A security market index is an indicator of a stock market, asset class, etc. prepared by aggregating the information of some representative constituent securities.

Price return index vs total return index

A price return index (or price index) just measures the movement in prices while a total return index also accounts for reinvestment of interest and dividends.

Price return over a single period can be calculated by dividing the change in index value by the opening value of the index.

Price\ Return =\frac{V_{n+1}- V_n}{V_n}

Price return can also be determined by finding the percentage change in the price of each constituent security and then multiplying it with the security’s weight in the total index and summing them up.

The total return can also be calculated using either of the above methods. The only difference is the inclusion of income in the numerator.

Total\ Return =\frac{V_{n+1}- V_n+I}{V_n}

Where Vn+1 and Vn are the relevant index values at the end and beginning of the period respectively and I is the total income attributable.

Index values (for both price return and total return) over multiple periods are determined by linking the single period returns.

Index construction and weighting methods

The first consideration in constructing an index is the identification of the target market and selection of constituent securities. The selection of securities in some indexes is based on rules related to market capitalization, number of outstanding shares, etc. while in others, it is determined objectively by committees.

There are four methods in which the constituent securities can be assigned weights:

Price-weighting

A method in which an index is constructed by summing up the prices of all securities and dividing it by the number of securities. Securities with high prices have a greater influence on such an index. Its advantage lies in its simplicity while its main disadvantage is that it assigns arbitrary weights to securities. Further, the divisor must be adjusted to reflect any stock split.

Equal weighting

A method in which equal weight is assigned to each constituent security. It over-represents securities with smaller market capitalization and underrepresented securities with high market capitalization. Its advantage is its simplicity, but it suffers from two disadvantages: (a) it assigns weights arbitrarily and (b) it requires rebalancing (because after a change in price, weights are no longer equal).

Market-capitalization weighting

A method in which weight assigned to each security equals its market capitalization divided by total market capitalization. The main advantage of a capitalization-weighted index is that the weights assigned are not arbitrary but represents the value of the security in the target market. However, such an index can potentially over-weight securities whose prices have risen (and hence may be overvalued) and under-weigh securities whose prices have declined (and hence may be undervalued).

Float-adjusted capitalization-weighting

Capitalization-weighted indices are sometimes based on the market float, i.e. they consider only such fraction of market capitalization which is available for the general investing public. In other words, float-adjusted market capitalization indices exclude shares held by controlling investors, major corporations and government.

Fundamental weighting

An indexing method in which stocks are assigned weights based on some fundamental indicator independent of the stock price, such as dividends, earnings, cash flow, etc. Fundamentally-weighted indices have a contrarian effect, i.e. they overweight stocks whose fundamentals relative to their market value are stronger.

Index rebalancing and reconstitution

Rebalancing refers to the periodic adjustments made to the weights of constituent securities of an index. A price-weighted index does not need any rebalancing because weights are dynamic and they change with change in stock prices. A capitalization-weighted index needs rebalancing only when there are mergers, takeovers, etc. An equal-weighted index needs frequent rebalancing.

Reconstitution stands for the process of changing constituent securities. Reconstitution creates significant turnover in an index because it changes the weights of the remaining securities. Some investment managers buy securities which they believe will be added to a popular index and sell securities which they believe will be deleted.

Uses of market indexes

Market indexes were created primarily to reflect market sentiment, but recently they have proved very useful as proxies for the market for the purpose of measuring and modeling risk and return. They are important for asset allocation because they function as proxies for different asset classes. Market indexes are used as benchmarks for actively managed portfolios. Further, many investment products such as index funds and ETFs are modeled on the basis of market indexes.

Equity indexes

Equity indexes have the following types:

  • Broad market indexes which generally cover almost all of the equity market. They approximate the market portfolio.
  • Multi-market indexes which aggregate global performance based on geographic region and stage of development)
  • Sector indexes which are typically a subset of a broad market index, primarily used for performance evaluation, and
  • Style indexes which classify stocked based on investment style and strategies:
  • Based on market capitalization: small-cap, mid-cap, and large-cap;
  • Based on whether they are value or growth.
  • Based on a combination of market capitalization and value/growth classification.

Types of fixed-income indexes

When compared to equity indexes, creation/replication of fixed income indexes is more challenging because:

  • The number of fixed income securities are far larger than equity securities
  • Fixed income securities mature, and new securities are issued leading to very high turnover.
  • Many fixed-income securities are illiquid and pricing information is available only from dealers or through estimation.

Fixed income indexes are classified based on sector, geographic region, and development stage. They are further classified based on the type of issuer (corporate, government), the currency of payments, maturity, credit quality, existence of inflation protection, etc. These indexes are further classified based on whether they are broad market, sector-specific, style-specific, etc.

Indexes of alternative investments

Three most popular alternative investment indexes relate to commodities, real estate, and hedge funds.

Commodities indexes

Commodities indexes are based on futures contracts of the constituent commodities. Some weigh commodities equally while others base it on liquidity measures and global production values. This causes the risk-return profile of indexes to be different from that of actual commodities. Performance of an actual portfolio of commodities can differ from index return because index return considers other factors such as risk-free interest rate, roll yield, etc.

Real estate indexes

Real estate indexes include both actual real estate assets and securities of real estate firms. They can be categorized as appraisal indexes, repeat sales indices, and real estate investment trust (REIT) indexes. REIT indexes are continuously updated because they are traded on an exchange and updated prices are available.

Hedge fund indexes

Hedge fund indexes are indexes of hedge fund returns. Since hedge funds are not required to make their information public, indexes are based on voluntary cooperation of funds. This leads to survivorship bias because only funds with good performance are inclined to share their performance.

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