Introduction to an Index
This sub‑topic introduces the concept of a stock market index, its purpose, and why it is a cornerstone of equity derivatives. Understanding how an index is constructed and calculated helps you answer exam questions on index‑linked futures and options. It also connects to SEBI’s definition of an index and the role of index providers.
Learning Objectives
- 1Define a stock market index and differentiate it from a single security.
- 2Identify the main components that make up an index.
- 3Explain the common weighting methods and how they affect index movement.
- 4Calculate an index level using the standard formula and interpret the divisor.
What is a Stock Market Index?
A stock market index is a statistical measure that reflects the performance of a selected group of stocks. SEBI defines an index as a “continuous series of numbers that represents the price movements of a basket of securities.”
Indices are created to provide a snapshot of market sentiment, sector health, or the overall economy. For example, the NIFTY 50 represents the top 50 large‑cap stocks on the NSE, while the S&P BSE Sensex tracks 30 prominent stocks on the BSE.
For the NISM exam, you must recognise that an index is not a tradable security itself; it is a benchmark used to price derivatives such as index futures and options. The exam often asks you to identify the underlying of an index derivative or to compute its payoff based on index movement.
Students sometimes treat the index value as the price of a single stock. Remember: the index is a composite measure; its level cannot be bought or sold directly, only through derivative contracts.
Key Components of an Index
Every index is built from three essential components: the basket of securities, the weighting scheme, and the divisor. The basket determines which stocks are included, often based on market‑capitalisation, sector representation, or liquidity criteria set by the index provider.
The weighting scheme decides how much each stock influences the index. Common schemes are price‑weighted, market‑cap weighted, and equal‑weighted. The choice of weighting changes the sensitivity of the index to price movements of large versus small constituents.
The divisor is a scaling factor that ensures continuity of the index when corporate actions (stock splits, dividends, additions, deletions) occur. It is adjusted so that the index level does not jump merely because of a technical change.
Weighting Methods
Price‑Weighted Index: Each stock’s price contributes equally, irrespective of its market size. The classic example is the Dow Jones Industrial Average. A high‑priced stock can dominate the index movement.
Market‑Cap Weighted Index: Stocks are weighted by their total market value (price × shares outstanding). This is the most common method in India, used for NIFTY and Sensex. Larger companies have a bigger impact.
Equal‑Weighted Index: Every constituent receives the same weight regardless of price or size. This method highlights the performance of smaller stocks and reduces concentration risk.
Exam‑wise, you may be asked to identify the weighting method of a given index or to predict how a price change in a large‑cap stock will affect a market‑cap weighted index.
Comparison of Common Index Weighting Methods
| Weighting Method | Calculation Basis | Typical Influence on Index | Example in India |
|---|---|---|---|
| Price‑Weighted | Sum of stock prices | High‑priced stocks dominate | Dow Jones (global example) |
| Market‑Cap Weighted | Sum of (price × shares) | Large‑cap stocks dominate | NIFTY 50, Sensex |
| Equal‑Weighted | Each stock gets 1/n weight | All stocks influence equally | NIFTY 100 Equal Weight (conceptual) |
Base Value and Divisor
The base value is the arbitrary starting point of an index, usually set at 100 or 1000 on a specific launch date. This makes historical comparison easier.
The divisor is a constant that scales the weighted sum of prices to the base value. When corporate actions occur, the divisor is adjusted so that the index level remains unchanged. For instance, if a constituent undergoes a 2‑for‑1 split, the divisor is halved.
Understanding divisor adjustments is crucial for exam questions that present a before‑and‑after corporate action scenario. You will need to state that the index level stays the same because the divisor is recalibrated.
Where:
P_{i}= Closing price of the i^{th} stock in the basket (₹)n= Number of stocks in the indexD= Divisor, adjusted for corporate actions (unitless)Worked Example
Given three stocks with closing prices P_{1}=120, P_{2}=80, P_{3}=200 and a divisor D=4: Step 1: Sum of prices = 120 + 80 + 200 = 400 Step 2: Index = 400 / 4 = 100 Verification: (120 + 80 + 200) / 4 = 100.
