Tag: Business economics

It is believed that holding two securities is less risky than having only one investment in a person’s portfolio. When two stocks are taken on a portfolio and if they have negative correlation, then risk can be completely reduced because the gain on one can offset the loss on the other.

The effect of two securities can also be studied when one security is more risky when compared to the other security. The following example shows a return of 13%. A combination of A and E will produce superior results to an investor rather than if he was to purchase only Stock-A and one-third of stock consists of Stock-B, the average return of the portfolio is weighted average return of each security in the portfolio.

Reduction of portfolio Risk through diversification: The process of combining securities in a portfolio is known as diversification. The aim of diversification is to reduce total risk without sacrificing portfolio return.

Domestic stocks

Stocks represent the most aggressive portion of your portfolio and provide the opportunity for higher growth over the long term. However, this greater potential for growth carries a greater risk, particularly in the short term. Because stocks are generally more volatile than other types of assets, your investment in a stock could be worth less if and when you decide to sell it.

Bonds

Most bonds provide regular interest income and are generally considered to be less volatile than stocks. They can also act as a cushion against the unpredictable ups and downs of the stock market, as they often behave differently than stocks. Investors who are more focused on safety than growth often favor US Treasury or other high-quality bonds, while reducing their exposure to stocks. These investors may have to accept lower long-term returns, as many bonds especially high-quality issues generally don’t offer returns as high as stocks over the long term. However, note that some fixed income investments, like high-yield bonds and certain international bonds, can offer much higher yields, albeit with more risk.

Short-term investments

These include money market funds and short-term CDs (certificates of deposit). Money market funds are conservative investments that offer stability and easy access to your money, ideal for those looking to preserve principal. In exchange for that level of safety, money market funds usually provide lower returns than bond funds or individual bonds. While money market funds are considered safer and more conservative, however, they are not insured or guaranteed by the Federal Deposit Insurance Corporation (FDIC) the way many CDs are.* When you invest in CDs though, you may sacrifice the liquidity generally offered by money market funds.

* You could lose money by investing in a money market fund. Although the fund seeks to preserve the value of your investment at $1.00 per share, it cannot guarantee it will do so. The Fund may impose a fee upon the sale of your shares or may temporarily suspend your ability to sell shares if the Fund’s liquidity falls below required minimums because of market conditions or other factors. An investment in the fund is not insured or guaranteed by the Federal Deposit Insurance Corporation or any other government agency. Fidelity Investments and its affiliates, the fund’s sponsor, have no legal obligation to provide financial support to the fund, and you should not expect that the sponsor will provide financial support to the fund at any time.

International stocks

Stocks issued by non-US companies often perform differently than their US counterparts, providing exposure to opportunities not offered by US securities. If you’re searching for investments that offer both higher potential returns and higher risk, you may want to consider adding some foreign stocks to your portfolio.

Sector funds

Although these invest in stocks, sector funds, as their name suggests, focus on a particular segment of the economy. They can be valuable tools for investors seeking opportunities in different phases of the economic cycle.

Commodity-focused funds

While only the most experienced investors should invest in commodities, adding equity funds that focus on commodity-intensive industries to your portfolio such as oil and gas, mining, and natural resources can provide a good hedge against inflation.

Real estate funds

Real estate funds, including real estate investment trusts (REITs), can also play a role in diversifying your portfolio and providing some protection against the risk of inflation.

Asset allocation funds

For investors who don’t have the time or the expertise to build a diversified portfolio, asset allocation funds can serve as an effective single-fund strategy. Fidelity manages a number of different types of these funds, including funds that are managed to a specific target date, funds that are managed to maintain a specific asset allocation, funds that are managed to generate income, and funds that are managed in anticipation of specific outcomes, such as inflation.

Diversification is a technique that reduces risk by allocating investments across various financial instruments, industries, and other categories. It aims to maximize returns by investing in different areas that would each react differently to the same event.

Most investment professionals agree that, although it does not guarantee against loss, diversification is the most important component of reaching long-range financial goals while minimizing risk. Here, we look at why this is true and how to accomplish diversification in your portfolio.

