Diversification

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Diversification Measurement

Intra-Portfolio Correlation

Intra-portfolio correlation is a means to quantify diversification . The range is from -1 to 1, with -1 being the most diversified and 1 being the least. We actually use a weighted average intra-portfolio correlation. This statistic is calculated as follows:

Where Q is the intra-portfolio correlation,

X i is the fraction invested in asset i,

X j is the fraction invested in asset j,

P ij is the correlation between assets i and j,

The expression is only computed when i j

The numerator represents the summation of all unique non-diagonal values in the matrix. The denominator represents the portfolio weight without the weight of irrelevant diagonal weights. This is because diagonal weights apply only to assets, not to the assets' relationships.

The IPC takes on the range of correlation value, and can be expressed in % format for uniform and simple reading.

IPC

% of diversifiable risk removed

1.00

0.00%

0.75

12.50%

0.50

25.00%

0.25

37.50%

0.00

50.00%

-0.25

62.50%

-0.50

75.00%

-0.75

87.50%

-1.00

100%

Concentration Coefficient

The concentration coefficient measures portfolio concentration in terms of the asset weightings. In an equal weighted portfolio the CC will be equal to the number of assets. As the portfolio becomes more concentrated in particular assets the CC will be proportionally reduced.

Introduced by Brandes Institute:

Thus, the CC is defined as:

Where:

  • P is the portfolio
  • N is the number of stocks held in the portfolio
  • W i,t is the weight of the i th stock in the portfolio at time t

Portfolio Dimension

KLD Dimension

Gravity Investments created dimensionality to represent the total diversification of a portfolio. More dimensions = more diversification. Normally, we think of having three dimensions to our world plus time as the fourth dimension. In mathematics, there are no limitations to the dimensionality. For example, the branch of physics investigating string theory has discovered that it takes 13 dimensions to attain harmony among their calculations. Every extra dimension that a portfolio has allows it to perform in a simultaneous and independent direction. A perfectly undiversified portfolio is one-dimensional. Think of a dot on a line. The dot can only move up the line or down the line. Now imagine a dot placed in a 5 dimensional space. That dot now has freedom to move up or down along each of the five directions. The direction is goes along one axis (dimension) does not connote anything about how it moves along another axis. The measure is patent pending.

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Investment Portfolio Diversification

Gsphere is visual asset allocation software rooted in portfolio diversification. Diversification is displayed in 3D as symmetry, equating portfolio balance to physical balance.
Meanwhile, the optimal asset allocation is obtained. Gsphere creates one globally efficient model portfolio, determining the equilibrium of diversification, risk and return.