  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 percent of the signal variance.
The condition of a minimal noise level has been applied to construct optimal
portfolios from selected shares. We show that implementation of a corresponding
threshold investment strategy leads to positive returns for historical data.
