Security Analysis and Portfolio Management Solved Question Paper May 2017
2017 (May)
COMMERCE (Speciality)
Course: 404 (Security Analysis and
Portfolio Management)
Full Marks: 80
Pass Marks: 24 Marks; Time: Three hours
The figures in the margin indicate
full marks for the questions
1. What do
you mean by the following (Answer in one sentence)? 1x8=8
a) Convertible security: A convertible security is a type of security, usually a bond or a preferred stock, that can be converted into a different form of security, normally equity shares.
b) Portfolio:
A portfolio is
a grouping of financial assets such as stocks, bonds, commodities, currencies
and cash equivalents, as well as their fund counterparts, including mutual,
exchange-traded and closed funds. A portfolio can also consist of non-publicly tradable
securities, like real estate, art, and private investments.
c) Full
form of CAPM: Capital Asset Pricing Model
d) Risk
Adjustment: Risk adjustment is a method to offset the cost of investments.
e) Unsystematic
risk: Unsystematic Risk refers to that portion of total risk that is unique or
peculiar to a firm or an industry, above and beyond that affecting securities
markets in general.
f) Diversification:
Risks involved in investment and portfolio management can be reduced through a
technique called diversification. Diversification is a strategy of investing in a variety of
securities in order to lower the risk involved with putting money into few
investments. The traditional belief is that diversification means “Not
putting all eggs in one basket.” Diversification helps in the reduction of
unsystematic risk and promotes the optimization of returns for a given level of
risks in portfolio management.
g) Beta:
Beta attempts to measure an investment's sensitivity to market movements. A
high beta means that an investment is highly volatile and that it will likely
outperform its benchmark in up markets, thus exceeding the benchmark's return,
and underperform it in down markets. A lower beta means an investment is likely
to underperform its benchmark in up markets, but is likely to do better when
the markets fall.
h) Market
timing: Market timing implies assessing correctly the direction of the market,
either bull or bear and positioning the portfolio accordingly.
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2. Write
short notes on the following: 4x4=16
a) Systematic risk
Ans:
Systematic Risk: Systematic Risk refers to that portion of
total variability (risk) in return caused by factors affecting the prices of
all securities. Economic, political, and sociological changes are the main
sources of systematic risk. Though it affects all the securities in the market,
the extent to which it affects a security will vary from one security to
another. Systematic risk cannot be diversified. Systematic risk can be measured
in terms of Beta (β), a statistical measure. The beta for market portfolio is
equal to one by definition. Beta of one (β=1), indicates that volatility of
return on the security is same as the market or index; beta more than one
(β>1) indicates that the security has more unavoidable risk or is more
volatile than market as a whole, and beta less than one (β<1) indicates that
the security has less systematic risk or is less volatile than market.
b) Efficiency frontier
Ans: The
Efficient Frontier
In order to compare investment
options, Markowitz developed a system to describe each investment or each asset
class with math, using unsystematic risk statistics. Then he further
applied that to the portfolios that contain the investment options. He looked
at the expected rate-of-return and the expected volatility for each investment.
He named his risk-reward equation The Efficient Frontier. The graph below is an example of what the Efficient Frontier
equation looks like when plotted.
The relationship securities have with
each other is an important part of the efficient frontier. Some securities'
prices move in the same direction under similar circumstances, while others
move in opposite directions. The more out of sync the securities in the
portfolio are (that is, the lower their covariance), the smaller the risk (standard deviation) of the portfolio that combines
them. The efficient frontier is curved because there is a diminishing marginal
return to risk. Each unit of risk added to a portfolio gains a
smaller and smaller amount of return.
The purpose of The Efficient Frontier
is to maximize returns while minimizing volatility. Portfolios along The
Efficient Frontier should have higher returns than is typical, on average, for
the level of risk the portfolio assumes. Notice that The Efficient Frontier
line starts with lower expected risks and returns, and it moves upward to
higher expected risks and returns. So people with different Investor Profiles
(determined by investment time horizon, tolerance for risk and personal
preferences) can find an appropriate portfolio anywhere along The Efficient
Frontier line. The Efficient Frontier flattens as it goes higher because there
is a limit to the returns investors can expect.
c) Security market line
Ans: Security
market line (SML) is the representation of the Capital asset pricing model. It
displays the expected rate of return of an individual security as a function of
systematic, non-diversifiable risk (its beta). It is also referred to as the
"characteristic line".
