# Calculating index values and performance

What is an index value?

Differences in how index values are calculated can occur depending on the index weighting scheme. For the sake of simplicity, we will explain the calculation of market cap-weighted index values.

As prices and market values of the stocks within an index rise and fall, the index reflects this movement using a series of index values. Index values are calculated and published daily after the market closes, and in some cases they are calculated in real time. The change in an index’s value from one point in time to the next represents the performance of the index (i.e., the performance of the market/segment it is designed to measure).

Calculating index values

Below is a hypothetical market cap-weighted index that includes five constituents.

STOCK NAME STOCK PRICE SHARES INCLUDED MARKET VALUE INDEX WEIGHT
A \$3 50 \$150 15%
B \$1 50 \$50 5%
C \$7 70 \$490 51%
D \$9 20 \$180 19%
E \$10 10 \$100 10%
TOTAL MARKET VALUE \$970 100%

The market value for each stock is calculated by multiplying its price by the number of shares included in the index, and each stock’s weight in the index is determined based on its market value relevant to the total market value of the index.

Stock A, for example, has a share price of \$3, and there are 50 shares of this stock in the index, so its market value is \$150 (\$3 X 50 shares = \$150).

The total market value of every stock in the index is \$970, so Stock A’s weight, or representation within the index is 15% (\$150 / \$970 = 15%).

When an index is first created, a starting (base) value is chosen. In our example, we will use 100 as the base value. Now that we have the total market value of our index and our base value, the next step is to determine the index divisor by dividing the total market value of the index by the base index value of 100 (\$970 / 100 = 9.7).

Each day, as the market values of the stocks in the index fluctuate based on changes to their prices, the new total market value of the index is divided by the same divisor (9.7) to produce a new index value:

DAY INDEX TOTAL MARKET VALUE DIVISOR INDEX VALUE
Day 1 \$970 9.7 100.0
Day 2 \$1010 9.7 104.1
Day 3 \$995 9.7 102.6
Day 4 \$1000 9.7 103.1

The divisor remains constant until the index constituency changes. For example, if a stock is delisted or a stock split occurs, the divisor will be recalculated to be reflective of the new index membership.

How are index values used to calculate performance?

Index performance between any two dates can be calculated by dividing the ending index value by the beginning index value as follows. Using our hypothetical index as an example:

Day 1 index value = 100.0

Day 4 index value = 103.1

((103.1 / 100) -1) x 100 = 3.1%

Why do index values vary so widely across indexes and index providers?

Comparing the values of indexes designed to measure the same market or market segment can be daunting, and in most cases irrelevant. Indexes can be started, or “launched” at different points in time and with different base values, so it is important not to get hung up on the values themselves, but rather the growth (or decline) of those values over time.

For example, if Index A had a base value of 100 in January of 2015 and that value increased to 150 as of January 2018, the index value increased by 50% over that 3-year period.

Index B measures the exact same market, but its starting base value was 1,000 in January of 2015, and its value grew to 1,500 as of January 2018. This value of this index also rose 50% over the same 3-year period.

Comparing their January 2018 values of 150 and 1,500 is irrelevant, as they were started with different base numbers. It’s their performance, not their values, that should be compared.

What is the difference between a price return and total return index values?

A price return value measures the changes in the stock prices and market values of the index constituents over time, as shown in the example above.

A total return value measures the changes in stock prices and market values as well, while also capturing the dividends paid to shareholders by the companies in the index by reinvesting the dividends. The dividend reinvestment and compounding is done at the total index level, not at the security level.

What is the difference between a Laspeyre index and a Paasche index?

Whether an index is a Laspeyre index or a Paasche index describes how changes to share quantities are reflected in the calculation of index values.

In a Laspeyre (or base-weighted) index, any changes in the prices of the underlying stocks are reflected in the calculation of the index value on a daily basis, but changes in share quantity are not factored in until the following day’s calculation.

In a Paasche (or current-weighted) index, any changes in the prices of the underlying stocks are reflected in the calculation of the index value on a daily basis, and share quantity changes are factored into the calculation of the index value same-day.

Neither method is subjectively better than the other, and both types of indexes are used in the industry. Both have their advantages and tradeoffs. For example, a Paasche index may be more up-to-the-minute than a Laspeyre index, but it can tend to overestimate values as well (compared to a Laspeyres, which can underestimate).

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