Where:
P_{i}= Closing price of the i^{th} stock (₹)Q_{i}= Number of shares outstanding of the i^{th} stockn= Number of stocks in the indexD= Divisor after adjustments (₹)Worked Example
Assume two stocks: Stock A – P=150, Q=10,000; Stock B – P=50, Q=30,000; divisor D=5,000. Step 1: Market cap A = 150 × 10,000 = 1,500,000 Step 2: Market cap B = 50 × 30,000 = 1,500,000 Step 3: Sum = 3,000,000 Step 4: Index = 3,000,000 / 5,000 = 600 Verification: (150×10,000 + 50×30,000) / 5,000 = 600.
Calculating Index Level – Step by Step
Step 1 – Identify the constituents and collect their latest closing prices. For a market‑cap weighted index, also gather the number of shares outstanding for each constituent.
Step 2 – Apply the appropriate weighting formula (price‑weighted or market‑cap weighted) to obtain the weighted sum.
Step 3 – Divide the weighted sum by the current divisor. The result is the index level that will be quoted to market participants.
In exam questions, the data is often presented in a table. Remember to keep units consistent (₹ for prices, number of shares for quantities) and to use the divisor supplied in the question.
Hypothetical NIFTY Index Levels Over Four Quarters
Practical Relevance for Equity Derivatives
Index futures and options derive their value from the underlying index level. The payoff of an NIFTY futures contract is directly proportional to the change in the NIFTY index from the entry price.
Because the index is a weighted aggregate, a large movement in a high‑cap constituent (e.g., Reliance Industries) can cause a sizable index shift, affecting the derivative’s mark‑to‑market. Understanding the weighting helps you anticipate which stocks will drive index volatility.
SEBI’s regulations require that index derivatives be settled in cash based on the final settlement price of the index. Exam questions may ask you to compute cash settlement amounts using the index level at expiry.
Scenario
An investor buys one NIFTY 50 futures contract at a price of 13,000 points. The contract size is ₹75 per index point. At expiry, the NIFTY index closes at 13,450 points.
Solution
Step 1: Determine the index point change = 13,450 – 13,000 = 450 points. Step 2: Multiply by contract size: 450 × ₹75 = ₹33,750. Step 3: Since the investor is long, the profit is +₹33,750. If the index had fallen, the same calculation would give a loss of the same magnitude.
Conclusion
The example shows that futures payoff is a simple multiplication of index movement and contract size, reinforcing why accurate index calculation matters for derivative pricing.
Students often forget to adjust the divisor after a stock split, leading to an incorrect index level. Always check the question for divisor changes before computing the final index.
Regulatory Perspective
SEBI mandates that index providers disclose methodology, constituent selection criteria, and divisor adjustment procedures. The regulations ensure transparency and prevent manipulation of index levels that could affect derivative contracts.
For the NISM exam, you may be asked which regulator oversees index calculation (SEBI) or what disclosures are mandatory for an index used as an underlying for derivatives.
Remember that any change in methodology requires prior approval from SEBI, and the index provider must publish the revised methodology at least 30 days before implementation.
⭐Exam Takeaways
- An index is a statistical measure of a basket of securities, not a tradable asset.
- Key components: constituent list, weighting method, and divisor.
- Price‑weighted, market‑cap weighted, and equal‑weighted are the three main weighting schemes.
- Index level = (Weighted sum of prices) ÷ Divisor; adjust the divisor for corporate actions.
- Derivatives settle in cash based on the final index level; contract size translates index points to rupees.
- SEBI regulates index methodology, requiring disclosure and approval for any changes.
- Common exam trap: forgetting divisor adjustments after splits or additions.
Practice Questions
8 questions on Introduction to an Index
A stock market index is best described as:
Which of the following is NOT a common weighting method used for constructing an index?
Using the price‑weighted formula, what is the index level for stocks priced at ₹120, ₹80 and ₹200 with a divisor of 4?
Why does a large‑cap stock’s price rise affect a market‑cap weighted index more than a price‑weighted index?
A price‑weighted index contains three stocks priced at ₹120, ₹80 and ₹200 with divisor 4, giving an index level of 100. If the ₹200 stock undergoes a 2‑for‑1 split, what should the new divisor be to keep the index unchanged?
An investor buys one NIFTY 50 futures contract at 13,000 points. The contract size is ₹75 per index point. At expiry the index closes at 13,450 points. What is the profit?
Which regulator requires index providers to disclose methodology and approve any changes to an index used for derivatives?
The component of an index that is adjusted to prevent jumps in the index level after corporate actions such as stock splits is: