Analysis of Risk Return Relationship In

7/24/2019 Analysis of Risk Return Relationship In

1/59

Project Report

Analysis of Risk-Return Relationship in

Indian Stock Market

Submitted in partial fulfillment of the requirements for degree of

B.A. (Hons.) Business Economics

By

Abhishek Gupta

(Roll No. - 11078208003)

Atul Panchal

(Roll No. - 11078208012)

Deepak Tiwari

(Roll No. - 11078208016)

Mayank Jain

(Roll No. - 11078208031)

Rahul Malhotra

(Roll No. - 11078208039)

Rohan Yadav

(Roll No. - 11078208041)

Supervisor:

Mr. Abhishek Kumar

Assistant Professor(University of Delhi)


2/59

DECLARATION

This is to certify that the material embodied in the present study entitled Analysis of Risk-Return

Relationship in Indian Stock Market is based on my original learning work and has not been

submitted in part or full time for any other college or degree of the university. Any indebtedness to other

work has been duly acknowledged.

Group Members: Project Supervisor:

ABHISHEK GUPTA MR. ABHISHEK KUMAR

(Roll No. - 11078208003) Assistant ProfessorATULPANCHAL (University of Delhi)

(Roll No. - 11078208012)

DEEPAK TIWARI

(Roll No. - 11078208016)

MAYANK JAIN

(Roll No. - 11078208031)

RAHUL MALHOTRA

(Roll No. - 11078208039)

ROHAN YADAV

(Roll No. - 11078208041)


3/59

ACKNOLEDGEMENT

It is great pleasure for us to acknowledge the kind of help and guidance received to us during our

research work. We were fortunate enough to get support from a large number of people to whom we

shall always remain grateful.

We sincerely thank Mr. Abhishek Kumar, Assistant Professor (University of Delhi), Person of

amiable personality, for assigning such a challenging project work which has enriched our work

experience and for his extended guidance, encouragement, support and reviews without whom this

project would not have been a success.


4/59

CONTENTS

DC ..................................................................................................................................................... 1

.......................................................................................................................................... 1

.............................................................................................................................................. 10

D .................................................................................................................................................. 10

C A ............................................................................................................................. 13

E ........................................................................................................................................ 16

BECE E D ................................................................................................................................... 18

A E D................................................................................................................................ 18

AABE EEC .......................................................................................................................................... 19

EAE EE ........................................................................................................................................... 20

ECA AA........................................................................................................................................... 25

1 CA ( A) ..................................................................................................... 25

............................................................................................................................. 26

............................................................................................................................................... 28

......................................................................................................................................... 29

2 CA (C A) ............................................................................................... 31

............................................................................................................................................... 31

A .......................................................................................................................................... 32

......................................................................................................................................... 36

3 E ............................................................................................................................. 37

............................................................................................................................................... 37

4 ......................................................................................................................... 46

............................................................................................................................................... 46

.................................................................................................................................... 49CC ...................................................................................................................................................... 53

DAA CE & EECE ............................................................................................................................. 55


5/59

1

INTRODUCTION

Indian Stock Market

CNX Nifty

The CNX Nifty, also called the Nifty 50 or simply the Nifty, is National Stock Exchange of India's

benchmark index for Indian equity market. Nifty is owned and managed by India Index Services and

Products Ltd. (IISL), which is a wholly owned subsidiary of the NSE Strategic Investment Corporation

Limited.CNX Nifty has shaped up as a largest single financial product in India, with an ecosystem

comprising: exchange traded funds (onshore and offshore), exchange-traded futures and options (at NSE

in India and at SGX and CME abroad), other index funds and OTC derivatives (mostly offshore).

The CNX Nifty covers 22 sectors of the Indian economy and offers investment managers exposure to the

Indian market in one portfolio. Our study has used nifty as representing the market portfolio comprising

of all assets. The CNX Nifty index is a free float market capitalisation weighted index. The index was

initially calculated on full market capitalisation methodology. From June 26, 2009, the computation was

changed to free float methodology.

CNX Bank Index

The CNX Bank Index is an index comprised of the most liquid and large capitalized Indian Banking

stocks. It provides investors and market intermediaries with a benchmark that captures the capital market

performance of the Indian banks. The Index has 12 stocks from the banking sector, which trade on the

National Stock Exchange (NSE).

CNX Bank Index is computed using free float market capitalization method, wherein the level of the

index reflects the total free float market value of all the stocks in the index relative to particular base

market capitalization value. CNX Bank Index can be used for a variety of purposes such asbenchmarking fund portfolios, launching of index funds, ETFs and structured products.

Top 10 Constituents by Weightage

Company' s Name Weight (%)

HDFC Bank Ltd. 30.52

ICICI Bank Ltd. 28.42


6/59

2

State Bank of India 11.6

Axis Bank Ltd. 8.71

Kotak Mahindra Bank Ltd. 7.16

IndusInd Bank Ltd. 4.36

Bank of Baroda 2.58

Yes Bank Ltd. 2.15

Punjab National Bank 1.91

Bank of India 0.94

CNX Energy Index

CNX Energy sector Index includes companies belonging to Petroleum, Gas and Power sectors. The Index

comprises of 10 companies listed on National Stock Exchange of India (NSE).

CNX Energy Index is computed using free float market capitalization method, wherein the level of the

index reflects the total free float market value of all the stocks in the index relative to particular base

market capitalization value. CNX Energy Index can be used for a variety of purposes such as

benchmarking fund portfolios, launching of index funds, ETFs and structured products.

Portfolio Characteristics

Methodology: Free Float Market Capitalization

No. of Constituents: 12

Launch Date: September 15, 2003

Base Date: January 1, 2000Base Value: 1000

Calculation Frequency: Real-time Daily

Index Rebalancing: Semi-Annually

Index PE: 10.99



Reliance Industries Ltd. 46.32

Oil & Natural Gas Corporation Ltd. 16.25

NTPC Ltd. 10.42

Cairn India Ltd. 6.47


7/59

3

CNX Finance Index

The CNX Finance Index is designed to reflect the behavior and performance of the Indian financial

market which includes banks, financial institutions, housing finance and other financial services

companies. The CNX Finance Index comprises of 15 stocks that are listed on the National Stock

Exchange (NSE).

CNX Finance Index can be used for a variety of purposes such as benchmarking fund portfolios,

launching of index funds, ETFs and structured products.

GAIL (India) Ltd. 5.05

Power Grid Corporation of India Ltd. 4.76

Tata Power Co. Ltd. 4.46

Bharat Petroleum Corporation Ltd. 2.94

Indian Oil Corporation Ltd. 1.71

Reliance Power Ltd. 1.62




Launch Date: 1-Jul-05

Base Date: 1-Jan-01

Base Value: 1000Calculation Frequency: Real-time Daily


Index PE: 10.15



Housing Development Finance Corporation Ltd. 24.43

HDFC Bank Ltd. 22.49

ICICI Bank Ltd. 20.94


Axis Bank Ltd. 6.41

Kotak Mahindra Bank Ltd. 5.28


8/59

4

CNX FMCG Index

The CNX FMCG Index is designed to reflect the behavior and performance of FMCGs (Fast Moving

Consumer Goods) which are non-durable, mass consumption products and available off the shelf. The

CNX FMCG Index comprises of 15 stocks from FMCG sector listed on the National Stock Exchange

(NSE).





Base Date: December 1, 1995

Base Value: 1000



Index PE: 37

IDFC Ltd. 2.24

Shriram Transport Finance Co. Ltd. 1.98

Mahindra & Mahindra Financial Services Ltd. 1.44






Base Date: January 1, 2004

Base Value: 1000



Index PE: 13.02


9/59

5

CNX IT Index

The CNX IT index provides investors and market intermediaries with an appropriate benchmark that

captures the performance of the Indian IT companies. The CNX IT Index comprises of 20 companies

listed on the National Stock Exchange (NSE).

The CNX IT index is computed using free float market capitalization method with a base date of Jan 1,

1996 indexed to a base value of 1000 wherein the level of the index reflects total free float market value

of all the stocks in the index relative to a particular base market capitalization value. The base value of

the index was revised from 1000 to 100 with effect from May 28, 2004.




