Risk Minimization through Portfolio Replication

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.

12 pages, APFA5 conference

References in corpus (4)

• Noise Dressing of Financial Correlation Matrices
• Universal and non-universal properties of cross-correlations in financial time series
• Modelling fluctuations of financial time series: from cascade process to stochastic volatility model
• Noisy Covariance Matrices and Portfolio Optimization II

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