The Index: Construction, Weighting and What Inclusion Means

An index is a rule for turning the prices of a chosen set of companies into a single number. The rule fixes which companies are in it, how much each one counts, and how the number is held steady through corporate actions. An index is a construction defined by the methodology that built it, not an observation of a market.

A rule of that kind hides more work than it announces. Every part of the number is a decision somebody wrote down: which companies were eligible, how many were taken, what each was measured by, and what happens on the day one of them issues shares. Two of the inputs to those decisions are already established. Market capitalisationWhat the quoted price puts on the whole equity of a company once every share in issue is counted at it. Nothing about revenue, assets or headcount enters it. was settled earlier in this sequence, and so was free floatWhatever part of the shares is actually loose in the market, after promoter and other locked in holdings are taken out. A proportion of the count, never a verdict on the business.. An index takes both of them, puts them inside a construction, and turns them into a weight.

What is an index, once it stops being treated as a thermometer?

Think about a school that reports one number for how the class did in an exam. The headmaster could take the plain average of thirty marks. He could weight every mark by the number of subject periods the student sat. He could drop the five lowest. Each of those is defensible, each produces a different number, and none of them is the class. The number is the rule, applied to the marks.

An equity index works exactly that way. Somebody writes a methodology document, the document says what goes in and how much each thing counts, and the number falls out. Two different rules applied to the very same set of prices on the very same day produce two different numbers. An index measures a market only in the sense its methodology defines. There is no underlying quantity called the market that the index is trying to estimate and sometimes gets wrong. There is a rule, and the rule has an output.

Here is the concrete version, using an unnamed illustrative index of fifty companies. Suppose one constituent rises 10 per cent on a day when nothing else moves at all. Under a rule that gives every constituent the same weight, each one counts 2.00 per cent, so the number rises 0.20 per cent. Under a rule that weights by free float capitalisation, that same constituent counts 0.20 per cent, so the number rises 0.02 per cent. Same market, same day, same prices, and the two answers are ten times apart.

How is an index actually built, decision by decision?

Five decisions, in order, and each one narrows what the number can possibly mean.

The first is the universe. Somebody says which companies are even eligible to be considered: listed on a stated exchange, of a stated kind, with a stated minimum trading record. The second is the selection criteria applied inside that universe. The criteria typically look at size and at how readily the shares trade. The third is the count, meaning how many names are taken, fifty or a hundred or five hundred. The count is a pure choice with no correct answer. The fourth is the weighting basis, and the basis decides how much each selected company counts. The fifth is the maintenance rule set: what happens on a corporate action, how often the list is reviewed, and how the number is kept continuous across both.

Every one of those five is a decision taken by people and written down, and the resulting number inherits all five of them. An index cannot be read without knowing its methodology. A reader who cannot say what the universe was, or how many names were taken, or what the weighting basis is, is reading a number whose meaning has not been established.

What does weighting decide?

Weighting decides whose price movements the number is actually reporting. If a company carries 0.20 per cent of the index, then a move in its price arrives in the number multiplied by 0.002, and a move in a company carrying 6 per cent arrives multiplied by 0.06. The index is a weighted average of price changes, and the weights are the whole of the transmission.

Under capitalisation weighting a larger company moves the number more. The rule sounds obvious until its practical consequence is spelt out: a heavily weighted handful can carry the index up on a day when most of the constituents fell. The lopsided result is not a flaw in the number. The number is doing exactly what its rule says. Weighting fixes whose movements the number is reporting and whose it is quietly ignoring, so weighting is the single most consequential choice in the whole construction.

The weighting basis is also where the tracking fundA fund that holds the constituents of an index in the index's own proportions, so that its return follows the index rather than a manager's selection. How such funds are run is a separate subject. enters. A fund built to follow an index has to hold the weights the methodology specifies. If it cannot hold them, it cannot follow the index, and the gap between what it holds and what the index says shows up in its returns. So a weighting basis is not only a measurement choice. A weighting basis is a promise that somebody has to keep with real money.

Why weight on the free float rather than on the whole company?