The SML essentially graphs the results
from the capital asset pricing model (CAPM) formula. The x-axis represents the
risk (beta), and the y-axis represents the expected return. The market risk
premium is determined from the slope of the SML. The security market line is a
useful tool in determining whether an asset being considered for a portfolio
offers a reasonable expected return for risk. Individual securities are plotted
on the SML graph. If the security's risk versus expected return is plotted
above the SML, it is undervalued because the investor can expect a greater
return for the inherent risk. A security plotted below the SML is overvalued
because the investor would be accepting less return for the amount of risk
assumed.
d)
Portfolio
performance measures
Ans: Portfolio performance measurement can be
defined as a feedback and control mechanism which is used by the portfolio
managers and investment analysts to make the process of portfolio/investment
management more effective. Expert Portfolio managers have to show superior
performance over the market; for that they have to evaluate their performance
in comparison with other portfolio managers. Portfolio manager have an
objective to achieve an optimum risk return adjustment. Whether they are
heading towards this objective or not will be found out only if they evaluate
their portfolios periodically. However, in conducting such an evaluation, a
means for determining the appropriate standard or benchmark must be
established. Two major factors which influence the performance are the rate of
return earned and the associated risk over the relevant period. The return is
defined to include changes in the value of the fund over the performance period
plus any income earned over that period. Risk is the variability surrounding
the return. The manager has to diversify completely into different industries,
assets and instruments so as to reduce the unsystematic risk to the minimum for
a given level of return. The systematic or market related risk has to be
managed by a proper selection of beta for the securities.
Methods of assessing performance
The portfolio performance is evaluated
by measuring and comparing the portfolio return and associated risk and hence
risks adjusted performance. For this purpose there are essentially three major
methods of assessing performance:
a) Return
per unit of risk.
b) Differential
return.
c) Components
of performance.
GROUP-A (New Course)
3. Discuss
the process of valuation of fixed and variable securities. 14
Ans:
Valuation of Fixed Securities: Fixed securities also known as fixed
income securities refers to those investments that provides their owners fixed
rate of income irrespective of market forces. Risks in case of fixed securities
are minimum and returns are also low as compared to common stock. Classic
examples of fixed securities are debentures and bonds.
(A)
BOND OR DEBENTURE VALUATION: Bonds/debentures are instrument of
debt issued by a business house or a government unit against the floating
charge of its assets. The bonds/debentures may be issued at par, premium or
discount. The par value is the amount stated on the face of the
bond/debentures. It states the amount the firm borrows and promises to repay at
the time of maturity. The bonds/debentures carry a fixed rate of interest
payable at fixed intervals of time. The interest is calculated by multiplying
the value of bonds with rate of interest.
Valuation of Bonds/debentures with a Maturing Period
When the
bonds/debentures have a definite maturity period, its valuation is determined
by considering the annual interest payments plus its maturity value. The
following formula can be used to determine the value of a bond:
Valuation
of Bonds/debentures Redeemable in Installments
A company
may issue a bond or debenture to be redeemed periodically. In such a case,
principal amount is repaid partially each period instead of a lump sum at
maturity and hence cash outflows each period include interest and principal.
The amount of interest goes on decreasing each period as it is calculated on
the outstanding amount of bond/debenture. The value of such a bond can be
calculated as below:
Valuation
of Bonds/debentures in Perpetuity
Perpetuity
bonds are the bonds which never mature or have infinitive maturity period.
Value of such bonds is simply the discounted value of infinite streams of
interest (cash) flows.
Valuation
of Variable securities: The term variable securities also
known as variable-income security refers to investments that provide their
owners with a rate of return that is dynamic and determined by market
forces. Variable-income securities provide investors with both greater
risks as well as rewards. Variable-income
securities are typically valued by investors looking for higher returns than
those offered by fixed-income securities. The classic example of a
variable-income security is common stock, which can offer investors virtually
unlimited up-side growth as well as the complete loss of principal.
