  A well-interpretable measure of information has been recently proposed based
on a partition obtained by intersecting a random sequence with its moving
average. The partition yields disjoint sets of the sequence, which are then
ranked according to their size to form a probability distribution function and
finally fed in the expression of the Shannon entropy. In this work, such
entropy measure is implemented on the time series of prices and volatilities of
six financial markets. The analysis has been performed, on tick-by-tick data
sampled every minute for six years of data from 1999 to 2004, for a broad range
of moving average windows and volatility horizons. The study shows that the
entropy of the volatility series depends on the individual market, while the
entropy of the price series is practically a market-invariant for the six
markets. Finally, a cumulative information measure - the `Market Heterogeneity
Index'- is derived from the integral of the proposed entropy measure. The
values of the Market Heterogeneity Index are discussed as possible tools for
optimal portfolio construction and compared with those obtained by using the
Sharpe ratio a traditional risk diversity measure.
