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CHAPTER 7: PORTFOLIO ANALYSIS
This chapter deals with the risks and returns on investments in securities.
Portfolio Management activities include:
Selection of securities for investment;
Construction of possible portfolios;
Deciding the weights / proportions of different securities in the
portfolio and arriving at an Optimal Portfolio for the concerned
investor.
The main objective of a rational investor is to identify the Efficient Portfolios
out of the different Feasible Portfolios and to zero in on the Optimal Portfolio
suiting his risk appetite. An Efficient Portfolio has the highest return
among all Feasible Portfolios having identical Risk and has the
lowest Risk among all Feasible Portfolios having identical Return.
The other Objectives of Portfolio management are:
a. Security/Safety of Principal;
b. Stability of Income;
c. Capital Appreciation;
d. Marketability & Liquidity;
e. Minimisation of risk;
f. Diversification;
g. Suitable tax considerations.
All investments are to be looked in the above areas before taking a call on
investment or continuing with the amount invested.
Investment management is a complex task, and requires special knowledge
and skills to deal with the identification and form of Portfolio.
Phases of portfolio Management: The various phases are:
a. Security Analysis: Securities are analysed under Fundamental
Analysis (EPS of the Co., Dividend Payout ratio, Competition faced by
the company, market share etc.) & Technical Analysis (Trends in share
price movements etc.) As per Efficient Market Hypothesis, share price
movements are random and not systematic. Consequently, neither
fundamental analysis nor technical analysis is of value or of use in
generating trading gains on a sustained basis.
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b. Portfolio analysis: After identifying the securities in which
investments are to be made, next comes the formation of Portfolio.
Portfolio is a combination of securities with different proportions of
investments. Different feasible portfolios are constructed and the
return and risk of each portfolio is ascertained. As per the risk
appetite of the investor, and his preferences, appropriate portfolio is
identified for investment.
c. Portfolio Revision: Economy and financial markets are dynamic in
nature, changes take place in these variables almost on a daily basis
and securities which were once attractive may cease to be so and vice
versa with the passage of time. Having made investments as per the
risk appetite of investors, the portfolio is watched continuously and
suitable changes to it are made as per changing market conditions and
risk appetite of the investor.
d. Portfolio Evaluation: Performance of the portfolio over a selected
period of time in terms of return and risk is ascertained. It involves
quantitative measurement of actual return realized and the risk borne
by the portfolio over the period of investment. The objective of
constructing a portfolio and revising it periodically is to maintain its
optimal risk return characteristics. Various types of measures of
performance evaluation have been developed for use by investors and
portfolio managers.
Risk Analysis: The risk in an investment is the variation in its returns. This
variation in returns is caused by a number of factors. The factors which
produce variations in the returns from an investment are called the elements
of risk which can be depicted by the following figure:
Total risk = Systematic risk + Unsystematic risk
Elements of Risk
Systematic Risk Unsystematic Risk
Interest Risk Market Risk
Purchasing Power Risk Business Risk Financial Risk Social Risk Default Risk
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Systematic risk refers to the variability of return on stocks or portfolio
associated with changes in return on the market as a whole. Systematic Risk
arises due to external factors that are macro in nature and usually out of
control of the company. It arises due to risk factors that affect the overall
market such as changes in the nations‟ economy, tax reform by the
Government or a change in the world energy situation. These are risks that
affect securities overall and, consequently, cannot be diversified away. This
is the risk which is common to an entire class of assets or liabilities. The
value of investments may decline over a given time period simply because of
economic changes or other events that impact large portions of the market.
Asset diversification can protect against systematic risk because different
portions of the market tend to underperform at different times. This is also
called market risk.
Systematic risk is further classified into:
a. Interest Rate Risk: The change in the interest rate has a bearing on
the welfare of the investors. As the interest rate goes up, the market
price of existing fixed income securities falls and vice versa. This is
because the buyer of a fixed income security would not buy it at its
par value or face value if its fixed interest rate is lower than the
prevailing interest rate on a similar security.
b. Social or Regulatory Risk: The social or regulatory risk arises, where
an otherwise profitable investment is impaired as a result of adverse
legislation, harsh regulatory climate, or in extreme instance
nationalization by a socialistic government. Eg. Latest Land acquisition
Act.
c. Market risk: At times prices of securities, equity shares in particular,
tend to fluctuate. Major cause appears to be the changing psychology
of the investors. The irrationality in the security markets may cause
losses unrelated to the basic risks. These losses are the result of
changes in the general tenor of the market and are called market
risks.
d. Purchasing Power Risk: Inflation or rise in prices lead to rise in
costs of production, lower margins, wage rises and profit squeezing
etc. The return expected by investors will change due to change in real
value of returns.
Unsystematic risk refers to risk unique to a particular company or
industry. This arises due to factors within the company and usually micro in
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nature and is controllable to a great extent. This is the risk of price change
due to the unique circumstances of a specific security as opposed to the
overall market. This risk can be virtually eliminated from a portfolio through
diversification.
Unsystematic risk is further classified into:
a. Business Risk: As a holder of corporate securities (equity shares or
debentures) one is exposed to the risk of poor business performance.
This may be caused by a variety of factors like heightened
competition, emergence of new technologies (SLR cameras to digital
cameras), development of substitute products, shifts in consumer
preferences, inadequate supply of essential inputs, changes in
governmental policies and so on. Often of course, the principal factor
may be inept and incompetent management.
b. Default Risk: Default risk refers to the risk arising from the fact that
a borrower may not pay interest and / or principal on time. Except in
the case of highly risky debt instrument, investors seem to be more
concerned with the perceived risk of default rather than the actual
occurrence of default. Even though the actual default may be highly
unlikely, they believe that a change in the perceived default risk of a
bond would have an immediate impact on its market price.
c. Financial Risk: This relates to the method of financing, adopted by
the company, high leverage leading to larger debt servicing problem or
short term liquidity problems due to bad debts, delayed receivables
and fall in current assets or rise in current liabilities.
Diversion of Risk: Each Security has two types of risks. Viz. Systematic
Risk and Unsystematic Risk. Unsystematic risk can be minimised by
increasing the size of the portfolio (say around 25 scrips.)
The following graph shows the relationship between the number of scrips
and the risk of portfolio. As the number of scrips increases, unsystematic
risk reduces (and thus total risk as well) and eventually gets minimised and
we will be left with only systematic risk of the portfolio.
Risk is usually measured by calculating Variance or Standard Deviation of
the returns of security / portfolio. Variance and standard deviation indicate
the extent of variability of possible returns from the expected return.
