Wednesday, May 15, 2019

Dibrugarh University B.Com 4th Sem: SAPM Solved Papers (May' 2015)


2015 (May)
The figures in the margin indicate full marks for the questions.
1. What do you mean by the following:                  1x8=8

a) Valuation of securities: The process of determining how much a security is worth is called valuation of securities. Security valuation is highly subjective, but it is easiest when one is considering thevalue of tangible assets, level of debt, and other quantifiable data of the company issuing a security.
b) In order to compare investment options, Markowitz developed a system to describe each investment or each asset class with math, using unsystematic risk statistics. Then he further applied that to the portfolios that contain the investment options. He looked at the expected rate-of-return and the expected volatility for each investment. He named his risk-reward equation The Efficient Frontier.
c) Market risk: The price of a stock may fluctuate widely within a short span of time even though earnings remain unchanged. The causes of this phenomenon are varied, but it is mainly due to a change in investors’ attitudes towards equities in general, or toward certain types or groups of securities in particular. Variability in return on most common stocks that is due to basic sweeping changes in investor expectations is referred to as market risk.
d) Risk Adjustment: Risk adjustment is a method to offset the cost of investments.
e) Systematic return is the part that depends upon the benchmark return and is calculated as beta times benchmark excess return.
f) Diversification: Risks involved in investment and portfolio management can be reduced through a technique called diversification. Diversification is a strategy of investing in a variety of securities in order to lower the risk involved with putting money into few investments. The traditional belief is that diversification means “Not putting all eggs in one basket.” Diversification helps in the reduction of unsystematic risk and promotes the optimization of returns for a given level of risks in portfolio management.
2. Write short note on:                                                 4x4=16
a) Nature of options.
b) Arbitrage.
c) Portfolio Management: Portfolio management is a dynamic concept and requires continuous and systematic analysis, judgement and operations. It is a process involving many activities of investment in assets and securities. Firstly, it involves construction of a portfolio based upon the data base of the client/investor, his objectives, constraint preferences for risk and return etc. On the basis of above mentioned facts, selection of assets and securities is made. Secondly, it involves monitoring/reviewing of the portfolio from time to time in light of changing market conditions. Accordingly changes are effected in the portfolio. Thirdly, it involves evaluation of the portfolio in terms of targets set for risk and return and making adjustments accordingly. Basically, portfolio management involves a proper decision making as to what to purchase and what to sell. It requires detailed risk and return analysis and proper money management in terms of investments in a basket of assets, the basic objective being reduction of risk and maximization or return.
d)  Convertible Securities: A convertible security is a type of security, usually a bond or a preferred stock, that can be converted into a different form of security, normally equity shares.
3. (a) What do you mean by unsystematic risk. What are its sources? How can it be managed? Discuss out with examples.                                                                
Ans: Unsystematic risk: Unsystematic Risk refers to that portion of total risk that is unique or peculiar to a firm or an industry, above and beyond that affecting securities markets in general. Factors like consumer preferences, labour strikes, management capability etc. cause unsystematic risk (variability of returns) for a company’s stock. Unlike systematic risk, the unsystematic risk can be reduced/avoided through diversification. Total risk of a fully diversified portfolio equals to the market risk of the portfolio as its specific risk becomes zero.
Sources of Unsystematic risk
a)      Business risk: Business risk relates to the variability of the sales, income, profits etc., which in turn depend on the market conditions for the product mix, input supplies, strength of competitors, etc. The business risk is sometimes external to the company due to changes in government policy or strategies of competitors or unforeseen market conditions. They may be internal due to fall in production, labour problems, raw material problems or inadequate supply of electricity etc. The internal business risk leads to fall in revenues and in profit of the company, but can be corrected by certain changes in the company’s policies.
b)      Financial Risk: This relates to the method of financing, adopted by the company; high leverage leading to larger debt servicing problems or short-term liquidity problems due to bad debts, delayed receivables and fall in current assets or rise in current liabilities. These problems could no doubt be solved, but they may lead to fluctuations in earnings, profits and dividends to share holders. Sometimes, if the company runs into losses or reduced profits, these may lead to fall in returns to investors or negative returns. Proper financial planning and other financial adjustments can be used to correct this risk and as such it is controllable.
