Lp Regularized Portfolio Optimization

27 Pages Posted: 16 Apr 2014

See all articles by Fabio Caccioli

Fabio Caccioli

University College London

Imre Kondor

Parmenides Foundation; London Mathematical Laboratory

Matteo Marsili

Abdus Salam International Centre for Theoretical Physics (ICTP)

Susanne Still

University of Hawaii

Date Written: April 15, 2014


Investors who optimize their portfolios under any of the coherent risk measures are naturally led to regularized portfolio optimization when they take into account the impact their trades make on the market. We show here that the impact function determines which regularizer is 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 (equivalent to a ban on short selling) eliminates it. We demonstrate these effects on the important special case of Expected Shortfall (ES) that is on its way to becoming the next global regulatory market risk measure.

Suggested Citation

Caccioli, Fabio and Kondor, Imre and Marsili, Matteo and Still, Susanne, Lp Regularized Portfolio Optimization (April 15, 2014). Available at SSRN: https://ssrn.com/abstract=2425326 or http://dx.doi.org/10.2139/ssrn.2425326

Fabio Caccioli (Contact Author)

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Imre Kondor

Parmenides Foundation ( email )

Kirchplatz 1
Munchen, 82049

London Mathematical Laboratory ( email )

14 Buckingham St
London, WC2N 6DF
United Kingdom

Matteo Marsili

Abdus Salam International Centre for Theoretical Physics (ICTP) ( email )

Strada Costiera 11
Trieste, 34014

Susanne Still

University of Hawaii ( email )

Honolulu, HI 96822
United States

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