NISM Series V-D · Chapter 14: Understanding Index

L1 · Foundation

Foundation — What an index is and the four ways of building one

The definition of an index and why the percentage change matters more than the number, the three uses of a stock index, and the four construction methods — market capitalisation weighted, free float, price weighted and equal weighted — each worked through the chapter's own figures.

14 min read · Worth 3% of the paper · Written from pages 330–338 of the official NISM workbook · Updated 18 September 2026

14.1 What an index is

"An index is a STATISTICAL INDICATOR that measures changes in the ECONOMY IN GENERAL OR SPECIFIC AREAS. In case of financial markets, an index is a PORTFOLIO OF SECURITIES THAT REPRESENT A PARTICULAR MARKET OR A PORTION OF A MARKET."

"Each index has its OWN CALCULATION METHODOLOGY and usually is expressed IN TERMS OF A CHANGE FROM A BASE VALUE. The base value might be as recent as THE PREVIOUS DAY or MANY YEARS IN THE PAST. Thus, THE PERCENTAGE CHANGE IS MORE IMPORTANT THAN THE ACTUAL NUMERIC VALUE."

That last sentence is the key to reading any index. The number 82,000 means nothing by itself — it is simply where a base of 100 has travelled to. What carries information is how far it moved, and from what.

"Financial indices are created to measure price movement of STOCKS, BONDS, T-BILLS AND OTHER TYPE OF FINANCIAL SECURITIES. More specifically, a STOCK INDEX is created to provide market participants with the information regarding the AVERAGE SHARE PRICE MOVEMENT IN THE MARKET. BROAD INDICES are expected to CAPTURE THE OVERALL BEHAVIOUR OF EQUITY MARKET and need to REPRESENT THE RETURN OBTAINED BY TYPICAL PORTFOLIOS IN THE COUNTRY."

14.2 The three uses of a stock index

"A stock index is an INDICATOR OF THE PERFORMANCE OF THE OVERALL MARKET OR A PARTICULAR SECTOR."
"It serves as a BENCHMARK FOR PORTFOLIO PERFORMANCE - Managed portfolios, belonging either to individuals or mutual funds, use the stock index as a measure for EVALUATION OF THEIR PERFORMANCE."
"It is used as an UNDERLYING FOR FINANCIAL APPLICATION OF DERIVATIVES – Various products in OTC and exchange traded markets are based on indices as the underlying asset."

The three uses are worth keeping distinct, because they explain why the rest of the chapter matters. If an index is merely a thermometer, small errors do not matter. But once it becomes a benchmark that decides whether a fund manager is judged good or bad, and then an underlying on which billions of rupees of contracts settle, the construction method, the liquidity of the constituents and the independence of the index agency all become serious questions.

14.3 The four construction methods

"Indices can be designed and constructed in various ways. Depending upon their METHODOLOGY, they can be classified as under."

Market capitalization weighted index

"Each stock is given a WEIGHT ACCORDING TO ITS MARKET CAPITALIZATION. So HIGHER the market capitalization of a constituent, HIGHER is its weight in the index. Market capitalization is the MARKET VALUE OF A COMPANY, calculated by MULTIPLYING THE TOTAL NUMBER OF SHARES OUTSTANDING TO ITS CURRENT MARKET PRICE."

The chapter's own illustration: "ABC company with 5,00,00,000 shares outstanding and a share price of Rs 120 per share will have market capitalization of 5,00,00,000 × 120 = Rs 6,00,00,00,000 i.e., 600 CRORES."

Now the worked index, with a base value of 100 set on 1 January 1995:

Stock	Old Price (Rs)	Shares (lakhs)	Old M.Cap (Rs lakhs)	Old Weight	New Price (Rs)	New M.Cap (Rs lakhs)	New Weight
AZ	150	20	3,000	0.16	650	13,000	0.31
BY	300	12	3,600	0.19	450	5,400	0.13
CX	450	16	7,200	0.38	600	9,600	0.23
DW	100	30	3,000	0.16	350	10,500	0.25
EU	250	8	2,000	0.11	500	4,000	0.09
Total			18,800	1.00		42,500	1.00

"The market capitalization of the index on January 1, 1995 is Rs 18,800 which is the sum of the market price MULTIPLIED BY the quantity of shares for each stock... With the change in market prices, the market capitalization of these stocks increases from Rs 18,800 lakhs to Rs 42,500 lakhs. The market capitalization on January 1, 1995 IS EQUATED TO 100. Hence, the new value of the index is calculated as (42500 lakhs / 18800 lakhs) × 100, which works out to 226.06. Since the index has risen from a base of 100 to a new value of 226.06, THE CHANGE IN THE INDEX VALUE IS 126.06 PER CENT."

