# Price & Value Weighted Indexes

Updated: Apr 25, 2021

An index is a measurement of a basket of securities. For example, I could create a Canadian stock market index which was made up of the 100 largest companies in Canada.

When creating an index we must assign a weight to each company, doing this allows us to calculate the change of the index value over time. The two types of indexes are:

1) Price-weighted

2) Value-weighted

In order to calculate the value of a price-weighted index, we sum the value of one share of each company in the index.

In order to calculate the value of a value-weighted index, we multiply the # ofhares by the price of a share for each company and then add them together.

Using these methods can produce some very odd numbers, often very large numbers as well. Of course, we can begin an index at any number we choose, perhaps a round number like 100 or 1000, and adjust periodically based on the percent change in the index value.

Example:

Starting value 100

Price-weighted value at time 0 = 30

Price weighted value at time 1 = 35

% change in price weighted index = 35/30 or 16.67%

Ending index value = 100*1.1667 = 116.67

### Accounting for Share Splits

Splits occur when the number of shares increases. For example in a 2:1 split, called a "two for one" split each shareholder will own two shares after the split for each one share they owned before the split,

Impact on the value-weighted index:

When shares split (2:1) the value of the share should halve. The net result should be zero. No adjustment needed. Observe below that XYZ shares double and share price halves resulting in the same index value.

Impact on the price-weighted index:

A price-weighted index will see the weight of the split shares decrease when the stock splits. In order to hold an index constant despite splits, we do the following.

Value of index pre-split = \$30 (20+10)

Value of index after split = \$20 (10+10)

In order to back out the effect of the split we do the following

old value = (P1+P2)/x

30=(10+10)/x

30x=20

x=.6667

Therefore, we can use the new share prices \$10 and \$10 but divide the sum by .6667 to keep the value constant

Index value = (10+10)/.6667 =

Index Value = 30

The same process can be repeated for future splits using the divisor adjusted value as the original value.

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