Let’s say you have a portfolio that only has airline stocks. Share prices will drop following any bad news, such as an indefinite pilot strike that will ultimately cancel flights. This means your portfolio will experience a noticeable drop in value.

You can counterbalance these stocks with a few railway stocks, so only part of your portfolio will be affected. In fact, there is a very good chance that these stock prices will rise, as passengers look for alternative modes of transportation.

You could diversify even further because of the risks associated with these companies. That’s because anything that affects travel will hurt both industries. Statisticians may say that rail and air stocks have a strong correlation. This means you should diversify across the board different industries as well as different types of companies. The more uncorrelated your stocks are, the better.

Be sure to diversify among different asset classes, too. Different assets such as bonds and stocks don’t react the same way to adverse events. A combination of asset classes like stocks and bonds will reduce your portfolio’s sensitivity to market swings because they move in opposite directions. So if you diversify, unpleasant movements in one will be offset by positive results in another.

And don’t forget location, location, location. Look for opportunities beyond your own geographical borders. After all, volatility in the United States may not affect stocks and bonds in Europe, so investing in that part of the world may minimize and offset the risks of investing at home.

Purpose of portfolio diversification

 The fundamental purpose of portfolio diversification is to minimize the risk on your investments; specifically unsystematic risk.

Unsystematic risk also known as specific risk is risk that is related to a specific company or market segment. By diversifying your portfolio, this is the risk you hope to cut. This way, all your investments would not be uniformly affected in the same way by market events.

Portfolio diversification is of the core tenets of investing and is crucial for better risk management. There are many benefits of diversification. However, it must be done with caution. Here’s how you can effectively diversify your portfolio:

Spread out your investments

Investing in equities is good but that doesn’t mean you should put all your wealth in a single stock or a single sector. The same applies to your investments in other options like Fixed Deposits, Mutual Funds or gold too.

For instance, you might invest in six stocks. But if the whole market suddenly takes a tumble, you could have a problem. This problem is compounded if the stocks belonged to the same sector like manufacturing. This is because any news item or information that affects the performance of one manufacturing stock could as well affect the other stocks in some way or other.

So, even if you choose the same asset, you can diversify by investing in different sectors and industries. There are so many different industries and sectors to explore with exciting opportunities like pharmaceuticals, Information Technology (IT), consumer goods, mining, aeronautics, energy and so on.

Explore other investment avenues

You could also add other investment options and assets to your portfolio. Mutual funds, bonds, real estate and pension plans are other investments you can consider. Also, make sure that the securities vary in risk and follow different market trends. 

It has been generally observed that the bond and equity markets have contrasting movements. So, by investing in both these avenues, you can offset any negative results in one market by positive movements in the other. This way, you can ensure that you are not in a lose-lose situation.

Consider Index or Bond Funds

A sound diversification strategy, adding Index or bond funds to the mix provides your portfolio with the much-needed stability. Also, investing in Index funds is highly cost-effective as the charges are quite low compared to actively managed funds.

At the same time, investing in bond funds hedges your portfolio from market volatility and uncertainty and prevents gains from being wiped out during market volatility.

Keep Building Your Portfolio

This is another portfolio diversification strategy. You need to keep building your portfolio by investing in different asset classes, spreading across equities, debt and fixed-return instruments. Adopting this approach helps you better ride volatility.

Also, if you are investing in mutual funds, adopting the SIP route is advisable as it helps you stay invested across market cycles and gain from the concept of rupee cost averaging.

Know When to Get Out

Portfolio diversification also entails knowing the time when you must exit your investments. If the asset class you have been investing hasn’t performed up to the mark for a long period and if there have been any changes in its fundamental structure that don’t align with your goals and risk appetite, then you must exit.

Also, note that if you have invested in any market-linked instrument, then don’t exit following short-term volatility.

Keep an Eye on Commissions

This is another crucial thing to watch out for. If you are taking services of a professional, check out the fees you are paying in lieu of the services availed.

