How is a stock market index calculated?

In India, stock market indices like the S&P BSE Sensex and the NSE Nifty 50 are calculated using specific methodologies. Here’s a breakdown of the processes:

1. Index Selection:

• Sensex: Comprises 30 of the largest and most actively traded stocks on the Bombay Stock Exchange (BSE).
• Nifty 50: Comprises 50 of the largest and most liquid stocks on the National Stock Exchange (NSE).

2. Weighting Method:

Both indices use the Free-Float Market Capitalization method, where the weight of each stock in the index is based on its free-float market capitalization rather than its total market capitalization.

• Free-Float Market Capitalization: It refers to the market capitalization of a company’s shares that are readily available for trading (excluding shares held by promoters, government, etc.).

• Formula:

  Free-Float Market Capitalization=Market Price of Stock×Number of Free-Float Shares\text{Free-Float Market Capitalization} = \text{Market Price of Stock} \times \text{Number of Free-Float Shares}Free-Float Market Capitalization=Market Price of Stock×Number of Free-Float Shares

3. Index Calculation:

• Base Year and Base Value: Both indices have a base year and a base index value, which provides a reference point. For example, the Sensex has a base year of 1978-79 and a base value of 100.

• Index Value Calculation: The value of the index is calculated using the following formula:

  Index Value=∑(Free-Float Market Capitalization of All Companies in Index)Index Divisor\text{Index Value} = \frac{\sum (\text{Free-Float Market Capitalization of All Companies in Index})}{\text{Index Divisor}}Index Value=Index Divisor∑(Free-Float Market Capitalization of All Companies in Index)
  • Index Divisor: A predetermined figure that helps maintain the continuity of the index over time, even after corporate actions like stock splits or mergers.

4. Corporate Actions:

• Adjustments are made to the index to account for corporate actions like dividends, rights issues, stock splits, and mergers to ensure that these actions do not distort the index's value.

Example (Simplified):

If the free-float market capitalization of the companies in the index increases due to a rise in stock prices, the index value will increase accordingly.

Summary:

• Sensex and Nifty 50 are both calculated using the free-float market capitalization method.
• The indices reflect the weighted performance of the selected stocks, adjusted for corporate actions, to provide an overall indicator of the market's health.

This methodology ensures that the index reflects the current market trends accurately.