# An Iterated Greedy Heuristic for the 1/N Portfolio Tracking Problem

### Oliver Strub, Norbert Trautmann

#### Abstract

The 1/N portfolio represents a simple strategy to invest money in the stock market. Investors who follow this strategy invest an equal proportion of their investment budget in each stock from a given investment universe. Empirical results indicate that this strategy leads to competitive results in terms of risk and return compared to more sophisticated strategies. However, in practice, investing in all N stocks from a given investment universe can cause substantial transaction costs if N is large or if the market is illiquid. The optimization problem considered in this paper consists of optimally replicating the returns of the 1/N portfolio by selecting a small subset of the N stocks, and determining the respective weight for each selected stock. For the first time, we apply the concept of iterated greedy heuristics to this novel portfolio-optimization problem. For analyzing the performance of our heuristic approach, we also formulate the problem as a mixed-integer quadratic program (MIQP). Our computational results indicate that, within a limited CPU time, our heuristic approach outperforms the MIQP, in particular when the number of stocks N grows large.

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#### Paper Citation

#### in Harvard Style

Strub O. and Trautmann N. (2016). **An Iterated Greedy Heuristic for the 1/N Portfolio Tracking Problem** . In *Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-171-7, pages 424-431. DOI: 10.5220/0005827704240431

#### in Bibtex Style

@conference{icores16,

author={Oliver Strub and Norbert Trautmann},

title={An Iterated Greedy Heuristic for the 1/N Portfolio Tracking Problem},

booktitle={Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2016},

pages={424-431},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005827704240431},

isbn={978-989-758-171-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - An Iterated Greedy Heuristic for the 1/N Portfolio Tracking Problem

SN - 978-989-758-171-7

AU - Strub O.

AU - Trautmann N.

PY - 2016

SP - 424

EP - 431

DO - 10.5220/0005827704240431