(capm final)
DESCRIPTION
STOCKTRANSCRIPT
Chapter 1
Executive Summary
The last 15 years have seen a revolution in the way financial economists understand the
investment world. It was once thought that stock and bonds returns were essentially
unpredictable. But it is discovered that stock and bond returns have a substantial predictable
component at long horizons. once thought that the Capital asset pricing model provided a good
description of why average returns on some stocks, portfolios, funds or strategies were higher
than others. Now it is recognized that the average returns of many investment opportunities
cannot be explained by the CAPM.
Portfolio theories were developed by Markowitz (1952) and Tobin (1958) in the early 1950s and
1960s, which suggested that the risk of an individual security is the standard Deviation of its
returns – a measure of return volatility. Thus, the larger the standard deviation of security returns
the greater the risk. Markowitz observed that
(i) When two risky assets are combined their standard deviations are not additive,
provided the returns from the two assets are not perfectly positively correlated and
(ii) When a portfolio of risky assets is formed, the standard deviation of the portfolio is
less than the sum of standard deviations of its constituents. Best portfolio’s are
constructed when two securities are perfectly negatively correlated.
Markowitz was the first to develop a specific measure of portfolio risk and to derive the
expected return and risk of a portfolio. The Markowitz model generates the efficient frontier of
portfolios and the investors are expected to select a portfolio, which is most appropriate for
them, from the efficient set of portfolios available to them.
The application of Markowitz is very complicated as the number of correlations required to
calculate are huge. But Markowitz contribution to portfolio Theory cannot be ignored.
Ever since Markowitz introduced the concept of portfolio theory in 1952 one of the questions
predominant in the minds of financial theorists has been the consistency of the investors optimal
portfolio. Research into this area, which become known as capital market theory attempted to
1
analyze the equilibrium relationships between assets. One of the products of this research was
widely accepted Capital asset pricing model of Sharpe and lintner.
Sharpe (1964) developed a computationally efficient method, the single index model, where
return on an individual security is related to the return on a common index. The common index
may be any variable thought to be the dominant influence on stock returns.
Ri = α+ β Rm (1)
Where
Ri = Security Return
β=Relationship of security with Common Index Generally Market Index
Rm =Market Index
α =Risk free return
The single index model can be extended to portfolios as well. This is possible because the
expected return on a portfolio is a weighted average of the expected returns on individual
securities.
When analyzing the risk of an individual security, however, the individual security risk must be
considered in relation to other securities in the portfolio. In particular, the risk of an individual
security must be measured in terms of the extent to which it adds risk to the investor’s portfolio.
Thus, a security’s contribution to portfolio risk is different from the risk of the individual
security.
Investors face two kinds of risks, Diversifiable (Unsystematic risk) is unique risk which is
specific to security and which can be eliminated by increasing the number of securities and non-
diversifiable (Systematic risk) is related with the market as a whole. It affect the entire economy
therefore is often referred to as the market risk. The market risk is the component of the total risk
that cannot be eliminated through portfolio diversification.
2
Chapter 2
Introduction
Investors and financial researchers, in order to test the relationship between Risk and Return,
have done numerous researches in the past. In order to assess the risk exposure to different
assets, practitioners all over the world use a plethora of models in their portfolio selection
process.
A stock’s contribution to the risk of a fully diversified portfolio depends on its sensitivity
to market changes. This sensitivity is generally known as beta. A security with a beta of 1.0 has
average market risk—a well-diversified portfolio of such securities has the same standard
deviation as the market index. A security with a beta of .5 has below-average market risk—a
well-diversified portfolio of these securities tends to move half as far as the market moves and
has half the market’s standard deviation.
Basis on which Investments is made
Risk: -
Risk can be defined as the uncertainty in achieving the expected return. It is the chance
that an investment's actual return will be different than expected. This includes the
possibility of losing some or all of the original investment. Risk is usually measured by
calculating the standard deviation of the historical returns or average returns of a specific
investment
Return: -
Return can be defined as the percentage annual accretion to the net wealth employed in
an investment avenue. In simple terms, it is the gain or loss of a security in a particular
period. The return consists of the income and the capital gains relative on an investment.
It is usually quoted as a percentage.
Return(y)= P1-P0+D1
3
P0
Timing: -
Timing involves at what time the investment avenue is being purchased or sold. There
are different investment styles that are present for making the investments at different
intervals. Portfolio Management involves time element and time horizon. The present
value of future returns /cash flows by discounting is useful for share valuation and bond
valuation.
4
Early Developments 2.1
The Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965), and Black (1972)
provides predictions for equilibrium expected returns on risky assets. More specifically, it states
that the expected excess return over the risk-free interest rate of an asset equals a coefficient,
times the (mean-variance efficient) market portfolio’s expected excess return over the risk-free
interest rate (equation 3). This relatively straightforward relationship between various rates of
return is difficult to implement empirically because expected returns and the efficient market
portfolio are unobservable. Despite this formidable difficulty, a substantial number of tests have
never the less been performed, using a variety of ex-post values and proxies for the unobservable
ex-ante variables.
Recognizing the seriousness of this situation quite early, Roll (1977) emphasized that tests
following such an approach provide no evidence about the validity of the CAPM. The obvious
reason is that ex-post values and proxies are only approximations and therefore not the variables
one should actually be using to test the CAPM.
Fama and MacBeth provided evidence
(i) Of a larger intercept term than the risk-free rate,
(ii) That the linear relationship between the average return and the beta holds and
(iii) That the linear relationship holds well when the data covers a long time period.
So CAPM passed the early scares and accepted as a useful tool.
2.1.1 CAPM
The Capital Asset Pricing Model is based on the two parameter portfolio analysis model
developed by Markowitz (1952). Markowitz drew attention to the common practice of portfolio
diversification and showed exactly how an investor can reduce the standard deviation of
portfolio returns by choosing stocks that do not move exactly together. This model was
simultaneously and independently developed by John Linter (1965), Jan Mossin (1966). In
equation form the model can be expressed as follows:
5
Where is expected return on the asset i, is the risk free rate of return, is expected
return on market proxy and is a measure of risk specific to asset i, and expected return on
market portfolio is also called the security market line. If CAPM is valid, all securities will lie in
a straight line called the security market line in the , frontier. The security market line
implies that return is a linearly increasing function of risk. Moreover only the market risk affects
the return and the investor receive no extra return for bearing diversifiable (residual) risk.
The assumptions employed in the CAPM can be summarized as follows [Brealey-Meyers
(2003)]:
1. Investment in U.S. Treasury bills is risk free. It is true that there is little chance of
default, but they don’t guarantee a real return. There is still some uncertainty about
inflation.
2. Investors can borrow money at the same rate of interest at which they can lend. Generally
borrowing rates are higher than lending rates.
CAPM also makes the following assumptions:
3. Investors are risk averse individuals who maximize the expected utility of their end of
period wealth. Implication: The model is a one period model.
4. Investors have homogenous expectations (beliefs) about asset returns. Implication: all
investors perceive identical opportunity sets. This is, everyone have the same information
at the same time.
5. Asset returns are distributed by the normal distribution.
6
6. There exists a risk free asset and investors may borrow or lend unlimited amounts of this
asset at a constant rate: the risk free rate (kf).
7. There is a definite number of assets and their quantities are fixed within the one period
world.
8. All assets are perfectly divisible and priced in a perfectly competitive marked
Implication. e.g. human capital is non-existing (it is not divisible and it can’t be owned
as an asset).
9. Asset markets are frictionless and information is costless and simultaneously available to
all investors. Implication: the borrowing rate equals the lending rate.
10. There are no market imperfections such as taxes, regulations, or restrictions on short
selling.
7
2.1.2 According to CAPM, a market portfolio includes riskless securities as well as risky
securities. It can also be written as:
Where,
• Portfolio Theory – ANY individual investor’s optimal selection of portfolio (partial
equilibrium)
• CAPM – equilibrium of ALL individual investors (and asset suppliers)
(general equilibrium)
E(return) = Risk-free rate of return + Risk premium specific to asset i
= Rf + (Market price of risk)x(quantity of risk of asset i)
CAPM tells us 1) what is the price of risk?
