Security Analysis and Portfolio Management Solved Question Paper May 2015
2015 (May)
COMMERCE (Speciality)
Course: 404 (Security Analysis and
Portfolio Management)
Full Marks: 80
Pass Marks: 32 Marks (Old Course)
Time: Three hours
The figures in the margin indicate
full marks for the questions
1. What do you mean by the following: 1x8=8
a) Valuation of securities: The process of determining how much a security is worth is called
valuation of securities. Security valuation is
highly subjective, but it is easiest when one is considering thevalue of tangible assets, level
of debt, and other quantifiable data of the company issuing a security.
b) 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.
c) Market risk: The price of a stock may
fluctuate widely within a short span of time even though earnings remain
unchanged. The causes of this phenomenon are varied, but it is mainly due to a
change in investors’ attitudes towards equities in general, or toward certain
types or groups of securities in particular. Variability in return on most
common stocks that is due to basic sweeping changes in investor expectations is
referred to as market risk.
d) Risk Adjustment: Risk adjustment is a
method to offset the cost of investments.
e) Systematic return is the part that depends upon the
benchmark return and is calculated as beta times benchmark
excess return.
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.
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2. Write short note on: 4x4=16
a) Nature of options.
b) Arbitrage.
c) Portfolio Management: Portfolio management is a dynamic concept and requires continuous
and systematic analysis, judgement and operations. It is a process involving
many activities of investment in assets and securities. Firstly, it involves
construction of a portfolio based upon the data base of the client/investor,
his objectives, constraint preferences for risk and return etc. On the basis of
above mentioned facts, selection of assets and securities is made. Secondly, it
involves monitoring/reviewing of the portfolio from time to time in light of
changing market conditions. Accordingly changes are effected in the portfolio.
Thirdly, it involves evaluation of the portfolio in terms of targets set for
risk and return and making adjustments accordingly. Basically, portfolio
management involves a proper decision making as to what to purchase and what to
sell. It requires detailed risk and return analysis and proper money management
in terms of investments in a basket of assets, the basic objective being
reduction of risk and maximization or return.
d) Convertible Securities: 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. Convertible securities include convertible
debentures (CDs), convertible pref. Shares (CPs), etc. CDs can be partly or
fully or optionally convertible into equity shares. CPs can be similarly
partly, fully or optionally convertible.
Convertible securities
give the investor initially fixed return and later on conversion might give
capital gain. When a company issues convertible bond, the conversion date, the
conversion price, the conversion ratio, etc. must be indentured. So, a company
issues convertible bonds of Rs. 60 each, convertible into 3 shares are
exchanged. The conversion price is, the face value of the bond divided by
conversion ratio, i.e., Rs. 60/3 = Rs. 20. If only the market price of the equity
shares is > 20, conversion will be effected. The market value of the
convertible bond does not affect the conversion will be affected. The market
value of the convertible bond does not affect the conversion price or
conversion ratio. The conversion ratio will be set, such that, it is not
lucrative to convert immediately. Say the current price of the share is Rs. 22.
Then the conversion value of the bond at this point of time is 3 x 22 = Rs. 66.
Say the bond goes at Rs. 70 in the market. Then, the conversion premium is said
to be Rs. 4 (i.e., Rs.70 – Rs. 66). As long as conversion premium exists,
conversion will not take place. To force conversion, the company may exercise
call provision and call the bonds for redemption, say at its face value of Rs.
60. The holders of the convertible bond will go for conversion as that gives
Rs. 6 more than call route redemption.
3. (a)
What do you mean by unsystematic risk. What are its sources? How can it be
managed? Discuss out with examples.
Ans: 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. Factors like
consumer preferences, labour strikes, management capability etc. cause unsystematic
risk (variability of returns) for a company’s stock. Unlike systematic risk,
the unsystematic risk can be reduced/avoided through diversification. Total
risk of a fully diversified portfolio equals to the market risk of the
portfolio as its specific risk becomes zero.
Sources of Unsystematic risk
a) Business risk: Business
risk relates to the variability of the sales, income, profits etc., which in
turn depend on the market conditions for the product mix, input supplies,
strength of competitors, etc. The business risk is sometimes external to the
company due to changes in government policy or strategies of competitors or
unforeseen market conditions. They may be internal due to fall in production,
labour problems, raw material problems or inadequate supply of electricity etc.
The internal business risk leads to fall in revenues and in profit of the
company, but can be corrected by certain changes in the company’s policies.
b) Financial Risk: This
relates to the method of financing, adopted by the company; high leverage
leading to larger debt servicing problems or short-term liquidity problems due
to bad debts, delayed receivables and fall in current assets or rise in current
liabilities. These problems could no doubt be solved, but they may lead to fluctuations
in earnings, profits and dividends to share holders. Sometimes, if the company
runs into losses or reduced profits, these may lead to fall in returns to
investors or negative returns. Proper financial planning and other financial
adjustments can be used to correct this risk and as such it is controllable.
c) Default or insolvency risk: The
borrower or issuer of securities may become insolvent or may default, or delay
the payments due, such as interest instalments or principal repayments. The
borrower’s credit rating might have fallen suddenly and he became default prone
and in its extreme form it may lead to insolvency or bankruptcies. In such
cases, the investor may get no return or negative returns. An investment in a
healthy company’s share might turn out to be a waste paper, if within a short
span, by the deliberate mistakes of Management or acts of God, the company
became sick and its share price tumbled below its face value.
d)
Other Risks:
Besides the above described risks, there are many more risks,
which can be listed, but in actual practice, they may vary in form, size and
effect. Some of such identifiable risks are the Political Risks, Management
Risks and Liquidity Risks etc. Political risk may occur due to the changes in
the government, or its policy shown in fiscal or budgetary aspects, changes in
tax rates, imposition of controls or administrative regulations etc. Management
risks arise due to errors or inefficiencies of management, causing losses to
the company. Marketability liquidity risks involve loss of liquidity or loss of
value in conversions from one asset to another say, from stocks to bonds, or
vice versa. Such risks may arise due to some features of securities, such as
callability; or lack of sinking fund or Debenture Redemption Reserve fund, for
repayment of principal or due to conversion terms, attached to the security,
which may go adverse to the investor. All the above types of risks are of
varying degrees, resulting in uncertainty or variability of return, loss of
income, and capital losses, or erosion of real value of income and wealth of
the investor. Normally the higher the risk taken, the higher is the return.
Can risk be avoided?
Every investor wants to guard himself
from the risk. This can be done by understanding the nature of the risk and
careful planning.
1) Market Risk Protection
a. The
investor has to study the price behaviour of the stock. Usually history repeats
itself even though it is not in perfect form. The stock that shows a growth
pattern may continue to do so for some more period. The Indian stock market
expects the growth pattern to continue for some more time in information
technology stock and depressing conditions to continue in the textile related
stock. Some stocks may be cyclical stocks. It is better to avoid such type of
stocks. The standard deviation and beta indicate the volatility of the stock.
b. The
standard deviation and beta are available for the stocks that are included in
the indices. The National Stock Exchange News bulletin provides this
information. Looking at the beta values, the investor can gauge the risk factor
and make wise decision according to his risk tolerance.
c. Further,
the investor should be prepared to hold the stock for a period of time to reap
the benefits of the rising trends in the market. He should be careful in the
timings of the purchase and sale of the stock. He should purchase it at the
lower level and should exit at a higher level.
2) Protection against Interest Rate
Risk
a. Often
suggested solution for this is to hold the investment sells it in the middle
due to fall in the interest rate, the capital invested would experience
tolerance.
b. The
investors can also buy treasury bills and bonds of short maturity. The
portfolio manager can invest in the treasury bills and the money can be reinvested
in the market to suit the prevailing interest rate.
c. Another
suggested solution is to invest in bonds with different maturity dates. When
the bonds mature in different dates, reinvestment can be done according to the
changes in the investment climate. Maturity diversification can yield the best
results.
3) Protection against Inflation
a. The
general opinion is that the bonds or debentures with fixed return cannot solve
the problem. If the bond yield is 13 to 15 % with low risk factor, they would provide
hedge against the inflation.
b. Another
way to avoid the risk is to have investment in short-term securities and to
avoid long term investment. The rising consumer price index may wipe off the
real rate of interest in the long term.
c. Investment
diversification can also solve this problem to a certain extent. The investor
has to diversify his investment in real estates, precious metals, arts and
antiques along with the investment in securities. One cannot assure that
different types of investments would provide a perfect hedge against inflation.
It can minimise the loss due to the fall in the purchasing power.
4) Protection against Business and
Financial Risk
a. To
guard against the business risk, the investor has to analyse the strength and
weakness of the industry to which the company belongs. If weakness of the
industry is too much of government interference in the way of rules and
regulations, it is better to avoid it.
b. Analysing
the profitability trend of the company is essential. The calculation of standard
deviation would yield the variability of the return. If there is inconsistency
in the earnings, it is better to avoid it. The investor has to choose a stock
of consistent track record.
c. The
financial risk should be minimised by analysing the capital structure of the
company. If the debt equity ratio is higher, the investor should have a sense
of caution. Along with the capital structure analysis. He should also take into
account of the interest payment. In a boom period, the investor can select a
highly levered company but not in a recession.
Or
(b) Discuss different measures to analyze the
fundamental and to technical factors in decision.
Ans: Tools and Techniques of fundamental
Analysis
Financial statement means a statement
or document which explains necessary financial information. Financial
statements express the financial position of a business at the end of
accounting period (Balance Sheet) and result of its operations performed during
the year (Profit and Loss Account). In order to determine whether the financial
or operational performance of company is satisfactory or not, the financial
data are analyzed. Different methods are used for this purpose. The main
techniques of financial analysis are:
The most commonly used techniques of financial analysis are as
follows:
1. Comparative Statements: These are the statements showing the
profitability and financial position of a firm for different periods of time in
a comparative form to give an idea about the position of two or more periods.
It usually applies to the two important financial statements, namely, balance
sheet and statement of profit and loss prepared in a comparative form. The
financial data will be comparative only when same accounting principles are
used in preparing these statements. If this is not the case, the deviation in
the use of accounting principles should be mentioned as a footnote. Comparative
figures indicate the trend and direction of financial position and operating
results. This analysis is also known as ‘horizontal analysis’.
Merits of Comparative Financial Statements:
a)
Comparison of financial statements
helps to identify the size and direction of changes in financial position of an
enterprise.
b)
These statements help to ascertain the
weakness and soundness about liquidity, profitability and solvency of an
enterprise.
c)
These statements help the management
in making forecasts for the future.
Demerits of Comparative Financial Statements:
a)
Inter-firm comparison may be
misleading if the firms are not of the same age and size, follow different
accounting policies.
b)
Inter-period comparison will also be
misleading if there is frequent changes in accounting policies.
2. Common Size Statements: These are the statements which
indicate the relationship of different items of a financial statement with a
common item by expressing each item as a percentage of that common item. The
percentage thus calculated can be easily compared with the results of
corresponding percentages of the previous year or of some other firms, as the
numbers are brought to common base. Such statements also allow an analyst to
compare the operating and financing characteristics of two companies of
different sizes in the same industry. Thus, common size statements are useful,
both, in intra-firm comparisons over different years and also in making
inter-firm comparisons for the same year or for several years. This analysis is
also known as ‘Vertical analysis’.
Merits of Common Size Statements:
a)
A common size statement facilitates
both types of analysis, horizontal as well as vertical. It allows both
comparisons across the years and also each individual item as shown in
financial statements.
b)
Comparison of the performance and
financial condition in respect of different units of the same industry can also
be done.
c)
These statements help the management
in making forecasts for the future.
Demerits of Common Size Statements:
a)
If there is no identical head of
accounts, then inter-firm comparison will be difficult.
b)
Inter-firm comparison may be
misleading if the firms are not of the same age and size, follow different
accounting policies.
c)
Inter-period comparison will also be
misleading if there is frequent changes in accounting policies.
