NISM Certifications · NISM-Series-VIII: Equity Derivatives

Understanding Index: formula sheet

Full chapter guide

Key formulas

Index as a barometer: Index movement = combined movement of the stocks in the basket; It reflects the market or sector, not any single stock.
Uses of an index: Market barometer + Benchmark + Base for index funds/ETFs + Underlying for derivatives; Remember these four uses; options often list them as choices.
Index percentage change: % change = (Closing index − Previous index) ÷ Previous index × 100; Use this to compare index returns with portfolio returns.
Settlement of index derivatives: Index cannot be delivered → cash settlement; Index futures and options settle in cash.
Market capitalisation: Market cap = Share price × Total number of issued shares; Used in full market cap weighted indices.
Free-float market capitalisation: Free-float market cap = Share price × Number of shares in free float; Free-float shares = issued shares less promoter, government and other locked-in holdings.
Index value (cap based): Index value = (Current market cap ÷ Base market cap) × Base value; Use free-float market cap for both current and base if the index is free-float based.
Price weighted index: Index = Sum of prices of constituent stocks ÷ Divisor; Divisor is adjusted for splits and constituent changes so the index does not jump.
Equal weighted index: Weight of each stock = 1 ÷ Number of stocks; Index moves with the simple average of the stocks' percentage returns, until weights drift and are rebalanced.
Index return: Index return % = (New index ÷ Old index − 1) × 100; Use this to find the percentage change between two index values.
Features of a good index: Representative + Liquid + Investable + Transparent + Stable + Diversified; Typical attributes tested. Representativeness and liquidity are the most commonly asked.
Index maintenance: Adjust for corporate actions so the index level stays continuous; Covers splits, bonus, rights, mergers, demergers. Not a change of constituents.
Rebalancing: Reset weights of existing constituents to target; Constituent list stays the same.
Reconstitution: Add or remove constituents as per eligibility criteria; Done periodically after review by the index committee under published rules.
Free-float market capitalisation: Free-float market cap = Price × Total shares × Free-float factor; Free-float factor is the fraction of shares available for public trading, between 0 and 1.
Index value: Index value = (Current free-float market cap ÷ Base market cap) × Base value; Used by both Nifty 50 and Sensex. Only the base date and base value differ.
Stock weight in index: Weight = Stock's free-float market cap ÷ Total free-float market cap of index; Larger free-float market cap means a larger weight and more impact on the index.
Key facts to recall: Nifty 50: NSE, 50 stocks, base 1000 at 3 Nov 1995 | Sensex: BSE, 30 stocks, base 100 at 1978-79 | Bank Nifty: NSE, 12 banks, base 1000 at 1 Jan 2000; Most factual MCQs test exactly these items.
Tracking difference: Tracking difference = Fund return − Index return; A simple gap over a period. It is usually negative for an index fund because of costs.
Tracking error: Tracking error = Standard deviation of (Fund return − Index return) over the periods; The usual definition in the workbook. It shows how much the gap varies. Lower is better.
Index futures contract value: Contract value = Index level × Lot size; Use the lot size set by the exchange for that index.
Settlement of index derivatives: Index derivatives are cash settled; No delivery of the underlying stocks takes place.

Quick revision

An index is a number that shows the combined movement of a basket of stocks.
Price weighted: stocks with higher prices get higher weight, regardless of company size.
Market cap weighted: weight depends on total market value of the company.
Free float market cap weighted: only shares available for public trading count.
Equal weighted: every stock gets the same weight at each rebalancing.
A good index is representative, investable, transparent and has low turnover.
Rebalancing resets weights; reconstitution changes the stocks in the index.
Corporate actions and changes in free float lead to index adjustments.
Nifty 50 is the NSE's flagship index; Sensex is the BSE's flagship index.
Index funds and ETFs aim to replicate an index, so the gap from the index is tracking error.
Index futures and options use an index as the underlying and are cash settled.

Common mistakes

Thinking you can buy an index directly. Fix: Remember an index is only a number. You trade it through index funds, ETFs, futures or options.
Treating an index as the price of one stock. Fix: Remember it summarises a whole basket of stocks.
Using total issued shares in a free-float index. Fix: Read the method first. If free-float is named, multiply price by free-float shares only.
Treating a high-priced stock as large in a market cap index. Fix: In cap weighted indices, size is price × shares. Price alone matters only in price weighted indices.
Using rebalancing and reconstitution as the same thing. Fix: Rebalancing changes weights only. Reconstitution changes the list of stocks.
Thinking a good index should change constituents often to stay current. Fix: Stability is a feature. Frequent change raises turnover and tracking cost for index funds.
Saying Sensex has 50 stocks or Nifty has 30. Fix: Link Nifty 50 with NSE and 50, Sensex with BSE and 30. The number 50 sits in the name Nifty 50.
Treating Bank Nifty as a broad-based index. Fix: Bank Nifty holds only banks, so it is a sectoral index.
Saying an ETF is bought at NAV from the fund house like a normal fund. Fix: Remember that ETF units trade on the exchange at market price. Index fund units deal at NAV with the fund house.
Thinking index funds are actively managed. Fix: Index funds and ETFs are passive. They copy the index, so no stock picking is involved.

Exam tips

Learn the four uses of an index as a list and match each to its keyword.
Watch for options that call an index a tradable security. They are wrong.
Remember index derivatives are cash settled because an index cannot be delivered.
Check whether the index in the question is broad-based or sectoral before choosing an answer.
Negative marking applies in this paper, so skip a question only if you cannot eliminate at least two options.
Read the method word first. Free-float and full market cap give different answers from the same data.
Questions often give a free-float factor. Multiply it by issued shares to get free-float shares.
If the index is based on a ratio, check for a direction error before calculating long figures.