2) what is the risk of asset i?
8
2.1.3 Example
Expected Return Standard Deviation
Asset i 10.9% 4.45%
Asset j 5.4% 7.25%
E(return) = Risk-free rate of return + Risk premium specific to asset i
= Rf + (Market price of risk)x(quantity of risk of asset i)
Question: According to the above equation, given that asset j has higher risk relative to asset i,
why wouldn’t asset j has higher expected return as well?
Possible Answers: (1) the equation, as intuitive as it is, is completely wrong.
(2) the equation is right. But market price of risk is different for different
assets.
(3) the equation is right. But quantity of risk of any risky asset is not
equal to the standard deviation of its return.
E(return) = Risk-free rate of return + Risk premium specific to asset i
= Rf + (Market price of risk)x(quantity of risk of asset i)
• The intuitive equation is right.
• The equilibrium price of risk is the same across all marketable assets
9
In the equation, the quantity of risk of any asset, however, is only PART of the total risk (s.d) of
the asset.
• Specifically:
Total risk = systematic risk + unsystematic risk
10
11
12
CAPM says:
(1)Unsystematic risk can be diversified away. Since there is no free lunch, if there is something
you bear but can be avoided by diversifying at NO cost, the market will not reward the holder of
unsystematic risk at all.
(2)Systematic risk cannot be diversified away without cost. In other words, investors need to be
compensated by a certain risk premium for bearing systematic risk.
E(return) = Risk-free rate of return + Risk premium specific to asset i
= Rf + (Market price of risk)x(quantity of risk of asset i)
13
Precisely:
[1] Expected Return on asset i = E(Ri)
[2] Equilibrium Risk-free rate of return = Rf
[3] Quantity of risk of asset i = COV(Ri, RM)/Var(RM)
[4] Market Price of risk = [E(RM)-Rf]
Thus, the equation known as the Capital Asset Pricing Model:
E(Ri) = Rf + [E(RM)-Rf] x [COV(Ri, RM)/Var(RM)]
Where [COV(Ri, RM)/Var(RM)] is also known as BETA of asset I
Or
E(Ri) = Rf + [E(RM)-Rf] x βi
14
15
16
17
18
Chapter 3
19
What is an equilibrium
3.1CONDITION 1:Individual investor’s equilibrium: Max U
• Assume:
• [1] Market is frictionless
=> borrowing rate = lending rate
=> linear efficient set in the return-risk space
[2] Anyone can borrow or lend unlimited amount at risk-free rate
• [3] All investors have homogenous beliefs
=> they perceive identical distribution of expected returns on ALL assets
=> thus, they all perceive the SAME linear efficient set (we called the line :
CAPITAL MARKET LINE
=> the tangency point is the MARKET PORTFOLIO
20
3.2 CONDITION 2: Demand = Supply for ALL risky assets
• Remember expected return is a function of price.
• Market price of any asset is such that its expected return is just enough to compensate its
investors to rationally hold it.
3.3 CONDITION 3: Equilibrium weight of any risky assets
• The Market portfolio consists of all risky assets.
• Market value of any asset i (Vi) = PixQi
• Market portfolio has a value of ∑iVi
• Market portfolio has N risky assets, each with a weight of wi
Such that
wi = Vi / ∑iVi for all i
3.4 CONDITION 4: Aggregate borrowing = Aggregate lending
• Risk-free rate is not exogenously given, but is determined by equating aggregate
borrowing and aggregate lending.
Chapter 4
21
Two-Fund Separation:
Given the assumptions of frictionless market, unlimited lending and borrowing,
homogenous beliefs, and if the above 4 equilibrium conditions are satisfied, we then have the 2-
fund separation.
TWO-FUND SEPARATION:
Each investor will have a utility-maximizing portfolio that is a combination of the risk-
free asset and a portfolio (or fund) of risky assets that is determined by the Capital market line
tangent to the investor’s efficient set of risky assets
Analogy of Two-fund separation
Fisher Separation Theorem in a world of certainty
Derivation of CAPM
22
• Using equilibrium condition 3
wi = Vi / ∑iVi for all i
market value of individual assets (asset i)
wi = ------------------------------------------------
market value of all assets (market portfolio)
• Consider the following portfolio:
hold a% in asset i
and (1-a%) in the market portfolio
• The expected return and standard deviation of such a portfolio can be written as:
E(Rp) = aE(Ri) + (1-a)E(Rm)
s(Rp) = [ a2si2 + (1-a)2sm
2 + 2a (1-a) sim ]
1/2
• Since the market portfolio already contains asset i and, most importantly, the equilibrium
value weight is wi
• therefore, the percent a in the above equations represent excess demands for a risky asset
• We know from equilibrium condition 2 that in equilibrium, Demand = Supply for all
asset.
Therefore, a = 0 has to be true in equilibrium.
Chapter 5
23
Beta
Beta is a measure of a stock's volatility in relation to the market. By definition, the market has a
beta of 1.0, and individual stocks are ranked according to how much they deviate from the
market. A stock that swings more than the market over time has a beta above 1.0. If a stock
moves less than the market, the stock's beta is less than 1.0. High-beta stocks are supposed to be
riskier but provide a potential for higher returns; low-beta stocks pose less risk but also lower
returns.
Beta is a key component for the capital asset pricing model (CAPM), which is used to
calculate cost of equity. Beta is a useful measure. A stock's price variability is important to
consider when assessing risk. Indeed, if you think about risk as the possibility of a stock losing
its value, beta has appeal as a proxy for risk.
24
5.1 Is Beta Dead
The Fama and French (1992) study has itself been challenged. The study’s claims most attacked
are these:
That the beta has no role for explaining cross-sectional variation in returns,
That the size has an important role,
That the book to-market equity ratio has an important role.
The studies responding to the Fama and French challenge generally take a closer look at the data
used in that study. Kothari, Shanken, and Sloan (1995) argue that Fama and French’s (1992)
findings depend critically on how one interprets their statistical tests. Kothari, Shanken, and
Sloan focus on Fama and French’s estimates for the coefficient on beta, which have high
standard errors and therefore imply that a wide range of economically plausible risk premiums
cannot be rejected statistically.
The view, that the data are too noisy to invalidate the CAPM, is supported by Amihud,
Christensen, and Mendelson (1992) and Black (1993). In fact, Amihud, Christensen, and
Mendelson (1992) find that when a more efficient statistical method is used, the estimated
relation between average return and beta is positive and significant. Black (1993) suggested that
the size effect noted by Banz (1981) could simply be a sample period effect: the size effect is
observed in some periods and not in others.
25
5.2 Is Beta Alive
The general reaction to the Fama and French (1992) findings, despite these challenges, has been
to focus on alternative asset pricing models. Jagannathan and Wang (1993) think that this may
not be necessary. Instead they show that the lack of empirical support for the CAPM may be due
to the inappropriateness of some assumptions made to facilitate the empirical analysis of the
model. Such an analysis must include a measure of the return on the aggregate wealth portfolio
of all agents in the economy, and Jagannathan and Wang say most CAPM studies do not do that.
Most empirical studies of the CAPM assume, instead, that the return on broad stock market
indexes, like the NYSE composite index, is a reasonable proxy for the return on the true market
portfolio of all assets in the economy.
However, in the United States, only one-third of nongovernmental tangible assets are owned by
the corporate sector, and only one-third of corporate assets are financed by equity. Furthermore,
intangible assets, like human capital, are not captured by stock market indexes. Jagannathan and
Wang (1993) abandon the assumption that the broad stock market indexes are adequate.
Following Mayers (1972), they include human capital in their measure of wealth. Since human
capital is, of course, not directly observable, Jagannathan and Wang choose the growth of labor
income, and build human capital into the CAPM this way: Then Jagannathan and Wang’s
version of the CAPM is show that the CAPM is able to explain 28 percent of the cross-sectional
variation in average returns in the 100 portfolios studied by Fama and French (1992). Thus,
Jagannathan and Wang (1993) directly respond to the challenge of Fama and French (1992).
Chapter -6
26
Indian Stock Market
6.1 WHAT IS STOCK
Share or stock is a document issued by a company, which entitles its holder to be one of the
owners of the company. A share is issued by a company or can be purchased from the stock
market.