Launch Date: -


Base Value: 100



Index PE: 21.66



I T C Ltd. 58.85

Hindustan Unilever Ltd. 13.96

United Spirits Ltd. 6.93

Godrej Consumer Products Ltd. 3.29

Dabur India Ltd. 2.91

Colgate Palmolive (India) Ltd. 2

Tata Global Beverages Ltd. 1.81

United Breweries Ltd. 1.8

Marico Ltd. 1.8

GlaxoSmithkline Consumer Healthcare Ltd. 1.58


10/59

6



Infosys Ltd. 41.31

Tata Consultancy Services Ltd. 27.94

Wipro Ltd. 8.78

HCL Technologies Ltd. 8.22

Tech Mahindra Ltd. 5.61

Oracle Financial Services Software Ltd. 1.84

MindTree Ltd. 1.04

MphasiS Ltd. 0.92

Hexaware Technologies Ltd. 0.79

Vakrangee Software Ltd. 0.62

CNX Metal Index

The CNX Metal Index is designed to reflect the behavior and performance of the Metals sector (including

mining). The CNX Metal Index comprises of 15 stocks that are listed on the National Stock Exchange

(NSE).



Sesa Goa Ltd. 19.84Coal India Ltd. 16.52

Tata Steel Ltd. 16.08

Hindalco Industries Ltd. 12.78

NMDC Ltd. 8.46

Jindal Steel & Power Ltd. 7.99

JSW Steel Ltd. 7.7

Steel Authority of India Ltd. 3.67

Bhushan Steel Ltd. 2.83

National Aluminium Co. Ltd. 1.33


11/59

7




Launch Date: July 12, 2011


Base Value: 1000



Index PE: 12.75

CNX Pharma Index

CNX Pharma Index captures the performance of the pharmaceutical sector. The Index comprises of 10

companies listed on National Stock Exchange of India (NSE).




Launch Date: July 1, 2005


Base Value: 1000



Index PE: 45.89



Sun Pharmaceutical Industries Ltd. 28.94

Dr. Reddy's Laboratories Ltd. 19.56

Cipla Ltd. 14.23

Lupin Ltd. 13.22

Glaxosmithkline Pharmaceuticals Ltd. 6.69

Glenmark Pharmaceuticals Ltd. 4.82

Divi's Laboratories Ltd. 4

Ranbaxy Laboratories Ltd. 3.31


12/59

8

Piramal Enterprises Ltd. 2.97

Cadila Healthcare Ltd. 2.27

CNX Auto Index

The CNX Auto Index is designed to reflect the behavior and performance of the Automobiles segment of

the financial market. The CNX Auto Index comprises 15 tradable, exchange listed companies. The index

represents auto related sectors like Automobiles 4 wheelers, Automobiles 2 & 3 wheelers, Auto

Ancillaries and Tyres.



No. of Constituents: 15Launch Date: July 12, 2011


Base Value: 1000



Index PE: 22.72



Tata Motors Ltd. 30.24

Mahindra & Mahindra Ltd. 19.26

Bajaj Auto Ltd. 13.5

Hero MotoCorp Ltd. 9.71

Maruti Suzuki India Ltd. 9.1

Bosch Ltd. 4.15Exide Industries Ltd. 3.01

Motherson Sumi Systems Ltd. 2.35

Eicher Motors Ltd. 1.77

MRF Ltd. 1.75


13/59

9

CNX PSU Bank Index

The CNX PSU Bank Index captures the performance of the PSU Banks. The Index comprises of 12

companies listed on National Stock Exchange (NSE).




Launch Date: August 30, 2007


Base Value: 1000



Index PE: 5.15




Bank of Baroda 12.13


Bank of India 4.42

Canara Bank 4.14

Union Bank of India 3.61

IDBI Bank Ltd. 2.88

Oriental Bank of Commerce 2.32

Allahabad Bank 2.23

Syndicate Bank 1.8


14/59

10

Portfolio Theory

The birth of modern theory of investment can be traced to 1950s when Markowitz developed the

portfolio theory. Before he came up with his theory, investors did not have a concrete measure of risk and

return, although they were not unaware of adages like "don't put all your eggs in one basket." It goes to

the credit of Markowitz that he developed mathematically the concept of diversification. Portfolio means

a mix of assets (both real and financial) invested in and held by an investor. Diversification is the act of

holding many securities to lessen risk. Markowitz proved that if investors balanced their investment

among several securities, it was possible to reduce risk. This possibility of risk reduction emerges if

securities do not move in lock-step fashion. The risk of a portfolio is diversified if stocks added to

portfolio do not co-vary (i.e. move together) too much in concordance with other stocks in the portfolio.

This helps investors constitute portfolios that attain the highest possible expected return for a given level

of risk or minimum risk for a given level of expected return.

The Markowitz's theory is based on the assumption that investors care only about the mean and variance

of return. That is why his theory is also known as mean-variance analysis. The investors are mean-

variance optimizer, and therefore, they seek and prefer portfolio with lowest possible return variance for

a given level of mean (expected) return. Simply put, it implies that investors prefer portfolios that

produce greatest amount of wealth with lowest amount of risk. This also suggests that variance-

dispersion in possible return outcomes is an appropriate measure of risk.

Before moving on to the main topic let us first understand the concept of risk

Defining Risks

The chance that an investments actual return will be less than its expected return is known as risk.

This risk of loss is linked to the expected variability in the investments return. The more volatile an

investments return is, the greater the chance investors will experience a loss

In finance, total risk of investing can be classified in two main groups


15/59

11

1. Systematic Risk

Systematic risk is due to the influence of external factors on an organization. Such factors are

normally uncontrollable from an organization's point of view.

It is a macro in nature as it affects a large number of organizations operating under a similar stream

or same domain. It cannot be planned by the organization.

For example, the risk of higher oil prices is a systematic risk factor. Higher oil prices affect

transportation costs, which in turn, affects the price of almost everything else in the economy. Higher oil

prices result in losses for car rental firms, trucking firms, shipping firms, and airlines. They cause higher

prices for food (all of which is transported from where it is grown to where it is sold to consumers), and

raw materials for manufacturers which leads to higher prices for finished goods. Since consumers must

pay higher prices for fuel, they have less money to spend on other consumer items which produces losses

for firms supplying these products.

Beta is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the

market as a whole. In other words, beta gives a sense of a stock's market risk compared to the greater

market. Beta is also used to compare a stock's market risk to that of other stocks. Investment analysts use

the Greek letter '' to represent beta. Beta is used in the capital asset pricing model (CAPM), as we

described in the previous section.

Beta is calculated using regression analysis, and one can think of beta as the tendency of a security's

returns to respond to swings in the market. A beta of 1 indicates that the security's price will move with

the market. A beta of less than 1 indicates that the security will be less volatile than the market. A beta of

greater than 1 indicates that the security's price will be more volatile than the market. For example, if a

stock's beta is 1.2, it's theoretically 20% more volatile than the market.

Here is a basic guide to various betas:

Negative beta- A beta less than 0 - which would indicate an inverse relation to the market - is

possible but highly unlikely. Some investors used to believe that gold and gold stocks should have

negative betas because they tended to do better when the stock market declined, but this hasn't proved to

be true over the long term.

Beta of 0- Basically, cash has a beta of 0. In other words, regardless of which way the market

moves, the value of cash remains unchanged.


16/59

12

Beta between 0 and 1- Companies with volatilities lower than the market have a beta of less

than 1 (but more than 0).

Beta of 1- A beta of 1 represents the volatility of the given indexused to represent the overall

market against which other stocks and their betas are measured. Nifty is such an index. If a stock has a

beta of 1, it will move the same amount and direction as the index. So, an index fund that mirrors the

Nifty will have a beta close to 1.

Beta greater than 1- This denotes a volatility that is greater than the broad-based index.

2. Unsystematic Risk

Unsystematic risk has two other names: firm-specific risk and diversifiable risk. Unsystematic risk is the

variability of returns (risk) caused by factors associated with a particular firm. Examples include the risk

of bad or fraudulent management, the risk of a plant fire, a labor strike, or a lawsuit. These risk factorsare not likely to be present in all the firms in a portfolio at the same time. Some firms will have them and

some wont. An investor holding a well-diversified portfolio (investments in firms in different industries

and locations) will not be concerned with unsystematic risk. For example, consider the quality of

management. Some of the firms in a portfolio will have good managers and some will have poor

managers. The net effect on the return of the portfolio will be nil. In effect, investors can diversify away

the risk posed by bad managers. The same is true for the other factors causing unsystematic risk.


