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.
