What an index measures

A level is a ratio, not a price 

The most common misreading of an index is to treat its level as a price. It is not one. No security trades at that number, no quantity of anything can be bought for it, and the currency it appears to be denominated in is a property of the shares underneath rather than of the index itself. An index level is the answer to a comparison: what is a defined basket of shares worth now, expressed as a proportion of what the identical basket was worth on a date the provider chose when the series began.

That starting point is the base date, and the number the provider assigns to it is the base value. The base value is arbitrary by design. A provider picks a round figure so that later readings are easy to interpret at a glance, and every subsequent level is that base value multiplied by the ratio between the basket's current worth and its worth on the base date. A reading of double the base value means the basket has doubled since the base date on the provider's own measure. It means nothing else at all.

One consequence follows immediately and is worth holding onto, because it disposes of a whole category of confusion. The absolute level of an index carries no information about whether the market it covers is expensive, large or important. An index that started life at a low base value in a recent decade will read lower than one that started at a high base value generations earlier, whatever the two markets have actually done. Levels are comparable with their own history and with nothing else.

The divisor, and why the series stays continuous 

A basket of shares does not stay still. Companies join the index and others leave it, a constituent splits its shares, another issues new ones, a third is taken over. Each of those events changes the arithmetic worth of the basket without anything having happened to the market that the index is trying to describe. Left alone, the series would jump on the day of every corporate event, and a chart of it would be unreadable as a measure of anything.

The device that prevents this is the divisor. The index level is the aggregate worth of the basket divided by a number the provider maintains, and whenever a change occurs that is not a market movement, the provider adjusts the divisor by exactly the amount needed to leave the published level unchanged at the moment of the change. The divisor absorbs the discontinuity; the series carries on. Every serious index in the world is maintained this way, and the divisor is republished by the provider so the calculation can be reproduced.

The divisor is also why an index review is not automatically an index movement. When a provider announces that a company joins and another leaves, the level on the day of the change is engineered to be continuous. What can move is the price of the two companies themselves, because funds tracking the index have to buy one and sell the other, and that flow is a real transaction in a real share.

Price return and total return 

Almost every index quoted in the media, and almost every index a derivative is written on, is a price return series. It measures the movement of constituent share prices and nothing else. When a company pays a dividend, its share price falls by roughly the amount distributed on the day the entitlement is removed, and a price return index records that fall as a decline. The cash the shareholder received is invisible to the series, because the series is only looking at prices.

A total return series treats the same event differently. It assumes each distribution is reinvested across the basket and includes it in the calculation, so the mechanical fall on the ex dividend date is offset by the cash it represents. Most providers publish both variants of the same index from the same constituent list, under names that differ by a suffix, and over long horizons the two diverge substantially: the whole of the distributed income is the gap between them.

Two practical points follow. First, a long run comparison between a price return index and any measure that includes income is not a like for like comparison, and the difference is not small. Second, because derivatives are written on the price return variant, the mechanical ex dividend decline is a known distortion in the contract rather than a market movement, which is why brokers conventionally apply a cash adjustment for it rather than allowing the contract to record a fall that the underlying basket did not economically suffer.

What a level cannot report 

An index compresses a market into one number, and compression discards information. Four things in particular are absent from the level and are routinely read into it anyway.

• Breadth. A level that is unchanged is consistent with every constituent being unchanged and equally consistent with half of them rising sharply while the other half falls. Providers publish breadth statistics separately for exactly this reason.
• Concentration. Where a weighting rule allows a handful of very large constituents to dominate, the level largely reports those companies. The number does not say so, and the constituent weights have to be looked up to find out.
• Survivorship. The list is maintained. Companies that fail are removed and replaced, so a long index series describes the performance of a rule for selecting companies, not the performance of the companies originally selected.
• Currency. A level is expressed in the currency of the market it covers, so a series that has risen in its home currency can have fallen when restated in another. The index makes no statement about this, and an unhedged position in a foreign index carries both movements at once.

Where practitioners disagree 

A genuine and unsettled argument runs underneath all of this: whether a broad index is best understood as a neutral description of a market or as an active strategy in disguise. One tradition holds that a rules based, capitalisation weighted list is the closest thing to an unopinionated measure available, since it holds every company in proportion to what the market itself says each is worth. The other points out that the rules embed choices at every step, in eligibility, in the free float adjustment, in the review calendar and in the treatment of secondary listings, and that a rule which mechanically holds more of whatever has risen is a momentum tilt whether or not it is labelled one. Both positions are defensible on the evidence, which is why index construction remains a live field rather than a settled one.