SAPM Solved Papers May' 2014, Dibrugarh University B.Com 4th/6th Sem

Security Analysis and Portfolio Management Solved Question Paper May 2014
2014 (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

The figures in the margin indicate full marks for the questions.

1. What do you mean by the following (in one sentence only)? 1x8=8

a) Investment.

Ans: Investment is the employment of funds with the aim of getting return on it. In general terms, investment means the use of money in the hope of making more money. In finance, investment means the purchase of a financial product or other item of value with an expectation of favorable future returns.

b) Diversification.

Ans: 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.

c) Risk.

Ans: Risk may be described as variability/fluctuation/deviation of actual return from expected return from a given asset/investment. Higher the variability, greater is the risk. In other words, the more certain the return from an asset, lesser is the variability and thereby lesser is the risk.

d) Option.  (Out of Syllabus)

e) Market timing.

Ans: . Market timing implies assessing correctly the direction of the market, either bull or bear and positioning the portfolio accordingly. When there is a forecast of declining market, the managers should position the portfolio properly by increasing the cash percentage of the portfolio or by decreasing the beta of the equity portion of the portfolio. When the forecast is of rising market, the managers should decrease the cash position or increase the beta of the equity portion of the portfolio.

f) Convertible securities.

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.

g) Portfolio.

Ans: Portfolio refers to the allocation of funds among a variety of financial assets available for investment.

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2. Write short notes on the following: 4x4=16

a) Future market. (Out of syllabus)

b) Factor models.

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.

c) Fundamental analysis.

Ans: Fundamental analysis is method of finding out the future price of a stock which an investor wishes to buy. Fundamental analysis is used to determine the intrinsic value of the share of a company to find out whether it is overpriced or under priced by examining the underlying forces that affect the well being of the economy, Industry groups and companies.

Fundamental analysis is simply an examination of future earnings potential of a company, by looking into various factors that impact the performance of the company. The prime objective of a fundamental analysis is to value the stock and accordingly buy and sell the stocks on the basis of its valuation in the market. The fundamental analysis consists of economic, industry and company analysis. This approach is sometimes referred to as a top-down method of analysis.

Types of fundamental analysis to be done before making Investment

The actual value of a security, as opposed to its market price or book value is called intrinsic value. The intrinsic value includes other variables such as brand name, trademarks, and copyrights that are often difficult to calculate and sometimes not accurately reflected in the market price. One way to look at it is that the market capitalization is the price (i.e. what investors are willing to pay for the company and intrinsic value is the value (i.e. what the company is really worth). The fundamental analysis consists of economic, industry and company analysis. This approach is sometimes referred to as a top-down method of analysis.

a)       At the economy level, fundamental analysis focus on economic data (such as GDP, Foreign exchange and Inflation etc.) to assess the present and future growth of the economy.

b)      At the industry level, fundamental analysis examines the supply and demand forces for the products offered.

c)       At the company level, fundamental analysis examines the financial data (such as balance sheet, income statement and cash flow statement etc.), management, business concept and competition.

d) Fixed securities.

Ans: 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.

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.

3. (a) Discuss the different avenues available to an investor for making investments.     11

Ans: Different methods of the classification of the investment avenues are available. Some of the methods are as follows:

1.       Physical Investments: Physical investments are tangible assets like motorcars, aero planes, ships, buildings, plant and machinery etc. some of the physical assets like machinery, equipment etc. are useful for further production whereas some like gold and silver ornaments, motor cars etc. are not useful for further production.

2.       Financial Investment: Financial assets are those which are used for consumption or for production of goods and services or for further creation of assets. Examples are shares, NSS certificates, bonds, etc.

3.       Marketable and Non-Marketable Investments: Some investments which are listed on the stock exchanges are easily marketable and can converted into cash in a short time e.g. shares, bonds and other instruments issues by government or companies. Non-marketable investments like bank deposits, provident funds, insurance schemes etc. cannot be bought or sold in the open market in the stock exchanges and thus are difficult to be converted into cash immediately.

4.       Transferable and Non-Transferable: Instruments like shares, bonds can be transferred in the name of others or can be sold or exchanged for cash or kind, whereas some instruments like insurance certificates, NSCs, cannot be transferred.

