LIQUIDITY RISK AND INSTABILITIES IN PORTFOLIO OPTIMIZATION

Fabio Caccioli, Imre Kondor, Matteo Marsili and Susanne Still
Additional contact information
Fabio Caccioli: Department of Computer Science, University College London, London WC1E 6BT, UK2Systemic Risk Centre, London School of Economics and Political Sciences, London, UK
Imre Kondor: Parmenides Foundation, Kirchplatz 1, Pullach, 82049, Germany
Matteo Marsili: Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Trieste, 34151, Italy
Susanne Still: Information and Computer Sciences, University of Hawai’i at Mānoa, 1680 East-West Road, Honolulu, 96822, Hawai’i, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 05, 1-28

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 ℓp with p > 1 makes the sensitivity of coherent risk measures to estimation error disappear, while regularizers with p < 1 do not. The ℓ1 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.

Keywords: Portfolio optimization; estimation error; expected shortfall (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (10)

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DOI: 10.1142/S0219024916500357

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