This is essential because commissions can ultimately take a toll on the end returns. A high commission can eat away into your gains.

Pros and Cons of Diversification

Now that you know the different portfolio diversification strategies let’s look at its advantages and disadvantages.

Advantages of Diversification

Makes Your Portfolio Better Shock-Proof

This is one of the major benefits of diversification. A well-diversified portfolio can better absorb the shocks during a market downturn. The risk is well-spread out when you invest in different asset classes.

Also, non-performance of one asset class is made up for by a different asset class. Simply put, with a well-diversified portfolio, you can contain the losses in a better manner.

Better Weather Market Cycles

Every economy goes through a cycle. During a cycle, markets move up, become stagnant, comes down and goes up again. With portfolio diversification, you can better weather market cycles and gain from its bullish run.

Also, following a crash when markets move up, it helps you gain from the rally. This is not the case, however, with a non-diversified portfolio that’s concentrated towards one asset class.

Enhance Risk-Adjusted Returns

This is another significant benefit of portfolio diversification. When two portfolios yield the same returns, a diversified one will take lesser risk than a concentrated one. The latter will be more volatile than the former.

Hence, for better risk-adjusted returns, it’s vital to have a diversified portfolio investing across asset classes.

Leverage Growth Opportunities Present in Other Sectors

When you invest across different assets in different sectors, you can leverage the growth opportunity present in them. For instance, of late gold has given spectacular returns and those having an exposure to the yellow metal have made quite significant gains.

Markets often see a cycle when one sector outperforms the other, and only when you have the exposure to this sector, you can take its advantage.

Provides Stability and Peace of Mind

Another significant advantage of diversification strategy is that it gives your portfolio the much-needed stability and peace of mind as you know, it can better combat a downturn. With a more predictable return, it cuts out the emotional quotient from investments, essential for achieving the desired goal.

Disadvantages of Diversification

Go Overboard

Sometimes in the name of portfolio diversification, investors tend to go overboard and end up investing in too many assets that they don’t even require.

For instance, often investors end up investing in too many equity funds holding the same stocks. This makes the portfolio bloated and dilutes returns.

Tax Complications

This is another major disadvantage of diversification. The tax structure differs across asset classes, and buying and selling them can lead to major complications. For example, taxation structure of equity mutual funds are different from debt funds. Similarly, income from bank FDs is taxed differently from that of real estate.

Hence, you need to be aware of the various tax structure while investing in different asset classes.

Risk of Investing in an Unknown Asset

Sometimes, in the name of diversification, you can end up investing in an asset that’s unknown to you. You may get caught off guard if investing in that asset isn’t legal in the country. Also, investing in an unknown asset may result in losing capital in the long run, which brings down returns of your overall portfolio.

Can Make Investments Complicated

 When you diversify too much, it can complicate investments. Before proceeding, you need to understand the structure and working of the asset class, and this can be a task too much.

On the other hand, when you invest in only a few asset classes, complications tend to be on the lower side.

Missed Windfalls

Another disadvantage of portfolio diversification is that if a single sector witnesses a spike, you can miss out on leveraging complete gains from it.

Often in the past, investors have regretted that only a small percentage of their holdings have made profits. Having said that, it’s pretty difficult to predict as to when that will happen to an asset class.

Harry M. Markowitz is credited with introducing new concepts of risk mea­surement and their application to the selection of portfolios. He started with the idea of risk aversion of average investors and their desire to maximise the expected return with the least risk.

Markowitz model is thus a theoretical framework for analysis of risk and return and their inter-relationships. He used the statistical analysis for measurement of risk and mathematical programming for selection of assets in a portfolio in an efficient manner. His framework led to the concept of efficient portfolios. An efficient portfolio is expected to yield the highest return for a given level of risk or lowest risk for a given level of return.

Markowitz generated a number of portfolios within a given amount of money or wealth and given preferences of investors for risk and return. Individuals vary widely in their risk tolerance and asset preferences. Their means, expenditures and investment requirements vary from individual to individual. Given the preferences, the portfolio selection is not a simple choice of any one security or securities, but a right combination of securities.