Investments Avenues

Wide varieties of investment avenues are now available in India. An investor can himself select the best avenue after studying the merits and demerits of different avenues. Even financial advertisements, newspaper supplements on financial matters and investment journals offer guidance to investors in the selection of suitable investment avenues. Investment avenues are the outlets of funds. A wide range of investment alternatives are available, they fall into two broad categories, viz, financial assets and real assets. Financial assets are paper (or electronic) claim on some issuer such as the government or a corporate body. The important financial assets are equity shares, corporate debentures, government securities, deposit with banks, post office schemes, mutual fund shares, insurance policies, and derivative instruments. Real assets are represented by tangible assets like residential house, commercial property, agricultural farm, gold, precious stones, and art object. As the economy advances, the relative importance of financial assets tends to increase. Some of the important investment alternatives are given below:

a)      Non-marketable Financial Assets: A good portion of financial assets is represented by non-marketable financial assets. A distinguishing feature of these assets is that they represent personal transactions between the investor and the issuer. For example, when you open a savings bank account at a bank you deal with the bank personally. In contrast when you buy equity shares in the stock market you do not know who the seller is and you do not care. These can be classified into the following broad categories:

1)      Post office deposits

2)      Company deposits

3)      Provident fund deposits

4)      Bank deposits

b)      Equity shares: By investing in shares, investors basically buy the ownership right to that company. When the company makes profits, shareholders receive their share of the profits in the form of dividends. In addition, when a company performs well and the future expectation from the company is very high, the price of the company’s shares goes up in the market. This allows shareholders to sell shares at profit, leading to capital gains. Investors can invest in shares either through primary market offerings or in the secondary market.

c)       Preference Shares: Preference shares refer to a form of shares that lie in between pure equity and debt. They have the characteristic of ownership rights while retaining the privilege of a consistent return on investment. The claims of these holders carry higher priority than that of ordinary shareholders but lower than that of debt holders. These are issued to the general public only after a public issue of ordinary shares.

d)      Debentures and Bonds: These are essentially long-term debt instruments. Many types of debentures and bonds have been structured to suit investors with different time needs. Debentures and Bonds are the instruments that are considered as a relatively safer investment avenues. Though having a higher risk as compared to bank fixed deposits, bonds, and debentures do offer higher returns.

e)      Mutual Fund Schemes: The Unit Trust of India is the first mutual fund in the country. A number of commercial banks and financial institutions have also set up mutual funds. Mutual funds have been set up in the private sector also. These mutual funds offer various investment schemes to investors. The number of mutual funds that have cropped up in recent years is quite large and though, on an average, the mutual fund industry has not been showing good returns, select funds have performed consistently, assuring the investor better returns and lower risk options.

f)        Money market instrument: By convention, the term "money market" refers to the market for short-term requirement and deployment of funds. Money market instruments are those instruments, which have a maturity period of less than one year. Examples of money market instruments are T-Bills, Certificate of Deposit, Commercial Paper etc.

g)      Life insurance: Now-a-days life insurance is also being considered as an investment avenue. Insurance premiums represent the sacrifice and the assured sum the benefit. Under it different schemes are:

1)      Endowment assurance policy

2)      Money back policy

3)      Whole life policy

4)      Term assurance policy

h)      Real estate: With the ever-increasing cost of land, real estate has come up as a profitable investment proposition.

i)        Bullion Investment: The bullion market offers investment opportunity in the form of gold, silver, and other metals. Specific categories of metals are traded in the metals exchange. The bullion market presents an opportunity for an investor by offering returns and end value in future. It has been observed that on several occasions, when the stock market failed, the gold market provided a return on investments.

j)        Financial Derivatives: These are such instruments which derive their value from some other underlying assets. It may be viewed as a side bet on the asset. The most important financial derivatives from the point of view of investors are Options and Futures.


(b) What do you mean by technical analysis? Differentiate between technical analysis and fundamental analysis. 4+7=11

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”.

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 discounts everything. The price of the security quoted represents the hope, fears and inside information received by the market players. Insider information regarding the issuance of bonus shares and right issues may support the prices. The loss of earnings and information regarding the forthcoming labor problem may result in fall in price. These factors may cause a shift in demand and supply, changing the direction of trends.

4.       The market always moves in the trends except for minor deviations.

Difference between technical and fundamental analysis

The key differences between technical analysis and fundamental analysis are as follows:

1.       Technical analysis mainly seeks to predict short term price movements, whereas fundamental analysis tries to establish long term values.