Variance (Sd2) = [ &#-667558785;&#-667558774;−&#-667558785; &#-667557936;∗��&#-667558769;&#-667558774;=&#-667557937;(&#-667558785;&#-667558774;)] Where,
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Xi = Possible returns on security i ; X = Expected Value of security /
Portfolio;
P(Xi) = Probability.
Standard Deviation is the Square Root of Variance.
Variance and Standard Deviation indicate the total risk associated with
security, i.e. Systematic risk + Unsystematic risk.
A rational risk-averse investor views the variance (or standard deviation) of
her portfolio‟s return as the proper risk of her portfolio. If the investor holds
only one security (or very few securities), the variance of that security‟s
return becomes the variance of the portfolio‟s return. Hence, the variance of
the security‟s return is the security‟s proper measure of risk.
An investor with diversified portfolio measures the beta of the security as a
proper measure of risk for the security since for him unsystematic risk is
minimised because of diversification. An investor who is evaluating the
systematic element of risk, that is, extent of deviation of returns vis a vis
the market, therefore considers beta as a proper measure of risk.
When risk is separated into systematic and unsystematic parts, the market
generally does not reward for diversifiable risk (unsystematic risk) since the
investor himself is expected to diversify the risk. However, if the investor
does not diversify he cannot be considered to be an efficient investor. The
market, therefore, rewards an investor only for the non-diversifiable
(systematic) risk. Hence, the investor needs to know how much non-
diversifiable risk he is taking. Non diversifiable risk is measured in terms of
beta.
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Further, an investor with varied diversified portfolio also considers variance
and standard deviation of the security as measure of the risk for the security
so far it impacts the variance and standard deviation of the portfolio. He will
not be per se interested in the variance or standard deviation of each
security, rather he is interested in their impact on the total portfolio.
Unsystematic risk is internal risk and is associated with the company. This
can be minimised by having another security in the portfolio with opposite
correlation and this process is known as diversification. A portfolio with
around 25 securities in it will have minimum unsystematic risk due to
diversification.
Measurement of Systematic Risk: Systematic risk relates to external
environment and is uncontrollable. Different Securities returns are affected
by different degrees due to changes in economy like inflation, interest rate,
etc. The average effect of a change in the economy can be represented by
the change in the stock market index. The systematic risk of a security can
be measured by relating that security‟s variability vis-à-vis variability in the
stock market index. A higher variability would indicate higher systematic risk
and vice versa.
The systematic risk of a security is measured by a statistical measure called
Beta. Input data required for the calculation of beta of any security are the
historical data of returns of the individual security and corresponding return
of a representative market return (stock market index). There are two
statistical methods i.e. correlation method and the regression method,
which can be used for the calculation of Beta.
Correlation Method: Formula used for calculation of Beta is:
&#-667558089;= &#-667558806;&#-667558768;&#-667558761;.&#-667558774;&#-667558770;
&#-667558764;��&#-667557936;&#-667558770; = &#-667558765;&#-667558774;&#-667558770;&#-667558764;��&#-667558774;&#-667558764;��&#-667558770;
&#-667558790;��&#-667557936;&#-667558770; = &#-667558765;&#-667558774;&#-667558770;&#-667558764;��&#-667558774;
&#-667558790;��&#-667558770; = &#-667558765;&#-667558767;&#-667558770;&#-667558764;��&#-667558767;
&#-667558790;��&#-667558770; Where,
rim = coefficient of correlation between scrip i and the market index m;
rpm = coefficient of correlation between portfolio p and the market index m
sdi = standard deviation of returns of stock i;
sdm = standard deviation of returns of market index,
sd2m = the variance of market returns; and
sdp = standard deviation of returns of portfolio.
Regression method: The general form of regression equation is:
&#-667558090;=&#-667558784;− &#-667558089;&#-667558785; Where,
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X = independent variable (market);
Y = dependent variable (security), and
&#-667558090;, &#-667558089; are constants.
Alpha indicates excess of return over expected return and Beta indicates
return of security vis a vis market return. Alpha indicates absolute figure
whereas Beta indicates relative figure.
Beta is calculated by the formula:
&#-667558089;= &#-667558769; &#-667558785;&#-667558784;−( &#-667558785;) ( &#-667558784;)
&#-667558769; &#-667558785;&#-667557936;− ( &#-667558785;)&#-667557936; where,
n = number of items;
X = Independent variable (market);
Y = Dependent variable (security);
XY = product of dependent and independent variable;
Alternative Formula:
&#-667558089;= &#-667558785;&#-667558784;−&#-667558769; &#-667558785;͞ &#-667558784;͞
&#-667558785;&#-667557936;− &#-667558769; &#-667558785;͞&#-667557936; = &#-667558785;&#-667558784;−( &#-667558785;) &#-667558784;͞
&#-667558785;&#-667557936;− ( &#-667558785;) &#-667558785;͞
X͞ & Y‾ are respective arithmetic means and rest of Notations have same
meaning as in above earlier formula.
To calculate return of individual security, following CAPM formula is used:
Ra = &#-667558090;+ &#-667558089;&#-667558791;&#-667558770; where,
Ra = Return of individual security,
Rm = Return on market index or Risk Premium
&#-667558148; = Return of the security when market is stationary
&#-667558089; = Change in return of individual security for unit change in return of
market index.
Significance of Beta: Beta measures the volatility of a security‟s returns
relative to the market, the larger the beta, the more volatile the security. A
beta of 1.0 indicates a security of average risk. A stock with beta greater
than 1.0 has above average risk i.e. its returns would be more volatile than
the market returns. For example, when market returns move up by 6%, a
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stock with beta of 2 would find its returns moving up by 12% (i.e. 6% x 2).
Similarly, decline in market returns by 6% would produce a decline of 12%
(i.e. 6% x 2) in the return of that security.
Positive beta of security: it indicates that return on security is dependent
on market return and will be in the same direction as that of market;
Negative beta of security: it indicates that return on security is dependent
on market return and will be in the opposite direction as that of market;
Zero beta: it indicates return on security is independent of market return.
Portfolio Beta: Systematic risk can be measured by using Beta (β). The
beta for the market is equal to 1.0. Beta explains the systematic relationship
between the return on a security and the return on the market by using a
simple linear regression equation. The return on a security is taken as a
dependent variable and the return on market is taken as independent
variable then,
Ri = Rf + β (Rm – Rf) where,
Ri = Return on security;
Rf = Risk free return on security;
Rm = Return on market
Β = Responsive of security returns to market returns.
