Introduction to Indices — how a market becomes one number

What an index is

Thousands of securities trade every day. No investor can watch them all. An index is a composite measure that reflects how a whole group of securities has moved.

The dictionary meaning of index is "a system of numbers used for comparing values of things that change according to each other or a fixed standard". A market index does exactly that: it shows how the value of the underlying has changed over a period and from its base value.

Four uses of an index

The first market index had one job. Charles H. Dow and Edward D. Jones introduced the Dow Jones Average in 1884 — the world's first security market index — simply to give a quick gauge of the market. Today indices do four things:

What makes one index different from another

There are over two million indices globally (the workbook's footnote cites an Index Industry Association study counting 2.96 million in 2019). They all track groups of securities. They differ on two things:

1. Sample size — how many stocks. BSE Sensex (30) and NIFTY 50 both track Indian large caps with different sample sizes. The sample must be representative of the population.
2. Weighting scheme — how much each stock counts. Four methods: price, value (market capitalisation), equal, and fundamental. The most popular is value weighting.

1. Price-weighted index

The simplest method. Add up the prices of the constituents and divide by a divisor. The Dow Jones Industrial Average is the classic example.

Index value = Sum of closing prices ÷ Adjusted divisor

The index divisor

The divisor is a number chosen at inception so the index starts at a convenient value such as 100 or 1,000 — the BSE Sensex started at 100. The index provider adjusts the divisor whenever something happens that should not move the index, such as a stock split or a change of constituents.

The workbook's illustration: five stocks priced ₹4, ₹6, ₹8, ₹9 and ₹10 sum to 37; with a divisor of 3.7 the index is 10. Stock E splits 2-for-1, so its price halves to ₹5 and the sum drops to 32. Nothing economic has happened, so the divisor is cut to 3.2 and the index stays at 10.

Merits and pitfalls

• Merit: easy to calculate — it is just an arithmetic mean of prices. That mattered before computers; it matters much less now.
• Pitfall 1 — high-priced stocks dominate. A 5% move in a ₹5,000 stock has more influence than a 50% move in a ₹50 stock.
• Pitfall 2 — downward bias. Fast-growing companies tend to have high prices and tend to split. Each split cuts their price and so their weight. Growth stocks consistently lose weight.

2. Value-weighted (market capitalisation) index

Each stock's weight is its market capitalisation (shares outstanding × current market price) — or its free-float market capitalisation — divided by the total for all constituents.

In the workbook's example, five stocks have a total market cap of ₹970. Stock A's cap of ₹150 gives a weight of 15.46%. To start the index at 100, the divisor is 9.7 (970 ÷ 100).

Three months later the total cap is ₹835, so the index is 835 ÷ 9.7 = 86.08. When stock A is replaced by stock X, the total cap becomes ₹1,230; the new divisor is set to 14.28 (1,230 ÷ 86.08) so the index stays at 86.08 after the change.

Key features:

• Large companies move the index more than small ones for the same percentage change.
• Automatic adjustment for stock splits and other capital changes — a split doubles shares and halves price, leaving market cap unchanged.
• This makes value weighting the ideal choice for index funds and index derivatives.

Two Indian dates worth knowing: BSE Sensex moved from full market cap to free-float methodology from 1 September 2003; NIFTY 50 moved to free float from 26 June 2009.

Free float

Free float measures the shares actually available for public investment. It separates strategic (control) shareholders — who hold for control, not for price — from investors who buy and sell on price and prospects. Generally excluded from free float:

• Shares held by founders, directors or acquirers with a control element.
• Shares held by persons or bodies with "controlling interest".
• Shares held by Government as promoter or acquirer.
• Holdings through the FDI route.
• Strategic stakes by private corporate bodies or individuals.
• Cross-holdings by associate or group companies.
• Equity held by Employee Welfare Trusts.
• Locked-in shares and shares that would not normally be sold in the open market.

3. Equal-weighted index

Every constituent has the same weight, whatever its price or size. A ₹2,500 stock counts the same as a ₹40 stock. It is like investing the same rupee amount in every stock.

The index moves by the arithmetic mean of the percentage price changes. In the workbook's example the five returns (67%, 50%, 14%, −11%, 11%) average 26%, so an index based at 100 moves to 126. Some equal-weighted indices use a geometric average instead.