2.       The focus of technical analysis is mainly on internal market data, particularly price and volume data. The focus of fundamental analysis is on fundamental factors relating to the economy, the industry, and the firm.

3.       Technical analysis appeals mostly to short-term traders i.e. speculators, whereas fundamental analysis appeals primarily to long-term investors.

4.       Technical analysis is the a simple and quick method on forecasting behaviour of stock prices. Whereas, fundamental analysis involves compilation and analysis of huge amount of data and is therefore, complex, time consuming and tedious in nature.

5.       The technical analysis is based on the premise that the history repeats itself. Therefore, the technical analysis answers the question “What had happened in the market” while on the basis of potentialities of market fundamental analysis answers the question, “What will happen in the market”.

6.       The technical analysis assumes that the market is 90 percent psychological and 10 percent logical, while the fundamental analysis believes that the market is 90 percent logical and 10percent psychological.

7.       The technical analysis seeks to estimate security prices rather than values, while the fundamental analysis estimates the intrinsic value of a security.

8.       According to technical analysts, their method is far superior than the fundamental analysis, because fundamental analysis is based on financial statements which themselves are plagued by certain deficiencies like subjectivity, inadequate disclosure etc.

4. (a) How can risk of an asset be calculated? Write a note on the diversification of risk. 2+10=12

Ans: Risk can be defined as the combination of the probability of an event occurring and the consequences if that event does occur. This gives us a simple formula to measure the level of risk in any situation. Risk = Likelihood x Severity.

Diversification of Risk

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.

 Diversification may take any of the following forms:

a)    Different Assets e.g. gold, bullion, real estate, government securities etc.

b)    Different Instruments e.g. Shares, Debentures, Bonds, etc.

c)    Different Industries e.g. Textiles, IT, Pharmaceuticals, etc.

d)    Different Companies e.g. new companies, new product company’s etc.

Proper diversification involves two or more companies/industries whose fortunes fluctuate independent of one another or in different directions. One single company/industry is always more risky than two companies/industries. Two company’s in textile industry are more risky than one company in textile and one in IT sector two companies/industries which are similar in nature of demand a market are more risky than two in dissimilar industries.

Some accepted methods of effecting diversification are as follows:

a)    Random Diversification: Randomness is a statistical technique which involves placing of companies in any order and picking them up in random manner. The probability of choosing wrong companies will come down due to randomness and the probability of reducing risk will be more. Some experts have suggested that diversification at random does not bring the expected return results. Diversification should, therefore, be related to industries which are not related to each other.

b)    Optimum Number of Companies: The investor should try to find the optimum number of companies in which to invest the money. If the number of companies is too small, risk cannot be reduced adequately and if the number of companies is too large, there will be diseconomies of scale. More supervision and monitoring will be required and analysis will be more difficult, which will increase the risk again.

c)    Adequate Diversification: An intelligent investor has to choose not only the optimum number of securities but the right kind of securities also. Otherwise, even if there are a large number of companies, the risk may not be reduced adequately if the companies are positively correlated with each other and the market. In such a case, all of them will move in the same direction and many risks will increase instead of being reduced.

d)    Markowitz Diversification: Markowitz theory is also based on diversification. According to this theory, the effect of one security purchase over the effects of the other security purchase is taken into consideration and then the results are evaluated.

Importance of Diversification in Portfolio Management

Diversification of investments is significant due to the following reasons:

1. Reduce the risk: Every stock or financial instrument carries some amount of risk with it except the risk-free investments. With portfolio diversification, one cannot completely remove the risks but can reduce the risk to a great extent. Without proper diversification amongst the different classes of the assets, the risk of investment rises with every investment we make. One needs to include both risky asset classes such as high- return generating stocks and to hedge their risk they should invest in fixed income assets. Diversification gradually reduces the risk of the portfolio over time.

2. Helps In Hedging: If investments are entirely made in stock market, then in case of excessive volatility the return on investments will dropped significantly. However, if they investors kept a certain amount of other investment assets like commodities, bonds, metals in their portfolio, their profits would have been higher because loss or low profits of the stock market would have been wiped off by the positive returns of the commodities market. Diversification helps in achieving desired or better returns even when the market is slow as there are other markets which make up for the negative or low yields of the former market. This way investors can hedge their investments and earn potential returns through portfolio diversification.

