SAPM Solved Papers May' 2017, Dibrugarh University B.Com 4th/6th Sem

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: 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.


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 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:



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: 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:




Expected Return

Risk (σ) of security






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.


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:


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)


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.


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


What are the factors that you would consider before making any investment decisions? Discuss.    11

4. Write a detailed note on Markowitz model.               11


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


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


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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