The Dow is a price-weighted index, and the average price of its thirty components is currently around $58. Both AAPL and GOOG have share prices in excess of $600, and their inclusion would cause day-to-day changes in the index to be driven largely by the behavior of these two securities. For instance, their combined weight in the Dow would be about 43% if they were to replace AA and TRV, which are the two current components with the lowest valuations. Furthermore, the index would become considerably more volatile even if the included stocks were individually no more volatile than those they replace.
To solve this problem, Debraj Ray and I have proposed a modification to the Dow formula that largely preserves the historical integrity of the data series, while allowing for the inclusion of securities regardless of their market price. Our modified index also leads to a smooth and gradual transition, as incumbent stocks are replaced, to a fully value-weighted index in the long run.
The proposed index is composed of two subindices, one price-weighted to respect the internal structure of the Dow, and the other value-weighted to apply to new entrants. The index has two parameters, both of which are adjusted whenever a substitution is made. One of these maintains continuity in the value of the index, while the other ensures that the two subindices are weighted in proportion to their respective market capitalizations. Stock splits require a change in parameters (as in the case of the current Dow divisor) but only if the split occurs for a firm in the price-weighted subindex.