3. Trend Analysis: It is a technique of studying the
operational results and financial position over a series of years. Using the
previous years’ data of a business enterprise, trend analysis can be done to
observe the percentage changes over time in the selected data. The trend
percentage is the percentage relationship, in which each item of different
years bear to the same item in the base year. Trend analysis is important
because, with its long run view, it may point to basic changes in the nature of
the business. By looking at a trend in a particular ratio, one may find whether
the ratio is falling, rising or remaining relatively constant. From this
observation, a problem is detected or the sign of good or poor management is
detected.
Merits of Trend analysis:
a)
Trend percentages can be presented in
the form of Index Numbers showing relative change in the financial statements
during a certain period.
b)
Trend analysis will exhibit the
direction to which the concern is proceeding.
c)
The trend ratio may be compared with
the industry, in order to know the strong or weak points of a concern.
Demerits of Common Size Statements:
a)
These are calculated only for major
items instead of calculating for all items in the financial statements.
b)
Trend values will also be misleading
if there is frequent changes in accounting policies.
4. Ratio Analysis: It describes the significant
relationship which exists between various items of a balance sheet and a
statement of profit and loss of a firm. As a technique of financial analysis,
accounting ratios measure the comparative significance of the individual items
of the income and position statements. It is possible to assess the
profitability, solvency and efficiency of an enterprise through the technique
of ratio analysis.
5.
Funds flow statement: The financial statement of the business indicates assets, liabilities
and capital on a particular date and also the profit or loss during a
period. But it is possible that there is enough profit in the business and the
financial position is also good and still there may be deficiency of cash or of
working capital in business. Financial statements are not helpful in analysing
such situation. Therefore, a statement of the sources and applications of funds
is prepared which indicates the utilisation of working capital during an
accounting period. This statement is called Funds Flow statement.
6.
Cash Flow Analysis: A Cash Flow Statement is similar to
the Funds Flow Statement, but while preparing funds flow statement all the
current assets and current liabilities are taken into consideration. But in a
cash flow statement only sources and applications of cash are taken into
consideration, even liquid asset like Debtors and Bills Receivables are
ignored. A Cash Flow Statement is a statement, which summarises the resources
of cash available to finance the activities of a business enterprise and the
uses for which such resources have been used during a particular period of
time. Any transaction, which increases the amount of cash, is a source of cash
and any transaction, which decreases the amount of cash, is an application of
cash. Simply, Cash Flow is a
statement which analyses the reasons for changes in balance of cash in hand and
at bank between two accounting period. It shows the inflows and outflows of
cash.
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.
4. (a) Write a detailed note on fraudulent portfolio analyses.
Or
(b) Write a detailed note
on Markowitz model.
Ans: MARKOWITZ MODEL
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 trade off 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.
PARAMETERS
OF MARKOWITZ DIVERSIFICATION
Based on thorough and scientific
research, Markowitz has set down his own guidelines for diversification:
b) The
investments have different types of risk characteristics. Some are systematic
or market related risks and the others are unsystematic or company related
risks.
c) His
diversification involves a proper number of securities not too less nor too
many.
d) The
securities have no correlation or negative correlation.
e) Last
is the proper choice of the companies, securities or assets whose returns are
not related and whose risks are mutually off setting to reduce the overall
risk.
Markowitz lays down three parameters
for building up the efficient set of portfolio:
a) Expected
returns.
b) Standard
deviation from mean to measure variability of returns.
c) Covariance
or variance of one asset return to other asset returns.
To generalize, higher the expected
return, lower will be the standard deviation or variance and lower is the
correlation. In such a case, better will be the security for investor choice.
If the covariance of the securities’ returns is negative or negligible, the total
risk of the portfolio of all securities may be lower as compared to the risk of
the individual securities in isolation.
By developing his model, Markowitz
first did away with the investment behaviour rule that the investor should
maximize expected return. This rule implied that the non-diversified single
security portfolio with the highest expected return is the most desirable
portfolio. Only by buying that single security can expected return be
maximized. The single security portfolio can be much preferred if the higher
return turns out to be the actual return. However, in real world, there are
conditions of so much uncertainty that most risk averse investors, joint with
Markowitz in adopting diversification of securities.