COMMON
STOCK OR EQUITY SHARE VALUATION
The
valuation of common stock or equity shares is relatively difficult as compared
to the bonds or preferred stock. The cash flows of the latter are certain
because the rate of interest on bonds and the rate of dividend on preference
shares are known. The cash flows expected by investors on common stock are
uncertain. The earnings and dividends on equity shares are expected to grow.
However, we can determine the value of equity shares (1) by developing certain
models based on capitalization of dividend, and (2) Capitalization of earnings.
Dividend capitalization models are the basic valuation models.
The Basic Valuation and Dividend Capitalization Models
The value
of an equity share is a function of cash inflows expected by the investors and
the risk associated with the cash inflows. The investor expects to receive
dividend while holding the shares and the capital gain on sale of shares. The
value of an equity share, in general, is the present value of its future stream
of dividends. Now, let us develop this idea in the form of valuation of models.
(a) One-Period Valuation Model: Suppose an
investor plans to buy an equity share to hold it for one year and then sell.
The value of the share for him will be the present value of expected dividend
at the end of one year plus the present value of the expected sale price at the
end of the year.
(b)
Two-Period Valuation Model
Suppose
now that the investor plans to hold the share for two years and then sell it.
The value of the share to the investor today would be:
(C)
n-Period Valuation Model
Similarly,
if the investor plans to hold the share for n years and then sell, the value of
the share would be:
If the
expected dividend in different periods is (D) constant, we can calculate the
value of the share by using annuity discount factor tables, as given below:-
DIVIDEND
VALUATION MODEL
Dividend
valuation model is the generalized form of common stock valuation. The concept
of this model is that many investors do not contemplate selling their share in
the near future. They want to hold the share for a very long period, say
infinity. In their case, the present value of the share is the capitalized
value of an infinite stream of future dividends.
Some Variations in the Dividend Valuation Model
(a) No growth case: If a firm has future
dividend pattern with on growth or where the dividends remain constant over
time, the value of the share shall be the capitalization of perpetual stream of
constant dividends:
(b) Constant growth case: It the dividends
of a firm are expected to grow at a constant rate forever, the value of the
share can be calculated as:
Or
Write a
detailed note on technical analysis.
14
Ans: Meaning
of technical analysis: In fundamental analysis, a value of a stock is
predicted with risk-return framework based on economic environment. An
alternative approach to predict stock price behaviour is known as technical
analysis. It is frequently used as a supplement rather than as a substitute to
fundamental analysis. Technical analysis is based on notion that security
prices are determined by the supply of and demand for securities. It uses
historical financial data on charts to find meaningful patterns, and using the
patterns to predict future prices.
In the words of Edwards and Magee:
“Technical analysis is directed towards predicting the price of a security. The
price at which a buyer and seller settle a deal is considered to be the one
precise figure which synthesizes, weights and finally expresses all factors,
rational and irrational quantifiable and non-quantifiable and is the only
figure that counts”.
Tools
of Technical Analysis:
Charting represents a key activity for
a technical analyst during individual stock analysis. The probable future
performance of a stock can be predicted and evolving and changing patterns of
price behaviour can be detected based on historical price-volume information of
the stock. Charts used to
study the trend in prices, price index, and also volume of transactions.
Technical analysis involves three basic types of charts. They are:
(a) Line charts,
(b) Bar charts, and
(3) Point and figure charts.
a)
A Line
Chart connects successive trading day’s closing price/price indices or volume
of trade as the case may. Each day’s price is recorded.
b)
A Bar
Chart is made up by a series of vertical bars of lines, each bar of line
representing; a particular day’s high and low prices. The closing price of a
day is indicated by a small horizontal dash on the day’s bar. Each day’s price
data are thus recorded.
c) Point
and figure charts are more complex than line and bar charts. Point and figure
chart are not only used to detect reversals in a trend, but also used to
forecasts the price, called price targets. The only significant price changes
are posted to point and figure charts. Three or five point price changes as
posted for high prices securities, only one point changes are posted follow
prices securities. While line and bar charts have two dimensions with vertical
column indicating trading day, point and figure chart represents each column as
a significant reversals instead of a trading day. For example, for a share in the price hand of Rs. 1000-1500
or so, a price change exceeding, say, Rs. 15 may be taken as significant,
whereas for a scrip in the price range of Rs. 100-150, a change in price of the
order of Rs. 3 or more may be taken as significant. Upward significant moves
are indicated by ‘x’ in the same column. Say for scrip of Rs. 3 change is taken
as significant. Another ‘x’ in the same column, above the previous ‘x’ is put.
