SAPM Solved Papers May' 2019, Dibrugarh University B.Com 4th/6th Sem

Security Analysis and Portfolio Management Solved Question Paper May 2019
2019 (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. Write on each of the following in one sentence: 1x8=8

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.

b) Real estate.

Ans: Real estate means property in the form of land, houses and buildings which can used for personal purpose or can be given on rent or can be sold for huge gain.

c) Market risk.

Ans: 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 are due to basic sweeping changes in investor expectations is referred to as market risk.

d) Diversification.

Ans: Diversification is a strategy of investing in a variety of securities in order to lower the risk involved with putting money into few investments.

e) Efficient market hypothesis.

Ans: In an efficient market, all the relevant information is reflected in the current stock price. Information cannot be used to obtain excess return, the information has already been taken into account and absorbed in the prices.

f) Treynor’s index.

Ans: The Treynor index 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).

g) Capital market line.

Ans: 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.

h) Stock selection.

Ans: Stock selection is the process of selecting quality stocks with low risk and high return probability while creating a portfoilio.

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2. Write short notes on the following (any four):              4x4=16

a) Portfolio management.

Ans: The concept of Portfolio Management was developed by Harry M. Markowitz, with the publication of a landmark paper. ‘Portfolio Selection’, in March 1952, in the journal or Finance. Later William F. Sharpe joined in the development of modern Portfolio Theory. In recognition of their contribution. 1990 Nobel Prize for Economics was awarded to Markowitz, Sharpe and Miller. So, the topic Portfolio Management is a Nobel prize winning topic.

Portfolio management means the planning, execution and control of activities concerning constructing and attainable sets of portfolios, identifying the efficient portfolios, choosing a portfolio and if need be, revision of portfolio. The world of investment is full of disk. Portfolio management enables risk diversification and hence return for unit risk can be maximized through efficient portfolio construction, selection and revision.

Every investor wants maximum return and minimum risk. Though risk and return move in the same direction. The scale of return per unit of risk can be maximized through careful allocation of funds across different investment avenues. And such careful allocation is nothing but portfolio management. Risk is minimises through diversification. But all diversification may not help reducing risk. So, there is an optimal level for diversification. It is achieved through efficient portfolio management. Hence the need for portfolio management.

b) Convertible securities.

Ans: 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.

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) Jensen’s model.

Ans: 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 cannot mitigate unsystematic risk, as his knowledge of market is primitive.

e) 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.

f) Valuation of bond.

Ans: 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.

3. (a) Define the term Investment. Discuss the investment process involved in a series of activities starting from the policy formulation. 4+10=14


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.

Investment of hard earned money is a crucial activity of every human being. Investment is the commitment of funds which have been saved from current consumption with the hope that some benefits will be received in future. Thus, it is a reward for waiting for money. Savings of the people are invested in assets depending on their risk and return demands.

Investment refers to the concept of deferred consumption, which involves purchasing an asset, giving a loan or keeping funds in a bank account with the aim of generating future returns. Various investment options are available, offering differing risk-reward tradeoffs. An understanding of the core concepts and a thorough analysis of the options can help an investor create a portfolio that maximizes returns while minimizing risk exposure.

Necessary steps in the process of Investments:

The following Steps are involved in the process of investment:

1.Policy Formulation: The first stage in investment journey is to determine the policy which an investor must following during entire process. It may also be called preparation of the investment policy stage. The investor must create a set of rules for himself which he must follow. Fixation of such rules depends on the knowledge of the investor. Key for success in investment is discipline and continuity. The investor has to see that he should be able to create an emergency fund, an element of liquidity and quick convertibility of securities into cash. This stage may, therefore; be considered appropriate for identifying investment assets and considering the various features of investments.

2. Objective and Source of the investments: The second important stage before making investment is to determine the objectives of the investments. It addition to this, the investor has to see that he should be able to create an adequate fund for investments. This stage is important because investments assets and their relative features are identified under this stage.

3. Analysis of various investment alternatives: When an individual has arranged a logical order of the types of investments that he requires on his portfolio, the next step is to analyse the various investment alternative for his portfolio. He must make a comparative analysis of the type of industry, kind of security and fixed vs. variable securities. Future behaviour or prices and stocks, the expected returns and associated risk must be taken into consideration while analysing various investment alternatives.