6.2 What is stock market
A market where dealing of securities is done is known as share market. There are basically two
types of share market in India:
1. Bombay Stock Exchange (BSE)
2. National Stock Exchange (NSE)6.3 DIFFERENCE BETWEEN PRIMARY AND SECONDARY
MARKET- In the primary market securities are issued to the public and the proceeds go
to the issuing company. Secondary market is a term used for stock exchanges, where
stocks are bought and sold after they are issued to the public.SECONDARY
MARKET
27Company
Companies get themselves listed on popular stock exchanges like BSE and NSE
BrokerStock Exchange Individual
Investors
CompanyIPO
Individuals apply to get shares of the company
Companies share ownership by issuing shares
6.4 DYNAMICS OF THE SHARE MARKET
Capital markets in India have considerable depth. There are 22 stock exchanges in India.
Ahmadabad, Delhi, Calcutta, Madras and Bangalore are major ones amongst the other
stock exchanges. These stock exchanges are served by 3,000 brokers and 20,000 sub-
brokers. A number of providers for merchant banking services exist. The market
capitalization of the Bombay Stock Exchange (BSE) alone was around Rs.5 trillion in
December 1994.This makes it one of the largest emerging stock markets in the world. A
28
Company
Companies get themselves listed on popular stock exchanges like BSE and NSE
BrokerStock Exchange Individual
Investors
Buyer BrokerStock
ExchangeBroker Seller
He pays the money to his broker
His broker pays it to the exchange
The exchange pays it to the seller’s broker
Seller’s broker finally pays the money to the seller
Similar process happens for the transfer of shares from the seller’s end.
number of other cities also have stock markets. There are two other exchanges in
Bombay:-National Stock Exchange (NSE)
Over The Counter Exchange of India (OTCEI)
The regulatory agency which oversees the functioning of stock markets is the Securities and
Exchange Board of India (SEBI), which is also located in Bombay. India has one of the most
active primary markets in the world, with roughly 130 public issues taking place each month.
The National Stock Exchange (NSE), Bombay Stock Exchange (BSE) and OTCEI have already
introduced screen-based trading. All other exchanges (except Guwahati, Magadh and
Bhubaneswar) are to introduce full computerization and screen-based trading by 30 June 1996.
This will bring about greater transparency for investors, reduce spreads, allow for more effective
monitoring of prices and volumes and speed up settlement.
6.4.1 TRANSACTION CYCLE IN SHARE MARKET
29
6..5 Major Stock Market In India
There are two major capital markets in India in terms of liquidity, volume of trades and the
volume if companies listed. These are:
1) NSE ( National Stock Exchange)
2) BSE (Bombay Stock Exchange)
6.5.1 Bombay Stock Exchange:
Bombay Stock Exchange is the oldest stock exchange in Asia with a rich heritage, now spanning
three centuries in its 133 years of existence. What is now popularly known as BSE was
established as "The Native Share & Stock Brokers' Association" in 1875. BSE is the first stock
exchange in the country which obtained permanent recognition (in 1956) from the Government
of India under the Securities Contracts (Regulation) Act 1956. BSE's pivotal and pre-eminent
30
role in the development of the Indian capital market is widely recognized. It migrated from the
open outcry system to an online screen-based order driven trading system in 1995. Earlier an
Association Of Persons (AOP), BSE is now a corporatised and demutualised entity incorporated
under the provisions of the Companies Act, 1956, pursuant to the BSE (Corporatisation and
Demutualisation) Scheme, 2005 notified by the Securities and Exchange Board of India (SEBI).
With demutualisation, BSE has two of world's best exchanges, Deutsche Börse and Singapore
Exchange, as its strategic partners. Over the past 133 years, BSE has facilitated the growth of the
Indian corporate sector by providing it with an efficient access to resources. There is perhaps no
major corporate in India which has not sourced BSE's services in raising resources from the
capital market. Today, BSE is the world's number 1 exchange in terms of the number of listed
companies and the world's 5th in transaction numbers. The market capitalization as on December
31, 2007 stood at USD 1.79 trillion.
The BSE Index, SENSEX, is India's first stock market index that enjoys an iconic stature,
and is tracked worldwide. It is an index of 30 stocks representing 12 major sectors. The
SENSEX is constructed on a 'free-float' methodology, and is sensitive to market sentiments and
market realities.
6.5.2 National Stock Exchange:
The NSE, located in Bombay, was set up in 1993 to encourage stock exchange reform through
system modernization and competition. NSE's reach has been extended to 21 cities, of which 6
cities do not have their own stock exchanges. NSE plans to cover 40 cities by end-1996. The
NSE has a very modern implementation of trading using contemporary technology in computers
and communication. It is an electronic screen based system where members have equal
opportunity and access for trading irrespective of their location, since they are connected by a
satellite network.
The number of members trading on the exchange has increased from the 227 at
commencement to 600 members as of November 1995. NSE, thus, helps to integrate the national
market and provides a modern system with a complete audit trail of all transactions. In a further
31
effort to improve the settlement system and minimize the risks associated therein, NSE has set
up a subsidiary - National Securities Clearing Corporation (NSCC). On par with clearing
corporations the world over, NSCC will shortly guarantee settlement of trades executed and
settled through it. The instruments traded are treasury bills, government security, and bonds
issued by public sector companies.
Currently, 200 large companies are traded on the NSE; that list is expected to gradually
expand as the exchange stabilizes. The NSE is a computerized market for debt and equity
instruments.
The government of India issues around Rs.70 billion of debt instruments per year. The market is
still nascent; but, trading volumes are steadily rising. Average daily turnover in stocks have
increased from Rs.70 million in November 1994 to Rs.990 million during July 1995.
6.5.2.1 Objectives:
To establish a nationwide trading facility for equities, debt instruments and hybrids.
To ensure equal access to investors all over the country through appropriate
communication network.
To provide a fair, efficient and transparent securities market to investors using an
electronic communication network.
To enable shorter settlement cycle and book entry settlement system.
To meet current international standards of securities market.
NSE-NIFTY: The national Stock Exchange on April 22, 1996 launched a new Equity Index The
NSE-50. The new Index which replaces the existing NSE-100 Index is expected to serve as an
32
appropriate Index for the new segment of futures and options. ―Nifty‖ means National Index for
Fifty Stock. The NSE-50 comprises 50 companies that represent 20 broad Industry groups with
an aggregate market capitalization of around Rs.170000crores. All companies included in the
index have a market capitalization in excess of Rs.500crores each and should have traded for
85% of trading days at an impact cost of less than 1.5%. The base period for the index is the
close of prices on Nov 3,1995 which makes one year of completion of operation of NSE‘s
capital market segment. The base value of the Index has been set at 1000.
Table 1
50 Companies of NIFTY as on 1st March, 2009
A B B Ltd. N T P C Ltd.
A C C Ltd. National Aluminium Co. Ltd.
Ambuja Cements Ltd. Oil & Natural Gas Corpn. Ltd.
Bharat Heavy Electricals Ltd. Power Grid Corpn. Of India Ltd.
Bharat Petroleum Corpn. Ltd. Punjab National Bank
Bharti Airtel Ltd. Ranbaxy Laboratories Ltd.
Cairn India Ltd. Reliance Capital Ltd.
Cipla Ltd. Reliance Communications Ltd.
D L F Ltd. Reliance Industries Ltd.
G A I L (India) Ltd. Reliance Infrastructure Ltd.
33
Grasim Industries Ltd. Reliance Petroleum Ltd.
H C L Technologies Ltd. Reliance Power Ltd.
H D F C Bank Ltd. Siemens Ltd.
Hero Honda Motors Ltd. State Bank Of India
Hindalco Industries Ltd. Steel Authority Of India Ltd.
Hindustan Unilever Ltd. Sterlite Industries (India) Ltd.
Housing Development Finance Corpn. Ltd. Sun Pharmaceutical Inds. Ltd.
I C I C I Bank Ltd. Suzlon Energy Ltd.
I T C Ltd. Tata Communications Ltd.
Idea Cellular Ltd. Tata Consultancy Services Ltd.
Infosys Technologies Ltd. Tata Motors Ltd.