The same day it moves to 107. One more ‘X’ is put. Next day price drifts by Rs.
2. No entry in price will he recorded in this column. If a significant increase
in price takes place, next column of ‘x’ will be charted.
Assumptions
of technical analysis:
Edwards and Magee formulate the basic
assumptions underlying technical analysis which are as follows:
1. The
market value of the scrip is determined by the interaction of demand and
supply.
2. Supply
and demand is governed by numerous factors, both rational and irrational. These
factors include economic variables relied by the fundamental analysis as well
as opinions, moods and guesses.
3. The
market always moves in the trends except for minor deviations.
4. As
the market always moves in trends, analysis of past market data can be used to
predict future price behavior.
5. Changes
in trends in stock prices are caused whenever there is a shift in the demand
and supply factors.
Advantages
of technical analysis
1) Simple
and quick: Technical analysis is simple and quick method on forecasting
behaviour of stock prices.
2) Helps
in identifying trend: Under the influence of crowd psychology, trends persist
for quite some time. Tools of technical analysis that help in identifying these
trends early are helpful in investment decision-making.
3) Short
term price prediction: Technical analysis try to predict short term market
price which is useful for speculators who want to make quick money.
4) Tracking
shift in demand and supply: Shifts in demand and supply are gradual, not
instant. Technical analysis helps in detecting these shifts rather early and
hence provides clues to future price movements,
Limitations
of technical analysis
1) Past
and historical data: Technical analysis is based on the past and historical
data. Unexpected future is not taken into consideration by it.
2) Analyst Bias: Just as
with fundamental analysis, technical analysis is subjective and our personal
biases can be reflected in the analysis.
3) No
explanation about the tools used: Most technical analysts are not able to offer
convincing explanations for the tools employed by them.
4) Chances
of wrong decision: False signals can always occur in the stock markets. If the
technical analysts act without confirmation, they would make mistakes and would
suffer unnecessary expenses and losses.
4. Discuss
the effects of combining securities with examples. 14
Ans: Effects
of combining two securities
Portfolio: A portfolio is
a grouping of financial assets such as stocks, bonds, commodities, currencies
and cash equivalents, as well as their fund counterparts, including mutual,
exchange-traded and closed funds. A portfolio can also consist of non-publicly tradable securities,
like real estate, art, and private investments.
Portfolio analysis deals with the
determination of future risk and return in holding various combinations of
individual securities. The portfolio expected return is the weighted average of
the expected returns, from each of the individual securities, with weights
representing the proportionate share of the security in the total investment.
The portfolio expected variance, in contrast, can be something less than a
weighted average of security variances. Therefore, an investor can sometimes
reduce risk by adding another security with greater individual risk compared to
any other individual security in the portfolio.
It is believed that holding two
securities is less risky than having only one investment in a person’s
portfolio. When two stocks are taken on a portfolio and if they have negative
correlation, then risk can be completely reduced because the gain on one can
offset the loss on the other.
The effect of two securities can also
be studied when one security is riskier when compared to the other
security. As per Markowitz, given the return, risk can be reduced by
diversification of investment into a number of securities. The risk of any two
securities is different from the risk of a group of two companies together.
Thus, it is possible to reduce the risk of a portfolio by incorporating into it
a security whose risk is greater than that of any of scrips held initially.
Example:
Given two securities A and B, with B considerably less risky than
A, a portfolio composed of some of A and some of B may be less risky than a
portfolio composed of only less risky B. Let:
|
|
A |
B |
|
Expected Return Risk (σ) of security |
40% 15% |
30% 10% |
|
Coefficient of correlation, between A and B can have any of the three possibilities i.e. -1, 0.5 or +1 Let us assume, investment in A is 60% and in
B 40% Return on Portfolio = (40 X 0.6) + (30 X
0.4) = 36% Risk on Portfolio = (15 x 0.6) + (10 x 0.4)
= 13%, Which is normal risk. |
Moreover, when two stocks are taken on
portfolio and if they have negative correlation, the risk can be completely
reduced, because the gain on one can offset the loss on the other. The effect
of two securities can also be studied when one security is more risk as
compared to the other security.