Markowitz emphasized that quality of a portfolio will be different from the quality of individual assets within it. Thus, the combined risk of two assets taken separately is not the same risk of two assets together. Thus, two securities of TISCO do not have the same risk as one security of TISCO and one of Reliance.

Risk and Reward are two aspects of investment considered by investors. The expected return may vary depending on the assumptions. Risk index is measured by the variance of the distribution around the mean, its range etc., which are in statistical terms called variance and covariance. The qualification of risk and the need for optimisation of return with lowest risk are the contributions of Markowitz. This led to what is called the Modern Portfolio Theory, which emphasizes the tradeoff between risk and return. If the investor wants a higher return, he has to take higher risk. But he prefers a high return but a low risk and hence the problem of a tradeoff.

A portfolio of assets involves the selection of securities. A combination of assets or securities is called a portfolio. Each individual investor puts his wealth in a combination of assets depending on his wealth, income and his preferences. The traditional theory of portfolio postulates that selection of assets should be based on lowest risk, as measured by its standard deviation from the mean of expected returns. The greater the variability of returns, the greater is the risk.

Thus, the investor chooses assets with the lowest variability of returns. Taking the return as the appreciation in the share price, if TELCO shares price varies from Rs. 338 to Rs. 580 (with variability of 72%) and Colgate from Rs. 218 to Rs. 315 (with a variability of 44%) during 1998, the investor chooses the Colgate as a less risky share.

As against this Traditional Theory that standard deviation measures the vari­ability of return and risk is indicated by the variability, and that the choice depends on the securities with lower variability, the modern Portfolio Theory emphasizes the need for maximization of returns through a combination of securities, whose total variability is lower.

The risk of each security is different from that of others and by a proper combination of securities, called diversification one can arrive at a combi­nation wherein the risk of one is offset partly or fully by that of the other. In other words, the variability of each security and covariance for their returns reflected through their inter-relationships should be taken into account.

Thus, as per the Modern Portfolio Theory, expected returns, the variance of these returns and covariance of the returns of the securities within the portfolio are to be considered for the choice of a portfolio. A portfolio is said to be efficient, if it is expected to yield the highest return possible for the lowest risk or a given level of risk.

A set of efficient portfolios can be generated by using the above process of combining various securities whose combined risk is lowest for a given level of return for the same amount of investment, that the investor is capable of. The theory of Markowitz, as stated above is based on a number of assumptions.

Assumptions of Markowitz Theory:

(1) Investors are rational and behave in a manner as to maximise their utility with a given level of income or money.

(2) Investors have free access to fair and correct information on the returns and risk.

(3) The markets are efficient and absorb the information quickly and perfectly.

(4) Investors are risk averse and try to minimise the risk and maximise return.

(5) Investors base decisions on expected returns and variance or standard deviation of these returns from the mean.

(6) Investors choose higher returns to lower returns for a given level of risk.

A portfolio of assets under the above assumptions is considered efficient if no other asset or portfolio of assets offers a higher expected return with the same or lower risk or lower risk with the same or higher expected return. Diversification of securities is one method by which the above objectives can be secured. The unsystematic and company related risk can be reduced by diversification into various securities and assets whose variability is different and offsetting or put in different words which are negatively correlated or not correlated at all.

Diversification of Markowitz Theory:

Markowitz postulated that diversification should not only aim at reducing the risk of a security by reducing its variability or standard deviation, but by reducing the covariance or interactive risk of two or more securities in a portfolio. As by combination of different securities, it is theoretically possible to have a range of risk varying from zero to infinity.

Markowitz theory of portfolio diversification attaches importance to standard deviation, to reduce it to zero, if possible, covariance to have as much as possible negative interactive effect among the securities within the portfolio and coefficient of correlation to have –1(negative) so that the overall risk of the portfolio as a whole is nil or negligible.

