Finding moving-band statistical arbitrages via convex–concave optimization

We propose a new method for finding statistical arbitrages that can contain more assets than just the traditional pair. We formulate the problem as seeking a portfolio with the highest volatility, subject to its price remaining in a band and a leverage limit. This optimization problem is not convex,...

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Published in:	Optimization and engineering Vol. 26; no. 2; pp. 1203 - 1224
Main Authors:	Johansson, Kasper, Schmelzer, Thomas, Boyd, Stephen
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Nature B.V 01.06.2025
Subjects:	Asset acquisitions Convexity Machine learning Optimization Prices Profits Stochastic control theory Time series
ISSN:	1389-4420, 1573-2924
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Abstract	We propose a new method for finding statistical arbitrages that can contain more assets than just the traditional pair. We formulate the problem as seeking a portfolio with the highest volatility, subject to its price remaining in a band and a leverage limit. This optimization problem is not convex, but can be approximately solved using the convex–concave procedure, a specific sequential convex programming method. We show how the method generalizes to finding moving-band statistical arbitrages, where the price band midpoint varies over time.
AbstractList	We propose a new method for finding statistical arbitrages that can contain more assets than just the traditional pair. We formulate the problem as seeking a portfolio with the highest volatility, subject to its price remaining in a band and a leverage limit. This optimization problem is not convex, but can be approximately solved using the convex–concave procedure, a specific sequential convex programming method. We show how the method generalizes to finding moving-band statistical arbitrages, where the price band midpoint varies over time.
Author	Johansson, Kasper Schmelzer, Thomas Boyd, Stephen
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Cites_doi	10.1093/rfs/hhj020 10.2307/1913236 10.1080/14697688.2018.1438642 10.3386/w20282 10.1080/14697688.2016.1164886 10.1016/j.ejor.2019.04.013 10.1561/2000000072 10.1007/s10690-017-9236-z 10.2139/ssrn.3862004 10.1016/j.jfineco.2003.10.004 10.3390/jrfm12010014 10.1109/SSP.2018.8450775 10.1111/joes.12153 10.1080/14697680500149370 10.1016/j.physa.2010.01.045 10.1080/00036846.2017.1305097 10.2139/ssrn.882536 10.1109/TSP.2019.2893862 10.1109/TSP.2018.2799193 10.2139/ssrn.2196391 10.1016/j.ejor.2010.06.043 10.1109/CDC.2016.7798400 10.1016/j.ejor.2016.10.031 10.1109/ACC.2008.4586628 10.1007/s11081-015-9294-x 10.3905/jpm.2005.470578 10.1007/978-3-319-67642-5_25 10.1016/S0304-405X(02)00206-4 10.1016/j.ejor.2008.03.025 10.3390/jrfm12010031 10.1145/2830556.2830562 10.1016/S0264-9993(99)00043-7 10.1111/acfi.12953 10.1057/jdhf.2009.4 10.1109/CDC.2012.6426072 10.1080/14697680903124632 10.1016/S0304-405X(02)00225-8 10.1007/978-981-33-6137-9_10 10.1017/CBO9780511804441 10.1080/14697688.2017.1374549
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