c)       Default or insolvency risk: The borrower or issuer of securities may become insolvent or may default, or delay the payments due, such as interest instalments or principal repayments. The borrower’s credit rating might have fallen suddenly and he became default prone and in its extreme form it may lead to insolvency or bankruptcies. In such cases, the investor may get no return or negative returns. An investment in a healthy company’s share might turn out to be a waste paper, if within a short span, by the deliberate mistakes of Management or acts of God, the company became sick and its share price tumbled below its face value.
d)      Other Risks: Besides the above described risks, there are many more risks, which can be listed, but in actual practice, they may vary in form, size and effect. Some of such identifiable risks are the Political Risks, Management Risks and Liquidity Risks etc. Political risk may occur due to the changes in the government, or its policy shown in fiscal or budgetary aspects, changes in tax rates, imposition of controls or administrative regulations etc. Management risks arise due to errors or inefficiencies of management, causing losses to the company. Marketability liquidity risks involve loss of liquidity or loss of value in conversions from one asset to another say, from stocks to bonds, or vice versa. Such risks may arise due to some features of securities, such as callability; or lack of sinking fund or Debenture Redemption Reserve fund, for repayment of principal or due to conversion terms, attached to the security, which may go adverse to the investor. All the above types of risks are of varying degrees, resulting in uncertainty or variability of return, loss of income, and capital losses, or erosion of real value of income and wealth of the investor. Normally the higher the risk taken, the higher is the return.
Can risk be avoided?
Every investor wants to guard himself from the risk. This can be done by understanding the nature of the risk and careful planning.
1) Market Risk Protection
a.       The investor has to study the price behaviour of the stock. Usually history repeats itself even though it is not in perfect form. The stock that shows a growth pattern may continue to do so for some more period. The Indian stock market expects the growth pattern to continue for some more time in information technology stock and depressing conditions to continue in the textile related stock. Some stocks may be cyclical stocks. It is better to avoid such type of stocks. The standard deviation and beta indicate the volatility of the stock.
b.      The standard deviation and beta are available for the stocks that are included in the indices. The National Stock Exchange News bulletin provides this information. Looking at the beta values, the investor can gauge the risk factor and make wise decision according to his risk tolerance.
c.       Further, the investor should be prepared to hold the stock for a period of time to reap the benefits of the rising trends in the market. He should be careful in the timings of the purchase and sale of the stock. He should purchase it at the lower level and should exit at a higher level.
2) Protection against Interest Rate Risk
a.       Often suggested solution for this is to hold the investment sells it in the middle due to fall in the interest rate, the capital invested would experience tolerance.
b.      The investors can also buy treasury bills and bonds of short maturity. The portfolio manager can invest in the treasury bills and the money can be reinvested in the market to suit the prevailing interest rate.
c.       Another suggested solution is to invest in bonds with different maturity dates. When the bonds mature in different dates, reinvestment can be done according to the changes in the investment climate. Maturity diversification can yield the best results.
3) Protection against Inflation
a.       The general opinion is that the bonds or debentures with fixed return cannot solve the problem. If the bond yield is 13 to 15 % with low risk factor, they would provide hedge against the inflation.
b.      Another way to avoid the risk is to have investment in short-term securities and to avoid long term investment. The rising consumer price index may wipe off the real rate of interest in the long term.
c.       Investment diversification can also solve this problem to a certain extent. The investor has to diversify his investment in real estates, precious metals, arts and antiques along with the investment in securities. One cannot assure that different types of investments would provide a perfect hedge against inflation. It can minimise the loss due to the fall in the purchasing power.
4) Protection against Business and Financial Risk
a.       To guard against the business risk, the investor has to analyse the strength and weakness of the industry to which the company belongs. If weakness of the industry is too much of government interference in the way of rules and regulations, it is better to avoid it.
b.      Analysing the profitability trend of the company is essential. The calculation of standard deviation would yield the variability of the return. If there is inconsistency in the earnings, it is better to avoid it. The investor has to choose a stock of consistent track record.
c.       The financial risk should be minimised by analysing the capital structure of the company. If the debt equity ratio is higher, the investor should have a sense of caution. Along with the capital structure analysis. He should also take into account of the interest payment. In a boom period, the investor can select a highly levered company but not in a recession.
