How do I calculate a price-weighted index with a divisor adjustment?

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AcadiFi · Accepted Answer

A price-weighted index is calculated as the sum of constituent prices divided by a divisor: Index = Σ Pi / D. Initially D = number of stocks. The divisor is adjusted after splits, spinoffs, or constituent changes so the index level is continuous. Example: An index contains four stocks at prices $140, $60, $90, $30. Sum = $320, initial divisor = 4, index = 80. If the $140 stock splits 2-for-1, its price becomes $70. New sum = $250. To keep index at 80, new divisor D' is solved from: 250 / D' = 80, so D' = 3.125. Note: after the split, a 1% move in the now-$70 stock changes the index by $0.70 / 3.125 = 0.224 points — less than before the split when a 1% move changed the index by $1.40 / 4 = 0.35 points. This exposes the core flaw of price-weighting: arbitrary share prices determine influence. A $720 stock (like Booking) would dwarf a $40 stock even if the latter's market cap were three times bigger. Constituent replacement: if CoreBright ($60) is removed and WintergaleAgri ($100) added, pre-change sum = $250, post-change sum = $290. New divisor adjusts: 290 / D'' = (pre-change index), recompute to maintain continuity. Only two major indices still use price-weighting: the DJIA and Nikkei 225.

How do I calculate a price-weighted index with a divisor adjustment?

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