17/59

13

Capital Asset Pricing Model

The core idea of CAPM is that only non-diversifiable risk is relevant in the determination of expected

return on any asset. Since the diversifiable risk can be eliminated, there is no reward for bearing it. The

corollary is, no matter how much total risk an asset has, only the non-diversifiable (systematic) portion is

pertinent in determining expected return. For instance, if there are two assets A and B, A has a total risk

(variance) of 40% and a systematic risk of 0.5, B has a total risk of 20% and a systematic risk of 1.5. It is

evident that A has more total risk, while on the contrary, B has more systematic risk. In the world of

CAPM, B rather than A will have higher expected return because A has more unsystematic portion of

risk that can be diversified away. Thus, the total risk (variance) of an asset itself is not an important

determinant of the asset's expected return.

As mentioned earlier the systematic risk is measured by . The coefficient tells us how much

systematic risk a particular asset has relative to a portfolio that contains all assets in the economy.

The portfolio that contains all assets in the economy is called market portfolio. This portfolio plays a

central role in CAPM. The market portfolio is unobservable, and therefore, it has to be proxied by

some index like stock market. Technically speaking, is the covariance of a stock's return with the

return on a market index scaled by variance of that index. It is also measured as slope in the

regression of a stock's return on market.

To derive the risk-return relation depicted by CAPM, let us consider two investments, one in the

Treasury bill and the other in the market portfolio. The investment in Treasury bill has a guaranteed

return, (risk-free return), and contains no systematic risk or has a of 0. The market portfolio

(proxied by index) has a of 1. By definition, is the ratio of covariance to variance. The covariance

of a variable [market portfolio] with itself is the variable's variance

Therefore, of the market portfolio has to be 1. Those who make investment in market portfolio take

average systematic risk, and therefore, require higher return than the Treasury bill. The difference

between the return on market and interest rate is termed as market risk premium. The Treasury bill has a

of 0 and its risk premium is zero. The market portfolio has a of 1 and risk premium RM RF. This

gives two benchmarks for calculating expected returns on any asset in the economy. CAPM predicts that

risk premium varies in direct proportion to . The return between expected return and posited by

CAPM can be stated in the following equation.


18/59

14

Above Equation can be interpreted as

The first expression is the reward for waiting, i.e. delaying consumption without taking risk. It amounts

to investing in Treasury bill, the least risky investment that provides guaranteed return and has a of

zero. The second expression is the reward per unit of risk borne. This component is return required due to

risk.

RM RF is the reward market offers for bearing average systematic risk in addition to waiting. The

amount of systematic risk present in a security is presented by i. Thus, the return on any asset is risk-free

rate plus the multiplied by the market risk premium.

CAPM assumes existence of risk-free asset. Black (1972) derived a more general version of CAPM

in which it is not necessary to assume existence of risk-free asset.

This does not alter the risk-return equation depicted earlier. The only difference is that risk-free return is

replaced with another value Rz expected return of a portfolio with a of zero. This portfolio has no

correlation with the market portfolio. This model is also known as zero-model. CAPM has a variety of

applications. The tools of CAPM are helpful not only for allocation of capital for real investment

(machineries and factories) but also for allocation of funds for financial investment (bonds, stocks, etc).

CAPM can be used for decisions concerning capital expenditure, corporate restructuring, financing,

Ri=RF+ (RM RF)i

Where Ri= Expected Return on security i

RF= Risk-free interest rate

i= Systematic risk for security i

RM= Expected Return on market portfolio

RM RF= Market risk premium

Expected return =Price of time + Price of Risk XAmount of Risk


19/59

15

investment, and evaluation of portfolio performance.

The capital expenditure decisions require estimation of cost of capital (required rate of return) for

discounting of future cash flows. CAPM helps in determination of cost of capital. To calculate the

cost of capital, the model requires three inputs: the stock's , the market risk premium, and risk-free

return.

Basic Assumptions of CAPM

All investors:

1. Aim to maximize economic utilities.

2. Are rational and risk-averse.

3. Are broadly diversified across a range of investments.

4. Are price takers, i.e., they cannot influence prices.

5. Can lend and borrow unlimited amounts under the risk free rate of interest.

6. Trade without transaction or taxation costs.

7. Deal with securities that are all highly divisible into small parcels.

8. Assume all information is available at the same time to all investors.


20/59

16

Equity Risk Premium

Equity risk premium is the price or premium which an investor gets for taking risk. It is a key component

into the expected return that we demand for a risky investment. This expected return, is a determinant

of both the cost of equity and the cost of capital. The size of the premium varies with the risk

inclusive in stocks.

The risk in return is usually measured by variance in actual returns around an expected return. So we can

say an investment is risk free when return is equal to expected.

What are the determinants of equity risk premiums? (Source- A. Damodaran)

Risk Aversion

The first and most critical factor, obviously, is the risk aversion of investors in the markets. As investors

become more risk averse, equity risk premiums will climb, and as risk aversion declines, equity risk

premiums will fall. While risk aversion will vary across investors, it is the collective risk aversion of

investors that determines equity risk premium, and changes in that collective risk aversion will

manifest themselves as changes in the equity risk premium. While there are numerous variables that

influence risk aversion, we will focus on the variables most likely to change over time.

a. Investor Age: There is substantial evidence that individuals become more risk averse as they get

older. The logical follow up to this is that markets with older investors, in the aggregate, should have

higher risk premiums than markets with younger investors, for any given level of risk. Bakshi and Chen

(1994), for instance, examine risk premiums in the United States and noted an increase in risk premiums

as investors aged.

b. Preference for current consumption: We would expect the equity risk premium to increase as

investor preferences for current over future consumption increase. Put another way, equity risk premiums

should be lower, other things remaining equal, in markets where individuals are net savers than in

markets where individuals are net consumers. Consequently, equity risk premiums should increase assavings rates decrease in an economy. Relating risk aversion to expected equity risk premiums is not as

easy as it looks. While the direction of the relationship is fairly simple to establish higher risk aversion

should translate into higher equity risk premiums- getting beyond that requires us to be more

precise in our judgments about investor utility functions, specifying how investor utility relates to wealth

(and variance in that wealth).


21/59

17

Economic Risk

The risk in equities as a class comes from more general concerns about the health and predictability of

the overall economy. Put in more intuitive terms, the equity risk premium should be lower in an economy

with predictable inflation, interest rates and economic growth than in one where these variables are

volatile.

Information

When you invest in equities, the risk in the underlying economy is manifested in volatility in the earnings

and cash flows reported by individual firms in that economy. Information about these changes is

transmitted to markets in multiple ways, and it is clear that there have been significant changes in both

the quantity and quality of information available to investors over the last two decades. During the

market boom in the late 1990s, there were some who argued that the lower equity risk premiums that

we observed in that period were reflective of the fact that investors had access to more information about

their investments, leading to higher confidence and lower risk premiums in 2000. After the accounting

scandals that followed the market collapse, there were others who attributed the increase in the equity

risk premium to deterioration in the quality of information as well as information overload. In effect,

they were arguing that easy access to large amounts of information of varying reliability was making

investors less certain about the future.

Catastrophic Risk

When investing in equities, there is always the potential for catastrophic risk, i.e. events that occur

infrequently but can cause dramatic drops in wealth. Examples in equity markets would include the great

depression from 1929-30 in the United States and the collapse of Japanese equities in the last 1980s. In

cases like these, many investors exposed to the market declines saw the values of their investments

drop so much that it was unlikely that they would be made whole again in their lifetimes. While

the possibility of catastrophic events occurring may below, they cannot be ruled out and the equity risk

premium has to reflect that risk


22/59

18

OBJECTIVE OF THE STUDY

To develop an understanding of the Capital Asset Pricing Model.

To test whether CAPM is valid in Indian Market.

To develop an understanding of Equity Risk Premium.

To test whether the theories for ERP hold same for Indian Market as for U.S.A. Market.

To find out risk & return for 9dominant industries & 2 market Indices of Indian Market.

To calculate ERP for 9 dominant industries of Indian Stock Market individually.

To test the effect of various variables on ERP.

To develop an understanding of the behavior of Risk with duration of Investment.

To find out the best holding (lock in) period for different industries &for Indian Stock Market.

To find out the industry that has given highest return.

To find out the industry that maximizes return in shortest time (holding period).

