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Liquidity risk and instabilities in portfolio optimization

Caccioli, F; Kondor, I; Marsili, M; Still, S; (2016) Liquidity risk and instabilities in portfolio optimization. International Journal of Theoretical and Applied Finance , 19 (5) , Article 1650035. 10.1142/S0219024916500357. Green open access

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Abstract

We show that including a term which accounts for finite liquidity in portfolio optimization naturally mitigates the instabilities that arise in the estimation of coherent risk measures on finite samples. This is because taking into account the impact of trading in the market is mathematically equivalent to introducing a regularization on the risk measure. We show here that the impact function determines which regularizer is to be used. We also show that any regularizer based on the norm ℓpℓp with p>1p>1 makes the sensitivity of coherent risk measures to estimation error disappear, while regularizers with p<1p<1 do not. The ℓ1ℓ1 norm represents a border case: its “soft” implementation does not remove the instability, but rather shifts its locus, whereas its “hard” implementation (including hard limits or a ban on short selling) eliminates it. We demonstrate these effects on the important special case of expected shortfall (ES) which has recently become the global regulatory market risk measure.

Type: Article
Title: Liquidity risk and instabilities in portfolio optimization
Open access status: An open access version is available from UCL Discovery
DOI: 10.1142/S0219024916500357
Publisher version: http://dx.doi.org/10.1142/S0219024916500357
Language: English
Additional information: Electronic version of an article published as International Journal of Theoretical and Applied Finance, 10.1142/S0219024916500357 © copyright World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijtaf.
Keywords: Portfolio optimization; estimation error; expected shortfall
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1450511
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