How are Market Indexes Calculated? – Definition & Examples

How are market indexes calculated?

How are price return and total return measured in market indexes?

What are index weighting methods?

How is each index weighting scheme calculated?

What are the terms of rebalancing and reconstitution?

If you’re looking for answers to these questions, this article will help you understand market indices.

Market Indexes Explained

Investors need to analyze security markets and compare return metrics continuously to assess their portfolios, portfolio managers, or find opportunities in the markets. Market indexes, such as Dow Jones Industrial Average (DJIA), Standard & Poor’s 500 (S&P 500), Nikkei 225, Hang Seng, FTSE 100, Dax, CAC 40 provides basic performance metrics of securities in financial markets.

Recent above-average returns of low-cost index funds boost the popularity of market indexes.

The table below indicates some well-known indexes showing different asset classes and weighting methods.

IndexWeighting Method
S&P 500Capitalization-weighted
DJIA (30 stocks)Price-weighted
FTSE 100Capitalization-weighted
Russell 2000Capitalization-weighted
CAC 40Capitalization-weighted
Topix (varies)Capitalization-weighted
Nikkei (225 stocks)Price-weighted
Hang Seng (50 stocks)Capitalization-weighted
Dax (30 stocks)Capitalization-weighted
Ibex 35Capitalization-weighted
Shanghai Composite (varies)Capitalization-weighted
MSCI All Country World IndexCapitalization-weighted
Bloomberg Barclays Global Aggregate Bond IndexCapitalization-weighted
iShares Long-Term Corporate Bond ETFCapitalization-weighted
Invesco S&P 500® Equal Weight ETFEqual-weighted
SPDR S&P Biotech ETFEqual-weighted
iShares Edge MSCI USA Quality Factor ETFFundamental-weighted

Price Return Index and Total Return Index

There are two versions of return calculation for the same index.

Price return index indicates the prices of securities within the index.

Total return index exhibits price return index + dividend return + interests + other distributions.

At the beginning of index creation, the values of price and total return indexes are equal. In the following periods, the total return index value is higher than the price return index with the effect of non-price variables (dividend, 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

Comparison of Price Return Index and Total Return Index

PeriodPrice Return (%)Income Return (%)
(dividend, interest, etc.)
Ending Value
(Price Return Index)
Ending Value
(Total Return Index)
010,000.0010,000.00
14,001,5010,400.0010,550.00
23,001,0010,712.0010,972.00
3-2,000,5010,497.7610,807.42

Index Weighting Schemes

Price-Weighted Indexes

Each member security is weighted in the percentage of its price per share in the index. High-priced securities have higher weights 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

SecurityBeginning PriceBeginning Weight (%)Ending PriceEnding Weight (%)Dividends Per SharePrice Ret. x Beg. Weight %Total Ret. x Beg. Weight %
ABC20.0026.6624.0030.002.505.338.66
DEF10.0013.338.0010.001.00-2.66-1.33
GHI40.0053.3342.0052.500.002.662.67
XYZ5.006.676.007.500.501.332.00
Total75.0010080.001006.6612.00
Index18.7520.00

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;

\(\frac{Ending\ Price + Dividends\ Per\ Share}{Beginning\ Price}\ Beginning\ Weight = Total\ Return\)

\(\frac{24.00+2.50}{20.00}\ 26.66\% = 8.66\%\)

Advantages

  • Simplicity
  • Long historical records of price-weighted indexes

Disadvantages

  • May not consider high market value companies
  • High-priced securities have higher weights
  • Stock splits change security prices

Capitalization-Weighted Indexes

Each member security is weighted according to the total market capitalization of the securities in the index. The market capitalization of each security is determined by multiplying the market price of a security and outstanding shares of a security. 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

SecurityBeg. PriceShares O/SBeg. Market CapBeg. Weight (%)Ending PriceDiv. Per ShareEnding Market CapPrice Ret. x Beg. Weight %Total Ret. x Beg. Weight %
ABC20.004,50090,00036.0024.002.50108,0007.2011.70
DEF10.007,00070,00028.008.001.0056,000-5.60-2.80
GHI40.001,00040,00016.0042.000.0042,0000.800.80
XYZ5.0010,00050,00020.006.000.5060,0004.006.00
Total250,000100266,0006.4015.70
Index10,00010,640