LIMITATIONS OF THE STUDY

Dividends distributed is totally ignored, therefore the return calculated by us is not perfect.

For CAPM analysis we did a short period analysis i.e. from 2004 to 2009.

For ERP also, data used for India is not for that much longer period as we used for U.S.A.

We took just 7 indices for cross sectional analysis of CAPM

Failure to amount adequately for riskless rate of interest, possible non-linearity in the risk return

relation, and distortion due to heteroscedasticity & other CNLRM assumptions as we did not

provided proof for them.

We jumped to results in case of optimum holding period just by considering simple average

return, which does not provide any kind of surety for receiving the same return and holding period

in future.


23/59

19

VARIABLE SELECTION

This empirical analysis has used particular software like Excel and SPSS and depends on both

availability of data and established statistical criteria that are frequently used in the selection of variables.

The National Stock Exchange Index (Nifty) has been considered as a proxy of the Indian Stock Market

and used to obtain a measure of market price movement of Indian securities since this index is

comprehensive.

To address the objective of this research government Treasury bill and 9 sectors namely auto, bank,

energy, finance, FMCG, IT, metal, Pharma & PSU Banks have been considered. CNX Auto Index has

been used as a proxy to Automobile Sector, CNX bank Index as a proxy to banking sector, CNX Energy

Index as a proxy to Energy Sector, CNX Finance Index as a proxy to financial Sector, CNX FMCG Index

as a proxy to FMCG Sector, CNX IT Index as a proxy to IT Sector, CNX Metal Index as a proxy to metal

sector, CNX PSU Banks Index as a proxy to public sector banks and CNX Pharma Index as a proxy to

Pharma Sector.

The empirical investigation is carried out using monthly data from January, 2004 to October, 2013 which

covers 118 monthly observations of all the sectors mentioned above and of 2 dominant Market Indices

i.e. SENSEX & Nifty. We also used monthly Consumer Price Index for India data from January, 2004 to

October, 2013 to calculate required inflation rate for different periods.

We also used yearly saving rate, ERP, Real interest rate & Inflation data of United States of America

(U.S.A.) from 1961 to 2012 from World Bank site.

Yearly saving rate, Sensex return, Treasury bill rate (365 days), Real interest rate, Gross Domestic

Product & Inflation data of India from 2004 to 2013 from World Bank & Reserve Bank of India site.


24/59

20

LITERATURE REVIEW

Capital Asset Pricing Model

A study by Sharpe and Cooper (1972) generally provided support for a positive relationship between

return and risk, although it was not completely linear. They formed equally weighted portfolio of all

stocks on NYSE dividing them into deciles on the basis of their beta calculated at a point if time using 60

months previous data. Sharpe and Cooper examined the average rate of returns for each of these

portfolios.

Results: they found that generally returns increased with high risk class except for the very high risk

classes where there was a tendency to level off and decline slightly. They also showed that the betas

for the portfolios were stable. Therefore it was possible to derive the average betas and the returnduring a subsequent period was generally consistent with the risk.

Jacob (1971) studied the validity of CAPM using 593 stocks of NYSE for which historical data were

used for the entire period of 1946-65. For the purpose of study Jacob divided this period into two sub-

periods of 1946-55 and 1956-65. Regression analysis was performed using both monthly as well as

yearly return on the securities.

Result: the result shows a significant positive relationship between realized return and risk during

each of the sub-periods. Although the relationship established by the study is all positive they are

weaker than predicted by CAPM.

Lintner (1969) used 301 stocks yearly return as his sample for testing CAPM. He regressed the

yearly return of each stock against the average return of all the stocks included in the sample (using it

as a market proxy), to estimate betas for each security. The first pass regression was of the form:

Rit=it+itRMtit+ eit

Whereit was the estimate of true of security i.

Lintner then performed the second pass cross-sectional regression of the following form:


25/59

21

Ri = a1+a2it +a3S2

eit+ n

Where S2

eitis the residual variance (the variance of e) from the first pass regression.

His results seem to violate the CAPM. The term representing the residual risk was statistically significant

and positive. The intercept term was larger than expected whilea2 although significant had value slightly

lower than reasonably expected.

Dougles (1969) employed similar methodology as used in Lintner (1969) and found similar results.

Dougles specifically examined the relationship between return and several measures of risk for individual

stocks. In the study he examined both total risk measure as well as systematic component of total risk

relative to return. The results were not consistent with CAPM, intercept was little larger than expected.

More importantly the coefficient of total risk variable was generally significant. Further the coefficient of

systematic risk variable was typically not significant.

Friend and Blume (1971) applied the test of CAPM on 10 portfolios out of NYSE common stocks

formed on the basis of estimated betas of each security. They tested them for three different periods in the

range of 1929-69 (1929-69, 1948-69 and 1956-69). Their results showed strong positive association

between return and beta for the period 1929-69. For the period 1948-69, while higher beta portfolio had

higher return than portfolios with low betas, there was little difference in return among portfolios with

>1. Moreover, the results showed no clear relationship between return and beta for the period 1956-69.

On this basis, they concluded that NYSE stocks with above average risk have higher returns than those

with below average risk but the premium for bearing additional risk on the portfolio composed of stocks

with above average betas was little.

Black, Jensen and Scholes (1972)were the first to conduct an in depth time series test of CAPM. They

took astheir basic time series model. Fitting the above equation on the time series data of the 10

portfolio, formed on the basis of the securities betas, to estimate the beta, intercept and correlation

coefficients for each portfolio, Black, Jensen and Scholes found that it explains the excess return quite

well, thereby lending support to the structure of the linear equation as a good explanation of security

returns. However, there was quite a variation in the intercept from zero. The intercept tend to be negative

when >1 and it tend to be positive when


26/59

22

Jensen and Scholes study provides substantial support for the hypothesis that the realized returns are a

linear function of the systematic return defined by the beta of the security or portfolio. Also, their study

shows that the relationship is significantly positive over long periods of time.

Indian Studies

Gupta and Sehgal (1993) tested CAPM over the period April 1979-March 1989. They employed 30

stocks forming BSE sensitive index and used portfolio method constructing three equally-weighted and

three value-weighted portfolios. They also explicitly addressed questions of non-linearity and the role of

residual risk in explaining returns. They concluded that CAPM did not seem to be a suitable descriptor of

asset pricing in the Indian capital market during the \study period. The risk-return relation over the period

is positive but weak. Madhusoodanan (1997) carried out his testing on a sample of 120 securities traded

on the BSE pertaining to the period January 1987 to March 1995. He used the portfolio technique testing

over several holding periods. In order to check the sensitivity of the result to the choice of index, he

employed both BSE index and NSE index. He did not find any positive relationship between and

return. The maximum risky portfolio gave the minimum return while the minimum risky portfolio

yielded comparably higher return. He suggested that high risk and high return strategy will not be

rewarding in the Indian context and it is better to opt for low stocks. He conjectures that as more

investors tilt their portfolio in favor of low stocks, a much tighter relationship between and return will

emerge. Madhusoodnan's study is not only disturbing for CAPM but also for the efficiency of the Indian

Capital Market. Sehgal (1997) reports that CAPM is not a suitable descriptor of asset pricing on the

Indian capital market for the period April 1994 to March, 1993. He finds the slope negative butinsignificant for the total period, implying absence of any significant relationship between and average

return.

Study by Yalwar, Y B (1988) attempts to test the following hypotheses of the CAPM:

1. Market portfolio explains significantly the variations in the returns on securities and portfolio.

2. Positive relationship between return and risk of securities or portfolio exists.

3. In a cross-sectional regression of expected return against beta, the intercept term is equal to the risk

free rate and the slope coefficient is equal to the market risk premium per unit of systematic risk i.e. RM-

RF.

Rit - RFt = 1+b1(RM RF) + eit


27/59

23

If CAPM is valid, a1 is expected to be zero andb1should be statistically significant. The author used a

sample of 122 stocks for which monthly return data for 5 continuous years were available. The study

revealed that, the beta estimate is positive and statistically significant at a significance level of 0.05, a1 -

was not statistically different from zero for 73 out of the 122 stocks included in the sample. These results

suggested that the market-index was an important explanatory variable to explain the variations in the

returns on securities traded on Bombay Stock Exchange and that CAPM is a good descriptor of activesecurity returns. To test the hypothesis concerning the return-risk relationships, cross-sectional regression

of the following form was carried out after eliminating the extreme observations observed.