3. Provide Higher Returns: Since the market keeps on changing, we need to diversify with asset classes which are not correlated. Correlation plays the most critical role in determining returns. If we are investing in one market which is connected to the other, when the former goes down, that will substantially affect the other. We need to choose investment vehicles which are entirely different from each other. That’s why we need a diversified portfolio.

4. Aligning Portfolio With Financial Aspirations: As per the Behavioural portfolio theory, either our investment will give us the potential for high-growth, or it will protect from negative returns. This theory states that when a portfolio is diversified, it corresponds to a pyramid structure. A properly diversified portfolio has the maximum of low-risk investments and provides value growth and steady income generation. ‘Blend’ funds comprise the top of this pyramid which is a mix of risky and low-risk investment instruments. The regular income generating investments will provide with periodic income, and the blend funds will grow in value, and together they bring stability of investment and higher wealth accumulation.

5. Investment Mix Adjustment: Portfolio diversification allows us to modify investment mix as per changing financial needs and market changes. With age, the investment mix also needs to be changed as the tenure for investments keeps on reducing. While we start off with high-risk investment instruments, with time flowing, we must reduce our risk by shifting more towards fixed income financial instruments for regular earnings. While an investor of 20’s age group can assign 90% of his investment into stocks, investor of 50’s age group must have not more than 40% allocated to equities. That’s why we need a diversified portfolio.

Problems of Diversification

Investment in too many assets may lead to the following problems:

1)      Purchase of bad stocks. While buying stocks at random, sometimes, the investor may purchase certain stocks which will not yield the expected return.

2)      Difficulty in obtaining information. When there are too many securities in a portfolio, it becomes difficult for the portfolio manager to obtain detailed information about their performance. In the absence of information he may not provide right advice as to what to buy and what not to buy.

3)      Increased research cost. Before the purchase of stocks, detailed analysis as to economic and technical performance of individual stock has to be carried out. This requires collecting and processing of information and storing the same. These procedures involve high costs in terms of salaries to be paid to the analysts who are specialized people in this field.

4)      Increased transaction cost. Some cost has to be incurred whenever a stock is to be purchased. Purchasing stocks in small quantities frequently involves higher transaction cost than the purchase of large quantity in one go.


(b) What do you understand by Portfolio Management? Write a note on the time value of money.   4+8=12

Ans: 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.

Time Value of Money (TVM)

Time value of money is the concept that the value of a rupee to be received in future is less than the value of a rupee on hand today. One reason is that money received today can be invested thus generating more money in near future. Another reason is that when a person opts to receive a sum of money in future rather than today, he is effectively lending the money and there are risks involved in lending such as default risk and inflation. Default risk arises when the borrower does not pay the money back to the lender. Inflation is the rise in general level of prices.

Time value of money principle also applies when comparing the worth of money to be received in future and the worth of money to be received in further future. In other words, TVM principle says that the value of given sum of money to be received on a particular date is more than same sum of money to be received on a later date.

While calculating time value the following points are taken into consideration:

Present Value: When a future payment or series of payments are discounted at the given rate of interest up to the present date to reflect the time value of money, the resulting value is called present value.

Future Value: Future value is amount that is obtained by enhancing the value of a present payment or a series of payments at the given rate of interest to reflect the time value of money.

Interest: Interest is charge against use of money paid by the borrower to the lender in addition to the actual money lent.

Time Value of Money Formula

The time value of money is an important concept not just for individuals, but also for making business decisions. Companies consider the time value of money in making decisions about investing in new product development, acquiring new business equipment or facilities, and in establishing credit terms for the sale of their products or services. A specific formula can be used for calculating the future value of money so that it can be compared to the present value:

 FV = PV x [1+ (i/n)] (nxt)


FV = the future value of money

PV = the present value

i = the interest rate or other return that can be earned on the money

t = the number of years to take into consideration

n = the number of compounding periods of interest per year

Application of Time Value of Money Principle

There are many applications of time value of money principle. For example, we can use it to compare the worth of cash flows occurring at different times in future, to find the present worth of a series of payments to be received periodically in future, to find the required amount of current investment that must be made at a given interest rate to generate a required future cash flow, etc.

5. (a) Discuss in detail the capital asset pricing model.    11

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.