Parameters of Markowitz Diversification:

Based on his research, Markowitz has set out guidelines for diversification on the basis of the attitude of investors towards risk and return and on a proper quantification of risk. The investments have different types of risk characteristics, some called systematic and market related risks and the other called unsystematic or company related risks. Markowitz diversification involves a proper number of securities, not too few or not too many which have no correlation or negative correlation. The proper choice of companies, securities, or assets whose return are not correlated and whose risks are mutually offsetting to reduce the overall risk.

For building up the efficient set of portfolio, as laid down by Markowitz, we need to look into these important parameters:

(1) Expected return.

(2) Variability of returns as measured by standard deviation from the mean.

(3) Covariance or variance of one asset return to other asset returns.

In general the higher the expected return, the lower is the standard deviation or variance and lower is the correlation the better will be the security for investor choice. Whatever is the risk of the individual securities in isolation, the total risk of the portfolio of all securities may be lower, if the covariance of their returns is negative or negligible.

Limitations of Markowitz model:

• Large number of input data required for calculations: An investor must obtain estimates of return and variance of returns for all securities as also covariances of returns for each pair of securities included in the portfolio. If there are N securities in the portfolio, he would need N return estimates, N variance estimates and N (N-1) / 2 covariance estimates, resulting in a total of 2N + [N (N-1) / 2] estimates. For example, analysing a set of 200 securities would require 200 return estimates, 200 variance estimates and

19,900 covariance estimates, adding upto a total of 20,300 estimates. For a set of 500 securities, the estimates would be 1,25,750. Thus, the number of estimates required becomes large because covariances between each pair of securities have to be estimated.

• Complexity of computations required: The computations required are numerous and complex in nature. With a given set of securities infinite number of portfolios can be constructed. The expected returns and variances of returns for each possible portfolio have to be computed. The identification of efficient portfolios requires the use of quadratic programming which is a complex procedure.

Traditional Portfolio theory is one of the subjective analysis but it has provided positive results to many some people who have invested keeping in mind the individual securities. Through this traditional theory, investors have been getting the maximum return at the minimum risk.

On the other hand, modern portfolio theory emphasizes on maximizing of return through a combination of securities. It discusses the relationship between different securities and then draws inter-relationships of risks between them.  This theory states that by combining a low risk security with the one with higher risk will ultimately result in a success by investor in making choice of investment.

Traditional portfolio analysis has been of a very subjective nature but it has provided success to some persons who have made their investments by making analysis of individual securities through evaluation of return and risk conditions in each security.

In fact, the investor has been able to get the maximum return at the minimum risk or achieve his return position at that indifferent curve which states his risk condition. The normal method of calculating the return on an individual security was by finding out the amount of dividends that have been given by the company, the price earning ratios, the common holding period and by an estimation of the market value of the shares.

The modern portfolio theory believes in the maximization of return through a combination of securities. The modern portfolio theory discusses the relationship between different securities and then draws inter-relationships of risks between them.

It is not necessary to achieve success, only by trying to get all securities of minimum risk. The theory states that by combining a security of low risk with another security of high risk, success can be achieved by an investor in making a choice of investment outlets.

Traditional theory was based on the fact that risk could be measured on each individual security through the process of finding out the standard deviation and that security should be chosen where the deviation was the lowest. Greater variability and higher deviations showed more risk than those securities which had lower variation.

The modern theory is of the view that by diversification risk can be reduced. Diversification can be made by the investor either by having a large number of shares of companies in different regions, in different industries, or those producing different types of product lines.

Diversification is important but the modern theory states that there cannot be only diversification to achieve the maximum return. The securities have to be evaluated and thus diversified to some limited extent within which the maximum achievement can be sought by the investor. The theory of diversification was based on the research work by Harry Markowitz.

Markowitz is of the view that a portfolio should be analysed depending upon:

(a) The attitude of the investor towards risk and return; and

(b) The quantification of risk

Thus, traditional theory and modern theory are both framed under the constraints of risk and return, the former analysing individual securities and the latter believing in the perspective of combination of securities.