Or
Discuss
the basic assumptions of Markowitz model. In what way this model is better than
other models? Discuss. 4+10=14
Ans: Dr. Harry M. Markowitz was the person who
developed the first modern portfolio analysis model. Markowitz used
mathematical programming and statistical analysis in order to arrange for the
optimum allocation of assets within portfolio. He infused a high degree of
sophistication into portfolio construction by developing a mean-variance model
for the selection of portfolio. Markowitz approach determines for the investors
the efficient set of portfolio through three importance variables - Return,
standard deviation and coefficient of correlation.
Markowitz model is called the “Full
Covariance Model”. Through this method the investor can find out the efficient
set of portfolio by finding out the tradeoff between risk and return, between
the limits of zero and infinity. Markowitz theory is based on several
assumptions these are:
ASSUMPTIONS
OF MARKOWITZ’S MODEL
a) The
markets are efficient and absorb all the information quickly and perfectly. So
an investor can earn superior returns either by technical analysis or
fundamental analysis. All the investors are in equal category in this regard.
b) Investors
are risk averse. Before making any investments, all of them, have a common
goal-avoidance of risk.
c) Investors
are rational. They would like to earn the maximum rate of return with a given
level of income or money.
d) Investors
base their decisions solely on expected return and variance (or standard
deviation) of returns only.
e) For
a given risk level, investors prefer high returns to lower returns. Similarly,
for a given level of expected return, they prefer less risk to more risk.
f)
The investor can reduce the risk if he
adds investments to his portfolio.
g) Investors
consider each investment alternative as being represented by a probability
distribution of expected returns over some holding period.
h) A
portfolio of assets under the above assumptions is considered to be efficient
if no other portfolio of assets offers higher expected return with the same (or
lower) risk or lower risk with the same (or higher) expected return.
How
Markowitz theory is superior to Traditional portfolio theory?
Dr. Harry M. Markowitz was the person
who developed the first modern portfolio analysis model. As against the
Traditional theory the modern Portfolio Theory emphasizes the need for
maximization of returns through a combination of securities whose total
variability is lower. It is not necessary that success can be achieved by
trying to get all securities of minimum risk.
The theory states that by combining a
security of low risk with another security of high risk, success can be
achieved by an investor in making a choice of investments. This theory, thus,
takes into consideration the variability of each security and covariance for
their returns reflected through their interrelationships. Thus, as per the
Modern Theory expected returns, the variance of these returns and covariance of
the returns of the securities within the portfolio are to be considered for the
choice of a portfolio. A portfolio is said to be efficient, if it is expected
to yield the highest return possible for the lower risk or a given level of
risk. The modern Portfolio Theory emphasizes the need for maximization of
returns, through a combination of securities, whose total variability is lower.
The risk of each security is different from that of others and by a proper
combination of securities, called diversification; one can arrive at a
combination, where the risk of one is off set partly or fully by that of the
other. Combination of securities can be made in many ways. Markowitz developed
the theory of diversification through scientific reasoning and method.
From the above discussion, the
following difference between Traditional Portfolio Theory and Modern Portfolio
Theory has been obtained:
1. Traditional theory deals with the
evaluation of return and risk conditions in each security. It deals with the
maximization of returns through a combination of different types of financial
assets.
2. Traditional theory is based on
measurement of standard deviation of particular scrip. But Markowitz model is
It is based on mainly diversification process. A portfolio of various classes
of assets is created for the purpose of diversification.
3. Traditional portfolio theory assumes
that market is inefficient. But Markowitz model assumes that market is perfect
and all information is known to public.
4. Traditional theory gives more
importance to standard deviation. But Markowitz model gives more importance to
beta. Beta attempts to measure an investment's sensitivity to market movements.
A high beta means that an investment is highly volatile and that it will likely
outperform its benchmark in up markets, thus exceeding the benchmark's return,
and underperform it in down markets. A lower beta means an investment is likely
to underperform its benchmark in up markets, but is likely to do better when
the markets fall.
