## WHAT IS 'Arithmetic Index'

Arithmetic index refers to a hypothetical portfolio of securities that uses an arithmetic sum to determine changes in its value, without taking the relative value of the securities into account. It is perhaps the simplest way to calculate a hypothetical portfolio, or index.

To calculate an arithmetic index, simply take the daily percent change of each included security, then divide by the total number of those securities. In this way, components with the most price movement in percentage terms exert the most influence on the index return.

There are very few arithmetic indexes, and most focus on equities. One of the best-known is the Value Line Arithmetic Index.

Next Up

## BREAKING DOWN 'Arithmetic Index'

An arithmetic index differs from most hypothetical stock portfolios, which are market-cap weighted. This means stocks backed by companies with the largest market values exert more influence on the index return than lesser-valued companies. Most well-known indexes including the Standard & Poor's 500 Index and the Nasdaq 100 are market-cap weighted.

Arithmetic indexes, however, are equal-weighted, in that each included stock represents the same percentage of the total.

However, not all equal-weighted indexes are arithmetic indexes. Some are geometrically weighted, meaning they take into account the effects of compounding over time. An example is the Value Line Geometric Index.

Neither an arithmetic index nor geometric index should be confused with a price-weighted index, which gives preference to the stocks with the highest prices. In this type of index, a stock moving from \$70 to \$80 carries more weight than a stock moving from \$7 to \$17, even though the latter is a much larger move in percentage terms. The Dow Jones Industrial Average is a price-weighted index.

## Pros and Cons of Arithmetic Index

An arithmetic index closely mimics the change of a theoretical portfolio if you held each of its components in equal amounts. It also tends not to be dominated by stocks with large market caps or, in the case of a price-weighted index, high prices. Therefore, it gives more representation to mid-and small-cap stocks.

However, investors don't always want this. Market-weighted indexes are more common because they more closely reflect reality: It takes significantly more money to move large-caps, and thus, these stocks seemingly deserve a heavier index weighting. Large-caps also tend to be more widely owned.

In addition, few investors want to hold a large portfolio of stocks in precisely equal amounts in real life, thus making an arithmetic index largely theoretical, and in some ways, impractical. It may be downright impossible for a large investor with tens of billions in the market to accumulate all components of an index in equal proportion, given the small available float of certain holdings, as well as trading costs.

RELATED TERMS
1. ### Weighted Average Market Capitalization

Weighted average market capitalization refers to a type of stock ...
2. ### Harmonic Mean

The harmonic mean is an average which is used in finance to average ...
3. ### Capitalization-Weighted Index

Capitalization-weighted index is a market index in which stocks ...
4. ### Average Strike Option

An average strike option is an option type where the payoff depends ...
5. ### Geometric Mean

The geometric mean is the average of a set of products - the ...
6. ### Weighted

Weighted is a description of adjustments to a figure to account ...
Related Articles
1. Investing

### The Pros and Cons of Indexes

Learn about the advantages and disadvantages of stock indexes and passive index funds. Discover how there is an opportunity cost to using index funds.

### Using index futures to predict the future

Want to know whether the stock market will open up or down? Learn about index futures and how they can help predict how the market will trade.
3. Insights

### An Introduction to Stock Market Indices

Lear more about the five most talked about stock indices and what makes them all different.

### CMT Association's Alan Shaw on Logarithmic Charts

After 46 years on Wall Street, retired analyst and CMT Association founder Alan Shaw shares his take on logarithmic versus arithmetic charts.
5. Investing

### ETF Tracking Errors: Protect Your Returns

Tracking errors tend to be small, but they can still adversely affect your returns. Learn how to protect against them.
6. Investing

### S&P 500 ETFs: Market Weight Vs. Equal Weight (RSP, SPY)

Both S&P 500 and S&P 500 EWI indexes include the same set of stocks, but different weighting strategies give them separate individual properties.
7. Investing

### Choosing The Right ETF Index To Reach Your Goals

The key to choosing ETFs for your portfolio is understanding how they pick stocks and making sure their investment philosophy matches yours.
8. Investing

### Strategies For Determining The Market's True Worth

Learn the strengths and weaknesses of passive and active management when trying to uncover the overall market's worth.
9. Investing

### How to calculate your investment return

How much are your investments actually returning? The method of calculation can make a significant difference in your true rate of return.
RELATED FAQS
1. ### What is the historical market risk premium?

Learn what the historical market risk premium is and the different figures that result from an analyst's choice of calculations ... Read Answer >>
2. ### What's the difference between the Dow Jones Industrial Average and the S&P 500?

The DJIA is a price-weighted average of 30 stocks whereas the S&P 500 is a market value-weighted index of 500 stocks. Read Answer >>

4. ### What are some examples of applications of the geometric mean?

Learn about applications of the geometric mean based on examples such as calculations of portfolio return, growth rates and ... Read Answer >>
5. ### How Do I Find Mutual Funds That Track Indexes?

Two good sources for finding index funds are Fidelity Investments and Vanguard. Read Answer >>
Hot Definitions
1. ### Intrinsic Value

Intrinsic value is the perceived or calculated value of a company, including tangible and intangible factors, and may differ ...
2. ### Current Assets

Current assets is a balance sheet account that represents the value of all assets that can reasonably expected to be converted ...
3. ### Volatility

Volatility measures how much the price of a security, derivative, or index fluctuates.
4. ### Money Market

The money market is a segment of the financial market in which financial instruments with high liquidity and very short maturities ...
5. ### Cost of Debt

Cost of debt is the effective rate that a company pays on its current debt as part of its capital structure.
6. ### Depreciation

Depreciation is an accounting method of allocating the cost of a tangible asset over its useful life and is used to account ...