Traditional theory believes that the market is inefficient and the fundamental analyst can take advantage of the situation. By analysing internal financial statements of the company, he can make superior profits through higher returns. The technical analyst believed in the market behaviour and past trends to forecast the future of the securities. These analyses were mainly under the risk and return criteria of single security analysis.

Modern portfolio theory, as brought out by Markowitz and Sharpe, is the combination of the securities to get the most efficient portfolio. Combination of securities can be made in many ways. Markowitz developed the theory of diversification through scientific reasoning and method.

Market index refers to a portfolio of securities that represent a particular section of the stock market. The securities that are part of a particular index often come with certain characteristics.

A market index measures the value of a portfolio of holdings with specific market characteristics. Each index has its own methodology which is calculated and maintained by the index provider. Index methodologies will typically be weighted by either price or market cap. A wide variety of investors use market indexes for following the financial markets and managing their investment portfolios. Indexes are deeply entrenched in the investment management business with funds using them as benchmarks for performance comparisons and managers using them as the basis for creating investable index funds.

Uses of Market Indexes

People from many walks of life use and are affected by market indexes. Economists and statisticians use stock-market indexes to study long-term growth patterns in the economy, to analyze and forecast business-cycle patterns, and to relate stock indexes to other time- series measures of economic activity.

Investors, both individual and institutional, use the market index as a benchmark against which to evaluate the performance of their own or institutional portfolios. The answer to the question, “Did you beat the market?” has important ramifications for all types of investors.

Market technicians in many cases base their decisions to buy and sell on the patterns that appear in the time series of the market indexes. The final use of the market index is in portfolio analysis.

In discussions of the market model and systematic it will be evident that the relevant riskiness of a security is determined by the relationship between that security’s return and the return on the market.

Among economists and statisticians one of the major uses of stock-market indexes is to use them as a leading economic indicator. Judging by how long they have been employed, leading indicators of economic activity must be considered in a forecasting success.

Unlike econometric modeling, the leading economic indicator approach to forecasting does not require assumptions about what causes economic behaviour. Instead, it relies on statistically detecting patterns among economic variables that can be used to forecast turning points in economic activity.

Real World Examples

Some of the market’s leading indexes include:

• S&P 500
• Dow Jones Industrial Average
• Nasdaq Composite
• S&P 100
• Russell 1000
• S&P MidCap 400
• Russell Midcap
• Russell 2000
• S&P 600
• S. Aggregate Bond Market
• Global Aggregate Bond Market

A stock index, or stock market index, is an index that measures a stock market, or a subset of the stock market, that helps investors compare current price levels with past prices to calculate market performance. It is computed from the prices of selected stocks (typically a weighted arithmetic mean).

An index is a statistical measure that represents the value of a batch of stocks. Investors use this measure like a barometer to track the overall progress of the market (or a segment of it).

There are various methods for calculating the stock market index. In this post, we will discuss some of the major methods to calculate stock market index

1. Full Market Capitalization method

In this method, to determine the scrips weighted in the index, the number of shares outstanding is multiplied by the market price of companies shares. The share with the highest market capitalization would have a higher weighted in the index and would be most influential in the index.  In the end, Market capitalization of all companies will be added and it will be the final value of that index.

The number of shares outstanding means the total number of shares currently held by all its shareholders, including shares held by institutional investors and restricted shares owned by the company’s officers and insiders. S&P 500 index in the USA uses this method.

Full Market Capitalization = No. of shares outstanding * Market Price of one share

2. Free Float Market Capitalization method

Free Float is the percentage of shares available in the market for trading. It excludes restricted shares held by the government in the form of strategic investment, shares held by companies officers and insiders, shares locked under employee stock option plan etc. Companies in the index are provided with the free float factors based on its percentage of shares in free float. Free float ranges from 0.05 to 1.0 Value of index through this method is calculated using following steps-

• Free float market Capitalization using the formula = Total number of free float shares * Market price of each share * Free float factor
• Add Market capitalization of all the companies in the index calculated through step 1.
• Calculate the index value with the help of following formula.

