Eur. Phys. J. B 57, 175-180 (2007)
https://doi.org/10.1140/epjb/e2007-00130-7

Risk minimization through portfolio replication

¹ CNRS, Univ. Paris Sud, UMR 8626, LPTMS, 91405 Orsay Cedex, France
² Science & Finance, Capital Fund Management, 6 boulevard Haussmann, 75009 Paris, France

Corresponding author: ^a ciliberti@roma1.infn.it

Received: 31 August 2006
Revised: 28 December 2006
Published online: 16 May 2007

Abstract

We use a replica approach to deal with portfolio optimization problems. A given risk measure is minimized using empirical estimates of asset values correlations. We study the phase transition which happens when the time series is too short with respect to the size of the portfolio. We also study the noise sensitivity of portfolio allocation when this transition is approached. We consider explicitely the cases where the absolute deviation and the conditional value-at-risk are chosen as a risk measure. We show how the replica method can study a wide range of risk measures, and deal with various types of time series correlations, including realistic ones with volatility clustering.