5. Discuss
the major factors associated with CAPM with examples. 14
Ans:
Capital Asset Pricing Model (CAPM): Capital market theory is an extension
of the Portfolio theory of Markowitz. The portfolio theory explains how
rational investors should build efficient portfolio based on their risk-return
preferences. Capital Market Asset Pricing Model (CAPM) incorporates a relationship,
explaining how assets should be prices in the capital market. The capital
market theory uses the results of capital market theory to derive the
relationship between the expected returns and systematic risk of individual
securities and portfolios.
Capital asset pricing
model is a tool used by investors to determine the risk associated with a
potential investment and also gives an idea as to what can be the expected
return on the investment. It was developed by William Sharpe along with a
formula for working out the risk as who states that with an investment come two
types of risks:
1) Systematic Risk:
These are risks that cannot be diversified away such as interest rates and
recessions. As the market moves and changes occur which affect the market, each
individual asset is affected to some degree and therefore they are sensitive to
change causing a high level of risk.
2) Unsystematic
(Specific): These risk can be diversified through increasing the size of an
investment portfolio as this risk is specific to individual stocks and
effectively represents no correlation between stocks and market movements.
CAPM states that
investors are compensated for taking systematic risk however not for taking
specific risk as an investor can diversify this risk away. Systematic risk
cannot be eliminated of course even by holding all the shares in a stock
market; therefore CAPM has introduced a method of calculating that risk.
Major elements of CAPM model
It
can be expressed mathematically with the help of following equation:
E(rA)
= rf + βA(E(rM) - rf)
where:
E(rA) is the expected return of the
asset: Expected
return is the profit or loss an investor anticipates on an investment
that has known or expected rates of return. It is
calculated by multiplying potential outcomes of an investment by the chances of
them occurring and then summing these results. Greater
the risk, the larger the expected return and the larger the chances of
substantial loss. Investments which carry low risk such as bonds will offer a
lower expected return than those which carry high risk such as equity stock of
a new company. A rational investor would have some degree of risk aversion, he
would accept the risk only if he is adequately compensated for it.
rf is the risk-free rate: It is an imaginary rate that
investors could expect to receive without any risk on investment. Normally
interest on government bonds and bank deposits are considered to be risk free.
E(rM) is the expected return of the
market portfolio: Expected return of the market portfolio is the
profit or loss an investor anticipates on investments in a portfolio of stock
or stock market that has known or expected rates of return.
It is calculated by multiplying potential outcomes of portfolio by the chances
of them occurring and then summing these results. Greater
the risk, the larger the expected return and the larger the chances of
substantial loss. Portfolios which carry low risk will offer a lower expected
return than those which carry high risk such as equity funds. A rational
investor would have some degree of risk aversion, he would accept the risk only
if he is adequately compensated for it.
βA
(Beta of an stock): Beta attempts to measure an
investment's sensitivity to market movements. A high beta means that an
investment is highly volatile and that it will likely outperform its benchmark
in up markets, thus exceeding the benchmark's return, and underperform it in
down markets. A lower beta means an investment is likely to underperform its
benchmark in up markets, but is likely to do better when the markets fall. The
first step in beta is measuring the volatility of a benchmark's returns in
excess of a risk-free asset's return, such as the Treasury bill. The
benchmark's beta is always 1.0. So a security with a beta of 0.83 is expected
to gain 17 percent less, on average, than the benchmark in up markets and
expected to lose, on average, 17 percent less in down markets. By contrast, a
security with a beta of 1.13, is expected to gain, on average, 13 percent more
than the benchmark in up markets, and lose, on average, 13 percent more in down
markets. However, beta does not calculate the odds of macroeconomic changes nor
does it take into consideration the herd-like behavior of investors and its
effect on the securities market.
The
general idea of CAPM is that investors should be compensated in two ways: time
value of money and risk. The time
value of money is represented by the risk-free (rf) rate in the formula and
compensates the investors for placing money in any investment over a period of
time. The other part of the formula
represents risk and calculates the amount of compensation the investor needs
for taking on additional risk. This is done by taking an estimate of risk,
(βA), and multiplying by the MRP, (E(rM) - rf).
Graphical Presentation of CAMP
An
asset is expected to earn the risk-free rate plus a reward for bearing risk as
measured by that asset’s beta. The chart below demonstrates this predicted
relationship between beta and expected return – this line is called the
Security Market Line.