Or
(b) Discuss different measures to analyze the fundamental and to technical factors in ­­decision.
Ans: Tools and Techniques of fundamental Analysis
Financial statement means a statement or document which explains necessary financial information. Financial statements express the financial position of a business at the end of accounting period (Balance Sheet) and result of its operations performed during the year (Profit and Loss Account). In order to determine whether the financial or operational performance of company is satisfactory or not, the financial data are analyzed. Different methods are used for this purpose. The main techniques of financial analysis are:
The most commonly used techniques of financial analysis are as follows:
1. Comparative Statements: These are the statements showing the profitability and financial position of a firm for different periods of time in a comparative form to give an idea about the position of two or more periods. It usually applies to the two important financial statements, namely, balance sheet and statement of profit and loss prepared in a comparative form. The financial data will be comparative only when same accounting principles are used in preparing these statements. If this is not the case, the deviation in the use of accounting principles should be mentioned as a footnote. Comparative figures indicate the trend and direction of financial position and operating results. This analysis is also known as ‘horizontal analysis’.
Merits of Comparative Financial Statements:
a)      Comparison of financial statements helps to identify the size and direction of changes in financial position of an enterprise.
b)      These statements help to ascertain the weakness and soundness about liquidity, profitability and solvency of an enterprise.
c)       These statements help the management in making forecasts for the future.
Demerits of Comparative Financial Statements:
a)      Inter-firm comparison may be misleading if the firms are not of the same age and size, follow different accounting policies.
b)      Inter-period comparison will also be misleading if there is frequent changes in accounting policies.
2. Common Size Statements: These are the statements which indicate the relationship of different items of a financial statement with a common item by expressing each item as a percentage of that common item. The percentage thus calculated can be easily compared with the results of corresponding percentages of the previous year or of some other firms, as the numbers are brought to common base. Such statements also allow an analyst to compare the operating and financing characteristics of two companies of different sizes in the same industry. Thus, common size statements are useful, both, in intra-firm comparisons over different years and also in making inter-firm comparisons for the same year or for several years. This analysis is also known as ‘Vertical analysis’.
Merits of Common Size Statements:
a)      A common size statement facilitates both types of analysis, horizontal as well as vertical. It allows both comparisons across the years and also each individual item as shown in financial statements.
b)      Comparison of the performance and financial condition in respect of different units of the same industry can also be done.
c)       These statements help the management in making forecasts for the future.
Demerits of Common Size Statements:
a)      If there is no identical head of accounts, then inter-firm comparison will be difficult.
b)      Inter-firm comparison may be misleading if the firms are not of the same age and size, follow different accounting policies.
c)       Inter-period comparison will also be misleading if there is frequent changes in accounting policies.
3. Trend Analysis: It is a technique of studying the operational results and financial position over a series of years. Using the previous years’ data of a business enterprise, trend analysis can be done to observe the percentage changes over time in the selected data. The trend percentage is the percentage relationship, in which each item of different years bear to the same item in the base year. Trend analysis is important because, with its long run view, it may point to basic changes in the nature of the business. By looking at a trend in a particular ratio, one may find whether the ratio is falling, rising or remaining relatively constant. From this observation, a problem is detected or the sign of good or poor management is detected.
Merits of Trend analysis:
a)      Trend percentages can be presented in the form of Index Numbers showing relative change in the financial statements during a certain period.
b)      Trend analysis will exhibit the direction to which the concern is proceeding.
c)       The trend ratio may be compared with the industry, in order to know the strong or weak points of a concern.
Demerits of Common Size Statements:
a)      These are calculated only for major items instead of calculating for all items in the financial statements.
b)      Trend values will also be misleading if there is frequent changes in accounting policies.
4. Ratio Analysis: It describes the significant relationship which exists between various items of a balance sheet and a statement of profit and loss of a firm. As a technique of financial analysis, accounting ratios measure the comparative significance of the individual items of the income and position statements. It is possible to assess the profitability, solvency and efficiency of an enterprise through the technique of ratio analysis.
5. Funds flow statement: The financial statement of the business indicates assets, liabilities and capital on a particular date and also the profit or loss during a period. But it is possible that there is enough profit in the business and the financial position is also good and still there may be deficiency of cash or of working capital in business. Financial statements are not helpful in analysing such situation. Therefore, a statement of the sources and applications of funds is prepared which indicates the utilisation of working capital during an accounting period. This statement is called Funds Flow statement.
