Theory and MethodologyMassively parallel processing of recursive multi-period portfolio models
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: 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.
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