Diversification
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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% |
Portfolio balance yes yes 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.