5. (a) Discuss the assumptions of CAPM model. Do you
think that it is acceptable in Indian context? Justify you argument with
examples.
Ans: 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.
Assumptions
of CAPM
The capital asset pricing model is
based on certain explicit assumptions regarding the behavior of investors. The
assumptions are listed below:
1. Investor
make their investment decisions on the basis of risk-return assessments
measured in terms of expected returns and standard deviation of return.
2. The
purchase or sale of a security can be undertaken in infinitely divisible unit.
3. Purchase
and sale by a single investor cannot affect prices. This means that there is
perfect competition where investors in total determine prices by their action.
4. There
are no transaction costs. Given the fact that transaction costs are small, they
are probably of minor importance in investment decision-making, and hence they
are ignored.
5. There
are no personal income taxes. Alternatively, the tax rate on dividend income
and capital gains are the same, thereby making the investor indifferent to the
form in which the return on the investment is received (dividends or capital
gains).
6. The
investor can lend or borrow any amount of fund desired at a rate of interest
equal to the rate of risk less securities.
7. The
investor can sell short any amount of any shares.
8. Investors
share homogeneity of expectations. This implies that investors have identical
expectations with regard to the decision period and decision inputs. Investors
are presumed to have identical expectations regarding expected returns,
variance of expected returns and covariance of all pairs of securities.
CAPM is acceptable in
India because of its various advantages which are stated below:
CAPM has been a
popular model for calculating risk for over 40 years now and is therefore a
proven method, some advantages are:
a) Ease-of-use: CAPM is a simplistic
calculation that can be easily stress-tested to derive a range of possible
outcomes to provide confidence around the required rates of return.
b) Systematic Risk: It
considers only systematic risk, reflecting a reality in which most investors
have diversified portfolios from which unsystematic risk has been essentially
eliminated.
c) Business and Financial Risk
Variability: When businesses investigate opportunities, if the business mix and
financing differ from the current business, then other required return
calculations, like weighted average
cost of capital (WACC)
cannot be used. However, CAPM can.
d) Determination of firm’s required return: To develop this
overall cost of capital, the manager must have an estimate of the cost of
equity capital. To calculate a cost of equity, some managers estimate the
firm’s beta (often from historical data) and use the CAPM to determine the
firm’s required return on equity.
e) Public
utility: The CAPM can also be used by the regulations of public utilities.
Utilities rates can be set so that all costs, including costs of debt and
equity capital, are covered by rates charged to consumers. In determining the
cost of equity for the public utility, the CAPM can be used to estimate
directly the cost of equity for the utility in question. The procedure is like
that followed for any other firm. The beta and risk-free and market rates of
return are estimated, and the CAPM is used to determine a cost of equity.
f)
Useful tool for investment managers:
Investment practitioners have been more enthusiastic and creative in adapting
the CAPM for their uses. The CAPM has been used to select securities, construct
portfolios, and are forecastle considered under-valued, that is, attractive
candidates for purchase.
g) Most reliable and effective tool: Furthermore, in the opinion
of most experts it is a more reliable and effective method of calculating risk
than other models such as the Dividend Growth Model as CAPM takes into account
a company's level of systematic risk against the stock market as a whole; this
is a benefit as it allows for a company to compare itself to the market.
Or
(b) Discuss the limitation
of factors models? In what way two factors model is better than one factor
model? Justify.
Ans: 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.
Limitations of factor models
a) Problems
in listing of various factors: The model requires listing of factors that have
impact on the stock under consideration. Finding and listing all factors can be
a difficult task and there is a risk that some or the other factor being
ignored. Also risk of accidental correlations may exist which may cause a
factor to become substantial impact provider or vice versa.
b) Expected
return of various factors: The expected returns for each of these factors will
have to be arrived at, which depending on the nature of the factor, may or may
not be easily available always.
c) Difficult
to measure Sensitivities of factors: The model requires calculating
sensitivities of each factor which again can be a tedious task and may not be
practically possible.
d) Change
in factors from time to time: The factors that affect the stock price for a
particular stock may change over a period of time. Moreover, the sensitivities
associated may also undergo shifts which need to be continuously monitored
making it very difficult to calculate and maintain.
e) Existence
of arbitrage is essential: The APT model will prevail only if there is a
opportunity of arbitrage. If arbitrage opportunity is not available, then this
model does not prevail.
f)
Uncertain size or sign of factors: APT
makes no statement about the size of sign of the factors.
g) Unrealistic
assumption: It is based on some assumptions which are not practical.
