Price-weighted index
Index = SUM(prices) / divisor
New divisor after a corporate action = new price sum / index level to be preserved
When the question gives only prices. The divisor starts as the number of stocks and must be re-solved after any split or constituent change.
- prices
- Market price of each constituent
- divisor
- Initially the number of stocks; adjusted to keep the index continuous
Value-weighted index
Index = (SUM(price x shares) / base market cap) x base index value
Shortcut: New index = Old index x (new aggregate cap / old aggregate cap)
The method the Sensex and Nifty use. Needs share counts as well as prices, and requires no adjustment for splits.
- price x shares
- Market capitalisation of each constituent
- base market cap
- Aggregate capitalisation on the base date
- base index value
- Index level assigned to the base date, e.g. 100 or 1,000
Equal-weighted index return
Return = (SUM of individual percentage returns) / number of stocks
When every constituent is to count the same. It over-weights small companies relative to the market and needs periodic rebalancing.
- individual return
- (new price - old price) / old price, per stock