Base value

An index is not a price. It is a ratio dressed up as a number. To turn "the basket is worth 2.26 times what it was" into a readable figure, the index provider picks a start date and assigns the basket a round starting number — the base value.

The workbook says each index "usually is expressed in terms of a change from a base value", and that the base value might be as recent as the previous day or many years in the past. The conclusion it draws is the important part: the percentage change is more important than the actual numeric value.

A Sensex at 80,000 and a Nifty at 25,000 are not "worth" different amounts in any meaningful sense. They started from different bases on different dates.

In the workbook's market capitalization weighted index, the combined market capitalization of the five stocks on the base date, 1 January 1995, is Rs 18,800 lakh. That figure is equated to the base value of 100. Every later value of the index is:

Index value = Current market capitalization ÷ Base market capitalization × Base value

When the market capitalization rises to Rs 42,500 lakh, the index is 42,500 ÷ 18,800 × 100 = 226.06 — a rise of 126.06%.

The equal weighted index example works the same way: the stocks are worth Rs 1,20,000 on 1 January 1995, the old index value is equated to 100, and at Rs 1,46,000 the index is 121.67.

The price-weighted index example does not rescale to 100 at all. Its value on the base date is simply the average price, (150 + 300 + 450 + 100 + 250) ÷ 5 = 250; today it is 510, an increase of 104%. Whether the base is 100 or 250 changes the number printed, and changes nothing about the percentage move.

Index value today = (Value of the basket today ÷ Value of the basket on base date) × Base value

% change in index = (Index today − Base value) ÷ Base value × 100

The workbook's market-cap weighted index (Chapter 2, section 2.3). Five stocks, base date 1 January 1995, base value 100.

Index today = 42,500 ÷ 18,800 × 100 = 226.06
Change      = (226.06 − 100) ÷ 100  = 126.06%

Change the base and nothing that matters changes (illustrative). Had the provider set the base value to 1,000 instead:

Index today = 42,500 ÷ 18,800 × 1,000 = 2,260.6
Change      = (2,260.6 − 1,000) ÷ 1,000 = 126.06%

Similarly, the workbook's price-weighted index moved from 250 to 510 — 104%. Rescaled to a base of 100 it would read 100 to 204. Same 104%.

This is why an investor who put Rs 1,00,000 into the market-cap basket on the base date would hold about Rs 2,26,064 today (1,00,000 × 42,500 ÷ 18,800), whichever base value the index happens to print.

Chapter 2, section 2.1, states that an index is expressed as a change from a base value and that the percentage change matters more than the number. Section 2.3 then computes the market capitalization weighted, price-weighted and equal weighted indices from their base dates. Expect a calculation of the current index value from base and current market capitalization, and a conceptual question on why the level of an index is less informative than its percentage change.

• The base value is arbitrary; the percentage change is what carries information.
• The base market capitalization is equated to the base value — the index is not the market capitalization itself.
• A base date can be recent or decades old — the workbook says it may be as recent as the previous day.
• Change in index % = (Index − Base) ÷ Base, so an index going from 100 to 226.06 has risen 126.06%, not 226.06%.
• Do not confuse base value of an index with the base price used in Chapter 6 for the operating ranges of futures contracts.