Stock Market Index

A stock market index is a statistical measure that combines the prices of a chosen group of shares into a single number, so that the movement of that number shows how the group as a whole has performed. Investors use indices as benchmarks, fund managers build products that copy them, and journalists quote them as shorthand for "the market".

An index is defined by a published rulebook: which companies listed on a financial exchange qualify, how each one is weighted, how often the list is reviewed and how dividends, share splits and rights issues are handled. Well-known examples include the S&P 500 and the Dow Jones Industrial Average in the United States, the FTSE 100 and the All Share Index family in the UK, and the KSE-100 Index in Pakistan.

Imagine trying to tell a friend whether prices at a weekly vegetable market went up or down. Listing every stall would take all day, so you pick a representative basket, perhaps onions, tomatoes and potatoes, and track what the whole basket costs each week. A stock index does the same for shares: it follows a basket and reports one figure.

The details matter, though. If the basket counts each stall by how big it is, a price change at the largest stall moves the total most. If every item counts equally, a jump in the price of a small item can move the figure just as much. Different indices make different choices, which is why two "market" numbers can tell slightly different stories on the same day.

The weighting method decides how much each company counts. The main approaches are:

• Capitalisation weighting. Each company counts in proportion to its market capitalization, the share price multiplied by the number of shares. Most modern benchmarks, including the S&P 500, use this method.
• Free-float weighting. A variation that counts only the shares available for trading, leaving out blocks held by founders, governments or parent companies. The KSE-100 moved to this method in 2012.
• Price weighting. Each company counts in proportion to its share price, regardless of size. The Dow Jones Industrial Average and Japan's Nikkei 225 work this way.
• Equal weighting. Every constituent gets the same weight at each rebalancing, which gives smaller companies more influence than in a capitalisation-weighted index.

A capitalisation-weighted index is calculated as:

• $I_t$ is the index level at time $t$.
• $P_{i,t}$ is the share price of company $i$.
• $Q_{i,t}$ is the number of shares counted for company $i$, either all shares or the free float.
• $D_t$ is the divisor, a scaling number set so that the index equals its chosen base value on the start date and adjusted later so that corporate actions do not cause artificial jumps.

Take an index of three companies. Company A trades at 50 with 1 million shares (value 50 million), B at 20 with 5 million shares (100 million) and C at 10 with 5 million shares (50 million). The total is 200 million. To start the index at 1,000, the divisor is set at 200,000. If A's price then rises 20% to 60, its value becomes 60 million, the total becomes 210 million and the index reads 210 million divided by 200,000, which is 1,050, a 5% rise.

A price-weighted index of the same three shares works differently. It adds the prices and divides by a divisor, here 3: (50 + 20 + 10) / 3 = 26.67. When A rises to 60, the index becomes 90 / 3 = 30, up 12.5%. The same price change moves the two indices by different amounts because A has the highest price but the smallest company value.

A price-return index tracks share prices only, so when a company pays a dividend and its share price drops by about that amount, the index falls even though shareholders have received cash. A total-return index assumes dividends are reinvested and so measures what an investor actually earned. Over long periods the gap is large, because reinvested dividends grow with compounding.

Most headline US and UK indices are quoted as price indices, with total-return versions published alongside. Some benchmarks are total-return by default: Germany's DAX is one, and the Pakistan Stock Exchange's methodology document describes the KSE-100 as adjusted for dividends, bonus shares and rights.

Indices serve as benchmarks for active fund managers and hedge funds, as the basis for index funds and exchange-traded funds, as underlyings for futures and options, and as a guide to price discovery across a market, as an economic signal watched alongside the yield curve and inflation. Funds that track an index must buy and sell constituents at each review, a process covered under ETF rebalancing.

The measure has limits. A capitalisation-weighted index can become dominated by a handful of very large companies, so its moves may reflect a few stocks rather than the broad market. Survivorship matters too: failing companies drop out and are replaced, which flatters long-run histories. And an index is not an economy: listed companies may be a small slice of national output, as with GDP in countries where most firms are unlisted. A broad capital market measure such as an all-share index reduces, but does not remove, these biases.

Index levels are also not comparable across markets. A reading of 1,050 or 100,000 says nothing on its own, since each index starts from its own base value and date; only percentage changes can be compared.

• Pakistan Stock Exchange: Free-float based KSE-100 Index methodology
• FTSE Russell: UK indices