Question

1. We have a market capitalization weighted index of 20 stocks. The total market capitalization of the index is $1 billion. Today, 18 of the stocks finished unchanged – that is, their return was 0.0%. The 19th stock was up 1% and has a market capitalization of $100 million. The 20th stock was down 1% and has a market capitalization of $10 million. What was the change in the index?

Answer 1

We can calculate the change in Market capitalization index as below

Number of Stocks on index = 20 stocks

Unchanged Stocks during the day = 18 stocks

Changes in Value of Stocks = 2 Stocks

Stock	Market Capitalization	Percentage Change	Change in Value
19th Stock	$ 100,000,000	1% Increase	(100,000,000 * 1%) $ 1,000,000 increase
20th Stock	$ 10,000,000	1% Decrease	( 10,000,000 * 1%) $ 100,000 decrease

Overall Change in Value = Increase in Value of 19th Stock - Decrease in Value of 20th Stock

= 1,000,000 - 100,000

= $ 900,000

So there is increase in the value of index by $ 900,000

Total Market Value of 19th and 20th Stock = $ 100,000,000 + 10,000,000

= $ 110,000,000

Percentage Change in the Index = Increase in Value / (Total Market value of 19th and 20th stock)

= 900,000 / 110,000,000

= 0.00818 or 0.82% Increase

So there is overall 0.82% increase in the index value.

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