Take Sarvani Coatings Limited, an invented paints and coatings maker. The company has 24.00 crore shares at an illustrative Rs 486/-, so its market capitalisation is Rs 11,664 crore. Its promoter and promoter groupWhoever controls the company, named as such in the shareholding pattern it files each quarter. What they hold is normally treated as parked rather than tradable. hold 52.4 per cent, which leaves 47.6 per cent as free float and Rs 5,552 crore of free float capitalisation. The other Rs 6,112 crore of capitalisation sits in shares that nobody in the market can go and buy.

Now weight the index on total capitalisation. A tracking fund is told to hold Sarvani Coatings in proportion to Rs 11,664 crore, but only Rs 5,552 crore of that exists as buyable shares. Multiply that across fifty constituents and the index has specified a portfolio which, in aggregate, nobody can assemble. As tracking money grows, the funds are all bidding for the same absent shares. Free float weighting exists to make the index replicable, and replicability rather than accuracy is the entire reason for it.

Notice how narrow the argument for the float is. Free float weighting does not make free float capitalisation a truer measure of a company's importance. On some readings total capitalisation is the more natural measure of size. The promoter's shares are shares too. The argument for the float is narrower and stronger than that: the index is meant to be followable, and a weight that cannot be held is not a weight.

Here is the demonstration on four named companies, with the remaining forty six constituents collapsed into one block so the aggregate still comes to Rs 27,76,000 crore of free float capitalisation. The capitalisation and the closely held proportion given to each of the three peers are illustrative.

Run the weights both ways and the shape of the problem appears. On the free float basis the four named constituents carry 0.20, 0.54, 0.05 and 0.24 per cent, and the block of forty six carries 98.97 per cent. On the total capitalisation basis they carry 0.26, 0.53, 0.11 and 0.20 per cent, and the block carries 98.90 per cent. Both sets add to 100.00 per cent, as they must. But on the total capitalisation basis, 38.31 per cent of the whole index weight corresponds to shares that are closely held and never come to market, and Rs 17,03,158 crore of that sits inside the block alone.

Work it out: what weight does Sarvani Coatings carry?

The weight is one division. Take the constituent's free float capitalisation and divide it by the aggregate free float capitalisation of every constituent in the index. Rs 5,552 crore over Rs 27,76,000 crore gives 0.002, or 0.20 per cent. The division is the whole calculation, and it is worth doing by hand once so the number stops feeling like a verdict and starts feeling like a ratio.

Now use the weight for what a weight is for. If Sarvani Coatings rises 10 per cent while every other constituent stands still, the index rises by 10 per cent multiplied by 0.20 per cent, or 0.02 per cent. On an illustrative index level of 1,000.00 that is a move to 1,000.20, or two tenths of a point. A weight is a transmission ratio, so a large move in a small constituent is a small move in the index, and reading the index for news about one constituent is reading the wrong instrument.

One more comparison finishes the free float argument, and it needs its assumption said out loud. Keep the aggregate exactly as given at Rs 27,76,000 crore and swap Sarvani Coatings' own number from its float to its whole capitalisation. The weight goes from 0.20 per cent to 0.42 per cent, or 2.10 times as much. The swapped numerator is only half the story. If instead the whole index switched basis, the denominator would move too, and Sarvani Coatings would land at 0.26 per cent. Either way the direction is the same and the reason is the same: the company is more closely held than the index average, so a rule that ignores the float hands it more weight than its buyable shares can support.

Put money on it. A tracking fund of Rs 1,000 crore holding the float weight buys Rs 2.00 crore of Sarvani Coatings. On the total capitalisation basis it is told to buy Rs 2.59 crore, of which Rs 1.36 crore corresponds to shares that are not for sale at any price. Against an average daily traded valueHow many rupees of a share typically change hands in one session, averaged across a period. A count of activity, never a promise about what a single order can achieve. of about Rs 42 crore, the Rs 2.00 crore purchase is around 4.8 per cent of a day, which is manageable. The Rs 1.36 crore of shares that never come to market is not manageable at any size.

What does inclusion in an index actually mean?

Inclusion means one thing, and the meaning is narrower than almost everybody assumes. On the review date, the company met the criteria written in the methodology. Nothing else is recorded.

Inclusion does not mean the company is well run. Inclusion does not mean the company is a good investment. Nothing about the business changed either. The criteria were size and tradability, and the company had already met them before anyone announced it. Inclusion is a record that a rule was applied on a date, and it carries no information about the quality of the company at all.

