Index Weighting: Price vs. Equal
The simplest form of weighting an index is price weighting. __Price weighting__ simply gives higher weights to higher priced stocks comprised in the index. The Dow Jones Industrial Average (DJIA) is one of the most popular indexes that utilizes price weighting.
Consider the following price weighted index.
| Security | Price | Shares | Weight |
|----------|-------|--------|--------|
| A | $30 | 50 | 10% |
| B | $10 | 50 | 3% |
| C | $70 | 50 | 23% |
| D | $90 | 50 | 30% |
| E | $100 | 50 | 33% |
Suppose that the securities are shown in order of market capitalization; A is the largest corporation, while E is the smallest. If security A rose in price by 1%, how might you characterize the effect on the index?
Exactly.
Ironically, the smallest company will have the largest impact on the index, simply because of the largely meaningless share price. This underscores the weakness of price indexes. The DJIA isn't popular because of its accuracy; but just because it's very old.
No.
Actually, a 1% price change in security B would have the smallest impact on the index.
No.
Actually, one of the smaller firms would have more impact, ironically.
You have been following a price-weighted index. Data for the index and its five securities are shown below:
| Security | Price | Shares | Weight |
|----------|-------|-------------|--------|
| A | $30 | 50 | 10% |
| B | $10 | 50 | 3% |
| C | $70 | 50 | 23% |
| D | $90 | 50 | 30% |
| E | $100 | 50 | 33% |
| Sum | 300 | | 100% |
| Divisor | 6 | Index value | 50 |
You heard some news about one of these securities this morning; security E has announced a two-for-one split. The new price for security E in the index will drop to $50. The total sum of the prices in the index will also drop to $250. You also recall that the weighting for the securities in a price-weighted index is the price of the security divided by the sum of the prices for all securities in the index.
How will this two-for-one split affect the weighting for these securities?
No.
Yes!
Since the sum of the prices has changed, the weights for all of the securities will change.
The change in the sum of the prices has you thinking: if the index value is the sum of the prices over the divisor, then the index value will drop because of this split. The way to adjust this so that the index value doesn’t drop because of a split is to change the divisor! The index manager will take the sum of the prices after the split and divide it by the value of the index before the split to get a new value for the divisor.
What will be the new divisor after this split to keep the value of the index unchanged?
Correct.
Since the new sum of the prices is 250, divide that by the index value before the split, which was 50, to get the new value of 5.
Not correct.
Just because the price of security E is one-half of its prior value doesn't mean you double the divisor to compensate for it. Since the new sum of the prices is 250, divide that by the index value before the split, which was 50, to get the new value of 5.
An __equal-weighted index__ simply gives each security in the index an equal weight. One of the main advantages is simplicity, like price weighting. For example, consider the following index:
| Security | Price | Shares | Weight |
|----------|-------|--------|--------|
| A | $45 | 1.644 | 20% |
| B | $60 | 1.233 | 20% |
| C | $70 | 1.057 | 20% |
| D | $90 | 0.822 | 20% |
| E | $105 | 0.705 | 20% |
How might you describe the relationship between price and the amount of shares in equally-weighted indexes?
Correct!
The calculation assigns an equal weight to each constituent security. By dividing the total of all of the securities' prices times the weight by the price for each security, you get to that security's number of shares.
Looking at the table again, the total value of the constituent securities is $370. If you take the total value and multiply it by the equal weight of 20%, you get $74. From there, you take $74 and divide it by each constituent security's price to get its respective shares.
Incorrect.
Securities with the lowest price will actually contain more shares in the index.
Incorrect.
Securities with the highest price will not have the same amount of shares as securities with the lowest price. Refer to the table to help find the correct answer.
One disadvantage of equally-weighted indexes is it is hard to maintain long term, as portfolios are rebalanced due to daily market fluctuations. Equally-weighted indexes may not take advantage of thriving markets, because they are only allotted so much weight in each security.
Another disadvantage involves representation. In an equally weighted index, will firms with a large market capitalization be underrepresented or overrepresented with respect to the tech sector as a whole?
Incorrect.
These firms have a larger value to the sector as measured by market capitalization, so they will be underrepresented, not overrepresented, in an equally weighted index.
Correct.
These firms have a larger value to the sector as measured by market capitalization, so they will be underrepresented in an equally weighted index.
To summarize:
[[summary]]
Any price changes in the constituent securities will cause the weighting to go out of balance and become unequal. That is another disadvantage of an equally weighted index. In a dynamic market where prices change constantly, an equally weighted index won’t stay equally weighted for long!
It would have the greatest impact
It wouldn't have as much impact as a 1% gain in security B
It wouldn't have as much impact as a 1% gain in security E
Only the weight for security E will change
The weights for all of the securities will change
The new divisor will be 5
The new divisor will be 10
Securities with the highest price will have the least amount of shares in an equally-weighted index
Securities with the lowest price will have an average amount of shares in an equally-weighted index
Securities with the highest price will have relatively the same amount of shares as securities with the lowest price
Overrepresented
Underrepresented
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