Risk Minimization through Portfolio Replication

Details Risk Minimization through Portfolio Replication Risk Minimization through Portfolio Replication

2006-08-03

arxiv.org/abs/physics/0608035v1

Physics

Physics and Society

12 pages, APFA5 conference

Scientific paper

10.1140/epjb/e2007-00130-7

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.

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