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Diversification - Definition and Overview |
| Related Words: Accommodation, Adaptation, Allotropy, Alteration, Analysis, Apostasy, Atomization, Break, Change, Continuity, Conversion, Defection, Degeneration |
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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%
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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:
- <math>
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}
<math>
Where Q is the intra-portfolio correlation,
<math>X_i<math> is the fraction invested in asset i,
<math>X_j<math> is the fraction invested in asset j,
<math>P_{ij}<math> is the correlation between assets i and j, and
n is the number of different assets.
See also
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