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Finding Near-Optimal Portfolios with Quality-Diversity

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Applications of Evolutionary Computation (EvoApplications 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14634))

Abstract

The majority of standard approaches to financial portfolio optimization (PO) are based on the mean-variance (MV) framework. Given a risk aversion coefficient, the MV procedure yields a single portfolio that represents the optimal trade-off between risk and return. However, the resulting optimal portfolio is known to be highly sensitive to the input parameters, i.e., the estimates of the return covariance matrix and the mean return vector. It has been shown that a more robust and flexible alternative lies in determining the entire region of near-optimal portfolios. In this paper, we present a novel approach for finding a diverse set of such portfolios based on quality-diversity (QD) optimization. More specifically, we employ the CVT-MAP-Elites algorithm, which is scalable to high-dimensional settings with potentially hundreds of behavioral descriptors and/or assets. The results highlight the promising features of QD as a novel tool in PO.

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Notes

  1. 1.

    In terms of their distance in the space of admissible portfolio weights or, more generally, some behavior space.

  2. 2.

    In the sense of the Euclidean distance between the portfolio weight vectors \(||\boldsymbol{w_1}-\boldsymbol{w_0}||\).

  3. 3.

    Van Eeghen [14] reports computation times of around 2 hours and more per run already for \(N>20\).

  4. 4.

    Environment, social and governance.

  5. 5.

    More precisely, the assets include the S &P 500 market index, Lehman Brothers Long Term Government Bond Index, and one-month Treasury bills. The original data is presented monthly and spans the period from 1980 to 1990, but the estimates are transformed into annual values in our work.

  6. 6.

    At the start of each QD run, niches are recalculated, discarding the old CVT results.

  7. 7.

    With constant variance set as the shrinkage target.

  8. 8.

    Similar approaches are employed in top-down investment strategies such as Tactical Asset Allocation (TAA) [35].

  9. 9.

    With the QuickHull algorithm [36], the execution time grows by \(n^{\lfloor \frac{d}{2} \rfloor }\), where n is the input size and d the dimensionality.

  10. 10.

    The choice of the estimation window size is a non-trivial issue that has been studied before [38,39,40], with larger sizes leading to reduced estimation errors at the price of assuming unrealistically long stationarity periods.

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia

    Bruno Gašperov, Marko Đurasević & Domagoj Jakobovic

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  1. Bruno Gašperov
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  2. Marko Đurasević
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  3. Domagoj Jakobovic
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Correspondence to Bruno Gašperov .

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Editors and Affiliations

  1. University of York, York, UK

    Stephen Smith

  2. University of Coimbra, Coimbra, Portugal

    João Correia

  3. University of Málaga, Málaga, Spain

    Christian Cintrano

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Gašperov, B., Đurasević, M., Jakobovic, D. (2024). Finding Near-Optimal Portfolios with Quality-Diversity. In: Smith, S., Correia, J., Cintrano, C. (eds) Applications of Evolutionary Computation. EvoApplications 2024. Lecture Notes in Computer Science, vol 14634. Springer, Cham. https://doi.org/10.1007/978-3-031-56852-7_1

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  • DOI: https://doi.org/10.1007/978-3-031-56852-7_1

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