The beta parameter (β) in the above equation represents the slope of the
above regression relationship. The portfolio beta is merely the weighted
average of the betas of individual securities included in the portfolio.
Portfolio beta, β = ∑ proportion of security × beta for security.
Beta is calculated from historical data on the presumption that future will
replicate history which may not always be correct.
Portfolio Analysis: Expected return of a portfolio is the sum of the
weighted average return of individual securities comprising the portfolio.
The weights to be applied for calculation of the portfolio return are the
fractions of the portfolio invested in respective securities. Formula is:
rp = ��&#-667558774;&#-667558769;&#-667558774;=&#-667557937;&#-667558765;&#-667558774; where
rp = expected return of portfolio;
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xi = proportion of funds invested in each security;
ri = expected return on securities; and
n = number of securities.
Covariance (a statistical measure) between two securities or two portfolios
or a security and a portfolio indicates how the rates of return for the two
concerned entities behave relative to each other. Covariance is calculated by
the formula;
CovAB = &#-667558791;&#-667558808;−&#-667558791;̅&#-667558808; (&#-667558791;&#-667558807;−&#-667558791;̅&#-667558807;)
�� where
RA = Return on security A;
R̅A = Expected or mean return of Security A;
RB = Return on security B;
R̅B = Expected or mean return of Security B.
Covariance of 2 securities is +ve if the returns consistently move in same
direction.
Covariance of 2 securities is -ve if the returns consistently move in opposite
direction.
Covariance of 2 securities is zero, if their returns are independent of each
other.
Coefficient of correlation is expressed by the formula:
rAB = &#-667558806;&#-667558768;&#-667558761;&#-667558808;&#-667558807;
&#-667558790;��&#-667558808;&#-667558790;��&#-667558807; where
rAB = Coefficient of correlation between A & B;
&#-667558858;����&#-667558860;&#-667558859; = Covariance between securities A & B
����&#-667558860; = Standard deviation of security A.
����&#-667558859; = Standard deviation of security B
Correlation coefficients may range from -1 to 1.
A value of +1 indicates a perfect positive correlation between the two
securities returns
A value of -1 indicates perfect negative correlation between the two
securities returns, and
A value of zero indicates that the returns are independent.
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Further, covariance can be expressed as the product of coefficient of
correlation between the securities and the standard deviation of each of the
securities as shown below:
&#-667558806;&#-667558768;&#-667558761;&#-667558808;&#-667558807; = rAB &#-667558790;��&#-667558808;&#-667558790;��&#-667558807;
Covariance between two securities may also be calculated by multiplying
respective betas and the variance of market.
&#-667558806;&#-667558768;&#-667558761;&#-667558808;&#-667558807;= βA βB sdm2
The Variance of a Portfolio consists of 2 components (unlike the return of
a portfolio where weighted average of individual securities is taken):
a. Aggregate of the weighted variances of the constituent securities and
b. Weighted covariances among different pairs of securities.
Calculation of risk In case of only 2 securities, A & B are there in
portfolio, then Variance of portfolio is given by the formula
Sdp2 = [XA2 SdA2 + XB2 SdB2] +2 [XAXB (rAB &#-667558790;��&#-667558808; &#-667558790;��&#-667558807;)]
Sdp2 = Variance of the portfolio;
XA = Proportion of funds invested in security A;
XB = Proportion of funds invested in security B;
SdA2 = Variance of security A;
SdB2 = Variance of security B;
����&#-667558860; = Standard deviation of security A;
����&#-667558859; = Standard deviation of security B, and
rAB = Correlation coefficient between the returns of A & B securities.
In case of perfect +ve correlation, coefficient of correlation, rAB = 1. So, the
variance of portfolio becomes:
Sdp = XA SdA + XB SdB
In case of perfect -ve correlation, coefficient of correlation, rAB = -1. So, the
variance of portfolio becomes:
Sdp = XA SdA - XB SdB
In case of perfect no correlation, rAB = 0. So, the variance of portfolio
becomes:
Sdp2 = XA2 SdA2 + XB2 SdB2 and
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Sdp = [XA2 SdA2 + XB2 SdB2]1/2
Portfolio Variance can also be calculated by the formula:
Sdp2 = [( &#-667558785;&#-667558774;&#-667558089;&#-667558774;)&#-667558769;&#-667558774;=&#-667557937;&#-667557936;&#-667558790;��&#-667558770;&#-667557936;]+[ &#-667558785;&#-667558774;&#-667557936;&#-667558788;&#-667558790;&#-667558791;&#-667557936;]&#-667558769;&#-667558774;=&#-667557937; Where,
Sdp2 = Variance of portfolio;
Xi = Proportion of the Stock in portfolio;
&#-667558147;&#-667558826; = Beta of the stock i in portfolio;
Sdm2 = Variance of the index;
USR = Unsystematic Risk
First component is weighted average of systematic risk and second
component is weighted average of unsystematic risk and sum of these is
total risk.
Optimum proportion of investment in case of 2 securities: Formula for
Optimum proportion of investment in case of 2 securities i & j is calculated
by the formula:
&#-667558785;&#-667558774;=
&#-667558790;��&#-667558773;&#-667557936;− &#-667558765;&#-667558774;&#-667558773; &#-667558790;��&#-667558774;&#-667558790;��&#-667558773;
&#-667558790;��&#-667558774;&#-667557936;+ &#-667558790;��&#-667558773;&#-667557936;− &#-667557936;&#-667558765;&#-667558774;&#-667558773; &#-667558790;��&#-667558774;&#-667558790;��&#-667558773;
=
&#-667558790;��&#-667558773;&#-667557936;− &#-667558806;&#-667558768;&#-667558761;.&#-667558774;&#-667558773;
&#-667558790;��&#-667558774;&#-667557936;+ &#-667558790;��&#-667558773;&#-667557936;− &#-667557936;&#-667558806;&#-667558768;&#-667558761;.&#-667558774;&#-667558773;
Where, &#-667558785;&#-667558774; is the proportion of investment in security i. Proportion of
investment in security j will be (1 – j).
Reduction or dilution of Portfolio Risk through Diversification: The
process of combining more than one security in to a portfolio is known as
diversification. The main purpose of this diversification is to reduce the total
risk by substantially mitigating the unsystematic risk, without sacrificing
portfolio return. Unsystematic Risk keeps reducing as more and more shares
are added to the portfolio say upto around 25 securities. Beyond this there
will not be any significant change in the unsystematic risk, despite addition
of securities to portfolio. Standard deviation of the portfolio keeps reducing
for the initial addition of around 25 securities. This happens in all cases
except when the shares are +vely correlated.