Larsen & Toubro Ltd. Tata Power Co. Ltd.
Mahindra & Mahindra Ltd. Tata Steel Ltd.
Maruti Suzuki India Ltd. Unitech Ltd.
Satyam Wipro Ltd.
Zee Entertainment Enterprises Ltd.
Chapter 7
Review of Literature
The process of selecting a portfolio may be divided into two stages. The first stage starts with
observation and experience and ends with beliefs about the future performances of available
securities. The second stage starts with the relevant beliefs about future performances and ends
with the choice of portfolio. This has been written by Markowitz (1952) in his research paper.
He has given as E-V rule, E-V rule states that that the investor would (or should) want to select
one of those portfolios which give rise to the (E, V) combinations indicated as efficient in the
figure; i.e., those with minimum V for given E or more and maximum E for given V or less. The
article presents a very comprehensive view to calculate highest expected return for a given level
of risk. The Markowitz approach only takes into account risky assets and there is no provision
34
for the risk free assets. Also the portfolio to be constructed must be based on the co-variances
between different securities and the securities which have minimum covariance must be
selected.
CAPM has been extensively used in various stocks markets and Portfolios. Michailidis,
Tsopoglou, Papanastasiou and Mariola(2006) in their study deals with 100 stocks listed on
Athens stock exchange for the period of January 1998 to December 2002. Regression analysis is
performed for the monthly return for the ten years. The findings of the study were not in favor of
the theory’s basic hypothesis that higher risk (beta) is associated with a higher level of return.
Klemkosky and Martin (1975), found the practical importance of beta effect on portfolio
diversification by comparing the residual risk of high and low beta stock portfolios containing
from two to twenty-five securities. These comparisons indicated that the levels of diversification
achieved for high versus low beta portfolios for a given portfolio size were significantly different
with high beta portfolios requiring a substantially larger number of securities to achieve the same
level of diversification as a low beta portfolio. This information should be of particular benefit to
the portfolio manager who seeks maximum diversification with a limited number of securities.
7.1 Literature on CAPM:
Jack Clark Francis and Frank Fabozzi (1979) conducted a study over a period of 73 months
between December 1965 and December 1971 on 694 stocks listed in NYSE. The study looked
into the stability of the single index market model (SIMM). The result of the study supports the
hypothesis that SIMM is affected by macroeconomic conditions. The inter-temporal instability
in the betas frequently observed could be due to this business cycle economics.
Richard Roll (1981) found the trading infrequency to be an important cause of bias in
short interval data. As the small firms are traded less frequently the risk measures for these firms
are downward biased. The bias is very large in daily data and is also present in returns from
monthly data. According to the author this bias can possibly explain effects like the small firm
effect, low P/E ratio effect and high dividend yield firm effects, present in the market.
35
Jeffrey F. Jaffe, Randolph Westerfield, M. A Christopher (1989) studied two sets of
indices from the US and one set each from Canada, Australia, England and Japan. The authors
find that Monday return for common stocks is negative only when market has declined in the
previous week. The findings are inconsistent with market efficiency. The inconsistency cannot
be explained by serial correlation arising from infrequent trading or higher risk on those
particular Mondays.
7.2 CAPM Tests in Indian Context
There are many studies has already been done on Capital Asset Pricing Model on the
Indian Capital Market. Vaidyanathan (1995) in his study found that Indian Capital market is not
efficient enough, and it is not having historical data on tapes and data has not been adjusted for
bonus/right etc over a long period of time which leads to market inefficiency. He also
recommended that in order to compete in twenty first century, we need to strengthen the
infrastructure, improve liquidity, minimize insider trading and enhance transparency.
Manjunatha and Mallikarjunappaa(2007) in their study deals with 66 stocks listed on the BSE
exchange. The stock was selected on based on two criteria: 1) the companies selected should
have been constituents of BSE Sensex 2) traded for the minimum time period of six months in a
36
year during the study period. The daily adjusted share prices and index from January 1990 to
June 2005 were used to study. The study revealed that the alpha of the CAPM was equal to the
risk-free rate of the returns, beta held the percentage returns when portfolios were formed with
market value weights, neither beta nor size variables explained the variation in portfolio returns.
A study conducted by Obaidullah (1994) used monthly stock price data for a period of sixteen
years (1976-91) for a sample of thirty stocks. The results from the exercise, however, do not lend
themselves to any supportive or contradictory interpretation. The coefficients of 2p are, in
general, not statistically significant. This is in conformity with the CAPM. However, in the
multiple regression model, the coefficients of p also in most cases become statistically
insignificant which is contrary to what the CAPM predicts. Hence he suggests that CAPM as a
description of asset pricing in Indian markets does not seem to rest on solid grounds.
Vaidyanathan & Gali (1994 a) studied the variation in various indices (Sensex, ET index and
Natex) and found that one scrip (Reliance) explained more than half of the variation in the
indices during 1989 and 1990. In case Hindustan Lever is also considered then the two scrips
explain around 70% of the variation in Sensex and Natex. Vaidyanathan & Gali (1994 b) studied
the efficiency of the stock market (weak form) using runs, serial correlation and filter tests at
four different points for the period 1980 to 1990 for ten scrips. The evidence from all the three
tests support the weak form of efficiency.
Chapter 8
Need of the Study
Over the years, there has been many significant studies has been done in order to know the
relation between Risk and Return. One of the most important contributions by researchers is in
the field of security market is the establishment of the relationship between Risk and Return by
the way of Capital Asset Pricing Model. After Markowitz (1952), Linter (1965) and Mossin
(1966) has given this concept, a large number of studies have been conducted to test CAPM. A
recent study on the same has been done by Michailidis, Tsopoglou, Papanastasiou, and Mariola
(2006) in the Greek Securities Market, whereas Vaidyanathan (1995) applied the CAP Model in
37
1995. Recently Manjunatha and Mallikarjunappa (2007) conducted a study on 66 stocks of BSE.
The Indian Stock Market is changing its dimensions in terms of liquidity and number of trades
on the stock market. Earlier derivatives and short selling was not allowed in the Indian Stock
Market but since 2001 it has been traded on the National Stock Exchange (India). The cost of
transaction has reduced. There have not been many studies found of Applicability of CAPM on
National Stock Market which is said to be more efficient than any other in terms of number of
transactions and the liquidity. So it is endeavored to conduct such a study from Indian
perspective.
Chapter 9
Research Objectives
The main objectives of the study are as follows:
1. To test the relation between risk (systematic risk) and return.
2. To study the effect on Portfolio Return with the diversification of risk.
38
Chapter 10
Research Methodology
Capital Asset Pricing Model is used in order measure the relationship among risk, return, and
effect of diversification on the portfolio risk in the Indian Stock Market. The first step is focused
to estimate a beta coefficient for each stock using monthly adjusted returns. For this, weekly
opening and closing prices, after adjusting with the bonus issue, right issue, and other factors, of
composite portfolio of 42 companies’ stocks of NSE representing all sectors of economy (index),
is taken as the sample for the study.
10.1 Data Collection:
39
The study used monthly stock returns from 42 Index companies listed on the NSE for the period
of July 2005 to June 2008. The data is obtained from the PROWESS, a data base maintained by
the CMIE Ltd. and from the websites of NSE and moneycontrol.
All stock returns have been adjusted for the dividends as required by the CAPM. The stock
prices are basically adjusted for the bonus and stock split. For example, if stock prices got a
bonus of 1:1 that means for every one stock you are getting one stock as bonus, the previous
stock prices that stock has been divided by two when the bonus credited to the shareholders and
like the same way if each stock has been splitted up into five parts then the previous prices of
that stock has been divided by five.
10.2 Beta Calculation
CAPM tells that return on security i, in time period t is a linear function of market return .
Where,
alpha is indicating the minimum level of return
The weekly return for the stocks from the stock prices was first calculated using the following
formula.
P1:- Opening price of the stock in Current Week i.e. on Monday
40
P0:- Opening Price of the stock in the Last Week i.e. on Monday
Further for the calculation of Beta covariance of stock return to market return has been
calculated by using the following equation.