• Merit: no price bias and no value bias.
• Drawback: an index fund tracking it must rebalance periodically — buying stocks that fell and selling stocks that rose to restore equal amounts — so it has high portfolio turnover and higher transaction costs.

4. Fundamental-weighted and factor-based index

A criticism of value weighting is that it overweights overvalued stocks and underweights undervalued ones — a stock's weight rises just because its price rose. Fundamental indices weight by business measures instead: book value, cash flows, dividends, sales, profits, net assets. These are also called alternative indices. One factor or a combination can be used; with several factors, each needs its own weight.

Workbook example: three companies with sales of ₹100 crore, ₹500 crore and ₹400 crore get weights of 10%, 50% and 40%. Their prices move +70%, +25% and −11.76%, so the index moves by (70% × 10%) + (25% × 50%) + (−11.76% × 40%) = 14.80%, to 114.80.

Behind factor indices sits a simple idea: some return factors are specific to one security, some are common to groups — and the risk premium is the reward for exposure to systematic risk factors.

Index methodology — how Sensex and NIFTY 50 pick stocks

Index providers make two big decisions — how many constituents and how to weight them — and then apply selection rules.

S&P BSE Sensex (methodology of January 2021, as the workbook cites)

Eligible universe: constituents of the S&P BSE 100. The company count is fixed at 30 (DVR share classes can make the stock count exceed 30).

Eligibility:

• Listing history of at least six months at BSE.
• Traded on every trading day at BSE in the six-month reference period.
• DVRs are aggregated with the company's common stock.

Construction, step by step:

1. Rank by average six-month float-adjusted market cap — identify the top 75.
2. Rank by average six-month total market cap — identify the top 75.
3. Combine, sort by annualised traded value; exclude companies with cumulative annualised traded value greater than 98%.
4. Sort by average float-adjusted market cap; exclude companies with weight below 0.5%.
5. Rank by average float-adjusted market cap and select:
   • the top 21 automatically, no sector consideration.
   • existing constituents ranked 22–39, in rank order, until 30 is reached.
   • if still short, non-constituents ranked 22–30, preferring under-represented sectors compared with the S&P BSE All Cap.
   • if still short, non-constituents in rank order.

Annualised traded value = the median of monthly medians of daily traded values over six months, annualised using 250 trading days. All additions and deletions are at the index committee's discretion. Constituents are weighted by float-adjusted market capitalisation.

NIFTY 50

• Trading frequency of 100% in the last six months.
• Average impact cost of 0.50% or less during the last six months for 90% of observations, for a portfolio of ₹10 crore.
• Average free-float market cap at least 1.5 times that of the smallest constituent.

Impact cost is the percentage mark-up suffered while buying or selling the desired quantity compared with the ideal price — (best buy + best sell) ÷ 2.

Index values are disseminated up to two decimal places.

Stock market index families

The NIFTY family (constituent examples as on December 2020)

• NIFTY 50 — 50 well-diversified companies, free-float market cap method.
• NIFTY Next 50 — the 50 companies in NIFTY 100 after excluding NIFTY 50.
• NIFTY 100 — NIFTY 50 + NIFTY Next 50.
• NIFTY 200 — NIFTY 100 + NIFTY Midcap 100.
• NIFTY 500 — top 500 companies by full market cap from the eligible universe.
• NIFTY Midcap 150 — the next 150 companies, ranked 101–250 by full market cap within NIFTY 500.

Stocks migrate between categories as their capitalisation changes.

Style indices — value vs growth

A growth manager follows the company's economic "story", with less regard to valuation. A value manager focuses on price, expecting a correction and possibly better fundamentals. Style indices have much higher turnover than broad indices, because valuation ratios change and stocks migrate between styles on reconstitution dates.

Total Return Index

A price index ignores dividends. A Total Returns Index includes returns from (a) price movements and (b) dividend receipts. Dividends are indexed on the ex-date and reinvested in the index. The base of the price index and the TR index is the same. An investor in index stocks should benchmark against the TR index, not the price index.

NIFTY50 USD

NIFTY 50 measured in dollars, for foreign investors.