Note carefully: the index value is 226.06, but the change is 126.06 per cent — the difference being the original 100. Confusing the two is a standard exam trap.

Notice also what the weights do. CX started as the biggest stock at 0.38 and ended at 0.23, while AZ climbed from 0.16 to 0.31. In a market cap weighted index the weights look after themselves — a stock that rises gains weight automatically, with no trading required.

"Popular indices in India, SENSEX AND NIFTY, WERE EARLIER DESIGNED ON MARKET CAPITALIZATION WEIGHTED METHOD."

Free-float market capitalization index

"In various businesses, equity holding is DIVIDED DIFFERENTLY among various stakeholders – PROMOTERS, INSTITUTIONS, CORPORATES, INDIVIDUALS, etc. The market has started to SEGREGATE THIS ON THE BASIS OF WHAT IS READILY AVAILABLE FOR TRADING AND WHAT IS NOT. The one available for IMMEDIATE TRADING is categorized as FREE FLOAT. And, if we compute the index based on weights of each security based on FREE FLOAT MARKET CAP, it is called FREE FLOAT MARKET CAPITALIZATION INDEX."

"A MAJORITY OF THE STOCK INDICES GLOBALLY, over a period of time, HAVE MOVED TO FREE FLOAT BASIS, INCLUDING THE INDIAN EQUITY INDICES - SENSEX, NIFTY AND SX40."

The reason is practical. If a company is 75 per cent held by its promoters, those shares are not going to be traded. Giving the company a weight based on its full market capitalisation would make the index claim an exposure that an actual investor could not buy.

Price-weighted index

"This is a stock index in which each stock influences the index IN PROPORTION TO ITS PRICE. Stocks with a HIGHER PRICE will be given MORE WEIGHT and therefore, will have a GREATER INFLUENCE over the performance of the Index."

Using the same five stocks: "the price index on January 1, 1995 = (150+300+450+100+250)/5 = 250", and "the current value of the index = (650+450+600+350+500) / 5 = 510. Thus, the increase in the value of the index is (510 − 250) / 250, i.e. 104%."

The verification table shows exactly where that 104 per cent comes from:

Stock	Price on 1 Jan 1995	Weight	Current price	% change in price	% change × weight
AZ	150	0.12	650	333.33%	40.00%
BY	300	0.24	450	50.00%	12.00%
CX	450	0.36	600	33.33%	12.00%
DW	100	0.08	350	250.00%	20.00%
EU	250	0.20	500	100.00%	20.00%
Total	1,250	1.00	2,550		104.00%

Look at what the weights are here: CX has the highest weight (0.36) purely because its price is Rs 450 — nothing to do with the size of the company. DW, with 30 lakh shares, carries the smallest weight (0.08) because its price is only Rs 100. In the market cap method those two stocks weighed 0.38 and 0.16; here they weigh 0.36 and 0.08.

"DOW JONES INDUSTRIAL AVERAGE and NIKKEI 225 are popular PRICE-WEIGHTED indices."

Equal weighted index

"An equal-weighted index is one in which ALL STOCKS included in the index have the SAME WEIGHTAGE. The NUMBER OF SHARES of each stock is ADJUSTED in such a way that the weight of each stock in the index is THE SAME. Subsequently, IF THERE IS ANY CHANGE IN THE MARKET PRICE of each stock, THE WEIGHT OF EACH STOCK WILL CHANGE. To MAINTAIN the same equal weights as earlier, THE FUND MANAGER NEEDS TO SELL THOSE STOCKS THAT HAVE INCREASED IN PRICE AND BUY THE STOCKS THAT HAVE FALLEN IN PRICE."

Stock	Price on 1 Jan 1995	Quantity	Value on 1 Jan 1995	Weight	Current price	Current value	Price change	Change × old weight
P	100	300	30,000	0.25	150	45,000	50.00%	12.50%
Q	150	200	30,000	0.25	130	26,000	−13.33%	−3.33%
R	125	240	30,000	0.25	200	48,000	60.00%	15.00%
S	200	150	30,000	0.25	180	27,000	−10.00%	−2.50%
Total			1,20,000	1.00		1,46,000		21.67%

"the number of shares of each stock is ADJUSTED in such a manner that the VALUE OF ALL STOCKS IN THE INDEX IS EQUAL... With a change in the stock prices, the current value... has changed from 120,000 to 146,000. If the old index value is equated to 100, the new index value will be 146000/120000×100, i.e. 121.67. As can be seen from the last column..., this is simply the percentage change in the stock price multiplied by the original weight of each stock, which equals to a rise of 21.67%."

