Conventional indexing certainly has its fan club. The classic version, started by Jack Bogle at Vanguard, is simple to understand: clients own shares on the market in the same proportions as the market itself.

For this school of thought, markets are efficient and any pricing anomalies are soon arbitraged out. Moving away from a market-cap weighting, in Bogle’s view, requires special insight — though more often it is driven by arrogance...

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