CAPM is based on single
factor model and APT is based on multiple factor model. Multiple factor model
is better than CAPM due the following reasons:
a) APT
model is a multi-factor model. So, the expected return is calculated taking
into account various factors and their sensitivities that might affect the
stock price movement. Thus it allows selection of factors that affect the stock
price largely and specifically.
b) APT
model is based on arbitrage free pricing or market equilibrium assumptions
which to a certain extent result in fair expectation of the rate of return on
the risky asset.
c) APT
based multi factor model places emphasis on covariance between asset returns
and exogenous factors unlike CAPM. CAPM places emphasis on covariance between
asset returns and endogenous factors.
d) APT
model works better in multi period cases as against CAPM which is suitable for
single period cases only.
e) APT
can be applied to cost of capital and capital budgeting decisions.
f) The APT model does not require any assumption about the empirical distribution of the asset returns unlike CAPM which assumes that stock returns follow a normal distribution and thus APT a less restrictive model.
6. Write notes on any two
of the following:
a) Sharpe model.
b) Treynor’s model.
c) Jansen model.
d)
Stock selection.
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
While a high and positive Sharpe Ratio
shows a superior risk-adjusted performance of a fund, a low and negative Sharpe
Ratio is an indication of unfavorable performance. This index gives a measure
of portfolios total risk and variability of returns in relation to the risk
premium. This method ranks all portfolios on the basis of St. Larger the value
of St, the better the performance of the portfolio.
The following figure gives a graphic
representation of Sharpe’s index. Sd measure the slope of the line emanating
from the risk less rate outward to the portfolio in question.
Example
|
Portfolio |
Average return |
S.D. |
Risk Free Rate |
|
A |
15% |
3% |
9% |
|
B |
20% |
8% |
9% |
SA = (15 – 9)/3 = 2
SB = (20 – 9)/8 = 1.375
Thus, portfolio A is ranked higher
because its index i.e. 2.0 is higher as compare to B’s index i.e. 1.375. This
is despite the fact that B has a higher return (20% >15%)
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.
Disadvantages of Sharpe ratio:
a) When risk free
rate is known, it is very difficult to find the right expected return and
standard deviation. In a stable market, it is very easy to predict expected
return but in today’s dynamic market it is very difficult to predict future
expected return.
b) This ratio is
not appropriate when evaluating individual stocks because it uses total risk
rather than systematic.
c) It is overstated if the return are smoothen
and historical prices are used.
d) It can be
manipulated by the fund managers if non-linear derivatives are used.
b) The Treynor Measure
Jack L. Treynor based his model on the
concept of characteristic line. This line is the least square regression line
relating the return to the risk and beta is the slope of the line. The slope of
the line measures volatility. A steep slope means that the actual rate of
return for the portfolio is highly sensitive to market performance whereas a
gentle slope indicates that the actual rate of return for the portfolio is less
sensitive to market fluctuations.
The Treynor index, also commonly known
as the reward-to-volatility ratio, is a measure that quantifies return per unit
of risk. This Index is a ratio of return generated by the fund over and above
risk free rate of return, during a given period and systematic risk associated
with it (beta). The
portfolio beta is a measure of portfolio volatility, which is used as a proxy
for overall risk – specifically risk that cannot be diversified. A beta of one
indicates volatility on par with the broader market, usually an equity index. A
beta of 0.5 means half the volatility of the market. Portfolios with twice the
volatility of the market would be given a beta of 2. Symbolically,
Treynor’s ratio can be represented as:
Treynor's
Index (Tt) = (Rt
– Rf)/Bt
Whereas,
Tt = Treynor’ measure of portfolio
Rt = Return of the portfolio
Rf = Risk free rate of return
Bt = Beta coefficient or volatility of the portfolio
All risk-averse investors would like to
maximize this value. While a high and positive Treynor's Index shows a superior
risk-adjusted performance of a fund, a low and negative Treynor's Index is an
indication of unfavorable performance. Treynor ratios can be used in both an ex-ante and ex-post
sense. The ex-ante form of the ratio uses expected values
for all variables, while the ex-post variation uses realized values.
