Investment strategy due to the minimization of portfolio noise level by observations of coarse-grained entropy

Using a recently developed method of noise level estimation that makes use of properties of the coarse-grained entropy, we have analyzed the noise level for the Dow Jones index and a few stocks from the New York Stock Exchange. We have found that the noise level ranges from 40% to 80% of the signal variance. The condition of a minimal noise level has been applied to construct optimal portfolios from selected shares. We show that the implementation of a corresponding threshold investment strategy leads to positive returns for historical data.