And then the rebalancing, which is the distinguishing feature of this method: "With the changed prices, stock P and stock R have a weight GREATER than 25% while stock Q and stock S have a weight LOWER than 25%. THE FUND MANAGER WILL THEN HAVE TO REBALANCE THE INDEX TO RESTORE EQUAL WEIGHTS. This can be done by SELLING appropriate quantities of stocks P and R and BUYING required quantities of stocks Q and S."

14.6 Major indices in India

"These are some of the popular equity indices in India:"

BSE family	NSE family	Other
S&P BSE Sensex	Nifty 50	SX 40
S&P BSE Sensex Next 50	Nifty Next 50
S&P BSE 100	Nifty 100
S&P BSE 200	Nifty 200
S&P BSE 500	Nifty 500

Think of it like this

The number tells you nothing; the journey tells you everything

An index "is usually expressed in terms of a CHANGE FROM A BASE VALUE. The base value might be as recent as THE PREVIOUS DAY or MANY YEARS IN THE PAST. Thus, THE PERCENTAGE CHANGE IS MORE IMPORTANT THAN THE ACTUAL NUMERIC VALUE." A milestone reading "412 km" means nothing until you know where the counting began. Two indices at 5,000 and 80,000 are not telling you that one market is sixteen times the other — only that they started counting from different bases in different years. This is why every comparison in this book is expressed as a percentage change over a stated period, never as a level.

Weighing the company or weighing the price tag

Take DW from the chapter's own table: 30 lakh shares at Rs 100, so a market capitalisation of Rs 3,000 lakh. In the market cap weighted index it carries a weight of 0.16. In the price weighted index it carries 0.08 — half as much — for no reason except that its share price is small. Meanwhile CX at Rs 450 carries a big weight in both, but in the price-weighted index purely because of its price tag. A price-weighted index effectively says "a Rs 450 share matters four and a half times as much as a Rs 100 share", which is a statement about share prices, not about companies. That is why the Dow Jones Industrial Average and the Nikkei 225 behave differently from the Sensex and Nifty.

Promoter shares are in the shop window, not on the shelf

Free float exists because "equity holding is divided differently among various stakeholders – promoters, institutions, corporates, individuals", and the market now segregates "what is READILY AVAILABLE FOR TRADING and what is not. The one available for IMMEDIATE TRADING is categorized as FREE FLOAT." If a promoter family holds 75 per cent of a company and will never sell, then an index weighting that company on its full market cap is promising investors an exposure they cannot actually buy. Like a shop displaying a stock of 100 sacks of rice when 75 are reserved for the owner's family — the sellable stock is 25. Hence "a majority of the stock indices globally... have MOVED TO FREE FLOAT BASIS, including... SENSEX, NIFTY AND SX40."

The index that never needs rebalancing, and the one that always does

In the market cap example, AZ rose from 0.16 to 0.31 and CX fell from 0.38 to 0.23 all by themselves — no trading was needed, because weight follows value automatically. Now look at the equal weighted index: after prices move, "stock P and stock R have a weight GREATER than 25% while stock Q and stock S have a weight LOWER than 25%. THE FUND MANAGER WILL THEN HAVE TO REBALANCE... by SELLING appropriate quantities of stocks P and R and BUYING required quantities of stocks Q and S." An equal weighted index is a discipline that forces you to sell winners and buy losers, permanently. That is either its great virtue or its great cost, depending on the market — but it is certainly work, and work has a cost.

226.06 is the value; 126.06 per cent is the change

The commonest arithmetic slip in this chapter. "the new value of the index is calculated as (42500 lakhs / 18800 lakhs) × 100, which works out to 226.06. Since the index has risen from a base of 100 to a new value of 226.06, THE CHANGE IN THE INDEX VALUE IS 126.06 PER CENT." The 100 you started with is your own money, not your gain. Same trap in the price weighted example: the index went from 250 to 510, a value of 510 and a change of 104 per cent, not 204. Read the question word for word — value or change — before reaching for the calculator.

Percentage change times original weight

Both the price-weighted and the equal-weighted tables end with the same elegant check: the index's rise equals the sum of (each stock's percentage price change × its original weight). In the price-weighted case 40.00 + 12.00 + 12.00 + 20.00 + 20.00 = 104.00%; in the equal-weighted case 12.50 − 3.33 + 15.00 − 2.50 = 21.67%. This is worth knowing as a cross-check in the exam — if your headline calculation and your weighted-contribution sum disagree, one of them is wrong. And it shows plainly which stock drove the index: in the price example, AZ alone contributed 40 of the 104 percentage points.