Index Value = (Current Free Float Market Capitalization of index / Base Free Float Market Capitalization of index) * Base Index Value

Free float market capitalization method is used by both BSE and NSE

3. Modified Capitalization Weighted

This method seeks to reduce the effect of largest stock in the index which would otherwise dominate the value of the index. This method sets a limit on percentage weight of the largest stock in the group of stocks. NASDAQ 100 uses this method.

4. Price weighted Index

In price-weighted index calculation method,   each stock influences the index in proportion to its price per share. The value of the index is calculated by adding the prices of each stock in the index and dividing them by the total number of stocks. Stocks with a higher price are given more weight which has a greater influence on the performance of the index. Dow Johns Industrial Average uses this method.

5. Equal Weighing

In this method, percentage weight of every stock in the index is equal. so, all the stocks have equal influence on the index value. Kansas City Board of Trade (KCBT) uses this method.

The value of money does not remain constant over time. It rises or falls and is inversely related to the changes in the price level. A rise in the price level means a fall in the value of money and a fall in the price level means a rise in the value of money. Thus, changes in the value of money are reflected by the changes in the general level of prices over a period of time. Changes in the general level of prices can be measured by a statistical device known as ‘index number.’

Index number is a technique of measuring changes in a variable or group of variables with respect to time, geographical location or other characteristics. There can be various types of index numbers, but, in the present context, we are concerned with price index numbers, which measures changes in the general price level (or in the value of money) over a period of time.

Price index number indicates the average of changes in the prices of representative commodities at one time in comparison with that at some other time taken as the base period. According to L.V. Lester, “An index number of prices is a figure showing the height of average prices at one time relative to their height at some other time which is taken as the base period.”

Features of Index Numbers:

(i) Index numbers are a special type of average. Whereas mean, median and mode measure the absolute changes and are used to compare only those series which are expressed in the same units, the technique of index numbers is used to measure the relative changes in the level of a phenomenon where the measurement of absolute change is not possible and the series are expressed in different types of items.

(ii) Index numbers are meant to study the changes in the effects of such factors which cannot be measured directly. For example, the general price level is an imaginary concept and is not capable of direct measurement. But, through the technique of index numbers, it is possible to have an idea of relative changes in the general level of prices by measuring relative changes in the price level of different commodities.

(iii) The technique of index numbers measures changes in one variable or group of related variables. For example, one variable can be the price of wheat, and group of variables can be the price of sugar, the price of milk and the price of rice.

(iv) The technique of index numbers is used to compare the levels of a phenomenon on a certain date with its level on some previous date (e.g., the price level in 1980 as compared to that in 1960 taken as the base year) or the levels of a phenomenon at different places on the same date (e.g., the price level in India in 1980 in comparison with that in other countries in 1980).

Uses:

• Index numbers are used in the fields of commerce, meteorology, labour, industry, etc.
• Index numbers measure fluctuations during intervals of time, group differences of geographical position of degree, etc.
• They are used to compare the total variations in the prices of different commodities in which the unit of measurements differs with time and price, etc.
• They measure the purchasing power of money.
• They are helpful in forecasting future economic trends.
• They are used in studying the difference between the comparable categories of animals, people or items.
• Index numbers of industrial production are used to measure the changes in the level of industrial production in the country.
• Index numbers of import prices and export prices are used to measure the changes in the trade of a country.
• Index numbers are used to measure seasonal variations and cyclical variations in a time series.

A collection of index numbers for different years, locations, etc., is sometimes called an index series.

• Simple Index Number: A simple index number is a number that measures a relative change in a single variable with respect to a base.
• Composite Index Number: A composite index number is a number that measures an average relative changes in a group of relative variables with respect to a base.

Types of Index Numbers

The following types of index numbers are usually used: price index numbers and quantity index numbers.

• Price Index Numbers: Price index numbers measure the relative changes in the price of a commodity between two periods. Prices can be either retail or wholesale.
• Quantity Index Numbers: These index numbers are considered to measure changes in the physical quantity of goods produced, consumed or sold for an item or a group of items.