4. Valuation of securities: The third step is perhaps the most important consideration of the valuation of investments. Investment value, in general, is taken to be the present worth to the owners of future benefits from investments. The investor has to bear in mind the value of these investments. An appropriate set of weights have to be applied with the use of forecasted benefits to estimate the value of the investment assets. Comparison of the value with the current market price of the asset allows a determination of the relative attractiveness of the asset. Each asset must be valued on its individual merit. Finally, the portfolio should be constructed.

5. Construction of portfolio:  Under features of an investment programme, portfolio construction requires knowledge of the different aspects of securities. While evaluating securities, the investor should realize that investments are made under conditions of uncertainty. These cannot be a magic formula which will always work. The investor should be concerned with concepts and applications that will satisfy his investment objectives and constantly evaluate the performance of his investments. If need be, the investor may consider switching over to alternate proposals.


(b) What do you mean by unsystematic risk? What are its sources? How can it be managed? Detail out with examples. 3+3+8=14

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 shareholders. 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 managed?

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.

4. (a) Write a detailed note on traditional portfolio analysis.       14

Ans: Traditional portfolio analysis: Traditional portfolio analysis has been of a very subjective nature for each individual. The investors made the analysis of individual securities through the evaluation of risk and return conditions in each security. The normal method of finding the return on an individual security was by finding out the amounts of dividends that have been given by the company, the price earning ratios, the common holding period and by an estimation of the market value of the shares. The traditional theory assumes that selection of securities should be based on lowest risk as measured by its standard deviation from the mean of expect returns. The greater the variability of returns the greater is the risk. Thus, the investor chooses assets with the lowest variability of returns.

Moreover, Traditional Theory believes that the market is inefficient and the fundamental analyst can take advantage of the situation. By analyzing internal financial statements of the company, he can make superior profits through higher returns. The technical analysts believed in the market behaviour and past trends to forecast the future of the securities. This analysis was mainly under the risk and return criteria of single security analysis.

Traditional Approach to Portfolio Construction

Under this approach, investor’s needs in terms of income and capital appreciation are evaluated and appropriate securities are selected. After that risk and return analysis is carried out. Finally, weights are assigned to securities like bonds, stocks and debentures keeping in view the risk and return involved and then diversification is carried out. The following steps may be carried out:

1. Analysis of the constraints: It involves analysis of constraints of the investor within which the objectives will be formulated. The constraints may be decided on the basis of:

a) Income needs: Investors need for current income and constant income.

b) Liquidity needs: Investors preference for liquid assets.

c) Safety of principal: Safety of principal value at the time of liquidation.

d) Time horizon: Life cycle stage and investment planning period of the investor.

e) Tax consideration: Tax benefits of investment in a particular asset.

f) Temperament: Risk bearing capacity of the investor.

2. Determination of Objectives of Investors: It involves formulation of objectives within the framework of constraints. The basic objective of all investors is to achieve the maximum level of return and minimize the risk involved. Other objectives such as safety, liquidity hedge against inflation etc. are the subsidiary objectives. Some common objectives of the investors are:

a) Current income

b) Growth in income

c) Capital appreciation

d) Preservation of capital

3. Selection of the Securities: The selection of the securities depends upon the various objectives of the investor:

a)       If objective is to earn adequate amount of current income, then more of debt and less of equity would be a good combination.

b)      If the investor wishes a certain percentage of growth in the income from his investment, then he may have more of equity shares (say more than 60%) and less of debt (say 0-40%) in his portfolio. Inclusion of debt in portfolio helps the investor to avail of tax benefits.

c)       If the investor wants to multiply his investment over the years, he may invest in land or housing schemes. These investments offer faster rate of capital appreciation but lack liquidity. In stock market, the value of shares multiplies at much higher rates but involve risk.

d)      The investor’s portfolio may consist of more of debt instruments than equity shares with a view to ensure more safety of the principal amount.

4. Risk and Return Analysis: The objective of portfolio management is to maximize the return and minimize the risk. Risk is uncertainty of income/capital appreciation or loss of both. The two types of risks evolved are:

a)       Systematic or market related risks arises due to non-availability of raw material, interest rates fluctuations, inflation, import and export policy of the government., taxation policy, government policies, general business risk, financial risk etc.

b)      Unsystematic risk or company related risk due to mismanagement, defective sales policies, increasing inventory, faulty financial policies, labour problems, defective marketing of products resulting into decreased demand etc.

