In the market place, diversification reduces risk and provides protection
against extreme events by ensuring that one is not overly exposed to individual
occurrences. We argue that diversification is best measured by characteristics
of the combined portfolio of assets and introduce a measure based on the
information entropy of the probability distribution for the final portfolio
asset value. For Gaussian assets the measure is a logarithmic function of the
variance and combining independent Gaussian assets of equal variance adds an
amount to the diversification. The advantages of this measure include that it
naturally extends to any type of distribution and that it takes all moments
into account. Furthermore, it can be used in cases of undefined weights
(zero-cost assets) or moments. We present examples which apply this measure to
derivative overlays.