Ri = 0+ 1b1i+ e

Where, 0 and1 are regression parameters.

Positive slope coefficient supported the hypothesis that there exists a positive relationship between return

and risk in Bombay Stock Exchange. Also t-statistics revealed that the estimates of 0 and 1were

statistically were not different from their expected value i.e. average bank return and average excess

return on the market index over average bank rate. Thus, the result indicated that the CAPM was a good

descriptor of security returns in the Indian equities market.


28/59

24

Equity Risk Premium

The main work done in the field of ERP is A. Damodarans work in ERP. His model is also the guideline

for us and helped us lot in making this project. The other works done in this field are as follows:

Bakshi and Chen (1994), for instance, examine risk premiums in the United States and noted an increase

in risk premiums as investors aged.

Lettau, Ludwig son and Wachter (2007)link the changing equity risk premiums in the United States to

shifting volatility in the real economy. In particular, they attribute that that the lower equity risk

premiums of the 1990s (and higher equity values) to reduced volatility in real economic variables

including employment, consumption and GDP growth. One of the graphs that they use to illustrate the

correlation looks at the relationship between the volatility in GDP growth and the dividend/ price

ratio (which is the loose estimate that they use for equity risk premiums).

Brandt and Wang (2003) argue that news about inflation dominates news about real economic

growth and consumption in determining risk aversion and risk premiums. They present evidence

that equity risk premiums tend to increase if inflation is higher than anticipated and decrease when

it is lower than expected. Reconciling the findings, it seems reasonable to conclude that it is not so much

the level of inflation that determines equity risk premiums but uncertainty about that level.

While much of the empirical work on liquidity has been done on cross sectional variation across stocks

(and the implications for expected returns), there have been attempts to extend the research to

look at overall market risk premiums. Gibson and Mougeot (2002) look at U.S. stock returns from

1973 to 1997 and conclude that liquidity accounts for a significant component of the overall equity

risk premium, and that its effect varies over time. Baekart, Harvey and Lundblad (2006) present

evidence that the differences in equity returns (and risk premiums) across emerging markets can be

partially explained by differences in liquidity across the markets.

The Equity Risk Premium Puzzle

While many researchers have focused on individual determinants of equity risk premiums, there isa related question that has drawn almost as much attention. Are the equity risk premiums that we have

observed in practice compatible with the theory? Mehra and Prescott (1985) fired the opening

shot in this debate by arguing that the observed historical risk premiums (which they estimated at

about 6% at the time of their analysis) were too high, and that investors would need implausibly

high risk-aversion coefficients to demand these premiums.


29/59

25

EMPIRICAL ANALYSIS

This Portion is divided into four parts:-

1.

In first, time series data is used to verify CAPM, calculate mean excess return of sectors & nifty & tocalculate betas for different sectors for further analysis.

2. In second, the output from the first part is used to verify CAPM from cross sectional data.

3. In third, relationship between various Variables & ERP is obtained for United States of America (U.S.A.)

& India.

4.

In forth, Optimum holding (lock in) period for Indian Stock Market & different sectors is obtained.

Part 1 CAPM Validity (Time Series Analysis)

Time Series Analysis

A time series is a sequence of data points, measured typically at successive points in time spaced at

uniform time intervals. Examples of time series are the daily closing value of the Dow Jones Industrial

Average and the annual flow volume of the Nile River at Aswan. Time series are very frequently plotted

via line charts. Time series are used in statistics, signal processing, pattern recognition, econometrics,

mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control

engineering, astronomy, and communications engineering.

Time series analysis comprises methods for analyzing time series data in order to extract meaningful

statistics and other characteristics of the data.

Descriptive Statistics

Descriptive statistics provides simple summaries about the sample and about the observations that have

been made. Such summaries may be either quantitative, i.e. summary statistics, or visual, i.e. simple-to-

understand graphs. These summaries may either form the basis of the initial description of the data as

part of a more extensive statistical analysis, or they may be sufficient in and of themselves for a particular

investigation.


30/59

26

Descriptive Statistics

Return N Mean Std. Deviation Variance Covariance

Excess_auto 64 0.296694 9.311588225 86.705675 48.83594541

Excess_bank 64 1.073299 12.6614555 160.31246 79.91402061

Excess_Energy 64 0.617695 9.624748707 92.635788 59.57133867

Excess_finance 64 1.170846 12.31653647 151.69707 80.20788658

Excess_FMCG 64 0.403208 7.504852227 56.322807 24.64266302

Excess_IT 64 -1.54762 14.26039793 203.35895 59.74401173

Excess_Metal 64 1.455102 14.88836932 221.66354 92.6659727

Excess_Pharma 64 -0.14573 8.139090261 66.24479 30.01475517

Excess_PSU 64 0.981596 13.15009769 172.92507 76.02589683

Excess_Nifty 64 0.571192 8.904230241 79.285316 79.28531618

CAPM Model:

RP= RF+ (RM RF)

RP- RF= (RM RF)

Excess RP= (Excess RM)

Statement Of Hypothesis

Null Hypothesis

All sectors (FMCG, Pharma, Auto, Energy, IT, PSU banks, banking, financial and metal) have no

independent returns and their excess returns are totally dependent on market excess returns. Here

measures the independent return and which is a measure of systematic risk shows the movement of

industry returns with market returns

This means


31/59

27

Ho: FMCG= 0 & Ho: FMCG= 0

Ho: PHARMA = 0 & Ho: PHARMA= 0

Ho: AUTO = 0 & Ho: AUTO= 0

Ho: ENERGY = 0 & Ho: ENERGY= 0

Ho: IT = 0 & Ho: IT= 0

Ho: PSU_BANKS = 0 &Ho: PSU_BANKS= 0

Ho: BANK = 0 & Ho: BANK= 0

Ho: FINANCE = 0 & Ho: FINANCE= 0

Ho: METAL = 0 & Ho: METAL= 0

Alternate Hypothesis

HA: FMCG 0 & HA: FMCG0

HA: PHARMA 0 & HA: PHARMA0

HA: AUTO 0 & HA: AUTO0

HA: ENERGY 0 & HA: ENERGY0

HA: IT 0 & HA: IT0

HA: PSU_BANKS 0 & HA: PSU_BANKS0

HA: BANK 0 & HA: BANK0

Ho: FINANCE 0 & HA: FINANCE0

HA: METAL 0 & HA: METAL0


32/59

28

Methodology

As per the CAPM, risk free securitys return has no sensitivity to market rate of return. It means of risk

free security is 0.

So, before moving ahead with our analysis we have checked the correlation of TB return (proxy of risk

free return) with Nifty return (proxy of market portfolio) and the result is 0.11. We know from our

statistical understanding that correlation below 0.3 is considered very weak, which allow us to use TB

return as risk free return.

Now we have calculated the excess return of our 9 industry indices and our market portfolio Nifty. For

calculating the excess return we have subtracted Treasury bill monthly return from our respective index

monthly return.

In this part, monthly data of excess return of an index lets say CNX Auto index is regressed with the

monthly data of excess return on Nifty and then this process is repeated by regressing other indices with

monthly data of excess return on Nifty.

For CAPM to hold, should not be statistically significant and (which measures the sensitivity of

portfolio with market portfolio) should be statistically significant.

Conditions to satisfy CAPM

1.

First and foremost the value of should not be statistically different from 0.

2.

The value of should be positive and should be statistically different from 0.

We obtain the following results after regressing the excess industry return with excess market return

Return Beta P-Value () Alpha P-Value () R2

Excess_FMCG 0.311 0.00 0.226 0.80 0.136

Excess_Pharma 0.379 0.00 -0.362 0.70 0.172

Excess_Auto 0.616 0.00 -0.055 0.95 0.347

Excess_Energy 0.751 0.00 0.189 0.83 0.483

Excess_IT 0.754 0.00 -1.978 0.22 0.221

Excess_PSU 0.959 0.00 0.434 0.73 0.422

Excess_bank 1.008 0.00 0.498 0.66 0.502

Excess_finance 1.012 0.00 0.593 0.58 0.535

Excess_Metal 1.169 0.00 0.788 0.56 0.489


33/59

29

As we can observe from the above table that the p-value of s (slope coefficient) are close to 0 and p-

value of s are very high. These findings are consistent with our model.

