# Understanding Market Indexes: Calculation, Weighting Methods, and More

Are you curious about how market indexes are calculated or how they measure price return and total return? Wondering about index weighting methods and how rebalancing and reconstitution come into play? This comprehensive guide will break down these essential concepts to help you better understand market indices and make informed investment decisions.

Market indexes, such as the Dow Jones Industrial Average (DJIA), Standard & Poor’s 500 (S&P 500), Nikkei 225, Hang Seng, FTSE 100, DAX, and CAC 40, are critical tools for investors. They help analyze security markets, compare return metrics, and identify investment opportunities. The growing popularity of low-cost index funds has also increased interest in understanding market indexes.

To give you a better idea of the diverse range of market indexes, here’s a table showcasing some well-known indexes, along with their asset classes and weighting methods:

## Price Return vs. Total Return Index

Understanding the difference between price return and total return indices is crucial for investors looking to analyze the performance of a particular index.

There are two ways to calculate returns for the same index: the price return index and the total return index.

1. Price Return Index: This index reflects the prices of the securities within the index. It gives investors an idea of how the underlying stocks have performed based on their price changes alone.
2. Total Return Index: This index considers not only the price return but also other factors, such as dividend returns, interest, and other distributions. As a result, it provides a more comprehensive view of an investment’s performance.

Initially, the values of the price and total return indexes are equal. However, over time, the total return index value typically becomes higher than the price return index due to the impact of non-price variables like dividends, interest, and other distributions.

The Value of a Price Return Index

The value of a price return index formula is as follows:

$$V_{PI}=\frac{\sum\limits_{i=1}^N P_i n_i}{D}$$

where:

$$V_{PI}$$ = value of the price return index

$$N$$ = the number of securities in the index

$$P_i$$ = the unit price of security $$i$$

$$n_i$$ = the number of units security $$i$$ retained in the index

$$D$$ = the value of the divisor

The Value of a Total Return Index

The value of a total return index formula is as follows:

$$V_{TI}=\frac{\sum\limits_{i=1}^N (P_i + Div_i + Int_i + Dist_i) n_i}{D}$$

where:

$$V_{TI}$$ = value of the total return index

$$N$$ = the number of securities in the index

$$P_i$$ = the unit price of security $$i$$

$$Div_i$$ = the dividend of security $$i$$

$$Int_i$$ = the received interest of security $$i$$

$$Dist_i$$ = the received distributions of security $$i$$

$$n_i$$ = the number of units security $$i$$ retained in the index

$$D$$ = the value of the divisor

## Index Weighting Schemes

### Price-Weighted Indexes: An Overview

In a price-weighted index, each security’s weight is determined by its price per share. Higher-priced securities carry more weight in the index return calculation. The price-weighted index formula is as follows:

$$w_i^P=\frac{P_i}{\sum\limits_{j=1}^N P_j}$$

where:

$$w_i^P$$ = weight of security $$i$$

$$P_i$$ = price of security $$i$$

### Example of Price-Weighted Index

How to Calculate Price Return and Total Return of Price-Weighted Security

Price return of ABC security;

$$\frac{Ending\ Price}{Beginning\ Price}\ Beginning\ Weight = Price\ Return$$
$$\frac{24.00}{20.00}\ 26.66\% = 5.33\%$$

Total return of ABC security;

$$\frac{Ending\ Price + Dividends\ Per\ Share}{Beginning\ Price}\ Beginning\ Weight = Total\ Return$$
$$\frac{24.00+2.50}{20.00}\ 26.66\% = 8.66\%$$

Simplicity: The calculation method is straightforward and easy to understand.

Long historical records: Many price-weighted indexes have a long-standing history in the financial markets.

Limited representation: High market value companies might not be adequately considered.

Overemphasis on high-priced securities: Higher-priced stocks have more significant influence, which could skew the index.

Impact of stock splits: Stock splits can change security prices, affecting the index’s overall representation.

### Capitalization-Weighted Indexes: An Overview

In a capitalization-weighted index, each security is weighted based on its total market capitalization. The market capitalization of a security is calculated by multiplying its market price by the number of outstanding shares. This approach gives greater weight to larger companies with higher market values. The capitalization-weighted index formula is as follows:

$$w_i^M=\frac{P_iQ_i}{\sum\limits_{j=1}^N P_jQ_j}$$

where:

$$w_i^M$$ = weight of security $$i$$

$$P_i$$ = price of security $$i$$

$$Q_i$$ = number of shares of security $$i$$

### Example of Capitalization-Weighted Index

How to Calculate Price Return and Total Return of Capital-Weighted Security

Price return of ABC security;

$$\frac{Ending\ Price}{Beginning\ Price}\ Beginning\ Weight = Price\ Return$$
$$\frac{24.00}{20.00}\ 36.00\% = 7.20\%$$

Total return of ABC security;

$$\frac{Ending\ Price + Dividends\ Per\ Share}{Beginning\ Price}\ Beginning\ Weight = Total\ Return$$
$$\frac{24.00+2.50}{20.00}\ 36.00\% = 11.70\%$$

More objective and explicit measure: The weighting is directly based on the market capitalization of each security, offering a clear, objective method for calculating index returns.

Limited rebalancing: As market capitalizations change, the index naturally adjusts, reducing the need for frequent rebalancing.

Investor-friendly: Investors can more easily replicate and hold securities in a capitalization-weighted index compared to other weighting schemes.

Overpriced securities can dominate: If a security becomes overvalued, it will have a more significant impact on the index, potentially distorting its representation of the market.

Overemphasis on large-cap securities: This method tends to give more weight to large-cap companies, which can overshadow smaller companies and limit diversification.

