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
IPC3
Intra Portfolio Correlation weighted Concentration Co-Efficient
IPC3 is perhaps the best single measure of diversification. The IPC3 computes the concentration coefficient and computes a concentration coefficient of the IPC values. The value obtained provides a basis for comparing portfolio diversification among a variety of portfolios
By combining each measure of diversification we can obtain a single value that explains diversification better than any. The CC can account for security risk but not market risk. The IPC accounts for market risk but not security risk. Since both risks are diversifiable a proper measure should account for both.
Intra Portfolio Correlation (IPC) is a perfect measure of diversification. IPC% calculates diversification as a percentage of the maximum statistical value. However, its utility is deceased because it can introduce significant model risk. This becomes important in portfolios with a smaller quantity of assets; therefore modeling an expected correlation becomes increasing important.
The concentration co-efficient (CC) measures diversification thought the quantity of assets held. It is also a definitive measure. However, the CC makes no quantification of the diversification in a portfolio by means of asset correlations.
IPC3 takes the form:
CC / (1-IPC %)
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