Also we have calculated R2(Coefficient of Determination)after running the regression.

In statistics, the Coefficient of Determination denoted R2and pronounced R squared, indicates how well

data points fit a line or curve. It is a statistic used in the context of statistical models whose main purpose

is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related

information. It provides a measure of how well observed outcomes are replicated by the model, as the

proportion of total variation of outcomes explained by the model.

In short, R2measures how much variation in excess return of our industries (dependent variable) is

explained by excess return on market portfolio(dependent variable).

Summarizing the above results

Return Beta Alpha

Excess_FMCG Significant Insignificant

Excess_Pharma Significant Insignificant

Excess_Auto Significant Insignificant

Excess_Energy Significant Insignificant

Excess_IT Significant Insignificant

Excess_PSU Significant InsignificantExcess_bank Significant Insignificant

Excess_finance Significant Insignificant

Excess_Metal Significant Insignificant

Results Obtained

1. The in all regression has p-value greater than 0.20 and this implies that the value of is notstatistically different from zero, and

2. All the values of are positive and has p-value equals to 0. This implies that for every sector the value

of is significant

(A 5% )


34/59

30

Inference

Thus, in above analysis both the conditions of CAPM are satisfied and we can say that the CAPM can be

used in Indian stock market to evaluate the return on security/portfolios.

In this model Excess return of market (Reward for bearing risk of 1) and the portfolios or risk are the

most significant determinants of the return on any portfolio.


35/59

31

Part 2 CAPM Validity (Cross Sectional Analysis)

Cross Sectional Data

Cross-sectional studies (also known as cross-sectional analyses, transversal studies, prevalence study)

form a class of research methods that involve observation of all of a population, or a representative

subset, at one specific point in time. They differ from case-control studies in that they aim to provide data

on the entire population under study, whereas case-control studies typically include only individuals with

a specific characteristic, with a sample, often a tiny minority, of the rest of the population.

In this we make use of the results of the above analysis and data for different sectors.

Similar CAPM equation is tested in this part, as used in above part, which is,

CAPM Model:

RP= RF+ (RM RF)

RP- RF= (RM RF)

Excess RP= (Excess RM)

But with little changes,

Mean(Excess RP) = (Mean(Excess RM))

Methodology

In Part 1, we calculated the Excess Monthly Return of all 9 industries and market representative index

Nifty.

For cross sectional analysis, we have calculated average of excess return of all 9 industries and Nifty

index.

For this analysis mean of expected return , total variance in returns of different sectors and (obtained in

Part 1) of different sectors is used as data , but the data for CNX FMCG and CNX IT sectors are not used

because of their extreme characteristics.

By following the above process we obtained 7 observations showing average of excess return of different

industries along with of different industries.


36/59

32

Then mean returns of 7 sectors is regressed with their respective s , to get a equation like,

Mean(Excess Rp)i= 1 + 2i

Here,

1 represents independent return of industry portfolio

2 represents the excess market return

Now for CAPM to hold (in Cross Sectional Data), 1should be 0 and 2which shows the excess return on

market portfolio should be statistically different from 0.

So stating the above conditions again, CAPM will hold if

1. 1 should not be statistically different from 0, so that all the returns should be explained by

only. Or in other words 1should be insignificant.

2. 2should be statistically significant and should be equal to mean of excess RM.

Now after regressing average of excess monthly return of 7 industries (Pharma, auto, energy, PSU banks,

banks, finance and metal) with their respective s, we got the following results.

1 P-Value(1) 2 P-Value(2) R2 Adjusted R

2

-0.925 0.00 2.023 0 0.996 0.996

The p-value of 1and 2is very low and close to 0.

Now from the above regression we obtain the following results

1.

1is statistically significant and different from 0.

2. 2is also statistically significant. Also it is different from mean of excess RM (0.57).

Thus CAPM model does not hold in cross sectional analysis with any significant effect. But in this

analysis also our model is significant with R2

of 0.996, and the isignificantly explain the return in any

portfolio although not exactly in the manner explained by the CAPM.

Assumption test

According to CAPM model (Systematic Risk) is the main determinant of excess return on any portfolio.

Although total risk in investing any security, is the sum total of systematic and unsystematic risk. But


37/59

33

CAPM says that unsystematic risk can be reduced by diversifying our portfolio. So it is the systematic

risk which explains excess return on any security.

To test the above assumption we have regressed average of excess monthly return of 7 industries

(Pharma, auto, energy, PSU banks, banks, finance and metal) by taking different independent variables:

The results of the above regressions are summarized in the table below:

RegressionDependent

Variable

Independent

Variable(s)1

P-Value

(1)2 ,3

P-Value

(2,3)Adjusted R

2

1Mean Of Excess

ReturnOf Time Series -0.093 0.00 2.023 0.00 0.996

2Mean Of Excess

Return

Of Time Series,

Total Risk(2)

-0.094 0.002.101,0.

000

0.00,0.

6610.995

3Mean Of Excess

ReturnTotal Risk(

2) -0.49 0.089 0.009 0.002 0.848

4Mean Of Excess

Return

Residual

Variance/

Unsystematic Risk

-0.51 0.361 0.017 0.046 0.50

5Mean Of Excess

Return

Of Time Series,

Residual Variance-0.913 0.00

2.078,-

0.001

0.00,

-0.4840.995

Note:-1 Constant Term (Measures Independent Return of a portfolio)

2 Coefficient of Independent Variable 1

3 Coefficient of Independent Variable 2


38/59

34

Regression 1:

Mean Of excess return of each industry was regressed with s of these industries (obtained in part 1).It

should be kept in mind that measures the systematic risk of investing in a particular security/portfolio.

1and 2 were statistically significant. Although the above findings are inconsistent with the model. But

taking into account adjusted R2, explains 99.6% of variation in our dependent variable.

Regression 2:

Mean Of excess return of each industry was regressed with s of these industries (obtained in part 1) and

variance of excess monthly return of the industries. It should be noteworthy that 2

(variance) is the

measure of total risk.

1and 2 were statistically significant but 3 was statistically insignificant.

By increasing on more independent variable (Total Risk) adjusted R2has fallen.


39/59

35

Regression 3:

Mean Of excess return of each industry was regressed with variance of excess monthly return of the

industries. This is done to check whether the total risk, independently, explains the total return better than

or not.

1was statistically insignificant but 2 was statistically significant.

Thus, looking at adjusted R2we can say that total risk only explains 84.8% variation in our dependent

variable. By comparing this with 99.6 % (adjusted R2for regression 1), we can say that is more relevant

than 2(variance).


40/59

36

Regression 4:

Mean Of excess return of each industry was regressed with residual variance of excess monthly return of

the industries. It should be kept in mind that residual variance is a measure of unsystematic risk i.e risk

which can be reduced with diversification.

1was statistically significant but 2 was statistically insignificant.

Thus, looking at adjusted R2we can say that residual variance only explains 50% variation in our

dependent variable.

Regression 5:

Mean Of excess return of each industry was regressed with s of these industries (obtained in part 1) and

residual variance of excess monthly return of the industries.

1and 2 were statistically significant, and 3 was insignificant.

Adjusted R2 was 99.5% .and thus only because of introducing in this regression, our model was

significant. And residual variance has insignificant presence in our model.

Results Obtained

1.

Thus, CAPM does not seem to work when we use cross-sectional data. One of the possible

reasons for this vague outcome could be the small sample size of 7 that we have used.

2.

Looking at our regression results we can conclude that is the best measure of risk which

explains the risk-return relationship. In nutshell, we can say that cross sectional analysis does not verify

Capital Asset Pricing model equation but it explains CAPM general theory very well i.e. explains the

excess return but with a different framework/equation.


41/59

37

Part 3 Equity Risk Premium

Methodology

To see the relationship between ERP and various factors we have taken data of US of last 50 years. For

saving rate and ERP we have simply collected data of US for 50 years from World Bank site and showed

correlation between them. For ERP and volatility in real interest rate of US, we made group of 6 years of

total time period. Then we have checked volatility in real interest rate for that period by taking standard

deviation, and we have taken average of ERP by taking geometric mean. The rationale behind taking

geometric mean instead of arithmetic mean is that ERP of different years are correlated and we are need

compounded return while arithmetic mean gives simple return. Also arithmetic mean may tend to

overstate the mean.

