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Measuring Portfolio Diversification

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.