The everyday version helps. A housing society keeps a list of the ten largest flats for a maintenance formula. Being on the list says a flat is large. The list says nothing about whether the flat is well kept, well located or a good buy. If somebody renovates and a bigger flat is built next door, the list changes and nothing at all has happened to the flat.

What does an index level report, and what does it not?

A level reports how the weighted set of prices has moved relative to the base value the methodology fixed when the index launched. A level reports nothing else, and the base value was a choice: somebody wrote down 100, or 1,000, or 10,000, and a date to attach it to.

A level depends entirely on a base value and a base date chosen at launch, so a level taken on its own carries no information at all and only changes in a level mean anything. An index standing at 4,000 is not lower, cheaper, smaller or worse than one standing at 20,000. The two levels are not on the same scale and were never meant to be.

The effect shows once an analyst chooses to rebaseTo restate a series so that it starts at a chosen number, usually 100, so two series that began at different values can be set side by side. Rebasing changes the presentation and not the movement. them. Consider an index that launched at a base of 1,000 and now stands at 4,000: it has multiplied 4.0 times, a rise of 300 per cent. A second index launched at a base of 10,000 and now stands at 20,000: it has multiplied 2.0 times, a rise of 100 per cent. The one with the smaller level did three times the work of the one with the bigger level. The levels told nothing; the changes told everything.

What happens when the constituents change?

Three things move under an index over time, and only one of them is prices. Constituents change at review. Weights change as prices and floats move between reviews. And corporate actions inside constituents change share counts. The number has to absorb those changes without recording anything. Sarvani Coatings' history has the classic case in it: a one for one bonusOne new share handed over free for each share already held. Twice the shares, roughly half the price, and the holder is left with the same value spread thinner. that took the count from 12.00 crore shares to 24.00 crore and the price from Rs 972/- to Rs 486/-.

Work the failure through. The failure is small and exact. The index level is the aggregate free float capitalisation divided by a divisor. Set the base at 1,000.00 against Rs 27,76,000 crore of aggregate float, and the divisor is Rs 2,776 crore of float for every index point. Now let the bonus happen and suppose the index takes the new price of Rs 486/- but keeps the old count of 12.00 crore shares. Sarvani Coatings' capitalisation appears to be Rs 5,832 crore, its float capitalisation appears to be Rs 2,776 crore instead of Rs 5,552 crore, the aggregate falls to Rs 27,73,224 crore, and the level prints 999.00. The index has just recorded a fall of 0.10 per cent on a day when no holder of any constituent lost a rupee.

The maintenance rule prevents that by restating the count on the same date as the price, so capitalisation stays at Rs 11,664 crore, the aggregate stays at Rs 27,76,000 crore, and the level stays at 1,000.00. The restatement rule from the corporate action material applies one level up: an index that did not restate would fall on every bonus issue among its constituents.

The divisor earns its keep on the other kind of change. At a review, suppose a constituent with Rs 3,000 crore of free float capitalisation leaves and one with Rs 4,200 crore enters. The aggregate rises to Rs 27,77,200 crore with no price having moved anywhere, and on the old divisor the level would print 1,000.43, a rise of 0.04 per cent that nobody earned. So the divisor is restated to Rs 2,777.20 crore per point and the level holds at 1,000.00. The divisor is the shock absorber: it moves whenever the aggregate changes for a reason that is not a price.

How does this get used at a desk, and by a household?

Meghna Iyer, an analyst on an equity desk, uses an index in three ways and treats each one carefully. When she compares a portfolio's return with an index, she first reads which universe and which weighting basis produced the index. A portfolio of mid sized companies compared against a large company index is not being measured against anything meaningful. When she looks at a constituent's weight, she treats it as a fact about the index rule rather than a fact about the company. And when a constituent's float is revised at a review, she expects the weight to move without any price having moved, so she does not read the flow that follows as a change of opinion about the business.

A household meets the same construction from the other side. Anyone who buys a fund that follows an index has bought the methodology: the universe somebody chose, the count somebody chose, and above all the weighting basis. Naming the methodology is not a criticism of the choice. The purchase consists of the methodology, and the methodology is published in advance, so a buyer can read what was bought. A difference of a few basis pointsOne hundredth of a per cent apiece, so fifty of them make half a per cent. Market people count in them to dodge the muddle of saying a percentage of a percentage. in weight is trivial; a difference in the weighting basis is not.