To see relationship between volatility in inflation and ERP of US similar procedure is done as done with

real interest rate.

In case of India we have no data available of ERP so we have to calculate ERP by-.

ERP= return in economy- risk free return

For calculating return in economy we have checked percentage change in price of stock market (for this

we have took Sensex price). After this we have subtracted risk free return i.e. return on Treasury bill from

this return to get ERP.

After calculating ERP we have simply shown the relationship between saving and ERP.

To see relation between volatility in inflation and ERP in India we have divide the period in group of 3

years. Then we have calculated the standard deviation of each of the group as a measure of volatility, and

then showed the correlation with ERP.

A similar kind of method is done for relation between volatility in interest rate and ERP in India. But

here we have divided the time period in 4 year group. And then found the standard deviation in realinterest rate. We also tried to find any relation between inflation and ERP.


42/59

38

ERP OF DIFFERENT INDUSTRIES IN INDIA

We have calculated the ERP paid by different industries in India to compare their performance. For this

we have taken group of 5 years to calculate ERP of these industries per year. The reason behind taking

group of 5 years is that ERP gives good result in long run.

For calculating ERP we need return of these industries over the period which we are considering that is

2004-2013. Then we made group of 5 years in this time period like: 2004-09, 2005-10, 2006-11, 2007-

12, and 2008-13. After grouping we calculated return in these industries based on the change in prices of

its stock (we have taken Sensex price).

For example Return (2004-09) = (closing price of 2009 closing price of 2004)/ closing price of 2004

After calculating the return its the time to find risk free return. For this we have taken government

Treasury bill rate.

ERP= Return in these industry government T-bill rate

Selecting risk free return

A major job in calculating ERP is selecting risk free return. For this we selected T-bill yield. And check

its correlation with overall return of economy. If there is very little correlation between return in

economy and government yield then we can select this yield as risk free return.

For calculating return in economy we have taken change in price of Sensex as our measure. And after

regressing the risk free return and Sensex return we have R2= 0.015, which means little or no correlation

so we can select our government yield as risk free return.

Note: Since we have given the annual yield on these T-bill we have adjusted these T-bill yields accordingto inflation taking year 2004 as base.

= 0.004 + 6.296

= 0.011

0

1

2

3

4

5

6

7

8

9

60 40 20 0 20 40 60 80

()

&


43/59

39

Results

1. Relationship between Volatility in interest rate & ERP

We have shown earlier that there is positive relationship between volatility in interest rate and ERP,

because higher volatility means higher risk. Thus the above graph is showing the positive relation

between ERP and volatility. So we can infer the relationship between ERP and volatility in interest rate

for U.S.A. but intercept and slope, both are not statistically significant.

But this relationship does not hold in case of India. Also intercept & slope, both are not statistically

significant.

= 0.999 + 1.413

= 0.292

0

0.5

1

1.5

2

2.5

33.5

4

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

& ()

= 17.33 + 64.17

= 0.055

20

0

20

40

60

80

100

0 0.5 1 1.5 2 2.5 3

& ()


44/59

40

2.

Relationship between Saving Rate & ERP

Since we have earlier shown that the relation between saving rate and ERP is negative. And same is

reflected through our graph of U.S.A. Here intercept is statistically significant and slope is not

statistically significant.

But this relationship does not hold for India. Here in this case we find that both intercept term and slope

are not statistically significant.

= 0.086 + 4.241

= 0.077

0

1

2

3

4

5

6

0 5 10 15 20 25

()

= 4.116 115.2

= 0.204

80

60

40

20

0

20

40

60

80

0 5 10 15 20 25 30 35 40

()


45/59

41

3. Relationship between Volatility in Inflation & ERP

The relation between ERP and volatility of inflation is positive. Higher the fluctuation, higher will be the

ERP. And same result is shown by our graph for U.S.A. also in this case the intercept term is statistically

significant and the slope term is not statistically significant.

The relation between ERP and volatility of inflation in US is not that clear by X-Y coordinate because

points are quite scattered. But graph line shows the correct relationship between ERP and average.

0

0.5

1

1.5

2

2.5

3

3.5

4

1961 1967 1973 1979 1985 1991 1997 2003 2009

&

& ()

E


46/59

42

This relation does not hold with India and both the terms, intercept and slope are not statistically

significant.

= 7.776 + 56.72

= 0.006

50

0

50

100

150

200

0 0.5 1 1.5 2 2.5 3

& ()

50

0

50

100

150

200

1997.2 2003 2006 2009 2012&

& ()

E


47/59

43

4.

Relation between Inflation & ERP

From the above graph it is clear that there is no relation between inflation and ERP. The intercept and

slope both are statistically not significant for both of the countries.

= 6E05 + 2.533

= 2E08

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10

& ()

= 4.413 + 35.84

= 0.080

80

60

40

20

0

20

40

60

80

& ()


48/59

44

5.

ERP of different industries in India

&

Here from the above graph it can be infer that in 2004-06, which was period of high economic growth,

when GDP was about 9.2 in both year 2005 and 2006. There was also huge capital formation in the

economy especially in private capital formation.

While during 2006-08 GDP was equal to 9.8 in 2007 but there was drastic fall in GDP in 2008 i.e. 3.8

when global economies were suffering from crisis, thus ERP of these industries also fell down.

Again in 2008-10 when Indian economy was coming back again at the path of restructuring, ERP of

these industries again started rising. But again in the period of 2010-13 ERP of these industries start

falling and become quite volatile.

100

50

0

50

100

150

200

200406 200608 200810 201012 201213

Year 2004 2005 2006 2007 2008 2009 2010 2011 2012

GDP 7.8 9.2 9.2 9.8 3.8 8.4 10.5 6.3 3.2


49/59

45

The other important point that can be infer from the graph above is that almost all industries in India have

paid volatile return in this period. Only pharmaceuticals are the only industry which has paid always

positive and constant return. The possible reason could be that demand of pharmaceuticals products is

least elastic.

Inference

Analysis of our Indian economy gave inverse relationship between ERP and its variables that what it

gave for U.S.A. & what we expected. Major reason behind such inverse relationship in case of India is

that Indian stock market is not that much organized as the U.S.A. Market i.e. Indian stock market is not a

proper indicator of economys health, thats why the earlier Analysis of our Indian economy gave inverse

relationship for India.


50/59

46

Part 4 Optimal Holding Period

In this section we will try to find out best holding (lock in) period for investing in Equity Market. Our

focus will be to check whether it is good to invest for shorter period or one should invest for longer

period to maximize returns.

We will also find out the industry which gives the maximum return and the optimum holding periods

within different industries.

Methodology

We have calculated return for different holding periods for Sensex & other 9 dominant industries indices

that we used in earlier two parts ( CNX Parma , CNX auto , CNX energy , CNX PSU banks, CNX banks

, CNX finance, CNX FMCG , CNX metal and CNX IT) from 2004 onwards.

We have calculated the annual return of all 10 indices for 1 month holding period by subtracting

M1(month1) closing price from M2(month2) closing price & dividing the result by M1. Then we

multiplied the result by 1200 to get the annual return. Following the same process we calculated the

return till October, 2013.

i.e. Annual Return(1 month holding period)

Similarly for calculating annual return for investing for 2 months we used the following formula

Annual Return (2 months holding period)

Following the above logic





51/59

47












52/59

48








Annual Return(108 months holding period)

Then we calculated average return & standard deviation for different holding periods for each of the 10

indices.


53/59

49

We also calculated inflation rate for each of these holding periods by using monthly CPI data from 2004

onwards till October 2013. We use the same methodology to compute inflation rate for different holding

periods which we used to find return. i.e. To calculate the annual inflation rate for 1month holding

period we subtracted CPI1 (Consumer price index of 1st month taken in consideration of 2004) value

from CPI2 (Consumer price index of 2nd month taken in consideration of 2004) value & divided the

result by CPI1. Then we multiplied the result by 1200 to get the annual inflation rate for 1 month holding

period. Similarly we calculated the inflation rate p.a. till October, 2013 for each 1 month holding period.

Similarly to calculate the annual inflation rate for 108months holding period we subtracted CPI1

(Consumer price index of 1stmonth taken in consideration of 2004) value from CPI109 (Consumer price

index of 109 month taken in consideration from 2004) value & divided the result by CPI1. Then we

multiplied the result by 100/9 to get the annual inflation rate for 108 month holding period. Similarly we

calculated the inflation rate p.a. 2013 for every holding period till October 2013.

