Diversification

Diversification is a measure of the commonality of a population. Greater diversification denotes a wider variety of elements within that population. Diversification is of central importance in investments. Diversification reduces the risk of a portfolio. It does not necessarily reduce the returns. This is why diversification is referred to as the only free lunch in finance.

Diversification can be quantified as the intra-portfolio correlation. This is a statistical measurement from negative one to one that measures the degree to which the various assets in a portfolio can be expected to perform in a similar fashion.

Intra-portfolio Correlation... Percent of Diversifiable Risk Eliminated...

        1                            0%
        .75                       12.5%
        .50                         25%
        .25                       37.5%
        0                           50%
        -.25                      62.5%
        -.50                        75%
        -.75                      87.5%
        -1                         100%

Portfolio balance occurs as the sum of all intra-portfolio correlations approaches negative one. Diversification is thus defined as the intra-portfolio correlation or, more specifically, the weighted average intra-portfolio correlation. Maximum diversification occurs when the intra-portfolio correlation is minimized. Intra-portfolio correlation may be an effective risk management measurement. The computation may be expressed as:

Q = Sigma XiXjPij / Sigma XiXj

Where Q is the intra-portfolio correlation, Xi is the fraction invested in asset i, Xj is the fraction invested in asset j, Pij is the correlation between assets i and j, The expression may be computed at least when i does not equal j.