Portfolio with more than two securities: The total risk of an individual
security comprises two components; the market related risk called
systematic risk and the unique risk of that particular security called
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unsystematic risk. By combining securities into a portfolio the unsystematic
risk specific to different securities is cancelled out. Consequently, the risk of
the portfolio as a whole is reduced as the size of the portfolio increases.
Ultimately when the size of the portfolio reaches a certain limit, it will
contain only the systematic risk of securities included in the portfolio. The
systematic risk, however, cannot be eliminated. Thus, a fairly large portfolio
has only systematic risk and has relatively little unsystematic risk. That is
why there is no gain in adding securities to a portfolio beyond a certain
portfolio size.
Calculation of Risk of Portfolio with more than two securities: The
portfolio variance and standard deviation depend on the proportion of
investment in each security as also the variance and covariance of each
security included in the portfolio. The formula for portfolio variance of a
portfolio with more than two securities is as follows:
Sdp2 = &#-667558785;&#-667558774; &#-667558785;&#-667558773; &#-667558806;&#-667558768;&#-667558761;&#-667558774;&#-667558773;&#-667558769;&#-667558774;=&#-667557937;&#-667558769;&#-667558774;=&#-667557937; = &#-667558785;&#-667558774; &#-667558785;&#-667558773; &#-667558765;&#-667558774;&#-667558773;&#-667558769;&#-667558774;=&#-667557937;&#-667558769;&#-667558774;=&#-667557937;&#-667558790;��&#-667558774; &#-667558790;��&#-667558773; where,
Sdp2 = Variance of Portfolio;
Xi = Proportion of funds invested in security i (the first of a pair of
securities).
Xj = Proportion of funds invested in security j (the second of a pair of
securities).
Covij = The Covariance between the pair of securities i and j;
��&#-667558826;&#-667558825; = Correlation Coefficient between securities i and j;
����&#-667558826; = Stabdard deviation of Security i;
����&#-667558825; = Stabdard deviation of Security j;
n = Total number of securities in the portfolio.
From a given set of 'n' securities, any number of portfolios can be created.
These portfolios may comprise of two securities, three securities, all the way
up to 'n' securities. A portfolio may contain the same securities as another
portfolio but with different weights. A new portfolio can be created either by
changing the securities in the portfolio or by changing the proportion of
investment in the existing securities.
Portfolio Analysis is Determination of expected return and risk (variance
or standard deviation) of each portfolio that can be used to create a set of
selected securities for portfolio management.
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Markowitz Model: This model is used to choose a particular portfolio
among alternative portfolios. Following are the assumptions:
a. The return on an investment summarises the outcome of the
investment.
b. The investors can visualise a probability distribution of rates of return.
c. The investors' risk estimates are proportional to the variance of return
they perceive for a security or portfolio.
d. Investors base their investment decisions on two criteria i.e. expected
return and variance of return.
e. All investors are risk averse. For a given expected return he prefers to
take minimum risk, for a given level of risk the investor prefers to get
maximum expected return.
f. Investors are assumed to be rational in so far as they would prefer
greater returns to lesser ones given equal or smaller risk and are risk
averse.
g. Return could be any suitable measure of monetary inflows like NPV but
yield has been the most commonly used measure of return, so that
where the standard deviation of returns is referred to it is meant the
standard deviation of yield about its expected value.
Markowitz has developed the concept of Efficient Frontier based on risk
return relationship. He says that a portfolio is not efficient if there exists
another portfolio with:
a. A higher expected value of return and a lower standard deviation
(risk).
b. A higher expected value of return and the same standard deviation
(risk)
c. The same expected value but a lower standard deviation (risk)
He says that if the portfolio of an investor is not efficient, then the investor
will:
a. Increase the expected value of return without increasing the risk.
b. Decrease the risk without decreasing the expected value of return, or
c. Obtain some combination of increase of expected return and decrease
risk.
He does this by switching his investment over the efficient frontier.
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He says that all investments are to be plotted on a risk return graph and
Efficient Frontier is to be marked containing all efficient portfolios. the
shaded portion represents all feasible solutions. An efficient portfolio has the
highest return among all portfolios with identical risk and the lowest risk
among all portfolios with identical return. In the above diagram, P Y R W
are on efficient frontier.
Lines c1, c2, and c3 are indifference curves for different customers with
regard to risks and associated returns of different portfolios. The investor
has to select a portfolio from the set of efficient portfolios lying on the
efficient frontier. This will depend upon his risk-return appetite. As different
investors have different preferences, the optimal portfolio of securities will
vary from one investor to another. Optimal portfolio to an investor will be
the point where the indifference curve meets the efficient frontier. For c3
customer, optimal portfolio will be at point R. At Point w, returns and risk
are at peak. Since this is not customer preference line, it is ignored.
Capital Asset Pricing Model (CAPM): CAPM provides a conceptual frame
work for evaluating any investment decision where capital is committed with
a goal of producing future returns. The Capital Asset Pricing Model was
developed by Sharpe, Mossin and Linter in 1960. The model explains the
relationship between the expected return, non diversifiable risk and the
valuation of securities. It considers the required rate of return of a security
on the basis of its contribution to the total risk. It is based on the premises
that the diversifiable risk of a security is eliminated when more and more
securities are added to the portfolio. However, the systematic risk cannot be
diversified and is related with that of the market portfolio. All securities do
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not have same level of systematic risk. The systematic risk can be measured
by beta. ß under CAPM, the expected return from a security can be
expressed as:
Expected return on security = Rf + Beta (Rm – Rf)
The model shows that the expected return of a security consists of the risk-
free rate of interest and the risk premium. The CAPM, when plotted on the
graph paper is known as the Security Market Line (SML). Usually Beta is
plotted on X Axis and required return on Y Axis. Security market line
measures the relation between systematic risk and return. Formula for
Security Line is:
y = &#-667558089;x +&#-667558090;
where, x is independent variable and y dependant variable.
Slope of security line indicates BETA. major implication of CAPM is that not
only every security but all portfolios too must be plotted on SML. This
implies that in an efficient market, all securities expected returns are
commensurate with their riskiness, measured by ß.
CAPM is based on following assumptions:
a. The investor‟s objective is to maximise the utility of terminal wealth;
b. Investors make choices on the basis of risk and return;
c. Investors have identical time horizon;
d. Investors have homogeneous expectations of risk and return;
e. Information is freely and simultaneously available to investors;
f. There is risk-free asset, and investor can borrow and lend unlimited
amounts at the risk-free rate;
g. There are no taxes, transaction costs, restrictions on short rates or
other market imperfections;
h. Total asset quantity is fixed, and all assets are marketable and
divisible.