### Equal-Weighted Indexes: An Overview

In an equal-weighted index, each security is assigned an equal weight, regardless of market capitalization. This approach provides a more balanced representation of the index’s constituents, offering potential benefits and drawbacks that investors should consider. The equal-weighted index formula is as follows:

$$w_i^E=\frac{1}{N}$$

where:

$$w_i^E$$ = weight of security $$i$$

$$N$$ = the number of securities in the index

### Example of Equal-Weighted Index​

How to Calculate Price Return and Total Return of Equal-Weighted Security

Price return of ABC security;

$$\frac{Ending\ Price}{Beginning\ Price}\ Beginning\ Weight = Price\ Return$$
$$\frac{24.00}{20.00}\ 25.00\% = 5.00\%$$

Total return of ABC security;

$$\frac{Ending\ Price + Dividends\ Per\ Share}{Beginning\ Price}\ Beginning\ Weight = Total\ Return$$
$$\frac{24.00+2.50}{20.00}\ 25.00\% = 8.13\%$$

Balanced representation: Large-cap securities are underweighted, resulting in a more diversified index that includes a broader range of companies.

Potential for higher returns: By giving equal weight to smaller-cap stocks, this approach may provide greater exposure to high-growth opportunities.

Fluctuating returns: The high concentration of small-cap securities can result in more volatile returns, which may not be suitable for all investors.

Less liquid securities: Due to the increased exposure to small-cap stocks, investors may encounter less liquid securities that can be harder to buy or sell.

Frequent rebalancing: Equal-weighted indexes require more frequent rebalancing to maintain equal weighting, which can lead to higher transaction costs and potential tax implications.

### Fundamental-Weighted Indexes: An Overview

Fundamental-weighted indexes assign weights to each security based on financial metrics, such as cash flow, revenues, earnings, dividends, and book value. This method is designed to counterbalance some of the disadvantages of capitalization-weighted indexes by offering a more stable and diversified representation of the market. The fundamental-weighted index formula is as follows:

$$w_i^F=\frac{F_i}{\sum\limits_{j=1}^N F_j}$$

where:

$$w_i^F$$ = weight of security $$i$$

$$F_i$$ = fundamental measure of security $$i$$

### Example of Fundamental-Weighted Index

How to Calculate Price Return and Total Return of Fundamental-Weighted Security

Price return of ABC security;

$$\frac{Ending\ Price}{Beginning\ Price}\ Beginning\ Weight = Price\ Return$$
$$\frac{24.00}{20.00}\ 73.39\% = 14.68\%$$

Total return of ABC security;

$$\frac{Ending\ Price + Dividends\ Per\ Share}{Beginning\ Price}\ Beginning\ Weight = Total\ Return$$
$$\frac{24.00+2.50}{20.00}\ 73.39\% = 23.85\%$$

Reduced overpricing: This approach is less prone to overpriced securities compared to capitalization-weighted indexes, as it focuses on fundamental financial metrics.

Enhanced small-cap representation: By using fundamental factors, this method can provide better representation of small-cap companies, potentially offering greater diversification and growth opportunities.

Subjective weighting scheme: The selection and weighting of financial metrics can be subjective, making it more challenging to compare and evaluate different fundamental-weighted indexes.

Incompatibility with some securities: Certain metrics may not be appropriate or applicable for all securities, leading to potential inconsistencies in the index’s construction.

Lack of transparency: Investors may not be fully aware of the index construction methodology, which can make it difficult to assess the potential risks and benefits associated with investing in a fundamental-weighted index.

## Rebalancing and Reconstitution: The Essentials for Maintaining Index Integrity

### Rebalancing: The Art of Adjusting Index Weightings

Rebalancing is the process of periodically adjusting the weightings of securities within an index to maintain the original or desired level of weighting or risk. This is typically done on a quarterly basis and involves buying and selling securities as needed.

• Price-weighted indexes do not require rebalancing, as their weightings are naturally adjusted through price changes.
• Capitalization-weighted indexes rebalance based on market capitalization. However, events like mergers, acquisitions, liquidations, and other security-related occurrences may prompt additional adjustments.
• Equal-weighted indexes rebalance to account for changes in the market capitalization of each security. These indexes may not remain equally weighted after their initial inception.
• Fundamental-weighted indexes rebalance according to specific fundamental metrics. Some of these metrics may not be publicly available, making it more challenging for investors to track.

### Reconstitution: Updating the Index to Reflect Market Changes

Reconstitution is the process of updating an index’s securities to accurately represent the current market landscape. This involves adding and removing securities to reflect changes in market capitalization or style. The reconstitution process can significantly impact the values of individual securities within the index.

By gaining a deeper understanding of the processes of rebalancing and reconstitution, investors can more effectively manage their investments and make better-informed decisions. This knowledge is particularly important when selecting index-based investments, as it provides insight into how the index is maintained and adjusted over time to accurately represent the market.

In conclusion, understanding the fundamentals of rebalancing and reconstitution in market indexes is crucial for investors who want to stay informed and make educated decisions. By grasping the inner workings of these processes, you’ll be better equipped to assess the performance of your investments, choose appropriate index-based products, and adapt your portfolio as needed.

Disclosure: I do not have any of the securities mentioned above. This article expresses my own views, and I wrote the article by myself. I am not receiving compensation for it. I have no business relationship with any company whose security is mentioned in this article.

Source: Improved Beta? A Comparison of Index-Weighting Schemes – EDHEC-Risk Institute

#### Mehmet E. Akgul

Covers investment, financial analysis and related financial market issues for BrightHedge. He has extensive experience in portfolio management, business consulting, risk management, and accounting areas.

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