# Security Market Indexes: Definition and Uses

## Introduction and Definition

• Security Market Index is a mathematical measure that shows the performance of a stock market. The market index is a hypothetical portfolio of marketable securities. The index is created by a few similar kinds of stocks that are chosen from amongst the securities already listed on the exchange and grouped together.
• The stocks included in the index are known as constituent securities. Any change taking place in the constituent securities prices will impact the overall value of the index. If the prices of most of the constituent securities rise, then the index will rise and vice-versa. The value of an index is updated regularly.
• An index can be represented in two versions as following:
• Price Return Index or Price Index: It depicts only the prices of the constituent securities. The return is based only on capital appreciation or depreciation.
1. Total Return Index: It depicts price, as well as reinvestment of all incomes, received since inception. The return calculation includes both the capital gains and dividend component to determine returns.

Illustration 1: Shares of ABC Ltd. is constituent security of a security market index, let us see how the two versions look like (with dividend and without the dividend)
Year Price Declared Dividend Price Return (Capital) Total Return (Capital + Dividend)
2012 (Period 1) 1000.00 0.00 0.00 0.00
2013 (Period 2) 1200.00 100.00 200.00 300.00
2014 (Period 3) 1240.00 100.00 40.00 140.00
2015 (Period 4) 1400.00 100.00 160.00 260.00
2016 (Period 5) 1300.00 100.00 -100.00 0.00
2017 (Period 6) 1270.00 100.00 -30.00 70.00
2018 (Period 7) 1310.00 50.00 40.00 90.00
• By observing the Price Return as well as Total Return it is very clear that the reinvestment or dividend has a significant impact on the returns, hence we can get a much clear picture in case of Total Return as compared to Price Return.
• At Initial Level or at the time of inception, the Price Return and Total Return are equal (as shown in the above illustration), but with time due to the addition of dividend and interest on it, the Total Return surpasses the Price Return (shown in the illustration above)

## Calculation of Single Time Period Return

Name Formula Detail
Price Return $${ PR }_{ I } = \sum _{ i=1 }^{ N }{ ({ w }_{ i }\times{ PR }_{ i }) }$$ PRis the Price Return of Index portfolio
wis the weight of the  constituent security
PRi is the Price Return of the  constituent security
N is the total number of securities in the Index.
Total Return $${ TR }_{ I }=\sum _{ i=1 }^{ N }{ ({ w }_{ i }\times { TR }_{ i }) }$$ TRis the Total Return of Index portfolio
wis the weight of the  constituent security
TRis the Total Return of the  constituent security
N is the total number of securities in the Index

## Calculation of Index Values over Multiple Time Period

The calculation of index values over multiple time periods requires geometric series linkage of index returns. The calculation becomes very difficult because the formula modifies as shown below:
$$V_{ PRIT }=V_{ PRI0 }(1+PR_{ I1 })(1+PR_{ I2 })……..(1+PR_{ IT })$$ Where,
VPRI0  is the value of the Price Return index at inception
VPRIT  is the value of the Price Return index at time t
PRIT  is the Price Return on the Index over period t = 1 to T
Also,
$$V_{ TRIT }=V_{ TRI0 }(1+TR_{ I1 })(1+TR_{ I2 })……..(1+TR_{ IT })$$Where,
VTRI0  is the value of the Total Return index at inception
VTRIT  is the value of the Total Return index at time t
TRIT  is the Total Return on the Index over period t = 1 to T

## Index Construction and Management

Construction of a market index constitutes the following steps:
1. Target Market Selection
2. Security Selection
3. Security Weight Selection
4. Index Rebalancing Duration
5. Re-examining Security Selection and Weight Selection

### Target Market and Security Selection

• This is the first step while creating a Market Index. A target market may be based on any of the following criteria (the list is not exhaustive):
• Asset Class (Equities, Fixed Income, Hedge, etc)
• Geographic Region (Country wise)
• Security Exchange (BSE, NSE, NYSE, etc)
• Other Factors (Investment Style, Duration, etc)
• After the target market is selected, the next step is to select appropriate securities from the target market. This includes the process of identifying the number of securities and specific securities to be included.

### Index Weighting

There are several methods to determine the weight of constituent securities, let use see them below:

Method Name Information Formula
Price Weighting   The weight of each security is determined by dividing its price by the sum of all the prices of the constituent securities. $$w_{ i }=\frac { P_{ i } }{ \sum P_{ i } }$$Where wis the weight of ith security, Pis the price of ith security and  $$\sum P_{ i }$$ is the sum of all constituent securities.
Equal Weighting This method assigns equal weight to all constituent security. $$w_{ i }=\frac { 1 }{ N }$$Where wi is the weight of  ith security and N is the total number of constituent securities
Market Capitalization Weighting This method assigns weight by dividing market capitalization of constituent security by total market capitalization. $$w_{ i }=\frac { Q_{ i }P_{ i } }{ ∑Q_{ i }P_{ i } }$$ Where wi  is the weight of ith security,Qi is the number of shares outstanding of  ith security and Pi is the share price of the ith security.
Fundamental Weighting This method uses the measure of a company’s fundamental size to determine the weight of each constituent security. The measures include book value, cash flow, revenue, earnings, etc. $$w_{ i }=\frac { F_{ i } }{ ∑F_{ i } }$$ Where wi  is the weight of ith security, Fi is the fundamental size measure of  ith company and $$∑F_{ i }$$  is the sum of fundamental size measure of all constituent securities.