Covariance =
The Data was arranged in the excel sheet and the covariance of the Nifty Index with Stock was
calculated using excel function i.e. =COVAR (array1, array2)
Variance =
The Variance of the Stock is also calculated by arranging the data in the excel sheet and using
excel function i.e. =VARP (number1, number2)
Beta is estimated by regressing the weekly security return to the return of index.
β = Cov Ri.Rm/σm2
The Beta is also calculated using Excel Sheet functions. The beta can be estimated by regressing
each stock’s monthly return against the market index according to the following equation:
10.3 Calculation of Various Risks: In the next stage, total market risk of the stock is calculated
for each stock which is the sum of total market risk and total non-market risk.
For calculating the total market risk, the variance of the stock is calculated, which is equal to the
total market risk. The variance of the stock has been calculated using the formula
Variance =
41
The Variance of the Stock is also calculated by arranging the data in the excel sheet and using
excel function i.e. =VARP (number1, number2). Total risk of the security is the sum of the total
market risk and total non-market risk.
Where variance of stock i representing the total risk is, is total market risk, and
is non-market risk.
10.4 Calculation of alpha: Further alpha of each stock is calculated for calculating the
minimum return expected from the stock. Alpha is a constant intercept indicating a minimum
level of return that is expected from the security I, if market remains flat is calculated in this
way:
Alpha (α) =
Where α is a constant intercept of security I, is a mean return of security I, is mean market
return of index, and is slope of the security i.
10.5 Calculation of Coefficient of Determination:
The Coefficient of determination in stock return is explained by the Index return, coefficient of
determination (R2) is calculated by dividing the systematic risk of the stock with the total market
risk of that stock.
10.6 Calculation of Expected return of securities and portfolio: The expected return of the
stocks has been calculated by using the following formula:
42
Where
α is the minimum level of return from the stock
β is the stock beta
is the average mean of the Index return.
Weighted average return of each stock will be taken in order to make the portfolio return. Here,
we will assume that equal weights to be given to each security in the portfolio. Symbolically,
portfolio return can be obtained as:
Where
Total risk of a portfolio will be the weighted average of total risk of individual securities, which
is composite of market and non-market risk. For better comparability of the market risk and
return, all securities will be arranged in the ascending order on the basis of the beta value and
then five portfolios will be made. The portfolio with the least beta (consisting of six securities)
will be the portfolio number one. Second portfolio will be the next six securities on the basis of
the beta and so on. The portfolio consisting with least beta will be the least responsive to the
market index. The portfolio with the highest six betas will be more responsive to the market
index.
The following equation will be used in order to estimate the portfolio betas:
43
Where,
.
The main objective is to test the relationship between risk (Systematic risk) and return, and
effect of diversification on the portfolio risk. To calculate the expected return of the securities
and portfolios here, the study has taken the average market return as market return which gave
0.46% weekly return to the market, and weekly interest on fixed deposit (0.11) has been taken as
risk free return.
Chapter 11
44
The Relation between Risk and Return
Our first objective is to find the relation between the risk and the expected return of the
securities. For this NIFTY-50 companies was taken as the sample size. Out of 50 companies,
data for 42 companies is available, as some of the companies were listed after July, 2005.
Pearson correlation coefficient between the stock beta and expected return (0.499) with high
degree of linear relationship between these two, and the total market risk and expected return
(0.527) signifies the high degree of relationship between risk and stock return. The proposition
of CAPM seems to be right here. Diversification has been carried out on the basis of the
arranging of securities according to the beta value. Stocks, which come in the first ranking, can
be categorized as less volatile as their respected beta is low. They remain less responsive to the
market up and downswings. On the other hand, stocks in the second end of ranking are of high
risk as their respected beta are highest, which shows the high degree of market volatile, showing
the high degree of market sensitivity in terms of upswings and downswings. The beta value
explains the proportional change in the security return due to the effective change in the market
return. The ups and downswings in the security return depended to the market return. To
determine the variation is the stock return is explained by the index return, coefficient of
determination (R2) is calculated for this purpose. So 1- R2 explains the variation in the stock
return that is not due to the index movement or index return. Coefficient of Determination is the
indication of the movement of the stock return due to the index return. If value of R2 is 0.71 then
it means that there is a 71% variation in the stock return due to the index return.
Table 2
45
Individual Stock return and Risk
Stock Beta
Variance
Stock
Alpha
Stock
Systemati
c Risk
Unsystematic
Risk R2 E(R)
HEROHONDA 0.46 16.50 -0.03 2.45 14.06 0.15 0.18
SUNPHARMA 0.46 16.92 0.40 2.49 14.44 0.15 0.61
CIPLA 0.56 29.35 -0.10 3.64 25.71 0.12 0.16
TCS 0.58 15.64 -0.03 3.86 11.78 0.25 0.24
RANBAXY 0.59 24.72 -0.17 4.06 20.67 0.16 0.11
SATYAMCOMP 0.62 18.05 0.16 4.50 13.55 0.25 0.45
INFOSYSTCH 0.65 16.46 0.02 4.88 11.58 0.30 0.32
HINDUNILVR 0.72 19.04 -0.08 5.97 13.08 0.31 0.25
AMBUJACEM 0.73 18.76 -0.04 6.12 12.65 0.33 0.29
ZEEL 0.77 42.06 0.07 6.86 35.20 0.16 0.42
ITC 0.77 19.50 0.06 6.93 12.57 0.36 0.42
GAIL 0.78 24.61 0.04 7.08 17.53 0.29 0.40
NTPC 0.78 17.26 0.09 7.08 10.18 0.41 0.45
BHARTIARTL 0.81 19.03 0.44 7.69 11.34 0.40 0.81
HCLTECH 0.82 24.34 -0.09 7.87 16.47 0.32 0.29
WIPRO 0.84 20.80 -0.18 8.18 12.62 0.39 0.21
BPCL 0.85 39.01 -0.46 8.35 30.67 0.21 -0.07
ACC 0.87 27.36 0.00 8.68 18.68 0.32 0.40
ABB 0.90 31.50 0.50 9.46 22.04 0.30 0.91
TATAMOTORS 0.92 21.92 -0.29 9.73 12.18 0.44 0.13
SIEMENS 0.93 33.99 0.22 9.94 24.05 0.29 0.64
MARUTI 0.94 27.45 -0.10 10.30 17.15 0.38 0.34
GRASIM 0.95 22.57 0.07 10.43 12.14 0.46 0.50
NATIONALUM 0.95 45.67 0.35 10.56 35.11 0.23 0.79
RELIANCE 0.96 21.04 0.45 10.79 10.25 0.51 0.90
M&M 0.99 26.25 0.05 11.40 14.84 0.43 0.51
ONGC 1.00 24.42 -0.18 11.49 12.93 0.47 0.27
46
HDFC 1.06 30.18 0.21 13.09 17.09 0.43 0.70
PNB 1.15 30.07 -0.35 15.32 14.75 0.51 0.18
TATAPOWER 1.15 32.16 0.28 15.35 16.82 0.48 0.81
HDFCBANK 1.16 26.93 -0.08 15.63 11.30 0.58 0.46
HINDALCO 1.17 37.37 -0.25 15.82 21.55 0.42 0.29
TATASTEEL 1.18 36.59 0.12 16.04 20.55 0.44 0.66
ICICIBANK 1.27 34.87 -0.13 18.71 16.15 0.54 0.46
TATACOMM 1.32 48.51 -0.11 20.28 28.23 0.42 0.50
LT 1.33 33.74 0.42 20.40 13.34 0.60 1.03
SAIL 1.34 45.84 0.31 20.81 25.03 0.45 0.93
BHEL 1.37 38.86 0.32 21.65 17.21 0.56 0.95
UNITECH 1.40 129.13 2.44 22.82 106.31 0.18 3.09
RELINFRA 1.41 47.64 -0.22 23.14 24.49 0.49 0.43
SBIN 1.41 47.64 -0.22 23.14 24.49 0.49 0.43
STER 1.51 58.05 0.71 26.27 31.78 0.45 1.40
The table explains the weekly expected return on the stocks. Whereas R2 is explaining the
coefficient of determination i.e. the proportion of stocks returns that came from the index value.