NIFTY50 USD = Closing value of NIFTY 50 × Exchange rate on base date ÷ Exchange rate for the day

Base date is the same as NIFTY 50 — 3 November 1995 — with base value 1,000. NIFTY 50 is also computed in Australian dollars and Canadian dollars.

Global equity indices

Many global indices cover over 90% of each market's investable market cap.

GDP-weighted vs market cap weighted

Market cap indices ignore unlisted companies — even though state-owned unlisted companies contribute heavily to many economies. They also tilt towards developed countries, which have higher market-cap-to-GDP ratios, so emerging and frontier markets are under-represented. The fix: weight countries by GDP. The MSCI World GDP Weighted Index — based on the MSCI World Index, 23 developed markets — was launched on 30 September 1988.

MSCI India Index

Different providers' methodologies make country indices hard to compare. MSCI computes consistent country indices. The MSCI India Index covers large and mid caps: 86 constituents, about 85% of the Indian equity universe. It emphasises liquidity (measured by impact cost), investability and replicability. Reviewed quarterly — February, May, August, November; in the May and November semi-annual reviews it is rebalanced and the large/mid cap cut-offs recalculated.

Bond market indices

Less famous, equally important. Building them is harder than equity indices because:

• the bond universe is much bigger and broader — governments, municipalities, corporates, financial institutions.
• one issuer can have many bond series with different risks and ratings.
• the universe changes constantly as new bonds are issued and old ones mature.

NIFTY G-Sec indices — six Macaulay duration buckets

Methodology: up to 3 liquid bonds per bucket by previous month's turnover; outstanding amount more than ₹5,000 crore; weights by amount outstanding; rebalanced and reconstituted monthly.

NIFTY T-Bill indices

Maturity indices for 30-day, 60-day, 91-day, 182-day and 1-year T-bills, plus the NIFTY All Maturity T-Bill Index. For 91-day, 182-day and 1-year, the most recently issued T-bill is the constituent; for 30-day and 60-day, the bill with residual maturity closest to 30 or 60 days.

The workbook is not consistent on two points here (Chapter 12, pp. 229–230): it says the all-maturity index aggregates performance across maturities and, a few lines later, aggregates 3 maturity-based indices; and it says the indices are reconstituted weekly, then that the index is rebalanced and reconstituted on every T-bill auction. Both versions are stated in the chapter.

Corporate bond indices

• NIFTY AAA, AA+, AA, AA− and Banking & PSU Bond Indices — across 6 Macaulay duration buckets; each index up to 14 issuers, each represented by its most liquid bonds. The liquidity score weights trading value 80%, days traded 10%, number of trades 10%.
• NIFTY A Bond Indices — 2 buckets: short (up to 3 years) and long (more than 3 years); all bonds with issuance above ₹50 crore; weights by issuance size; issuers selected on primary market issuances; monthly rebalancing.
• NIFTY AA Category Bond Indices — aggregate AA+, AA and AA− across 6 buckets, up to 14 most liquid issuers per sub-category.
• NIFTY Fixed Income Aggregate Indices — 13 indices across G-secs, corporate bonds, CPs, CDs, T-bills and overnight rate.

Other bond indices

• High yield bond index — bonds below investment grade.
• Global bond index — e.g. FTSE Russell: government, government-sponsored, collateralised and corporate bonds, more than 100 countries, 18,000+ unique bonds.
• Total return bond index — market-value-weighted return including price movements, accrued interest and cash flows (coupons, redemptions, repurchases).

The workbook states that Indian bonds are not yet part of any major global bond index and that the Government is working towards inclusion, which would attract foreign inflows.

Beyond the book: that statement is now out of date. J.P. Morgan added Indian government bonds to its GBI-EM emerging market bond index from June 2024, and other major providers have followed. For the exam, know the workbook's wording; in practice, know that inclusion has happened.

Stock–bond (composite) indices

Blend equity and bonds to benchmark hybrid portfolios. The NIFTY Hybrid Index series has 6 indices built from the total return versions of NIFTY 50 and fixed income aggregate indices. Weights drift between reset dates and are reset to pre-defined levels monthly.

Note: in the workbook's Table 12.10 the debt cell for the 25:75 index reads 25%, which conflicts with the index's own name (25:75). Go by the name if asked about the split, and be aware the table cell says otherwise.