Power mapping with dynamical adjustment for improved portfolio optimization |
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Authors: | Rudi Schäfer Nils Fredrik Nilsson Thomas Guhr |
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Institution: | 1. Department of Physics , University of Duisburg-Essen , Duisburg, Germany rudi.schaefer@uni-duisburg-essen.de;3. Department of Mathematical Physics , LTH, Lund University , Lund, Sweden;4. Department of Physics , University of Duisburg-Essen , Duisburg, Germany |
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Abstract: | For financial risk management it is of vital interest to have good estimates for the correlations between the stocks. It has been found that the correlations obtained from historical data are covered by a considerable amount of noise, which leads to a substantial error in the estimation of the portfolio risk. A method to suppress this noise is power mapping. It raises the absolute value of each matrix element to a power q while preserving the sign. In this paper we use the Markowitz portfolio optimization as a criterion for the optimal value of q and find a K/T dependence, where K is the portfolio size and T the length of the time series. Both in numerical simulations and for real market data we find that power mapping leads to portfolios with considerably reduced risk. It compares well with another noise reduction method based on spectral filtering. A combination of both methods yields the best results. |
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Keywords: | Econophysics Correlation structures Dynamic models Financial markets Monte Carlo methods Numerical simulation Portfolio optimization |
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