal of Operational Research

    (2012)
  • A. Chekhlov et al.

    Drawdown measure in portfolio optimization

    International Journal of Theoretical and Applied Finance

    (2005)
  • Chen, Z., Liu, J., Li, G., & Yan, Z. (2015).: Composite time-consistent multi-period risk measure and its application...
  • J.S. Cramer

    Logit models from economics and other fields

    (2003)
  • R.A. Davis et al.

    Structural break estimation for nonstationary time series models

    Journal of the Americal Statistical Association

    (2006)
  • V. DeMiguel et al.

    Optimal versus naive diversification: how inefficient is the 1/N portfolio

    Review of Financial Studies

    (2009)
  • B. Efron et al.

    The bootstrap method for assessing statistical accuracy

    Behaviormetrika

    (1985)
  • J.D. Farmer et al.

    Predicting chaotic time series

    Physical Review Letters

    (1987)
  • Cited by (0)

    View full text