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:
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