6. Cash Flow Analysis: A Cash Flow Statement is similar to the Funds Flow Statement, but while preparing funds flow statement all the current assets and current liabilities are taken into consideration. But in a cash flow statement only sources and applications of cash are taken into consideration, even liquid asset like Debtors and Bills Receivables are ignored. A Cash Flow Statement is a statement, which summarises the resources of cash available to finance the activities of a business enterprise and the uses for which such resources have been used during a particular period of time. Any transaction, which increases the amount of cash, is a source of cash and any transaction, which decreases the amount of cash, is an application of cash. Simply, Cash Flow is a statement which analyses the reasons for changes in balance of cash in hand and at bank between two accounting period. It shows the inflows and outflows of cash.
Tools of Technical Analysis:
Charting represents a key activity for a technical analyst during individual stock analysis. The probable future performance of a stock can be predicted and evolving and changing patterns of price behaviour can be detected based on historical price-volume information of the stock. Charts used to study the trend in prices, price index, and also volume of transactions. Technical analysis involves three basic types of charts. They are:
(a) Line charts,
(b) Bar charts, and
(3) Point and figure charts.
a)      A Line Chart connects successive trading day’s closing price/price indices or volume of trade as the case may. Each day’s price is recorded.
b)      A Bar Chart is made up by a series of vertical bars of lines, each bar of line representing; a particular day’s high and low prices. The closing price of a day is indicated by a small horizontal dash on the day’s bar. Each day’s price data are thus recorded.
c)       Point and figure charts are more complex than line and bar charts. Point and figure chart are not only used to detect reversals in a trend, but also used to forecasts the price, called price targets. The only significant price changes are posted to point and figure charts. Three or five point price changes as posted for high prices securities, only one point changes are posted follow prices securities. While line and bar charts have two dimensions with vertical column indicating trading day, point and figure chart represents each column as a significant reversals instead of a trading day. For example, for a share in the price hand of Rs. 1000-1500 or so, a price change exceeding, say, Rs. 15 may be taken as significant, whereas for a scrip in the price range of Rs. 100-150, a change in price of the order of Rs. 3 or more may be taken as significant. Upward significant moves are indicated by ‘x’ in the same column. Say for scrip of Rs. 3 change is taken as significant. Another ‘x’ in the same column, above the previous ‘x’ is put. The same day it moves to 107. One more ‘X’ is put. Next day price drifts by Rs. 2. No entry in price will he recorded in this column. If a significant increase in price takes place, next column of ‘x’ will be charted.
4. (a) Write a detailed note on fraudulent portfolio analyses.
Or
(b) Write a detailed note on Markowitz model.
Ans: MARKOWITZ MODEL
Dr. Harry M. Markowitz was the person who developed the first modern portfolio analysis model. Markowitz used mathematical programming and statistical analysis in order to arrange for the optimum allocation of assets within portfolio. He infused a high degree of sophistication into portfolio construction by developing a mean-variance model for the selection of portfolio. Markowitz approach determines for the investors the efficient set of portfolio through three importance variables - Return, standard deviation and coefficient of correlation.
Markowitz model is called the “Full Covariance Model”. Through this method the investor can find out the efficient set of portfolio by finding out the trade off between risk and return, between the limits of zero and infinity. Markowitz theory is based on several assumptions these are:
ASSUMPTIONS OF MARKOWITZ’S MODEL
a)      The markets are efficient and absorb all the information quickly and perfectly. So an investor can earn superior returns either by technical analysis or fundamental analysis. All the investors are in equal category in this regard.
b)      Investors are risk averse. Before making any investments, all of them, have a common goal-avoidance of risk.
c)       Investors are rational. They would like to earn the maximum rate of return with a given level of income or money.
d)      Investors base their decisions solely on expected return and variance (or standard deviation) of returns only.
e)      For a given risk level, investors prefer high returns to lower returns. Similarly, for a given level of expected return, they prefer less risk to more risk.
f)       The investor can reduce the risk if he adds investments to his portfolio.
g)      Investors consider each investment alternative as being represented by a probability distribution of expected returns over some holding period.
h)      A portfolio of assets under the above assumptions is considered to be efficient if no other portfolio of assets offers higher expected return with the same (or lower) risk or lower risk with the same (or higher) expected return.
