Index Calculation Primer

Index Calculation Primer

Roger J. Bos, CFA

Senior Index Analyst

Standard & Poor's

roger_bos@standardandpoors.com

July 17, 2000

Roger J. Bos, CFA - Standard & Poor's Quantitative Services 2

What is an index?

* An index is a single descriptive statistic that

summarizes the relative change in an

underlying group of variables.

* In an equity index, such as the S&P 500, the

underlying variables are stocks.

* The main differences among indexes is the

types of securities held and the weighting

scheme.

Roger J. Bos, CFA - Standard & Poor's Quantitative Services 3

Index Groupings

* There are many types of indexes, each

trying to measure different groups of stocks:

Broad based Narrow

Small Cap Economic Sector

Mid Cap Industry

Large Cap

Value

Growth

Geographic region

* Or any combination of the above.

Roger J. Bos, CFA - Standard & Poor's Quantitative Services 4

Index Groupings

* These groupings are usually based on

simple financial ratios.

* Size (small, mid, or large) is based on

market cap, which is price times shares

outstanding.

* Style (value or growth) is often based on

book to price ratio, which is the company's

common equity divided by its share price.

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Index Weightings

* Index constituents can be either equal weighted, price

weighted, or cap weighted.

* Lets say we wanted to form a new index comprised of the

five largest cap stocks in the S&P 500 as of May 31, 2000.

Sales Shares Price

* CISCO SYSTEMS INC 12,154.00 7000.939 56.938

* EXXON MOBIL CORP 160,883.00 3481.021 83.312

* GENERAL ELECTRIC CO 110,832.00 9882.338 52.688

* INTEL CORP 29,389.00 3348.987 124.688

* MICROSOFT CORP 19,747.00 5242.042 62.562

Roger J. Bos, CFA - Standard & Poor's Quantitative Services 6

Equal Weighted

* Equal weighting would consist of giving each stock equal

representation in the index. In this example that's a weight of 20%.

* To design such an index, we would designate some amount of fictional

money (say $10,000) to be invested in each stock. Then divide that

amount by the stock price to get how many shares to buy. Lets call

this number Index Shares.

Price Index Shares Dollar Holdings

* CISCO SYSTEMS INC 56.938 175.629 10,000

* EXXON MOBIL CORP 83.312 120.031 10,000

* GENERAL ELECTRIC CO 52.688 189.797 10,000

* INTEL CORP 124.688 80.200 10,000

* MICROSOFT CORP 62.562 159.841 10,000

Roger J. Bos, CFA - Standard & Poor's Quantitative Services 7

Price Weighted

* Price weighting would consist of buying an equal number of shares of

each stock in the index.

* The higher the price, the more weight the stock has in the index.

* For example, Intel has twice the weight of Microsoft, even though

Microsoft's market cap is larger then Intel's.

* The Dow Jones Industrial Average is price weighted because in 1890

(before computers) the easiest thing to do was to add up 12 prices and

divide by 12.

Price Index Shares Dollar Holdings

* CISCO SYSTEMS INC 56.938 10,000 569,380

* EXXON MOBIL CORP 83.312 10,000 833,120

* GENERAL ELECTRIC CO 52.688 10,000 526,880

* INTEL CORP 124.688 10,000 1,246,880

* MICROSOFT CORP 62.562 10,000 625,6200

Roger J. Bos, CFA - Standard & Poor's Quantitative Services 8

Cap Weighted

* Cap weighting is weighting by market capitalization, which is

shares times price.

* In this case index shares (how much one needs to hold to match

an index) are the same as shares outstanding (the number of

shares a company has issued).

* The S&P 500 Index is Cap weighted.

Index Shares Price Market Cap

* CISCO SYSTEMS INC 7000.939 56.938 398,619.44

*

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