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.

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. Price-Weighted Index

    A price-weighted index is a stock market index where each stock ...
  3. Average Strike Option

    An average strike option is an option type where the payoff depends ...
  4. Equal Weight

    Equal weight is a type of classification that gives the same ...
  5. Theoretical Dow Jones Index

    A method of calculating a Dow Jones index that assumes all index ...
  6. Index Futures

    Index futures are contracts based on a financial index, which ...
Related Articles
  1. Investing

    3 Types of Indexing for ETF Success

    ETF success relies on the index with which it is paired. Explore three index genres for tracking average market performance.
  2. Investing

    The Hidden Flaws of Index Investing

    Index investing isn't always better than active investing. Here's why.
  3. Insights

    An Introduction to Stock Market Indices

    Lear more about the five most talked about stock indices and what makes them all different.
  4. 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.
  5. 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.
  6. Investing

    4 Cases to Buy If the Stock Market Is at an All-Time High

    Learn about why someone would invest in the stock market, even if it has reached an all-time high. This article will review four cases for doing just that.
  7. Investing

    5 Stocks Commanding the Dow Bull Market (MMM, CVX)

    Just 5 stocks—United Healthcare, 3M, Chevron, Caterpillar and IBM—are responsible for 81% of the gain in the Dow Jones Industrial Average so far this year, which is up around 2.5% YTD.
  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.
  10. Investing

    Index Investing

    Get to know the most important market indices and the pros and cons of investing in them.
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 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 >>
  3. How Do I Find Mutual Funds That Track Indexes?

    Two good sources for finding index funds are Fidelity Investments and Vanguard. Read Answer >>
  4. What does the S&P 500 index measure and how is it calculated?

    Learn about what exactly the S&P measures and why it's used by market participants as a tool to understand the broader stock ... Read Answer >>
  5. How is the value of the S&P 500 calculated?

    The S&P 500 is a U.S. market index that gives investors an idea of the overall movement in the U.S. equity market. The value ... Read Answer >>
  6. Why do investors use the S&P 500 as a benchmark?

    Learn about the advantages and disadvantages of using the S&P 500 as a benchmark for portfolio performance, and understand ... Read Answer >>
Trading Center