Mathematical expression of CAPM: 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

rf is the risk-free rate

E (rM) is the expected return of the market portfolio

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.

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.

Advantages of CAPM

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.

Drawbacks of CAPM

Despite the consistent use of the model over the years there has been some criticism for a few reasons:

1)      Unrealistic assumptions: Capital asset pricing model is based on a number of assumptions that are far from the reality. For example it is very difficult to find a risk free security. A short term highly liquid government security is considered as a risk free security. It is unlikely that the government will default, but inflation causes uncertain about the real rate of return.

2)      Based on future expectations: The CAPM is based on expectations about the future but empirical tests and data for practical use are exclusively based on historical returns.

3)      Risk-free Rate (Rf): The commonly accepted rate used as the Rf is the yield on short-term government securities. The issue with using this input is that the yield changes daily, creating volatility.


(b) Compare and contrast between capital market line and security market line.

Ans: Capital Market Line (CML)

Capital Market Line (CML) is a line used in the capital asset pricing model to illustrate the rates of return for efficient portfolios depending on the risk-free rate of return and the level of risk (standard deviation) for a particular portfolio.

The CML is derived by drawing a tangent line from the intercept point on the efficient frontier to the point where the expected return equals the risk-free rate of return. The CML is considered to be superior to the efficient frontier since it takes into account the inclusion of a risk-free asset in the portfolio.

The CML is the relationship between the risk and the expected return for portfolio. The CML results from the combination of the market portfolio and the risk-free asset. All points along the CML have superior risk-return profiles to any portfolio on the efficient frontier, with the exception of the Market Portfolio, the point on the efficient frontier to which the CML is the tangent. From a CML perspective, this portfolio is composed entirely of the risky asset, the market, and has no holding of the risk free asset ,i.e., money is neither invested in, nor borrowed from the money market account.

Security market line (SML)

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.

Difference between Capital Market Line and Security Market Line

1. The CML is a line that is used to show the rates of return, which depends on risk-free rates of return and levels of risk for a specific portfolio. SML, which is also called a Characteristic Line, is a graphical representation of the market’s risk and return at a given time.

2. While standard deviation is the measure of risk in CML, Beta coefficient determines the risk factors of the SML.

3. While the Capital Market Line graphs define efficient portfolios, the Security Market Line graphs define both efficient and non-efficient portfolios.

4. The CML determines the risk or return for efficient portfolios, and the SML demonstrates the risk or return for individual stocks.

5. Where the market portfolio and risk free assets are determined by the CML, all security factors are determined by the SML.

6. While calculating the returns, the expected return of the portfolio for CML is shown along the Y- axis. On the contrary, for SML, the return of the securities is shown along the Y-axis.

7. The standard deviation of the portfolio is shown along the X-axis for CML, whereas, the Beta of security is shown along the X-axis for SML.

8. Finally, the Capital Market Line is considered to be superior when measuring the risk factors.

6. (a) What are the differences between Sharpe’s and Treynor’s measures of portfolio performance? Explain with a suitable example.  11

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

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.




Average return


Risk Free Rate









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%)

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


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:






Risk free Rate









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.

Difference between Sharpe’s and Treynor’s

Comparison of Sharpe’s and Treynor’s measures of portfolio performance





Sharpe used standard deviation as the risk measure to capture the overall risk of the portfolio.

Treynor used beta as the risk measure to capture the volatility of the portfolio relative to the market.


Sharpe ratio is applicable to all portfolios.

Treynor is applicable to well-diversified portfolios.

Performance measurement

Sharpe is a more forward-looking performance measure.

Treynor is used to measure historical performance.


According to Sharpe, investor is concerned about the total risk.

According to Treynor, investor is concerned about the systematic risk.


Sharpe Index (St) = (Rt - Rf)/Sd

Treynor's Index (Tt) = (Rt – Rf)/Bt


(b) Determine the Treynor’s and Jensen’s measures of portfolio performance from the given information:

      Average rate of return on market portfolio                     18%

      Average rate of return on this portfolio                            19%

      Average risk-free rate of return                                            12%

      Standard deviation of this portfolio                                    14%

      Beta of portfolio under consideration                                               0.95

7. (a) Write a note on the contract specifications in case of options. Discuss the process of trading of options.   5+6=11


(b) Differentiate between an option and a future. What are the essential specifications of a future contract? Explain. 5+6=11

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