Regensburg 2007 – scientific programme

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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 14: Financial Markets and Risk Management III

AKSOE 14.1: Talk

Thursday, March 29, 2007, 14:00–14:30, H8

Noise Reduction by Power Mapping for Improved Portfolio Optimization — •Rudi Schäfer, Nils Fredrik Nilsson, and Thomas Guhr — Mathematical physics, LTH, Lund university, P.O. Box 118, 22 100 Lund, Sweden

To construct an optimal portfolio it is of vital interest to know the correlations between different stocks. However, due to the finiteness of recorded time series the true correlations are covered by a considerable amount of noise [1]. This leads to a systematic underestimation of risk.

In 2003 Guhr and Kälber [2] introduced the power mapping to suppress this noise and thereby effectively “prolong” the time series. This method raises the absolute value of each matrix element to a power q while preserving the sign. There is a trade-off between suppressing the noise and destroying the true correlations in the matrix. We use the Markowitz portfolio optimization as a criterion for finding the optimal value for q. In particular, we investigate how this value is effected by changing the underlying correlation structure and the tail behavior of the random processes used to simulate the stock prices.

[1] L. Laloux et al, Phys. Rev. Lett. 83, 1467 (1999)

[2] T. Guhr, B. Kälber, J. Phys. A 36, 3009 (2003)