CAPM Advantages:
Risk Adjusted Return: CAPM provides a basis for estimating the required
return on an investment which has risk in built into it. Hence it can be used
as Risk Adjusted Discount Rate in Capital Budgeting.
No Dividend Company: It is useful in computing the cost of equity of a
company which does not declare dividend.
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CAPM has also some limitations:
a. Reliability of Beta: Statistically reliable Beta might not exist for
shares of many firms. It may not be possible to determine the cost of
equity of all firms using CAPM. All shortcomings that apply to Beta
value apply to CAPM too.
b. Other Risks: It emphasises only systematic risk while unsystematic
risks are also important to share holders who do not possess a
diversified portfolio.
c. Information Available: It is extremely difficult to obtain important
information on risk-free interest rate and expected return on market
portfolio as there are multiple risk-free rates for one while for another,
markets being volatile it varies over time period.
Under Valued and Over Valued Stocks:
The CAPM model can be used to buy, sell or hold stocks. CAPM provides the
required rate of return on a stock after considering the risk involved in an
investment. Based on current market price one can identify as to what would
be the expected return over a period of time. By comparing the required
return with the expected return the following investment decisions can be
made: If:
On Return Basis:
Expected Return < CAPM Return; Sell, since stock is overvalued.
Expected Return > CAPM Return; Buy, since stock is undervalued
Expected Return = CAPM Return; Hold.
On Price Basis:
Actual Market Price < CAPM price, stock is undervalued; so Buy
Actual market Price > CAPM price, stock is overvalued; so, sell.
Actual market Price = CAPM price, stock is correctly valued.;
Point of indifference.
Characteristic Line: Characteristic line represents the relationship
between the returns of two securities or a security and market return over a
period of time. The differences between Security Market Line and
Characteristic Line are as below:
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Sl. # Aspect Security Market Line Characteristic Line
1 Scheme
Represents relationship
between return and risk
measured in terms of
systematic risk of a security
or portfolio.
Represents the relationship
between the returns of two
securities or a security and
market return over a period
of time.
2 Nature of Graph Security Market Line is a
Cross Sectional Graph.
Characteristic Line is a Time
Series Graph.
3 Comparison Beta Vs. Expected Return
are Plotted.
Security Returns Vs. Index
Returns are Plotted.
4 Utility
Used to estimate the
expected return of a security
vis-a-vis its Beta.
Used to estimate Beta and
also to determine how a
security return correlates to
a market index return.
Beta in case of Leverage: The risk of a company changes with change in
the debt equity ratio. A company with no debt funds will be less risky than a
company with debts which has the commitments of interest and principal
repayments. A leveraged company will have the risk of an unleveraged
company and in addition to this it will also have risk related to the leverage.
To ascertain Beta for leveraged companies formula is:
&#-667558089;&#-667558771; = &#-667558089;&#-667558762;&#-667558771; [1 + (1 – T) D / E] = &#-667558089;&#-667558762;&#-667558771; + &#-667558089;&#-667558762;&#-667558771; &#-667557937;−&#-667558789; &#-667558805;/&#-667558804; Where,
&#-667558147;��= Leveraged &#-667558089;
&#-667558147;ul= Unleveraged &#-667558147;
D = Debt; E = Equity, and T = Rate of Tax
Arbitrage Pricing Theory Model: CAPM is single factor model, as against
Arbitrage Pricing Theory Model which uses 4 factors Viz., Inflation and
money supply, Interest Rate, Industrial Production, and personal
consumption. Under this method, expected return on investment is:
E (Ri) = Rf + λ 1βi1 + λ 2 βi2 + λ 3 βi3 + λ 4 βi4 where,
E(Ri) = Expected return on equity;
λ 1, λ 2 , λ 3 , λ 4 are average risk premium (Rm – Rf) for each of the four
factors in the model and βi1 , βi2 , βi3 , βi4 are measures of sensitivity of the
particular security i to each of the four factors.
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Sharpe Index Model: This model assumes that co-movement between
stocks is due to change or movement in the market index. Casual
observation of the stock prices over a period of time reveals that most of the
stock prices move with the market index. As per this model, expected
return on security i, is calculated by the formula;
R i = α i + β i R m + ∈i where,
Ri = expected return on security i
αi = intercept of the straight line or alpha co-efficient
βi = slope of straight line or beta co-efficient
Rm = the rate of return on market index
€i = error term.
Alpha of a stock can be found by the above formula or alternatively by fitting
a straight line with coordinates (x1, y1) and (x2, y2) where x1, x2 and y1, y2
are the expected returns of the market and the security in any 2 periods.
Alpha is the value of intercept on Y Axis. Equation of the line in 2 point form
is given by the formula:
&#-667558862;− &#-667558862;&#-667557937;=
&#-667558862;&#-667557936;− &#-667558862;&#-667557937;
&#-667558863;&#-667557936;− &#-667558863;&#-667557937;
(&#-667558863;− &#-667558863;&#-667557937;)
According to Sharpe, the return of stock can be divided into 2 components:
Return due to market changes (systematic risk)and
Return independent of market changes (unsystematic risk).
Beta indicates the sensitiveness of the stock returns to changes in the
market return.
The Variance of the security has 2 components:
Systematic or market risk, and
Unsystematic or unique risk.
So, the variance explained by the market index (i.e. Beta) is called
systematic risk and the variance not explained by market index is
unsystematic risk.
Total variance (Sdi2) = Systematic risk (ßi2 X Sdm2) + Unsystematic risk
Unsystematic risk will be the balancing figure.
Formula for systematic risk is:
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systematic risk = ßi2 X Variance of market index = ßi2 X Sdm2
Unsystematic risk = Total Variance – systematic risk
i.e. Unsystematic risk = Sdi2 - ßi2 X Sdm2
(Sdm = Standard deviation of Market index; ßi = Beta of security i; Sdi =
Standard deviation of security i)
When USR is given, Portfolio Variance is calculated by the formula:
Sdp2 = [( &#-667558785;&#-667558774;&#-667558089;&#-667558774;)&#-667558769;&#-667558774;=&#-667557937;&#-667557936;&#-667558790;��&#-667558770;&#-667557936;]+[ &#-667558785;&#-667558774;&#-667557936;&#-667558788;&#-667558790;&#-667558791;&#-667557936;]&#-667558769;&#-667558774;=&#-667557937; Where,
Sdp2 = Variance of portfolio;
Xi = Proportion of the Stock in portfolio;
&#-667558147;&#-667558826; = Beta of the stock i in portfolio;
Sdm2 = Variance of the index;
USR = Unsystematic Risk
First component is weighted average of systematic risk and second
component is weighted average of unsystematic risk and sum of these is
total risk.
