Index Weighting Methods

This week we want to share with you various Index Weighting Methods covered in the CFA Level 1 curriculum. The following explanation is taking directly from our latest CFA Level 1 Study Guide. If you haven’t purchased your copy yet, we invite you to check it out here.

Security Market Indices

A security market index aims at providing a reference for the performance of an asset class, a market or a segment of the market. In other words, it gives market participant an idea of how the market is doing so they can compare the performance of their portfolio. An index is a pool of securities called constituents that are amalgamated as a portfolio.

The value of an index is the sum of its constituents. The return of an index is the geometric mean of its periodic returns. Remember that the geometric mean is calculated as:

geometric mean formula

Index Weighting Methods

The value of the index depends on the weight of its constituents which indicates what proportion of each stock should be included in the index portfolio. There are five methods to measure the weights: price weighting, market capitalization weighting (aka value weighting), float-adjusted market capitalization weighting, fundamental weighting and equal weighting. The most popular method is the market capitalization weighting. We explain in details the price, value and equal weighting methods below.

Price Weighting

What?

The value of the price weighted index adds the prices of all the constituent stocks and divides by the number of constituents adjusted for stock splits. The most popular price weighted index are the Dow Jones Industrial Average (30 U.S. stocks) and the Nikkei 225 (225 top Japanese stocks).

Why?

The main advantage of the price weighting method is that it is easy to calculate. However, the price of a security does not mean anything and under the price weighting method, the highest priced securities will have a larger weight.

How?

Price Weighted Index Formula

Value (Market Capitalization) Weighting

What?

Value weighting uses the proportion of the stock’s market capitalization relative to the total market capitalization of all constituents. Alternatively, only the market float (shares available to the investing public) can be used to compute the weights. The S&P 500 is the most common example of a value weighted index.

Why?

The value weighted approach reflects better than the price or equal weighted approach the value of each constituent in the market. For instance, in the Nasdaq 100 index, Apple has a significant weight because the company is very large. It makes sense that it has a larger impact on the index since it does have an impact on the general market and many investors’ portfolios.

How?

Current Index Value

The base year index period for the S&P 500 for example is the 1941-1943 and the base level value is  10.

Equal Weighting

What?

Return of a portfolio that would have equal amount invested in each constituent stock.  Since different stocks will surely have different performance, the equal weighting does not last for long. The best performing stock increases more than the others ends up having a larger weight. This is why equal weighting indices need to be rebalanced periodically. An example of an equal weighting equity index is the MSCI World Equal Weighted Index.

Why?

They are simple to compute and do not discriminate against smaller companies like the value weighting or low-priced stocks like the price weighting. However, given the periodical rebalancing, one that would try to replicate an equal weighted index would incur large transaction costs.

 

How?

Since all constituents have the same weights, only their performance matters. Thus, the index performance is simply the average performance of its constituents.

Equal Weighted Index formula

Rebalancing and Reconstitution

Rebalancing is the adjustment of the weights of the constituents of the index. For price and value weighted indices, the rebalancing is done automatically since the price changes are reflected immediately on the index value. Therefore, rebalancing is performed only for equal weighted indices. Rebalancing is usually done on a quarterly basis.

Reconstitution is the process of adding and deleting securities from an index when they no longer meet the criteria of the index.  For example, the S&P 500 recently (June 2013) dropped Heinz from its list of constituents and re-added General Motors which was dropped back in 2009.

Purpose of Indices

  1. Reflects market sentiment. By looking at the performance of a general market index, investors can have an idea of what the market is doing. For instance, if you hear on the news that the Dow Jones dropped by 3%, you immediately understand that the market is rather gloomy on the prospects for the U.S. economy.
  2. Serve as a benchmark for asset managers. If you manage a French large capitalization portfolio, you would want to “beat” the CAC 40 index of French stocks.
  3. Measure the risk and return of asset classes. In study session 12, when we performed the mean variance optimization, we used ETFs that tracked various indices to represent asset classes. For example, to represent the performance of small capitalization stocks, we used the Russell 2000 index.
  4. Measure the market return and risk of individual stocks. In study session 12 when we performed our Beta analysis, we used the S&P 500 index as the independent variable to assess the systematic risk and expected return of Pfizer and Goldman Sachs. Risk and return was measured relative to the index using the CAPM formula.
  5. Serve as model portfolio for index funds. Passively managed mutual funds and exchange traded funds replicate an index. For example the SPY SPDR is a widely traded ETF that replicates the S&P 500.

 

Types of Indices

Equity indices

Types of Equity Indices

Fixed income indices

Since fixed income securities trade over-the-counter as opposed to equities that trade on an exchange, there is less transparency and liquidity in trading. Also, the bonds eventually mature and disappear. These factors make the construction of a fixed income index more tricky.

There are various fixed income indices. They can be constructed based on these characteristics, among others:

  1. Maturity
  2. Sectors,
  3. Geographies,
  4. Embedded options (calls, conversion…)
  5. Type of issuer
  6. Collateral
  7. Default risk
  8. Coupon rate
  9. Maturity

Examples of fixed income indices include the NYSE 7-10 Year Treasury Bond Index or the BofA Merrill Lynch Diversified Germany Bond Index.

Alternative investment indices

Alternative Investments

Most well known and followed indices

Most well known and followed indices

As always, we hope this provided you with valuable information in order to help you prepare for the latest CFA Level 1 exam. We also welcome your comments and suggestions and we invite you to share your thoughts in the comments sections below.

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