Using a recently developed method of noise level estimation [1] that makes use of properties of the coarse grained-entropy we have analyzed the noise level for the Dow Jones index and some stocks from the New York Stock Exchange as well as Warsaw Stock Exchange. We have found that the noise level ranges from 40 to 100 percent of the signal variance. The condition of the minimal noise level has been applied to construct optimal portfolios from selected shares [2]. We have observed that the level of noise is statistically correlated with the stock price changes and this fact has been used to create our investment strategy.

Using our method we have calculated 40000 recommendations for portofolio optimalization for periods 4-7 days at Warsaw Stock Exchange. The annual return received in such a way after substracting commissions was around 23%.

[1] K. Urbanowicz and J. A. Holyst, Phys. Rev. E 67, 046218 (2003).
[2] K. Urbanowicz and J.A. Holyst, Proceedings of the Conference Application of Physics in Financial Analysis 4, Physica A (2004).