11.1 Correlation Analysis
47
Correlation Analysis of Beta and Expected Return:
11.1.1 Table of Correlation between Beta and Expected Return
Correlations
Table 3
Beta Expected Return
Beta Pearson Correlation 1 .499(**)
Sig. (2-tailed) .001
N 42 42
Expected Return Pearson Correlation .499(**) 1
Sig. (2-tailed) .001
N 42 42
** Correlation is significant at the 0.01 level (2-tailed).
Interpretation: The correlation between the Beta and Expected return is 0.499 which signifies
the high level of correlation between the two and there exist a linear relation between the two as
its significance level is 0.001 which is very high. The standard error term should be less than
0.05 but our standard is very low i.e. 0.001 which shows that there is very less chance of the
error in the calculation of the correlation of the Beta and return from the stocks. The correlation
value varies between -1 to +1 and our analysis is showing that the relation between. Although
the Correlation is not that high but still it shows a good correlation between the two. Beta is the
slope of Systematic risk. The correlation is showing that with the increase in the slope of
Systematic Risk, the shareholders are getting moderate level of return. The proposition of
CAPM says that with the increase in the slope of Beta value, the expected return should also be
higher.
11.1..2 Correlation Analysis of Total Market Risk and Expected Return:
48
Table of Correlation between Total Market Risk and Expected Return
Table 4
Correlations
1 .527**
.000
42 42
.527** 1
.000
42 42
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Expected_Return
Systematic_Risk
Expected_Return
Systematic_Risk
Correlation is significant at the 0.01 level (2-tailed).**.
Interpretation: Pearson Coefficient of Correlation between the Total market Risk and the
Expected Return is showing a significant high level of relation which means, with the increase in
the risk related to stock the Return also increase. This relation shows that shareholder demands
higher return to face higher risk. The proposition of CAPM seems to be right here. High risk
yield high return to the stock. The proposition of CAPM is that if you invest in a risky security
you should get higher return for taking extra risk.
11.2 Regression Analysis
49
Variables Entered/Removedb
Betaa . EnterModel1
VariablesEntered
VariablesRemoved Method
All requested variables entered.a.
Dependent Variable: Expected_Returnb.
Model Summary
.499a .249 .230 .43775Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
Predictors: (Constant), Betaa.
Table 5
Coefficientsa
-.295 .242 -1.216 .231
.881 .242 .499 3.644 .001
(Constant)
Beta
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
Dependent Variable: Expected_Returna.
50
Interpretation: The correlation coefficient r, is the correlation between the observed and
predicted value of the dependent variable. The values of r for models produced but the
regression procedure range from 0 to 1. Larger value of r indicates stronger relationships.
The coefficient of determination, r2, indicates the proportions of variation in the
dependent variable explained by the regression model. The value of r2 ranges from 0 to 1.
The value of r2 0.249 explains that only 24.9% of the dependent variable is explained by
independent variable.
The regression is Y = -0.295 + 0.881X
There is high degree of significance exist between the Expected Return of the stock and
its beta, as the value of standard error is very low i.e. 0.001. This shows that there is high degree
of linear relationship exist between the stock beta and its expected return which signifies that
with the increase in the stock beta, its return also increases that means higher the risk higher the
return of the stock.
Our first objective to find the applicability of the CAPM in Indian Stock Market satisfies
as it shows the relationship between the Risk and Return.
51
Chapter 12
The Effect on Portfolio Return with the Diversification of Risk
In order to obtain the result of our second objective the beta of the stocks has been arranged in
the ascending order. A Stocks which come in the first end of ranking, can be categorized as less
volatile to the market, has been put in the first portfolio. On the other hand stock with highest
value of beta, showing high degree of volatility, is included in the last portfolio. With this, eight
portfolios have been constructed with 40 securities on the basis of beta value. The Excess two
securities has been included in the first and last portfolio that means first and last portfolio
consist of six securities and rest of the portfolio consist of five securities. Beta of the stock
integrates the stock to the market developments. The ups and downswing in the market rate of
return bring less or more proportional change in the return of security depending upon beta
value.
The List of portfolios and its securities are as follows:
Table 6
Portfolio 1
Stock Beta
Variance
Stock
Alpha
Stock
Systematic
Risk
Unsystematic
Risk R2 E(R)
HEROHONDA 0.46 16.50 -0.03 2.45 14.06 0.15 0.18
SUNPHARMA 0.46 16.92 0.40 2.49 14.44 0.15 0.61
CIPLA 0.56 29.35 -0.10 3.64 25.71 0.12 0.16
TCS 0.58 15.64 -0.03 3.86 11.78 0.25 0.24
RANBAXY 0.59 24.72 -0.17 4.06 20.67 0.16 0.11
SATYAMCOMP 0.62 18.05 0.16 4.50 13.55 0.25 0.45
52
Portfolio 2
Stock Beta
Variance
Stock
Alpha
Stock
Systematic
Risk
Unsystematic
Risk R2 E(R)
INFOSYSTCH 0.65 16.46 0.02 4.88 11.58 0.30 0.32
HINDUNILVR 0.72 19.04 -0.08 5.97 13.08 0.31 0.25
AMBUJACEM 0.73 18.76 -0.04 6.12 12.65 0.33 0.29
ZEEL 0.77 42.06 0.07 6.86 35.20 0.16 0.42
ITC 0.77 19.50 0.06 6.93 12.57 0.36 0.42
Portfolio 3
Stock Beta
Variance
Stock
Alpha
Stock
Systematic
Risk
Unsystematic
Risk R2 E(R)
GAIL 0.78 24.61 0.04 7.08 17.53 0.29 0.40
NTPC 0.78 17.26 0.09 7.08 10.18 0.41 0.45
BHARTIARTL 0.81 19.03 0.44 7.69 11.34 0.40 0.81
HCLTECH 0.82 24.34 -0.09 7.87 16.47 0.32 0.29
WIPRO 0.84 20.80 -0.18 8.18 12.62 0.39 0.21
Portfolio 4
Stock Beta
Variance
Stock
Alpha
Stock
Systematic
Risk
Unsystematic
Risk R2 E(R)
BPCL 0.85 39.01 -0.46 8.35 30.67 0.21 -0.07
ACC 0.87 27.36 0.00 8.68 18.68 0.32 0.40
ABB 0.90 31.50 0.50 9.46 22.04 0.30 0.91
TATAMOTORS 0.92 21.92 -0.29 9.73 12.18 0.44 0.13
SIEMENS 0.93 33.99 0.22 9.94 24.05 0.29 0.64
53
Portfolio 5
Stock Beta
Variance
Stock
Alpha
Stock
Systematic
Risk
Unsystematic
Risk R2 E(R)
MARUTI 0.94 27.45 -0.10 10.30 17.15 0.38 0.34
GRASIM 0.95 22.57 0.07 10.43 12.14 0.46 0.50
NATIONALUM 0.95 45.67 0.35 10.56 35.11 0.23 0.79
RELIANCE 0.96 21.04 0.45 10.79 10.25 0.51 0.90
M&M 0.99 26.25 0.05 11.40 14.84 0.43 0.51
Portfolio 6
Stock Beta
Variance
Stock
Alpha
Stock
Systematic
Risk
Unsystematic
Risk R2 E(R)
ONGC 1.00 24.42 -0.18 11.49 12.93 0.47 0.27
HDFC 1.06 30.18 0.21 13.09 17.09 0.43 0.70
PNB 1.15 30.07 -0.35 15.32 14.75 0.51 0.18
TATAPOWER 1.15 32.16 0.28 15.35 16.82 0.48 0.81
HDFCBANK 1.16 26.93 -0.08 15.63 11.30 0.58 0.46
Portfolio 7
Stock Beta
Variance
Stock
Alpha
Stock
Systematic
Risk
Unsystematic
Risk R2 E(R)
HINDALCO 1.17 37.37 -0.25 15.82 21.55 0.42 0.29
TATASTEEL 1.18 36.59 0.12 16.04 20.55 0.44 0.66
ICICIBANK 1.27 34.87 -0.13 18.71 16.15 0.54 0.46
TATACOMM 1.32 48.51 -0.11 20.28 28.23 0.42 0.50
LT 1.33 33.74 0.42 20.40 13.34 0.60 1.03
54
Portfolio 8
Stock Beta
Variance
Stock
Alpha
Stock
Systematic
Risk
Unsystematic
Risk R2 E(R)
SAIL 1.34 45.84 0.31 20.81 25.03 0.45 0.93
BHEL 1.37 38.86 0.32 21.65 17.21 0.56 0.95
UNITECH 1.40 129.13 2.44 22.82 106.31 0.18 3.09
RELINFRA 1.41 47.64 -0.22 23.14 24.49 0.49 0.43
SBIN 1.41 47.64 -0.22 23.14 24.49 0.49 0.43
STER 1.51 58.05 0.71 26.27 31.78 0.45 1.40
Testing of Portfolio Risk and Return:
Eight portfolios have been constructed in order to test the relation between portfolio risk and
return.