For
example, a stock with a beta of 1.5 would be expected to have an excess return
of 15% in a time period where the overall market beat the risk-free asset by
10%. The CAPM model is used for pricing an individual security or a portfolio.
For individual securities, the security market line (SML) and its relation to
expected return and systematic risk (beta) shows how the market must price
individual securities in relation to their security risk class.
As
the CAPM predicts expected returns of assets or portfolios relative to risk and
market return, the CAPM can also be used to evaluate the performance of active
fund managers. The difference is “excess return”, which is often referred to as
alpha (α). If α is greater than zero, the portfolio lies above the Security
Market Line.
Or
Write a
detailed note on two-factor model. 14
Ans: Factor Models: In
portfolio management computation of expected return, risk and covariance for
every security included in the portfolio is crucial process and it proves a bit
difficult too. Factor
models relatively make the process easier as security return is assumed to be
in correlation with one factor(s) or other(s). Factor models captured macro
economic factors that systematically influence prices of
securities. Any aspect of a
security’s return unexplained by the factor model is taken as security
specific. Factor models are otherwise known as index models. Securities return when
assumed to be related to return on a market index, such model is called as
market index model. Similar to return on market index, other factors to which
security returns stand related can be modeled and used to estimate returns as
securities. Similarly portfolio returns as related to identified factors can be
found and used in portfolio management. And this will ease the
problem of computing returns. One
factor (say Market Return, Growth rate of gross Domestic Product or Inflation rate), two factors (any two of
macro economic factors) and multi-factors models can be through of.
Single Factor Model
CAPM is base on the
single factor model. According to this model, the asset price depends on a
single factor, say gross national product or industrial productions or interest
rates, money supply and so on. In general, a single factor model can be
represented in the equation form as follows:
R = E + Bf + e
Where, E = Uncertain
return on security
B = Security’s
sensitivity to change in the factor
f = The actual return
on the factor
e = error term
Thus, this model only
state that the actual return on a security equals the expected return plus
sensitivity times factor movement plus residual risk.
Multiple
Factor Model
The Arbitrage pricing theory based
model aims to do away with the limitations of one factor model (CAPM) that
different stocks will have different sensitivities to different market factors
which may be totally different from any other stock under observation. In
layman terms, one can say that not all stocks can be assumed to react to single
and same parameter always and hence the need to take multifactor and their
sensitivities. The formula includes a variable for each factor, and then a
factor beta for each factor, representing the security’s sensitivity to movements
in that factor. A two-factor version of the arbitrage pricing theory would look
like as:
r = E(r) + B1F1 +
B2F2 + e
r = return on the security
E(r) = expected return on the security
F1 = the first
factor
B1 = the
security’s sensitivity to movements in the first factor
F2 = the
second factor
B2 = the
security’s sensitivity to movements in the second factor
e = the idiosyncratic component of the
security’s return
As the formula shows, the expected
return on the asset/stock is a form of liner regression taking into
consideration many factors that can affect the price of the asset and the
degree to which it can affect it i.e. the asset’s sensitivity to those factors.
If one is able to identify a single
factor which singly affects the price, the CAPM model shall be sufficient. If
there are more than one factor affecting the price of the asset/stock, one will
have to work with a two factor model or a multi factor model depending on the
number of factors that affect the stock price movement for the company.
6. Write
detailed notes on any two of the following: 7x2=14
a) Relation between risk and return
Ans: The entire scenario of security analysis
is built on two concepts of security: Return and risk. The risk and return
constitute the framework for taking investment decision. Return from equity
comprises dividend and capital appreciation. To earn return on investment, that
is, to earn dividend and to get capital appreciation, investment has to be made
for some period which in turn implies passage of time. Dealing with the return
to be achieved requires estimated of the return on investment over the time
period. Risk denotes deviation of actual return from the estimated return. This
deviation of actual return from expected return may be on either side – both
above and below the expected return. However, investors are more concerned with
the downside risk.
The risk in holding security deviation
of return deviation of dividend and capital appreciation from the expected
return may arise due to internal and external forces. That part of the risk
which is internal that in unique and related to the firm and industry is called
‘unsystematic risk’. That part of the risk which is external and which affects
all securities and is broad in its effect is called ‘systematic risk’.
