# Capitalization-weighted Index

Capitalization-weighted Index (also called cap-weighted or value-weighted index) is a capital market index in which the constituent securities are weighted based on their market capitalization, which equals the product of its price per share and total number of common shares outstanding. The weight of each security is calculated by the ratio of its market capitalization to the sum of market capitalization of all constituent securities.

Many stock market indices such as FTSE 100, S&P500, NASDAQ Composite, etc. are capitalization-weighted indices.

## Formula

A market-capitalization weighted index value at any point can be calculated using the following formula:

Market Capitalization-weighted Index
=w1×p1 + w2×p2 + ... + wn×pn

Where,
w1 is the weight of first stock,
p1 is the price of first stock,
w2 is the weight of second stock,
p2 is the price of second stock,
wn is the weights of nth stock and
pn is the price of nth stock and so on

Weight of each security can be calculated as follows:

$$w_n\\=\frac{Market\ Capitalization\ of\ Security\ n}{Sum\ of\ Market\ Capitalizations}\\=\frac{q_n\times p_n}{q_1\times p_1+q_2\times p_2+...+q_n\times p_n}$$

## Example

Work out the index value on 1 Jan 2017 and 31 Dec 2017 based on the following data:

Stock Shares
Outstanding
(Q)
Stock Price Market Capitalization
1 Jan 2017
(P0)
31 Dec 2017
(P1)
1 Jan 2017
(Q×P0)
31 Dec 2017
(Q×P1)
A 25,000 $15$20 $375,000$500,000
B 50,000 $34$40 $1,700,000$2,000,000
C 100,000 $52$60 $5,200,000$6,000,000
D 50,000 $120$100 $6,000,000$5,000,000

Assume that the divisor is 1.

Now, we can work out the relevant weights as follows:

$$Weight\ of\ Stock\ A\ on\ 1\ Jan\ 2017\\=\frac{375,000}{375,000+1,700,000+5,200,000+6,000,000}\\=2.82\%$$

Similarly, we work out that weights of Stock B, C and D are 12.81%, 39.17% and 45.20% respectively.

The weights for Stock A, B, C and D as on 31 Dec 2017 are 3.77%, 15.07%, 45.20% and 37.66%.

You can see that weights have increased where the stock price has increased and vice versa.

Index as at 1 Jan 2017
= 2.82%×$15 + 12.81%×$34 + 39.17%×$52 + 45.20%×$120
= 79.38

In the same fashion, we find out that the index value as at 31 Dec 2017 is 71.56. The biggest drag on the index is the drop in price of Stock D because it has the highest weight.