Table 7
Testing of Portfolio Risk and Return
Beta Variance
Stock
Alpha
Stock
Systematic
Risk
Unsystematic
Risk
R2 E( R )
P1 0.55 23.03 0.04 6.33 16.70 0.27 0.29
P2 0.73 25.45 0.00 8.43 17.01 0.33 0.34
P3 0.81 23.00 0.06 9.37 13.63 0.41 0.43
P4 0.89 31.87 -0.01 10.34 21.52 0.32 0.41
P5 0.96 29.04 0.16 11.14 17.90 0.38 0.61
P6 1.10 27.38 -0.02 12.80 14.58 0.47 0.48
P7 1.25 34.49 0.01 14.53 19.96 0.42 0.59
P8 1.41 54.54 0.56 16.32 38.22 0.30 1.21
It can be observed from the table that with the increase in the portfolio beta, the return of
respected portfolio is also increasing. As first portfolio has beta value of 0.55 its expected return
55
is 0.29 and portfolio eight whose beta value is high among all portfolios is also giving high
return to the investors.
12.1 Correlation Analysis
12.1.1 Correlation between Portfolio Beta and Portfolio Return:
It can be said from the table that correlation coefficient between portfolios’ beta and portfolio
expected return, and between portfolios’ market risk and portfolio return, is very which are
supposed to be positive according to CAPM.
Correlations
1 .841**
.009
8 8
.841** 1
.009
8 8
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
P_Beta
P_Expected_Return
P_BetaP_Expected_
Return
Correlation is significant at the 0.01 level (2-tailed).**.
Table 8
Interpretation: The Pearson Correlation Coefficient is the correlation between Portfolio Return
and Portfolio Beta. The values of Correlation range from 0 to 1. Larger value of correlation
indicates stronger relationships. Here we can see that there exist stronger relation between the
Portfolio Beta and Portfolio Return. The value of correlation is very high i.e. 0.841 and the
significance level is also very high. The significance value should be low and should be less than
0.05. Here the value of significance is 0.009 that is very high and which is showing a very high
degree of relation between the Portfolio Beta and Portfolio Return.
The correlation between the two showing the applicability of the Capital Asset Pricing
Model applies Indian Stock Market. It shows that with the increase in the Systematic Risk attach
to a certain security, the investors demands higher return.
56
12.1.2 Correlation between Portfolio Return and Portfolio Systematic Risk:
The Systematic Risk is the market risk which we cannot control and is affected by the market factor.
Correlations
1 .837**
.010
8 8
.837** 1
.010
8 8
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
P_Expected_Return
Systematic_Risk
P_Expected_Return
Systematic_Risk
Correlation is significant at the 0.01 level (2-tailed).**.
Table 9
Interpretation: The Pearson Correlation Coefficient between Portfolio Systematic and
Portfolio Return shows the relation between these two. The values of Correlation range from 0 to
1. Larger value of Correlation indicates stronger relationships if the correlation between two is
negative, it shows that if the one variable is increasing the other variable will decrease and vice
versa.
Here we can see that there is high degree of correlation between portfolio return and
portfolio systematic risk. The value of correlation is 0.837 which is significant also. The value of
Significance is 0.01 which should not be higher than 0.05. The relation shows that with the
increase in the return of the portfolio with beta, the systematic risk is also increasing. The
proposition of Capital Asset Pricing Model is that with the increase in the risk, the return of that
security should also increase. With the relation we find, we can say that this propositions fits to
Indian Stock Market.
We can interpret that the diversification helps in reducing the risk. If we invest in
diversified portfolio, we can increase our return with given level of risk.
57
12.2 Regression Analysis
4.3.1 Regression Analysis of Portfolio Beta and Portfolio Return:
Model Summary
.841a .707 .659 .16978Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
Predictors: (Constant), P_Betaa.
Coefficientsa
-.291 .228 -1.279 .248
.868 .228 .841 3.809 .009
(Constant)
P_Beta
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
Dependent Variable: P_Expected_Returna.
Table 10
Interpretation:
The correlation coefficient r, is the correlation between the observed and predicted value of the
dependent variable. The values of r for models produced but the regression procedure range
from 0 to 1. Larger value of r indicates stronger relationships.
The coefficient of determination, r2, indicates the proportions of variation in the dependent
variable explained by the regression model. The value of r2 ranges from 0 to 1.
The value of r2 0.707 explains that only 70.7% of the dependent variable is explained by
independent variable which is showing that there is high degree of effect of portfolio beta on
portfolio return.
The regression is Y = -0.291 + 0.868X
The significant level is very high between the Expected Return of the stock and its beta,
as the value of standard error is very low i.e. 0.009. This shows that there is high degree of linear
relationship exist between the portfolio beta and its portfolio return which signifies that with the
increase in the portfolio beta, its portfolio return also increases that means higher the risk higher
the return of the portfolio. It also conclude that if we invest in diversified securities then we can
maximize our return with given level of risk
58
Chapter 13
Security Market Line:
When Capital Asset Pricing Model is depicted graphically, it is called Security Market Line. It
shows the relation between the portfolios’ beta and expected return. It also suggests the expected
return that an investor should earn in the market for any level of market sensitivity (Beta). We
can obtain SML by joining the portfolios’ beta to the corresponding portfolios’ expected return.
Figure 1, provides the empirical SML representing various combinations of portfolios return,
and the portfolios’ beta, and is observed to be very close to theoretical SML, asserting the
positive and linear relationship.
Figure 1
59
The security market line (SML) expresses the return an individual investor can expect in terms
of a risk-free rate and the relative risk of a security or portfolio. The SML with respect to
security i can be written as:
E (Ri) = Rf + βi (E (Rm-Rf))
Where βi
σ i Rm/ σ m or Cov (Ri, Rm)/ σ2 m
Equation (3) is a version of the CAPM. The set of assumptions sufficient to derive the CAPM
version of (3) are the following:
(i) The investor’s utility functions are either quadratic or normal,
(ii) All diversifiable risks are eliminated and
(iii) The market portfolio and the risk-free asset dominate the opportunity set of risky assets.
The SML is applicable to portfolios as well. Therefore, SML can be used in portfolio analysis to
test whether securities are fairly priced, or not.
60
Chapter -13
Capital Market Line
To test the closeness to theoretical CML, the empirical capital market line is made hat signifies
the positive and linear relationship between total market risk of the portfolio and portfolio
expected return. Diversification, generally, involves holding more than one stock in the
portfolio, which differs from each other on some common attributes. But for the sale of
convenience, here diversification was carried on the basis of beta value each stock
Figure 2
61
The capital market line (CML) specifies the return an individual investor expects to receive on a
portfolio. This is a linear relationship between risk and return on efficient portfolios that can be
written as:
E (RP) = Rf + σ p (E (Rm)-Rf))/σ m
Where,
RP = portfolio return
Rf = risk-free return
Rm = market portfolio return,
σ p = standard deviation of portfolio returns, and
σm = standard deviation of market portfolio returns.
The CML is valid only for efficient portfolios and expresses investors’ behavior regarding the
market portfolio and their own investment portfolios.