The fact that investors do not hold a
single security which they consider most profitable is enough to say that they
are not only interested in the maximization of return, but also minimization of
risks. The unsystematic risk is eliminated through holding more diversified
securities. Systematic risk is also known as non-diversifiable risk as this can
not be eliminated through more securities and is also called ‘market risk’.
Therefore, diversification leads to risk reduction but only to the minimum
level of market risk. The investors increase their required return as perceived
uncertainty increases. The rate of return differs substantially among
alternative investments, and because the required return on specific
investments change over time, the factors that influence the required rate of
return must be considered.
b) Advantages
of Sharpe model
Ans: The
Sharpe Measure
In this model, performance of a fund
is evaluated on the basis of Sharpe Ratio, which is a ratio of returns
generated by the fund over and above risk free rate of return and the total
risk associated with it. According to Sharpe, it is the total risk of the fund
that the investors are concerned about. So, the model evaluates funds on the
basis of reward per unit of total risk. Symbolically, it can be written as:
Sharpe
Index (St) = (Rt - Rf)/Sd
Where,
St = Sharpe’s Index
Rt=
represents return on fund and
Rf=
is risk free rate of return.
Sd=
is the standard deviation
Advantages
of Sharpe’s Ratio:
a) The main advantage of this ratio is
that it is easy to calculate and it is used widely.
b) This index gives a measure of
portfolios total risk and variability of returns in relation to the risk
premium.
c) The Sharpe ratio also standardizes the relationship between
risk and return and therefore can be used to compare different asset classes
i.e., comparison of stocks with commodities.
d) An
advantage of Sharpe ratio is that a beta estimate is not required.
c) Limitations
of Jensen model
Ans: Jensen Model
Jensen's model proposes another risk
adjusted performance measure. This measure was developed by Michael Jensen and
is sometimes referred to as the Differential Return Method. This measure
involves evaluation of the returns that the fund has generated vs. the returns
actually expected out of the fund given the level of its systematic risk. The
surplus between the two returns is called Alpha, which measures the performance
of a fund compared with the actual returns over the period. Required return of
a fund at a given level of risk (b) can be calculated as:
Rt – R = a + b (Rm
– R)
Where,
Rt = Portfolio Return
R = Risk
less return
a =
Intercept the graph that measures the forecasting ability of the portfolio manager.
b = Beta
coefficient, a measure of systematic risk
Rm
= Return of the market portfolio
Thus, Jensen’s equation involves two
steps:
(i) First he calculates what the
return of a given portfolio should be on the basis of b, Rm and R.
(ii) He compares the actual realised
return of the portfolio with the calculated or predicted return. Greater the
excess of realised return over the calculated return, better is the performance
of the portfolio.
Disadvantages
of this model:
a) Weakness of Treynor’s ratio is that
it requires an estimate of beta, which can differ a lot depending on the source
which in turn can lead to mis-measurement of risk adjusted return. Many
investors accomplish that a beta cannot give a clear picture of risk involved
with the investment.
b) It does not consider the advantage
of a diversified portfolio.
c) Jensen’s alpha doesn’t take the
portfolio’s volatility and takes into account, only the expected return.
d) It will miss out on characteristics
such as returns kurtosis and skewness, which are of great importance in
determining whether you’ll go broke before you realize profits.
e) Limitation of this model is that it
considers only systematic risk not the entire risk associated with the fund and
an ordinary investor can not mitigate unsystematic risk, as his knowledge of
market is primitive.
GROUP-B (Old Course)
3. What
do you mean by risk? What are the different components of unsystematic risk?
Discuss. 4+7=11
Or
What are the factors that you would consider
before making any investment decisions? Discuss. 11
4. Write a detailed note on Markowitz
model. 11
Or
Write a detailed note on location of the
efficiency frontier. 11
5. In what way ‘capital market line’ and
‘security market line’ are valuable indicators for a better portfolio
formulation? Explain. 11
Or
Discuss the disadvantages of CAPM. Do you
think any other existing model can replace CAPM? Justify. 11
6. Write a comparative note on Sharpe and
Treynor performance measures. 11
Or
Discuss the various factors influencing the
portfolio investment performance. 11
7. Write short notes on (any two): 6x2=12
a) Option
b) Futures
c) Market Projections
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