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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 = \frac{\sum_{i=1}^n\sum_{j=1}^n X_i X_j P_{ij}}{\sum_{i=1}^n\sum_{j=1}^n X_i X_j}

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, and n is the number of different assets.

See also

Last updated: 08-19-2005 22:56:02
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