Coefficient of Determination (r2): Coefficient of determination (r2) gives
the percentage of variation in the security‟s return that is explained by the
variation of the market index return
Systematic and Unsystematic risk can also be found by the formulas:
Systematic risk (β) = variance of security X r2 = Sdi2 X r2
Unsystematic risk = variance of security (1 – r2) = Sdi2 (1 – r2)
r2 = Coefficient of Determination.
Sharpe and Treynor ratios: These two ratios measure the Risk Premium
per unit of Risk for a security or a portfolio of securities and provide the tools
for comparing the performance of diverse securities and portfolios.
Sharpe Ratio = (Ri – Rf)/Sdi and
Treynor Ratio = (Ri – Rf)/ βi Where,
Ri = Expected return on stock i
Rf = Return on a risk less asset
Sdi = Standard Deviation of the rates of return for the ith Security
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βi = Expected change in the rate of return on stock i associated with one
unit change in the market return
Higher the Risk Premium generated by a security or portfolio per unit of risk,
the better and these ratios provide a useful tool for comparing securities and
portfolios with diverse risk return profiles. While the Sharpe Ratio uses the
standard deviation (i.e. total risk) as the measure of risk, the Treynor Ratio
uses the beta (i.e. systematic risk) as the measure of risk.
Sharpe’s Optimal Portfolio: The steps for finding out the stocks to be
included in the optimal portfolio are as below:
a. Find out the “excess return to beta” ratio for each stock under
consideration.
b. Rank them from the highest to the lowest.
c. Calculate Ci for all the stocks/portfolios according to the ranked order
using the following formula:
Ci =
&#-667558894;��&#-667558874;&#-667557936; (&#-667558895;��−&#-667558895;��)����
��&#-667558894;&#-667558895;&#-667557936;
&#-667558873;��=&#-667557937;
&#-667557937;+&#-667558894;��&#-667558874;&#-667557936; ����&#-667557936;
��&#-667558894;&#-667558895;&#-667557936;&#-667558873;��=&#-667557937;
Where,
&#-667558790;��&#-667558770;&#-667557936; = Variance of the index;
Ri = Expected return on stock i
Rf = Return on a risk less asset
βi = Expected change in the rate of return on stock i associated with one
unit change in the market return
USR = Unsystematic Risk i.e., variance of stock movement not related to
index movement.
d. Compute the cut-off point which is the highest value of Ci and is taken
as C*. The stock whose excess-return to risk ratio is above the cut-off
ratio are selected and all whose ratios are below are rejected. The
main reason for this selection is that since securities are ranked from
highest excess return to Beta to lowest, and if particular security
belongs to optimal portfolio all higher ranked securities also belong to
optimal portfolio.
e. Calculate the percent to be invested in each security by using the
following formula:
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% to be invested = &#-667558783;&#-667558774;
&#-667558783;&#-667558774;&#-667558769;&#-667558774;=&#-667557937;
Where,
Zi = &#-667558089;&#-667558774;
&#-667558788;&#-667558790;&#-667558791;&#-667557936;(
&#-667558791;&#-667558774;−&#-667558791;��
&#-667558089;&#-667558774;
− &#-667558806;∗)
Formulation of Portfolio Strategy: There are 2 main strategies of
portfolio, viz.
a. Active Portfolio Strategy and
b. Passive Portfolio Strategy.
Active Portfolio Strategy: Most of the investment professionals follow this
strategy. “Active” fund managers try to identify and invest in stocks of
those companies that they think will produce better returns and beat the
overall market (or Index). Principles involved in this strategy are:
a. Market Timing
b. Sector Rotation
c. Security Selection
d. Use of Specialised Investment Concept
Passive Portfolio Strategy: Passive strategy, is based on the principle that
capital market is fairly efficient with respect to the available information.
Hence they search for superior return. Basically, passive strategy involves
adhering to two guidelines.
a. Create a well diversified portfolio at a predetermined level of risk.
b. Hold the portfolio relatively unchanged over time unless it became
adequately diversified or inconsistent with the investor risk return
preference.
Funds which are passively managed are called index funds.
Portfolio Balancing: Balancing of portfolio comprises of 2 issues. Viz., one
Balancing the value of the portfolio and another Balancing the composition of
the portfolio. Balancing is done by following the below policies:
A. Buy and Hold Policy: This is a Do Nothing policy where shares and
bonds are bought in a predetermined ratio and retained as such.
a. Gives rise to a straight line pay off.
b. Provides a definite downside protection.
c. Performance between Constant mix policy and CPPI policy.
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B. Constant Mix Policy: This is a Do Something policy where shares
and bonds are bought at predetermined ratio and reviewed when
significant changes take place and the portfolio is reset to
predetermined ratio by taking appropriate action.
a. Gives rise to concave pay off drive.
b. Doesn‟t provide much downward protection and tends to do
relatively poor in the up market
c. Tends to do very well in flat but fluctuating market.
C. CPPI Policy: This is Constant Proportion Portfolio Insurance Policy,
where the portfolio is frequently reviewed to ensure the investments in
shares is maintained as per the following formula:
Investment in shares = m * (Portfolio value – Floor Value)
Floor Value is the value which market expects at end of the period of
investment and m is a constant factor.
a. Gives rise to a convex pay off drive.
b. Provides good downside protection and performs well in up
market.
c. Tends to do very poorly in flat but in fluctuating market.
d. As market increases more funds will be diverted to market and
vice versa.
Hedge Funds: Hedge Fund is an aggressively managed portfolio of
investments that uses advanced investment strategies such as leverage,
long, short and derivative positions in both domestic and international
markets with the goal of generating high returns (either in an absolute sense
or over a specified market benchmark). Investments in hedge funds are
illiquid as they often require investors to keep their money in the fund for a
minimum period of at least one year. Hedge funds (unlike mutual funds) are
mostly unregulated because they cater to sophisticated investors.
Features of Hedge Funds:
a. Utilize a variety of financial instruments to reduce risk, enhance
returns
b. Hedge funds vary enormously in terms of investment returns, volatility
and risk. Many, but not all, hedge fund strategies tend to hedge
against downturns in the markets being traded.
c. Hedge funds have the ability to deliver non-market correlated returns.
