## Noise Reduction by Power Mapping for Improved Portfolio Optimization

### Rudi Schäfer

Matematisk Fysik, LTH

**Friday, 14 September 2007, 14:00**

MatFys Library

**Abstract**:

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)