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;

\(\frac{Ending\ Price + Dividends\ Per\ Share}{Beginning\ Price}\ Beginning\ Weight = Total\ Return\)

\(\frac{24.00+2.50}{20.00}\ 36.00\% = 11.70\%\)

Advantages

  • More objective and explicit measure
  • Limited rebalancing
  • Investors can hold securities easier than other weighting schemes

Disadvantages

  • Overpriced securities dominate the index
  • Large-cap securities are represented more

Equal-Weighted Indexes

Each member security is weighted equally. 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

SecurityBeg. PriceShares O/SBeg. Market CapBeg. Weight (%)Ending PriceDiv. Per ShareEnding Market CapPrice Ret. x Beg. Weight %Total Ret. x Beg. Weight %
ABC20.00125.002,5002524.002.503,0005.008.13
DEF10.00250.002,500258.001.002,000-5.00-2.50
GHI40.0062.502,5002542.000.002,6251.251.25
XYZ5.00500.002,500256.000.503,0005.007.50
Total10,00010010,6256.2514.38
Index10,00010,625

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;

\(\frac{Ending\ Price + Dividends\ Per\ Share}{Beginning\ Price}\ Beginning\ Weight = Total\ Return\)

\(\frac{24.00+2.50}{20.00}\ 25.00\% = 8.13\%\)

Advantages

  • Large-cap securities are underweighted and more diversified

Disadvantages

  • High concentration of small-cap securities may result in fluctuating returns
  • Less liquid securities due to small-cap bias
  • Frequent rebalancing

Fundamental-Weighted Indexes

Each member security is weighted according to metrics such as cash flow, revenues, earnings, dividends, book value to stabilize the disadvantages of capitalization-weighted indexes. 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

SecurityBeg. PriceTotal SalesBeg. Weight (%)Ending PriceDiv. Per ShareEnding Weight (%)Price Ret. x Beg. Weight %Total Ret. x Beg. Weight %
ABC20.002 Bil73.3924.002.5077.1714.6823.85
DEF10.00500 Mil9.178.001.006.43-1.83-0.92
GHI40.00200 Mil14.6842.000.0013.500.730.73
XYZ5.00300 Mil2.756.000.502.890.550.83
Total54,500 Billion62,200 Billion14.1324.50
Index10,00011,412.84

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;

\(\frac{Ending\ Price + Dividends\ Per\ Share}{Beginning\ Price}\ Beginning\ Weight = Total\ Return\)

\(\frac{24.00+2.50}{20.00}\ 73.39\% = 23.85\%\)

Advantages

  • Less overpriced securities than capitalization-weighted indexes
  • More small-cap representation

Disadvantages

  • Subjective weighting scheme
  • Some metrics may not be suitable for some securities
  • Investors may not be aware of index construction methodology

Rebalancing and Reconstitution

Rebalancing

Rebalancing is the process of adjusting the weightings of the member securities in the index. The index’s original or desired level of weighting or risk is maintained by periodically (usually quarterly) buying and selling securities.

  • Price-weighted indexes need not be rebalanced because these indexes are price-adjusted.
  • Capitalization-weighted indexes rebalance according to market capitalization. However, mergers, acquisitions, liquidations, and other security-related events are reasons for rebalancing adjustments.
  • Equal-weighted indexes rebalance after market-cap changes of each security. The equal-weighted index is not equally weighted after the inception of the index.
  • Fundamental-weighted indexes rebalance according to fundamental metrics. Some metrics of fundamental-weighted indexes may not be publicly available and not easy to follow.

Reconstitution

Reconstitution is the process of buying and selling the member securities in the index to reflect the current style and market-cap. The addition and removal of securities during the reconstitution process of the index may have a significant impact on security values.

Knowing the basic understanding of security market indexes’ structure and management helps investors and users in their decision-making process.

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

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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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Important Information

The investment information, comments and recommendations contained herein are not subject to investment advice. The comments and recommendations contained herein are based on personal views. These views may not fit your financial situation and your risk and return preferences. For this reason, based only on the information contained herein, investment decisions may not have the appropriate outcome.