July 31, 2018

Over the last decade we seen a have surge in popularity the so called fundamentally weighted index, a type of equity index in which components are chosen based on fundamental criteria as opposed to market capitalization. Here we show that in a general equilibrium setting we know that the fundamentally weighted index must converge to the capitalization weighted index. Thus if there is a manager that is using a fundamentally weighted index that diverges from the market cap, there has to be other managers holding the remaining stocks in the index not being held by the fundamentally weighted index. This generates an excess demand for the fundamentally over weighted stocks and an excess supply for the fundamentally underweighted stocks. Equilibrium requires a change in the absolute and relative price of the stocks. The price of the fundamentally over weighted stocks increases while the price of the fundamentally underweighted stocks declines. Once equilibrium is restored, the fundamentally weighted index and the market capitalization weighted index become one and the same.

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