Now for calculating inflation adjusted returns for each holding period for each of the indices we

subtracted the corresponding inflation rate calculated for each of the holding period from annual returns

calculated above.

We also took a reinvestment assumption at 7% so we discounted each of the average holding period

return for each of the indices to get the inflation adjusted discounted rate of return.

Results and Findings

1)Risk Analysis

We observed that together with the increase in the holding period the standard deviation of returns have

decreased. Which suggest that, in holding period of shorter span there is more risk as compared to the

risk in holding periods of larger span. In other words with the increase in holding period risk (s.d.)

decreases.


54/59

50

Holding

period

Sensex Auto

sector

Banking

sector

Energy Finance FMCG IT Metal Pharma PSU

bank

1 month 89 106.42 133.74 98.96 127.73 76.88 140.96 161.33 84.88 145.31

2 months 67.3 77.78 99.7 71.04 96.92 55.02 104.74 122.96 61.68 106.78

3 months 56.88 69.34 83.71 58.05 82.46 45.2 88.62 110.51 51.36 88.44

4 month 51.2 64.56 71.57 50.3 71.6 39.44 80.18 100.85 46.39 74.59

5 months 47.2 62.16 62.94 45.59 63.83 36.17 75.23 93.11 41.99 65.1

6 months 43.85 60.54 57.77 42 58.96 33.05 68.72 87.77 39.07 59.55

7 months 40.79 57.43 53.13 38.61 54.25 29.89 63.61 81.58 36.69 54.73

8 months 38.26 56.15 48.76 35.87 50.22 28.59 59.22 77.98 34.02 50.41

9 months 35.97 53.89 45.19 33.53 46.72 27.45 56.06 75.51 32.34 46.92

10 months 34.24 52.22 42.43 31.54 43.75 26.62 53.19 72.79 30.92 43.8

11 months 32.76 49.85 39.75 29.66 40.78 26.12 50.39 69 29.21 41.3412 months 31.55 48.31 37.9 28.3 38.91 25.58 48.05 67.5 27.83 39.35

5 quarters 29.26 43.47 33.95 25.35 35.7 23.36 41.88 60.71 23.01 35.92

6 quarters 28.81 41.75 33.63 23.53 35.56 23.09 38.63 53.45 20.4 36.47

7 quarters 28.17 40.16 29.83 21.71 31.78 21.45 36.47 51.51 17.3 30.75

8 quarters 27.39 36.13 26.11 21.06 28.26 18.76 33.25 51.29 15.6 27.22

3 years 24.44 22.34 20.27 20.19 24.77 13.37 20.33 41.37 14.59 18.51

4 years 16.3 18.66 15.49 15.6 18.39 12.44 15.53 36.99 13.13 15.41

5 years 14.44 10.84 13.17 13.96 15.71 8.62 11.22 30.09 12.34 14.47

6 years 14.97 12.5 15.64 11.37 17.77 9.12 11.77 30.84 7.96 18.29

7 years 10.63 10.37 11.77 6.63 12.2 7.93 10.48 22.67 8.9 13

8 years 5.02 5.35 8.9 2.89 9.19 9.82 11.82 11.61 7.27 9.46

9 years 3 4.27 6.14 3.06 6.22 12.46 17.53 4.9 5.31 5.39

2) Optimal Holding Period

By calculating the inflation adjusted returns we observed that:-

On an average the maximum return for a holding period of up to 5 years for most of the industries was

obtained between 9-12 months of holding period which means there is no additional advantage of locking

the money in stock market for more than 1 year till 5 years.

FMCG industry which has provided 52.11% return annually for holding period of 9 years, followed by

finance industry providing 32.59% annual return for 9 years of holding period.

D


55/59

51

Holding

period

Sense

x

Auto

sector

Banking

sectorEnergy Finance FMCG IT Metal Pharma

PSU

Banks

1 month 8.28 12.37 12.43 2.89 13.21 12.65 -0.98 9.71 10.16 8.5

2 months 8.4 12.6 12.99 3.64 13.93 12.99 0.15 12.03 10.06 9.09

3 months 8.48 12.97 13.07 3.42 14.26 13.42 0.48 12.96 10.21 8.35

4 month 8.83 13.58 13.23 3.36 14.66 13.91 0.54 14.58 10.93 8.04

5 months 9.65 14.43 13.44 3.5 15.13 14.61 0.91 16 11.37 7.98

6 months 10.28 15.53 14.39 4.2 16.17 15.32 2.31 17.42 11.66 9.03

7 months 10.58 15.94 14.65 4.46 16.52 15.68 3.41 17.94 12 9.4

8 months 10.81 16.59 14.82 4.59 16.77 16.07 4.15 18.45 12.06 9.66

9 months 10.88 17.13 15.21 4.82 17.19 16.54 4.78 19.18 12.12 10.03

10 months 11.07 17.69 15.57 4.91 17.55 16.94 5.07 19.58 12.31 10.4311 months 11.15 18.04 15.85 4.97 17.85 17.38 5.26 19.72 12.25 10.84

12 months 11.13 18.27 15.82 4.98 17.88 17.58 5.55 19.82 12.1 10.83

5 quarters 11.03 18.26 15.14 4.77 17.54 17.84 5.89 18.92 11.29 10.26

6 quarters 11.09 18.88 15.12 4.68 17.71 18.19 6.25 18.25 10.54 10.56

7 quarters 11 19.16 14.24 4.7 17 17.94 6.34 19.02 9.69 9.59

8 quarters 10.76 18.51 13.32 4.74 16.24 17.55 5.75 19.82 9.8 8.89

3 years 9.27 15.27 14.07 5.49 17.41 16.01 2.27 20.31 11.94 10.11

4 years 6.42 14.79 13.79 4.67 16.64 16.63 0.81 20.08 12.84 11.06

5 years 5.34 13.43 12.47 3.22 14.94 16.65 -0.51 16.29 14.67 10.55

6 years 8.21 17.43 17.84 4.51 21.52 21.16 -0.29 22.11 15.21 14.53

7 years 9.77 19.5 19.25 3.35 23.82 26.17 -0.23 17.67 18.43 11.72

8 years 13.01 25.63 20.4 2.83 26.35 39.38 -0.02 11.21 17.25 9.25

9 years 16.92 29.48 26.41 2.88 32.59 52.11 -3.36 8.52 26.01 8.93

By calculating the discounted annual return at assumption of reinvestment at 7%, we observed that:-

On an average the optimization holding period is 11 months for most of the indices.

Metal sector is the one which has provided the highest optimized return followed by Auto sector.

A A


56/59

52

Holding

period

Sens

ex

Auto

sector

Banking

sectorEnergy Finance

FMC

GIT Metal Pharma

PSU

Banks

1 month 8.23 12.3 12.36 2.88 13.14 12.58 -0.97 9.65 10.1 8.46

2 months 8.3 12.45 12.84 3.6 13.76 12.84 0.15 11.89 9.94 8.98

3 months 8.33 12.75 12.85 3.36 14.01 13.18 0.47 12.74 10.03 8.21

4 month 8.63 13.26 12.93 3.28 14.33 13.59 0.53 14.24 10.68 7.86

5 months 9.37 14.02 13.05 3.4 14.7 14.19 0.88 15.54 11.04 7.75

6 months 9.93 15 13.9 4.05 15.62 14.79 2.23 16.82 11.26 8.72

7 months 10.15 15.31 14.06 4.28 15.86 15.06 3.27 17.22 11.52 9.02

8 months 10.31 15.84 14.14 4.38 16.01 15.34 3.97 17.62 11.51 9.22

9 months 10.33 16.26 14.43 4.57 16.31 15.7 4.53 18.21 11.5 9.52

10 months 10.45 16.69 14.69 4.63 16.56 15.99 4.78 18.47 11.61 9.84

11 months 10.46 16.92 14.86 4.66 16.74 16.31 4.94 18.5 11.49 10.1712 months 10.38 17.04 14.75 4.64 16.68 16.4 5.18 18.49 11.28 10.1

5 quarters 10.11 16.74 13.88 4.37 16.08 16.35 5.4 17.34 10.35 9.4

6 quarters 9.98 17.01 13.62 4.21 15.95 16.38 5.63 16.44

Documents

Analysis of Risk Return Relationship In