### Rebalancing of Security

• Rebalancing is the process of re-assigning a weight to all the constituent securities of an index. It is very important to carry out the process of rebalancing periodically to account for a change in price, market capitalization, or any other important factor about the constituent security of the index.

### Reconstitution of Security

• Reconstitution is the process of changing the constituent securities of an index. The securities which do not follow the criteria of the constituent securities are replaced with securities that meet the criteria. After the list of revised security is finalized the process of reconstitution is followed by rebalancing to assign proper weight to the securities.
• The reconstitution date is the date on which the constituent securities, are reviewed and it is decided whether a particular security is to be retained or changed or retained in the index.

## Use of Market Indexes

Indexes were created to get a view of the performance of the security market on a given day if the index value increase then the market performance is assumed to be good and vice-versa
There are few other uses of the Market Indexes as explained below:
1. A measure of Market Sentiment: The increase and decrease in the index give an idea about the behaviour and sentiment of market participants.
2. Risk and Return Modelling: The historical trends of market index serves as a base to fund managers to manage the funds and assets by establishing an equilibrium between risk and return.
3. Benchmark for other Portfolios: Market Indices are extensively used by Investors to estimate and calculate the returns on their active investments; however, the choice of index is a very important factor. If the performance of the fund is better than the index it is said to have outperformed the index and if the performance of the fund is low as compared to index the fund is said to have underperformed the index.
4. Passive Investment/Model Portfolio: Passive Investment refers to investing in a portfolio that contains exactly the stocks of the Index. Investors. This helps in calculating and estimating the return on the investment portfolio.

## Equity Indexes

1. Broad Market Index: Broad Equity Market Index includes stocks from companies of all sizes viz. large-cap, mid-cap, and small-cap based on the values of the companies according to their stock prices and total outstanding shares. E.g. BSE 100 and BSE 500.
2. Multi-Market/World Index: A multi-market index represents multiple index security markets around the world. E.g. Dow Jones World Stock Index.
3. Sectorial Index: This index measures the performance of different sectors of the economy. E.g. BSE Bankex and CNX IT.
4. Style Index: This index focusses on investment strategy/style (growth, income, value) rather than the underlying stock. E.g. Emerging Growth Fund, Balanced Income Fund.

## Fixed Income Indexes

Fixed Income Index includes the fixed term instrument or the Debt segment as the constituent Stocks. The creation of management of Fixed income Index is very different and difficult than the Equity Index due to the following reasons:
1. The fixed-term instruments are very large in number as compared to the equity segment instruments. The Fixed-term instruments include bonds, securities, debts, etc.
2. Unlike Equities most Fixed Term instruments have a fixed life after which they mature and hence it is important to keep track of it.
3. The population of fixed-term instruments is continuously changing because of new issues, maturities, etc.
4. Every entity has its own security and characteristics regarding its instruments thereby creating a lack of homogeneity throughout the globe.
5. Fixed-term Instruments are traded via a dealer that adds an extra layer in its trading thereby reducing its liquidity.
Fixed Income Instruments can be classified in all categories like Equity Index; however, it has a few additional categories as below:
• Based on Issuer (Government or Private)
• Currency Involved (Domestic or Foreign)
• Maturity
• Credit Quality (Rating)

## Alternative Investment Indexes

1. Commodity Indexes: These include a future contract of one or more commodities like energy, grains, metals, food and fibre, and livestock. Commodity index returns reflect the risk-free interest rate and the changes in future prices. Hence, a commodity index return can be very different from the return based on changes in the prices of the underlying commodities.
2. Real Estate Investment Trust Indexes (REIT Index): This can be understood as a sector index of the Real Estate Sector. REIT is public or private corporations organized to invest in real estate, either through ownership of properties or investment in mortgages, this index tracks the shares of various REIT.
3. Hedge Fund Indexes: Hedge funds are private investment instruments that use long and short investment strategies with a promise of significantly high returns, this index tracks various hedge funds as its constituent stocks. The biggest problem associated with the hedge funds is the fact that the reporting of fund performance is voluntary which leads to no/very less reporting of low performing funds. Due to voluntary reporting and volatility in hedge funds, managing the index is a difficult task. 