A negative contribution is still a contribution

The equal weighted table is the only one in the chapter containing falls: Q dropped 13.33 per cent and S dropped 10 per cent, contributing −3.33 and −2.50 percentage points. The index still rose 21.67 per cent, because P and R contributed 12.50 and 15.00. This is the practical meaning of an index as "a statistical indicator" — it is an average, and an average conceals as much as it reveals. A client who says "the market is up 21 per cent, so my shares must be up" has forgotten that two of the four stocks in this index lost money.

The BSE and NSE index families run in parallel

The list of major Indian indices has a pleasing symmetry worth using as a memory aid. The BSE family runs Sensex, Sensex Next 50, BSE 100, BSE 200, BSE 500; the NSE family runs Nifty 50, Nifty Next 50, Nifty 100, Nifty 200, Nifty 500; and SX 40 stands alone. The numbers in the names tell you the breadth of each index, which connects directly to Chapter 11's rule that a narrow fund needs a narrow benchmark and a broad fund a broad one — and to this chapter's finding that diversification stops helping much beyond about 100 stocks.

Key terms in this chapter

Attributes of a good index: It should reflect market behaviour, be computed by an independent third party free from the influence of any market participant, and be professionally maintained.
Base value: The starting point against which an index is measured. It may be as recent as the previous day or many years in the past, which is why two index levels cannot be compared with each other directly.
Bid-ask spread: The difference between the best buy and best sell orders. It represents the transaction cost the market charges for a small trade — buying and immediately selling leaves the trader poorer by the spread.
Diversification and liquidity trade-off: A good index balances the two. Going from 10 to 20 stocks sharply reduces risk, from 50 to 100 reduces it very little, and beyond 100 causes almost zero decline — while each additional stock is less liquid and raises the cost of trading the index.
Equal weighted index: An index in which every stock carries the same weight, achieved by adjusting the number of shares so each holding has equal value. Because prices then move the weights apart, the manager must rebalance by selling the stocks that rose and buying those that fell.
Exchange Traded Fund (ETF): A basket of securities that trades like an individual stock on an exchange, allowing intraday transactions and basket trading in smaller denomination at low transaction cost.
Free float: The portion of a company's equity readily available for immediate trading, as distinct from holdings of promoters and others that will not be traded. An index weighted on free float market capitalisation reflects what an investor could actually buy.
Ideal price: The average of the best bid and the best offer. In an infinitely liquid market even large transactions would execute very close to it.
Impact cost: The percentage degradation experienced against the ideal price when shares are bought or sold. It varies with transaction size, differs between the buy and sell sides, and is never separately billed — it arises purely from lack of liquidity.
Index: A statistical indicator measuring changes in the economy in general or in specific areas. In financial markets it is a portfolio of securities representing a market or a portion of one, expressed as a change from a base value — so the percentage change matters more than the numeric level.
Index Committee: The specialised committee that takes the final decision on including or removing a security from an index, once the pre-determined eligibility criteria are satisfied.
Index construction: Choosing the index stocks and deciding the calculation methodology, guided by pre-determined qualitative and quantitative parameters — with the final decision on inclusion or removal taken by the Index Committee.
Index derivatives: Derivative contracts with an index as the underlying asset. Index options and index futures are the most popular derivative contracts worldwide, and they are useful as a tool to hedge against market risk.
Index fund: A fund investing in the stocks of a specific index in the proportions in which they exist in that index, aiming to generate returns equivalent to the index — subject to a small tracking error arising from fund management expenses and the cash held for redemptions.
Index maintenance: Adjusting the index for corporate actions such as bonus issues, rights issues, stock splits, consolidations and mergers, so that it stays comparable across time. It is triggered by a corporate action.
Index revision: Changing the composition of the index by replacing existing stocks with new ones, because the trading paradigm of a stock has changed or market participants' interest has shifted. Unlike maintenance, it is a continuous exercise.
Liquidity: In stock market terms, a market where large orders are executed without moving prices.
Market capitalization: The market value of a company — total number of shares outstanding multiplied by the current market price.
Market capitalization weighted index: An index in which each stock's weight follows its market capitalisation, so the larger the company the greater its influence. Weights adjust themselves as prices move, requiring no trading.
Price-weighted index: An index in which each stock influences the index in proportion to its share price, so a higher-priced share carries more weight regardless of the size of the company. Computed as the sum of prices divided by the number of stocks.
Prudential norms for non-benchmark index derivatives: Under SEBI's circular of 30 October 2025 — a minimum of 14 constituents, a top constituent weight of no more than 20 per cent, a combined top-three weight of no more than 45 per cent, and a descending weight structure.

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Original explanatory writing based on the official NISM workbook for Series V-D, which is published and copyrighted by NISM. Check figures against the current edition at nism.ac.in.

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