Price-weighted and equal-weighted indexes

What choices does an index provider make?

Building an index is like building a portfolio, and the provider answers five questions. Each answer changes the index’s return, so two indexes of “the same market” can differ.

The first is the target market : the market, segment or asset class the index represents. It can be broad (all shares in a country) or narrow (small technology companies in one region). The second is security selection : nearly all of the securities in that market, or a representative sample. Some indexes fix the number of constituents and put it in the name; others let the number vary. Selection may follow mechanical rules or a committee’s judgment.

The third choice is how to weight the securities. The last two are when to rebalance (reset the weights) and when to re-examine the list. Those two come up in lesson 4.

Building an indexsimilar to building a portfolio

• Target market Know the idea which market, segment or asset class it represents
• Security selection Know the idea nearly all of the market, or a representative sample
• Weighting Memorize how much of each security
  • Price weighting weight follows share price
  • Equal weighting each constituent gets 1 ÷ N
  • Market-cap and fundamental weighting next lesson
• Rebalancing Know the idea when weights are reset
• Reconstitution Know the idea when the member list is re-examined

Exam tip Weighting is the choice with the biggest effect on index value and return. The rest of this lesson and the next one work through the four weighting methods.

How does price weighting work?

In price weighting each constituent’s weight is its share price divided by the sum of all the prices. The index value is the sum of prices divided by a divisor . Holding the index is like owning one share of each constituent.

$$V = \frac{\sum_i P_i}{D}$$

$$w_i = \frac{P_i}{\sum_j P_j}, \qquad R = \frac{\sum P_1 - \sum P_0}{\sum P_0}$$

This lesson and the next use one three-stock table. Prices are in USD, shares outstanding in millions and dividends per share are paid during the period.

Stock	Start price	End price	Shares (m)	Dividend
X	80	88	50	2.00
Y	25	24	200	0.50
Z	45	54	40	0.00

What happens when a share splits?

A split divides a share’s price, so the sum of prices falls even though nothing economic has changed. To stop the index from dropping, the provider changes the divisor so that the index value is the same just after the split as just before.

$$D_{new} = \frac{\sum P_{after}}{V_{before}}$$

Price weighting is simple and has a long history. Its weakness is that the weights are arbitrary: they depend on price levels, which splits change. The same divisor adjustment is needed when a constituent is replaced.

How does equal weighting work?

In equal weighting every constituent gets the same weight, 1 ÷ N, at the start of the period. The index return is then the simple average of the constituents’ returns.

$$w_i = \frac{1}{N}, \qquad R = \frac{1}{N}\sum_i R_i$$

Equal weighting is also simple. It avoids concentration in the biggest names, but it has two drawbacks. First, small companies are overweighted and large ones underweighted relative to their share of the market, and small companies are less liquid and harder to replicate. Second, weights drift as prices move. After one period here the weights are X 33.7%, Y 29.4%, Z 36.8%, so the provider has to rebalance often to restore 33.3% each.

How do the two methods compare on the same table?

They give different returns because the weighting rule is different. Price weighting follows the change in the sum of prices (10.67%). Equal weighting averages the returns (8.67%). A third method, market-cap weighting, gives 5.19% on the same table, and the next lesson shows how.

Go deeper Why price-weighted indexes survive, and what splits do over decades

Price weighting is the oldest method. It needs only prices and a divisor, so it could be calculated by hand a century ago. Some of the most quoted indexes still use it. Because companies tend to split their shares as prices rise, the shares that have done best get the lowest prices per share, and so lose weight. Over decades a price-weighted index drifts away from the winners. That is a quirk of the method, not a view about the companies.

Go deeper The hidden tilts of equal weighting

Giving the same weight to a very small company and a giant means equal weighting holds far more small companies than the market does. It also sells winners and buys losers each time it rebalances, which is a mild contrarian pattern. Both tilts mean its returns can differ from a market-cap index even when the target market is the same.