62
Chapter-15
Problems with the CAPM
Subsequent studies, however, provided weak empirical evidence on these relationships. Issue in
the CAPM is whether investors face only one risk arising from uncertainty about the future
values of assets. In all likelihood, investors face many sources of risk, as shown by Merton’s
(1973) inter-temporal asset pricing model. As we have discussed capital asset pricing model was
developed 40 years ago by Sharpe (1964) and Lintner (1965) and was the first apparently
successful attempt to show how to assess the risk of the cash flow from a potential investment
project and to estimate the project’s cost of capital, the expected rate of return that investors will
demand if they are to invest in the project. In a major development (1992), tests by Fama and
French, said, in effect, that the CAPM is useless for precisely what it was developed to do. Since
then, researchers have been scrambling to figure out just what’s going on. What’s wrong with
the CAPM?
Are the Fama and French results being interpreted too broadly?
Must the CAPM be abandoned and a new model developed?
Can the CAPM be modified in some way to make it still a useful tool?
The mixed empirical findings on the return-beta relationship prompted a number of responses:
(i) The single-factor CAPM is rejected when the portfolio used as a market proxy is inefficient.
For example, Roll (1977) and Ross (1977). Even very small deviations from efficiency can
produce an insignificant relationship between risk and expected returns (Roll and Ross, 1994;
Kandel and Stambaugh, 1995).
(ii) Kothari, Shanken and Sloan (1995) highlighted the survivorship bias in the data used to test
the validity of the asset pricing model specifications.
Fama concluded after his studies in (1992) “beta as a sole valuable in explaining return on stock
is dead”. Though the three-factor models have better empirical explanatory power than the
original CAPM to explain cross sectional returns the economic reason for why size and BV/MV
63
to be priced is not known. In their later articles, Fama and French, The CAPM is Wanted, Dead
or Alive (1996) give reasoning that the small stocks with high BV/MV ratio are firms that have
performed poorly and are vulnerable to financial distress and hence command a premium, which
they call as 'distress premium'.
Banz (1981) tested CAPM by checking whether the size of the firms involved can explain the
residual variation in average returns across assets that are not explained by the CAPM’s beta.
Banz challenges the CAPM by showing that size does explain the cross-sectional variation in
average returns on a particular collection of assets better than beta. He found that during the
1936–75 period, the average return to stocks of small firms (those with low values of market
equity) was substantially higher than the average return to stocks of large firms after adjusting
for risk using the CAPM. This observation becomes known as the size effect.
Challenge
The CAPM was quite successful until 1981. In 1981, however, empirical studies suggested that
it might be missing something. A decade later, in 1992 another study suggested that it might be
missing everything, and the debate about the CAPM’s value is on.
64
Chapter 16
Findings and Recommendations
Findings
1. A positive relationship exists between portfolios’ beta and portfolios’ return, i.e. the
coefficient of correlation between the two is statistically significant. Study shows that as
the value of beta attached to the respected security keeps on increasing, its return
expectation among the investors also increases. Thus it proves that the higher beta gives
higher return.
2. The results of the study found that Capital Asset Pricing Model does applicable to Indian
Stock Market so all the assumptions that Capital Asset Pricing Model takes apply to
Indian Market.
3. The study found that the investors are Risk averse individuals who maximize the expected
utility of their end of period wealth.
4. The investors have homogenous expectations about asset returns.
5. The non-market risk of the portfolio will go on declining as portfolio is diversified.
6. The study also proves that in Indian Capital Market, as the systematic risk attached to a
security increase the return also increases so there is statistically significant relations exist
between the two.
65
Recommendations
1. The financial engineer should use this study to develop such instruments where the
higher risk is accompanied with the higher returns. This will help the investors to
diversify their risk attached to the security and will lead them to higher return at given
level of risk.
2. For calculating the risk adjusted rate CAPM is advisable.
3. The study has been carefully conducted under certain assumptions and between the
periods July 2005 to June 2008, and should not be blindly applied.
66
Chapter -17
Conclusion
The study aims to find the relation between risk and reward. The study used weekly stocks
return from the 42 companies listed in the National Stock Exchange from July 2005 to June
2008.
The finding of the study is in support of the theory’s basic hypothesis that the higher risk
(beta) is associated with the higher level of return.
The model does explain, however, excess returns. The results obtained lend support to
the linear structure of the CAPM equation being a good explanation of security returns. The
high value of the estimated correlation coefficient between the risk and the slope indicates
that the model used, explains excess returns.
The objective of the study was to find the linear relation between the risk and the return
on the Indian Stock Market and study is very much successful in finding the relation between
these two. The study indicates that as the risk attached to a certain security increases, the
expected return to that security should also be in linear relation to that.
The theory thus applies to Indian Stock market, but it needs to be tested time to time and
its applicability to other stock market in India should also be tested. The investors should not
blindly believe on this model, they should take care of the assumption taken by the Capital
Asset Pricing Model.
67
Chapter-18
Bibliography
Brealey-Meyers(2003), “Principles of Corporate Finance”, The McGraw-Hill Companies, Delhi
pp. 152-203
Francis, Jack Clark and Frank J. Fabozzi, (1979),“The Effects of Changing Macroeconomic
Conditions on the Parameters of the Single Index Market Model”, Journal of Financial and
Quantitative Analysis, June, Vol. 14, No.2, pp. 351-360.
Jaffe, Jeffrey F., Randolph Westerfield and MA Christopher, 1989,“A Twist on the Monday
Effect in Stock Prices: Evidence from the U.S. and Foreign Stock Markets”, Journal of Banking
and Finance, September, Vol. /3, No.4/5, pp. 641-50.
Klemkosky R.C. and Martin J.D. (1975),“The Effect of Market Risk on the Portfolio
Diversification”, the Journal of Finance, March 1975
Linter J (1965), “Security Prices, Risk and Maximum Gains from the Diversification”, Journal
of Finance, December 1965
Manjunatha T. and Mallikarjunappa T. (2007),“Capital Asset Pricing Model: Beta and Size
Tests”, AIMS International, January 2007.
Markowitz H (1952), “Portfolio Selection”, the Journal of Finance, March 1952
Michailidis G, Tsopoglou S, Papanastasiou D and Mariola E (2006), “Testing the Capital Asset
Pricing Model (CAPM): The Case of the Emerging Greek Securities Market”, International
Research Journal of Finance and Economics, Issue 4, 2006
68
Obaidulllah, M., 1994, “Indian Stock Market: Theories and Evidence”, Hyderabad: ICFAI.
Palaha, Satinder, 1991, Cost of Capital and Corporate Policy, Anmol Publications.
Roll, Richard, 1981,”A Possible Explanation of the Small Firm Effect”, Journal of Finance,
September, Vol.36, No.4, pp. 879-88.
Vaidyanathan R, (1995), “Capital Asset Pricing Model: The Indian Context”, The ICFAI
Journal of APPLIED FINANCE, July 1995
Zikmund.(2003). Business Research Methods, Akash Press, Delhi, pp. 102-105.
69
Chapter-19
Annexure
List of 42 Companies included in NIFTY as on 30th June, 2008
HERO HONDA LTD. SIEMENS
SUN PHARMACEUTICAL LTD. MARUTI UDYOG LTD.
CIPLA GRASIM INDUSTRIES
TATA CONSULATNCY SERVICES NATIONAL ALUMINIUM COMPANY
RANBAXY RELIANCE INDUSTRIES
SATYAM COMPUTER SERVICES MAHINDRA AND MAHINDRA
INFOSYS TECHNOLOGIES ONGC
HINDUSTAN UNILEVER LTD HOUSING DEVELOPMENT FINANCE CORPORATION
AMBUJA CEMENT PUNJAB AND NATIONAL LTD.
ZEE LTD. TATA POWER LTD.
ITC LTD. HDFC BANK LTD.
GAIL HINDALCO INDUCTRIES
NTPC TATA STEEL LTD.
BHARTI AIRTEL ICICI BANK LTD.
HCL TECHNOLOGIES TATA COMMUNICATIONS
WIPRO LARSEN AND TURBO
BHART PETROLEUM CORPORATION LTD STEEL AUTHORITY OF INDIA LTD
ACC BHART HEAVY ELECTRICALS LTD.
ABB UNITECH
TATA MOTORS LTD. RELIANCE INFRASTRUCTURE LTD.
STERLITE INDUSTRIES LTD STATE BANK OF INDIA
70