A Deep Dive

Read the title again and think about the first thing that comes to your mind? To me: market- a place of exchange between a willing buyer and seller acting in their own interest. An efficient market? One where the exchange happens at a price that reflects all information about the value of the subject matter of exchange. An index? the simplest meaning of an index would be a representative measure, ostensibly originating from ‘indicate’. In the current sense, an index would be a representative number indicating the value of a group of numbers relative to its chosen base, which are often market prices of the stocks which constitute the very index.

Are they equally weighted? you may ask, is the index a simple average of the prices of the stocks? or are they given a weightage? if yes, what’s the rationale behind this weightage? Well, let’s find out.

Exhibit A:

For our understanding, we’ve chosen 5 imaginary securities & prices on the day of the inception of such index. A simple change occurred on day 2, although highly unlikely in the real market due to the presence of circuit breakers but sufficient to give us a conceptual understanding. What are circuit breakers? For now think of them as quantitative boundaries that the stock price can’t cross on any given trading day, applicable in both directions. What’s the change?

Let’s break it down:

1. As you can observe, the total price of all 5 securities on day 1, which is 75, increases to 150 on day 2, Therefore a 100% increase in price [((150-75)/75)*100].
2. Similarly, even the prices of each of the securities has increased by 100%. Pretty intuitive.
3. What’s most important is the value of the index, in this case set at 10 on day 1. This number is known as the base number and this could be absolutely anything and there is no rationale for it’s selection. As mentioned earlier, its merely representative.
4. The divisor, although is the only number that links the base number to the index. As illustrated, the value of the divisor most often remains the same (except to adjust for corporate and other actions such as stock splits etc.- not useful in our illustration).
5. The divisor at inception is arrived at, by dividing the Total (Aggregate) Price by the base number. (In this case B8/B10).
6. Finally, you may notice, as the price of the individual stocks increased on day 2, so did the aggregate price, but the weightage (Column G) remained same, because the change in price was constant (100%) across all stocks. Where this brings us, is to an index value of 20 on Day 2 which as earlier illustrated would be the Aggregate Price in F8 divided by the constant divisor in F11 (150/7.5).

This is what a price weighted index looks like. (Where the weightage of individual stocks on the index is determined by its price).

Fairly similarly, stock market indexes are usually market capitalisation (cap) weighted, and most often, they are free float market cap weighted. Simply put, the market cap of a stock is the current market price per share * the total number of outstanding shares in the market. Outstanding (o/s) shares are those currently held by such company’s shareholders. They’re outstanding because the company still owes that per share amount to each of it’s shareholders.

Free Float Market Cap on the other hand are those shares that are readily available for the public to invest in. These exclude all those shares that are held by the company’s promoters, if any held by the government as a promoter, held through the FDI (Foreign Direct Investment) route and by companies in the same group. Free Float market cap often excludes those shares that inherently posses some element of control in the company. The outstanding shares are then multiplied by their free float factor (amount of o/s shares available for the public to invest in/amount of total o/s shares of the company) to arrive at the free float market cap that would be reflected in the index.

Exhibit B:

Contrary to Exhibit A, Exhibit B uses the free float market cap (FFMC) of the constituent securities instead of their per share market price. The FFMC is the resultant product of the per share market price, number of shares o/s and its respective free float factor which determines the individual weightage of a constituent security in an index. Again, since the change in prices and no. of shares o/s are constant across all constituents, weights remain the same and the revised index value of 2000 reflects that very change in price (100%), with the constant divisor being the only link to the base number as illustrated above.

The S&P BSE Sensex (often referred to as Sensex in common parlance) is based on this methodology, where the level of index at any point of time reflects the Free-float Market Cap of 30 component (constituent) stocks relative to a base period.  (1978-1979 in this case with base value as 100)

Now you know exactly what it means when the Sensex moves up/down by any number of points.

The real market scenario would differ in terms of differing outstanding shares per company, differing degrees of price changes of such stocks (often restricted to upper/ lower circuits) and therefore commensurate changes in the weights reflecting in the index. Although fundamentally, the aforementioned structure is how free float market cap weighted indexes are constructed and maintained. To understand any index, the knowledge of its weighting method, quantitative details of constituents therein and base value should suffice.

On the Bombay Stock Exchange website, this illustrative alphabetical matrix of all 30 constituent stocks in the Index are dynamically displayed, providing a bird’s eye view of all constituents in the Sensex.

Consider the following questions:

1. Have you ever thought why the Sensex often depicts the mood of the market?
2. Why is it the most sought after measure of the overall performance of the market (akin to Nifty 50 on the National Stock Exchange)? OR
3. Why is it said to be a recognized gauge of market sentiment?

Well, one of the biggest reasons is the diversity of the sectors represented by the companies in the index and the criteria for selecting stocks that form part of the Sensex, illustrated below:

This brings us to our final question. Who & What determines which stock forms part of the Sensex?

Broadly, the following quantitative criteria determines constitution of a stock in the Sensex, inter alia:

The Security should find itself in the Top 100 companies listed on the exchange (Bombay Stock Exchange) as per total market cap, have a listing history of at least one year on BSE, and shall be traded on each trading day for the last one year. But this is just the tip of the iceberg, the quantitative requisites are further enlisted unequivocally on the BSE website.

We do need to keep in mind that any security included in the index is not immediately removed upon being unable to satisfy one or more quantitative or qualitative criterion. At least 6 weeks are provided as a buffer period for any announced reconstitution in the index to be implemented.

I do hope that questions like “What does ‘x’ market index really mean?” will never bother you again.

In fact, you’re one of those who can now answer it best.