Index weighting methods

Why weighting is the decision that matters 

An index provider makes three choices when it builds a series: which companies are eligible, how many of them to include, and how much influence each one gets. The first two are the ones that get named in the instrument. The third is the one that determines behaviour. Two indices drawn from the identical list of companies, differing only in the weighting rule applied to them, produce different levels, different volatility and different correlations with everything else, and over a long horizon they can tell materially different stories about the same market.

The mechanism is simple to state. Every index level is a weighted sum of constituent prices, and a weight is the answer to a single question: when this company's share price moves by one percent, how much of that movement reaches the index. A weighting rule is nothing more than a formula for answering that question consistently across every constituent and across time.

Capitalisation weighting 

The dominant rule worldwide weights each constituent by its market capitalisation, which is its share price multiplied by the number of shares in issue. A company worth twice as much as another exerts twice the influence. The appeal is that the rule requires no judgement about which company deserves prominence: it delegates the question to the market, which has already priced every company relative to every other.

The rule also has a property that keeps maintenance cheap and is the main reason it became standard. Because a weight is proportional to a value that moves with the share price, the weights update themselves as prices change, and no trading is required to hold the basket in line. A capitalisation weighted portfolio that is left completely alone stays correctly weighted. Every other rule described below has to be traded back into shape on a schedule.

The cost is concentration. When a small number of companies grow far larger than the rest, the rule hands them a correspondingly large share of the index, and the published level increasingly reports those companies rather than the market as a whole. This is not a malfunction. It is the rule working exactly as specified, and it is the reason concentration statistics are published alongside the level rather than being inferable from it.

Free float adjustment 

Nearly every capitalisation weighted index in current use applies a further correction before the weight is set. Shares held by a founding family, by a parent company, by a government or by another strategic holder are not available to be bought, so counting them inflates the weight of a company relative to the shares that actually change hands. The free float adjustment counts only the portion available to the market.

The example is not an extreme case. Markets where family ownership, cross holdings or state stakes are common contain many companies whose free float is a minority of their capitalisation, and in those markets the adjustment reorders the index substantially. It also creates a scheduled event: when a strategic holder sells down, the free float factor is revised at the next review, the constituent's weight rises, and every fund tracking the index has to buy the difference on a known date.

Price weighting 

A small number of long established indices, including the underlying benchmarks referenced by the Wall Street 30 and Japan 225 contracts, weight constituents by share price alone. A company whose shares are quoted at a high price exerts more influence than one quoted at a low price, regardless of how large either company is. The rule predates modern computation, and its survival is a matter of continuity rather than of anyone arguing it is the better measure.

Its defining oddity is that a share price is an arbitrary number. A company can halve its share price overnight by splitting its shares, without any change in what it is worth, and a price weighted index responds by halving that company's influence. The provider adjusts the divisor so the published level does not jump, but the weight has genuinely changed, and it changed because of a decision the company made about the denomination of its stock rather than about its business.

For anyone reading a price weighted contract, the practical consequence is that the constituents worth watching are the highest priced ones, which are frequently not the largest. It is also why a price weighted index and a capitalisation weighted index covering broadly the same market can diverge for weeks at a time without either being wrong.

Equal weighting 

An equal weighted index gives every constituent the same influence, so the smallest company in the list moves the level exactly as much as the largest. The rule removes concentration entirely and, by construction, tilts the series toward the smaller half of whatever universe it is applied to. It is most often published as a companion to a capitalisation weighted flagship, precisely so the two can be compared: a persistent gap between them is one of the standard ways market breadth is measured.

The rule is expensive to maintain in a way the capitalisation rule is not. Prices move constantly, so weights drift away from equality continuously, and restoring them requires selling whatever has risen and buying whatever has fallen at every review. That trading is real and it recurs, which is one reason equal weighted variants are more common as published series than as the reference for a heavily traded derivative.

What the rule does to a contract written on the index 

A CFD references the published level, so the weighting rule reaches the contract in full and unaltered. Three effects are worth naming because each one is observable rather than theoretical.

1. Sensitivity to single companies. On a concentrated capitalisation weighted index, an earnings report from one constituent can move the whole contract. On an equal weighted or broad index the same report is diluted almost to nothing.
2. Sector exposure that nobody chose. Weighting by size means the index inherits whatever sector composition the market's largest companies happen to have, and that composition changes slowly and without announcement.
3. Scheduled flow. Free float revisions, constituent changes and equal weight restorations all happen on published review dates, and the trading they compel lands on the constituents, not on the index arithmetic.