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d. Many hedge funds have as an objective consistency of returns and
capital preservation rather than magnitude of returns.
e. Hedge funds are managed by experienced investment professionals
who are generally disciplined and diligent.
f. Pension funds, endowments, insurance companies, private banks and
high net worth individuals and families invest in hedge funds.
g. Most hedge fund managers are highly specialized and trade only within
their area of expertise and competitive advantage.
h. Hedge funds benefit by heavily weighting hedge fund managers‟
remuneration towards performance incentives, thus attracting the best
brains in the investment business.
Hedging Strategies:
a. Selling Short
b. Using Arbitrage
c. Trading Options or Derivatives
d. Investing in Anticipation of a Specific Event
e. Investing in Deeply Discounted Securities
f. Many of the strategies used by hedge funds benefit from being non-
correlated to the direction of equity markets.
Styles of Hedge Funds:
a. Aggressive Growth
b. Distressed Securities
c. Emerging Markets
d. Funds of Hedge Funds: : Mix and match hedge funds and other pooled
investment vehicles
e. Income
f. Macro: Participates in all major markets - equities, bonds, currencies
and commodities - though not always at the same time.
g. Market Neutral: Off sets positions.
h. Market Timing
i. Opportunistic
j. Multi Strategy
k. Short Selling
l. Special Situations
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m. Value: Invests in securities perceived to be selling at deep
discounts to their intrinsic or potential worth.
Random Walk Theory: Many investment managers and stock market
analysts believe that stock market prices can never be predicted because
they are not a result of any underlying factors but are mere statistical ups
and downs. This hypothesis is known as Random Walk hypothesis which
states that the behaviour of stock market prices is unpredictable and that
there is no relationship between the present prices of the shares and their
future prices. Proponents of this hypothesis argue that stock market prices
are independent. A British statistician, M. G. Kendell, found that changes in
security prices behave nearly as if they are generated by a suitably designed
roulette wheel for which each outcome is statistically independent of the
past history. The fact that there are peaks and troughs in stock exchange
prices is a mere statistical happening – successive peaks and troughs are
unconnected. In the layman's language it may be said that prices on the
stock exchange behave exactly the way a drunkard would behave while
walking in a blind lane, i.e., up and down, with an unsteady way going in
any direction he likes, bending on the side once and on the other side the
second time etc. Views of supporters of this theory are as below:
a. Prices of shares in stock market can never be predicted.
b. The reason is that the price trends are not the result of any underlying
factors, but that they represent a statistical expression of past data.
c. There may be periodical ups or downs in share prices, but no
connection can be established between two successive peaks (high
price of stocks) and troughs (low price of stocks)
Factors Affecting Investment Decision In Portfolio: Objectives of
investment Decision are varied:
a. Growth oriented or income oriented
b. Duration of investment
c. Risk appetite of investor
d. Whether investment is being made to hedge.
e. To invest in Bonds or Stocks; etc.
Impact of Government Policies on Securities:
a. Licensing Policy
b. Restrictions on commodity and stock trading in exchanges
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c. Changes in FDI and FII rules.
d. Export and import restrictions
e. Restrictions on shareholding in different industry sectors
f. Changes in tax laws and corporate and Securities laws.
Efficient Market Theory: This theory states that at any given time, all
available information is fully reflected in securities' prices. Thus this theory
implies that no investor can consistently outperform the market as every
stock is appropriately priced based on available information. Thus it is
impossible to either purchase undervalued stocks or sell stocks for inflated
prices as stocks are always traded at their fair value on stock exchanges.
Hence the only way to outperform market is through expert stock selection
or market timing and that is the way an investor can possibly obtain higher
returns by purchasing riskier investments.
Several researchers like Kendall, Roberts, Oshorne etc. have conducted
several tests on price behaviour of stocks and all the results indicated that
stock price movements are like the movement of a drunkard in an open
area. No predictions can be made. The reason for this is efficient and
perfect markets due to which any special information of a stock will find its
way into market and accordingly the shares get repriced. Following are the
Reasons for random movement of stock prices:
a. Information is freely and instantaneously available to all market
participants.
b. Price change is only response to new information that is unrelated to
previous information and therefore unpredictable.
c. Keen competition among the market participants ensures that market
will reflect intrinsic values since participants fully impound all available
information.
Misconception about Efficient Market Theory: Efficient Market Theory
signifies that prices impound all available information and so it implies that
market does not possess perfect forecasting abilities.
Although prices tend to fluctuate they cannot reflect fair value. This is
because the future is uncertain and the market springs surprises continually
as fluctuations in prices reflect the surprises.
The random movement of stock prices suggests that stock market is
irrational.
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Inability of institutional portfolio managers to achieve superior investment
performance implies that they lack competence in an efficient market. It is
not possible to achieve superior investment performance since all portfolio
managers do their job well in a competitive setting.
Three forms of Efficient Market Hypothesis: The Efficient Market Theory
lays stress on the speed of information that affects the prices of securities.
As per research studies, it was observed that if information is slowly
incorporated in the price, it provides an opportunity to earn excess profit.
However, once the information is incorporated then investor cannot earn this
excess profit. There are 3 levels of market efficiency:
a. Weak form efficiency: Prices reflect all information found in the
record of past prices and volumes.
b. Semi – Strong efficiency: Prices reflect not only all information
found in the records of past prices and volumes but also all other
publicly available information.
c. Strong form efficiency: Prices reflect all available information public
as well as private.
Proof of weak form of efficiency: According to the Weak form Efficient
Market Theory current price of a stock reflects all information found in the
record of past prices and volumes. This means that there is relationship
between the past and future price movements. This is affirmed through 3
tests:
a. Serial Correlation Test: In this test, price changes in one period are
correlated with price changes in another period. Price changes are
considered to be serially independent. Serial correlation studies
employing different stocks, at different time lags and different time
periods have been conducted to detect serial correlation but no
significant serial correlation could be discovered. These studies were
carried on short term trends viz. daily, weekly, fortnightly and monthly
and not in long term trends in stock prices as in such cases, Stock
prices tend to move upwards.
b. Run Test: Given a series of stock price changes each price change is
designated + if it represents an increase and – if it represents a
decrease. The resulting series may be -, +,+ ,+, - , -, - , +, +.
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A run occurs when there is no difference between the sign of two
changes. When the sign of change differs, the run ends and new run
begins.