Graphically Treynor’s measure is
depicted as:
Example
|
Portfolio |
Return |
Volatility |
Risk free Rate |
|
A |
20% |
5% |
8% |
|
B |
24% |
8% |
8% |
Treynor’s index has ranked portfolio A
as the better performer because value is higher (2.4 > 2.0) despite the fact
that portfolio B has a higher return (24% > 20%). It is due to the
difference in volatility of two portfolios.
Advantages
of Treynor’s ratio:
a)
The main advantage to the
Treynor Ratio is that it indicates the volatility a stock brings to an entire
portfolio.
b)
The Treynor Ratio should be used only as a ranking mechanism for investments
within the same sector. In a situation where rate of return from various
investments alternatives are same, investments with higher Treynor Ratios are
less risky and better managed.
c)
It is proper measure for diversified portfolio.
d)
This method is easy to calculate and simple to understand.
Limitations
of Treynor’s ratio:
a) It is only a ranking criterion. It
does not consider any values or metrics calculated by means of the management
of portfolios or investments.
b) A Treynor ratio is a
backward-looking design. This ratio gives importance to how the portfolio
behaved in pas. It is possible that a portfolio may perform differently in
future from how it has done in the past.
c) 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.
d) It can be overstated if market
neutral strategies are used and assets used in the portfolio are highly
leveraged.
c) 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.
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.
Graphic representation of Jensen’s
model is a given in the following figure:
The figure shows three lines showing
negative, neutral and positive values. The negative line shows that the
management of the performed portfolio is inferior. The positive line shows that
superior quality of management of funds. The neutral value shows that the
performance of the fund is similar to the performance of the market portfolio.
A comparison between the three models
shows that the intercept of the line is Sharpe and Treynor models is always at
the origin, where as Jensen’s model it may be at the origin (a = 0), above the
origin (a > 0) and even be below the origin indicating a negative value (a
< 0). The risk adjusted measures have been criticized for using a market surrogate
instead of the true market portfolio. These measures have been unable to
statistically distinguish luck or change from skill except over very long
period of time. Moreover, these models rely heavily on the validity of CAPM. If
in estimating the measures the analyst assumes the wrong from of the CAPM in
the market place, he will get based measure of performance, usually in favour
of low risk portfolios.
Advantages of this model:
a) This model is very easy to interpret.
b) It helps to
measure how much of the portfolio's rate of return is attributable to deliver
above-average returns, adjusted for market risk. The higher the ratio, the
better the risk adjusted returns.
c) Because it is estimated from a regression equation,
it is possible to make statements about the statistical significance of the
manager’s skill level.
d) It is flexible
enough to allow for alternative models of risk and expected return than the
CAPM.
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.
d) Stock
Selection: Overall performance of the fund can be
examined in terms of superior or inferior stock selection and the normal return
associated with a given level of risk. Thus, Total Excess Return = Selecting +
Risk. To earn average returns, the fund managers have to diversify. The
market pays returns only on the basis of systematic risk. The level of
diversification can be judged on the basis of the correlation between the
portfolio returns and the returns for a market portfolio. A completely
diversified portfolio is perfectly correlated with the market portfolio, which
is in turn completely diversified. To earn the above average return, fund
managers will generally have to forsake some diversification that will have its
cost in terms of additional portfolio risk. Hence some additional return is
needed for this additional diversification risk. Capital Market Line (CML)
helps in determining the risk commensurate with the incurred risk.
7. (a)
Calculate the full price of a 3 months (91 days) call and put options with
exercise price of 120 for a stock quoting at Rs. 100. Assume interest rate of
10% and S.D. of 0.8.
Or
(b) Stock PQR is currently priced at Rs. 1010. A put option with exercise price of Rs. 980 is available for Rs. 42. What are the intrinsic value and time value?
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