5. Diversification: The unsystematic risks or company related risks involved in investment and portfolio management can be reduced and returns can be optimized through diversification i.e. by carefully selecting variety of the assets, instruments, industry and scrip of companies/government securities. When different assets are added to the portfolio, the total risk tends to decrease.


(b) Simron hold portfolio of two companies P and Q with the following details:




Security return

Security variance

Investment proportion









Under the Markowitz model, what are the portfolio return and portfolio risk?      14

5. (a) Explain the arbitrage pricing theory (APT). What are its limitations?            9+5=14

Ans: Arbitrage Pricing Theory (APT)

Arbitrage Pricing Theory (APT) is an alternate version of Capital Asset Pricing Model (CAPM). This theory, like CAPM provides investors with estimated required rate of return on risky securities. It is a multifactor mathematical model used to describe the relation between the risk and expected return of securities in financial markets. It computes the expected return on a security based on the security’s sensitivity to movements in macroeconomic factors. The resultant expected return can then be used to price the security.

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.

Limitations of Arbitrage Pricing Theory:

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.


(b) Discuss the limitations of factor models. In what way two-factor model is better than one-factor model? Justify your answer.     6+8=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.

Limitations of factor model

1.    It is very difficult for factor model analyst is to identify the right factors. It depends to too many considerations. If the data set is affected by high inter correlation and other violation of regression assumptions, then the model can become unstable.

2.    One task of the task of factor model analyst is deciding how many factors are to be considered. There are a variety of methods for determining this but all methods are not suitable in every situation.

3.    At times adding more factors might not explain the effect on the dependent variable and therefore the model might reach a particular limit and that might not be too extensive to justify the time, money, and effort that goes into such analysis.

4.    Factor models involves high cost. They require the use of advanced statistical techniques which in turn require expensive technology and therefore cannot be used the retail investors or small companies with limited financial resources.

5.    Since advanced mathematical calculation involved in factor model calculation, highly qualified and skilled human capital required which are either not available or if available, cost of such human capital is too high.

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.

Multiple factor model is superior to single factor model due to the following advantages:

a)       In Multiple-factor model, 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)      Multiple-factor 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)       Multiple-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)      Multiple-factor model works better in multi period cases as against CAPM which is suitable for single period cases only.

e)      Multiple-factor model can be applied to cost of capital and capital budgeting decisions.

f)        The Multiple-factor 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 Multiple-factor model based APT is a less restrictive model.

6. (a) What are the differences between Sharpe’s and Treynor’s measures of portfolio performance? Explain with a suitable example.  14

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) Compare between Treynor’s index and Sharpe’s index for the following data and comment:   14




Riskless Return













Full Marks: 80

Pass Marks: 32

Time: 3 hours

1. Write on each of the following in one sentence:  1x8=8

a)          Investment.

b)         Redeemable debenture.

c)          Diversification.

d)         Portfolio analysis.

e)         Combining securities.

f)           Market risk.

g)          Call option.

h)         Efficient market hypothesis.

2. Write short notes on the following (any four):  4x4=16

a)          Fundamental analysis.

b)         Markowitz model.

c)          Risk of buying and selling options.

d)         Future market.

e)         Arbitrage pricing theory.

f)           Effects of combining securities.

3. (a) How would you differentiate Risk from Uncertainty? Do you think that all risks can be avoided? Justify your answer.  5+6=11


(b) Distinguish between:                        

1)         Investment and Gambling.

2)         Investment and Speculation.

4. (a) Discuss the uses of modern portfolio theory in other disciplines of finance.      12


(b) Stock x and y have yielded the following returns for the past two years:                                        12






2016 – 17

2017 – 18





1)         What is the expected return on portfolio made up to 60% of x and 40% of y?

2)         Find out the standard deviation of each stock.

3)         What is the covariance and co-efficient of correlation between x and y?

4)         What is the portfolio risk of a portfolio made up to 60% of x and 40% of y?

5. (a) Discuss the assumption of CAPM model. Do you think that it is acceptable in Indian context? Justify your argument with example.        11


(b) Calculate the equilibrium rate of return for the following three securities:                                   11








– 0.5






6. (a) Explain in brief Sharpe’s and Treynor’s performance evaluation models?     


(b) Discuss with examples why Jensen’s alpha is better than other contemporary models of portfolio performance.   11

7. (a) Define ‘option’. Explain the different types of options. Discuss the uses of options.   2+4+5=11


(b) What is ‘Future Contract’? Distinguish between future and forward contract. Explain the different types of margin in future contract.      2+4+5=11


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