Price Incr. / Decr. +,+,+,-,-,+,-,+,-,-,+,+,+,-,+,+,+,+
Run 1 2 3 4 5 6 7 8 9
To test a series of price change for independence, the number of runs
in that series is compared with a number of runs in a purely random
series of the same size to determine whether it is statistically different.
The results of these studies strongly support the Random Walk Model.
Calculation: To test efficiency, following procedure is adopted:
First, number of runs r is calculated.
Secondly, N+ & N- are calculated. These are the number of +ve & -
ve signs in the sample.
Thirdly, N is calculated. N = N+ + N- = Total observations – 1
Fourthly, As per Null hypothesis, the number of runs in a sequence of
N elements as random variable whose conditional distribution is given
by observations of N+ and N- is approximately normal with Mean µ
which is calculated as
µ= &#-667557936; ��+��−
��+ &#-667557937;
Fifthly, Standard deviation, �� is calculated by the formula:
��= µ−&#-667557937; (µ−&#-667557936;)
��−&#-667557937;
Sixthly, If the sample size is N, then it will have (N - 1) degrees of
freedom. For this particular degrees of freedom, and the given level of
significance, using the value ‘t’ from t-table, Upper and Lower limits
are found by the formula:
Upper / Lower Limit = µ ± t * ��
Lastly, If the value of r falls within the upper and lower limits, it is
called weak form of efficiency, and if it falls outside the limits, it is
called strong form of efficiency.
c. Filter Test: Under this test, if the price of a stock increases by at
least N% buy and hold it until its price decreases by at least N% from
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a subsequent high. When the price decreases at least N% or more, sell
it. If the behaviour of stock price changes is random, filter rules should
not be applied and in such case a buy and hold strategy is to be
adopted. Studies suggest that filter rules do not outperform a single
buy and hold strategy particularly after considering commission on
transaction.
Proof of Semi Strong Efficiency: According to Semi-strong form efficient
market theory stock prices adjust rapidly to all publicly available
information. By using publicly available information, investors will not be
able to earn above normal rates of return after considering the risk factor.
To test semi-strong form efficient market theory, a number of studies were
conducted to answer the following queries:
Whether it is possible to earn the above normal rate of return after
adjustment for risk, using only publicly available information? and
How rapidly prices adjust to public announcement with regard to
earnings, dividends, mergers, acquisitions, stock splits?
Several studies have been made on the above issues and it is observed that,
the prices of stocks moved up significantly before announcements than after
announcements. The studies have also brought out following observations:
Stock price adjust gradually not rapidly to announcements of
unanticipated changes in quarterly earnings.
Small firms‟ portfolio seemed to outperform large firms‟ portfolio.
Monday‟s return is lower than return for the other days of the week.
Thus it is affirmed that random movement of stock prices holds good.
Proof of Strong Efficiency: According to Strong form efficient market
theory stock prices adjust rapidly to all publicly and privately available
information.
To test this theory, the researchers analysed returns earned by certain
groups viz. Corporate insiders, specialists on stock exchanges, mutual fund
managers who have access to internal information (not publicly available),
or posses greater resource or ability to intensively analyse information in the
public domain. They suggested that corporate insiders (having access to
internal information) and stock exchange specialists (having monopolistic
exposure) earn superior rate of return after adjustment of risk.
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Mutual Fund managers do not on an average earn a superior rate of return.
No scientific evidence has been formulated to indicate that investment
performance of professionally managed portfolios as a group is better than
that of randomly selected portfolios.
This indicates that persons who are privy to certain information earn more
than others who are not privy to such information.
Challenges of Efficient Market Theory: Information is not freely available
and even if available, the authenticity cannot always be vouched. At times
corporates deliberately allow wrong information to get propagated. Other
challenges are:
a. Limited information processing capabilities: Human information
processing capabilities are sharply limited. Every human organism
lives in an environment which generates millions of new bits of
information every second but the bottle necks of the perceptual
apparatus does not admit more than thousand bits per second or
possibly much less.
Further, under conditions of anxiety and uncertainty, with a vast
interacting information grid, the market can become a giant.
b. Irrational Behaviour: It is generally believed that investors‟
rationality will ensure a close correspondence between market prices
and intrinsic values. But in practice this is not true. All sorts of
considerations enter into the market valuation which is in no way
relevant to the prospective yield. This was confirmed by L. C. Gupta
who found that the market evaluation processes work haphazardly
almost like a blind man firing a gun. The market seems to function
largely on hit or miss tactics rather than on the basis of informed
beliefs about the long term prospects of individual enterprises.
c. Monopolistic Influence: A market is regarded as highly competitive.
No single buyer or seller is supposed to have undue influence over
prices. In practice, powerful institutions and big operators wield great
influence over the market. The monopolistic power enjoyed by them
diminishes the competitiveness of the market. Due to monopolistic
powers, prices are rigged for gains.
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Statutory Warning: Investing all Liquid
assets, and / or converting all fixed assets
into liquid assets and investing in Stock
Market will be injurious to your wealth.
Questions:
a. Briefly explain the objectives of “Portfolio Management”.
b. Distinguish between „Systematic risk‟ and „Unsystematic risk‟.
c. Discuss the various kinds of Systematic and Unsystematic risk?
d. What sort of investor normally views the variance (or Standard
Deviation) of an individual security‟s return as the security‟s proper
measure of risk?
e. What sort of investor rationally views the beta of a security as the
security‟s proper measure of risk? In answering the question, explain
the concept of beta.
f. Write short note on Factors affecting investment decisions in portfolio
management.
g. Explain the Efficient Market Theory and what are major misconceptions
about this theory?
h. Explain the different levels or forms of Efficient Market Theory and
what are various empirical evidence for these forms?
i. Explain the three form of Efficient Market Hypothesis.
j. Explain different challenges to Efficient Market Theory.
k. Discuss the Capital Asset Pricing Model (CAPM) and its relevant
assumptions.
l. Discuss the Random Walk Theory.
m. Discuss how the risk associated with securities is affected by
Government policy.
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Correlation: Correlation indicates the strength of relationship between two
variables.
Covariance (a statistical measure) between two securities or two portfolios
or a security and a portfolio indicating how the rates of return for the two
concerned behave relative to each other. Covariance between 2 securities
can be +ve, -ve or zero.
Coefficient of Correlation: Coefficient of Correlation is a statistical
measure which indicates the degree to which changes to the value of a
variable indicates the change in the value of the other variable. In positively
correlated variables, the value of the variable increases or decreases in
tandem with the value of another variable and the change depends on the
degree of coefficient. In negatively correlated variables, the change will be
vice versa.

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