This has led to other ways of constructing indices, with the aim of achieving diversification by spreading risk equally across constituents.
Because of this diversification objective, an equal risk contribution index has similarities to an equally weighted index. But equal risk contribution is a more sophisticated approach because it takes into account those two additional characteristics: stocks’ individual risk and the correlations between them.
The diagrams below, called Lorenz curves, show how concentrated indexes are when the three weighting approaches (by capitalization, equally weighted and by equal risk contribution) are applied. The more the Lorenz curve extends towards the top left of each diagram, the more concentrated the index.
Lorenz Curves for Different Weighting Methodologies
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In both diagrams the capitalization-weighted index (shown by the light blue line) is the most concentrated.
In the left diagram, which measures the cumulative weights of stocks for a given percentage of constituents, the equally weighted index (the blue line) is the least concentrated. In terms of concentration by stock weights, the equal risk contribution index (the red line) lies between the equally weighted and cap-weighted indexes.
But when the cumulative contribution to risk of the constituents is measured (in the right diagram), the equal risk contribution index is the least concentrated approach. This time the Lorenz curve of the equally weighted index lies between the curves representing the equal risk contribution index and the cap-weighted index.
Bringing stocks’ individual risk levels and intra-stock correlations into the index methodology makes calculating index weights a more complex process. In fact, this is done by means of a mathematical optimization, an algorithm that works out the lowest possible index-level volatility for a given starting set of index constituents, individual stock volatilities and correlations.
As we have seen, different types of index can serve a similar overall objective, such as enhanced diversification.
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