PARAMETERS OF MARKOWITZ DIVERSIFICATION
Based on thorough and scientific research, Markowitz has set down his own guidelines for diversification:
b)      The investments have different types of risk characteristics. Some are systematic or market related risks and the others are unsystematic or company related risks.
c)       His diversification involves a proper number of securities not too less nor too many.
d)      The securities have no correlation or negative correlation.
e)      Last is the proper choice of the companies, securities or assets whose returns are not related and whose risks are mutually off setting to reduce the overall risk.
Markowitz lays down three parameters for building up the efficient set of portfolio:
a)      Expected returns.
b)      Standard deviation from mean to measure variability of returns.
c)       Covariance or variance of one asset return to other asset returns.
To generalize, higher the expected return, lower will be the standard deviation or variance and lower is the correlation. In such a case, better will be the security for investor choice. If the covariance of the securities’ returns is negative or negligible, the total risk of the portfolio of all securities may be lower as compared to the risk of the individual securities in isolation.
By developing his model, Markowitz first did away with the investment behaviour rule that the investor should maximize expected return. This rule implied that the non-diversified single security portfolio with the highest expected return is the most desirable portfolio. Only by buying that single security can expected return be maximized. The single security portfolio can be much preferred if the higher return turns out to be the actual return. However, in real world, there are conditions of so much uncertainty that most risk averse investors, joint with Markowitz in adopting diversification of securities.
5. (a) Discuss the assumptions of CAPM model. Do you think that it is acceptable in Indian context? Justify you argument with examples.
Ans: Capital market theory is an extension of the Portfolio theory of Markowitz. The portfolio theory explains how rational investors should build efficient portfolio based on their risk-return preferences. Capital Market Asset Pricing Model (CAPM) incorporates a relationship, explaining how assets should be prices in the capital market. The capital market theory uses the results of capital market theory to derive the relationship between the expected returns and systematic risk of individual securities and portfolios.
Capital asset pricing model is a tool used by investors to determine the risk associated with a potential investment and also gives an idea as to what can be the expected return on the investment. It was developed by William Sharpe along with a formula for working out the risk as who states that with an investment come two types of risks:
1) Systematic Risk: These are risks that cannot be diversified away such as interest rates and recessions. As the market moves and changes occur which affect the market, each individual asset is affected to some degree and therefore they are sensitive to change causing a high level of risk.
2) Unsystematic (Specific): These risk can be diversified through increasing the size of an investment portfolio as this risk is specific to individual stocks and effectively represents no correlation between stocks and market movements.
Assumptions of CAPM
The capital asset pricing model is based on certain explicit assumptions regarding the behavior of investors. The assumptions are listed below:
1.       Investor make their investment decisions on the basis of risk-return assessments measured in terms of expected returns and standard deviation of return.
2.       The purchase or sale of a security can be undertaken in infinitely divisible unit.
3.       Purchase and sale by a single investor cannot affect prices. This means that there is perfect competition where investors in total determine prices by their action.
4.       There are no transaction costs. Given the fact that transaction costs are small, they are probably of minor importance in investment decision-making, and hence they are ignored.
5.       There are no personal income taxes. Alternatively, the tax rate on dividend income and capital gains are the same, thereby making the investor indifferent to the form in which the return on the investment is received (dividends or capital gains).
6.       The investor can lend or borrow any amount of fund desired at a rate of interest equal to the rate of risk less securities.
7.       The investor can sell short any amount of any shares.
8.       Investors share homogeneity of expectations. This implies that investors have identical expectations with regard to the decision period and decision inputs. Investors are presumed to have identical expectations regarding expected returns, variance of expected returns and covariance of all pairs of securities.
CAPM is acceptable in India because of its various advantages which are stated below:
CAPM has been a popular model for calculating risk for over 40 years now and is therefore a proven method, some advantages are:
a)      Ease-of-use: CAPM is a simplistic calculation that can be easily stress-tested to derive a range of possible outcomes to provide confidence around the required rates of return.
b)      Systematic Risk: It considers only systematic risk, reflecting a reality in which most investors have diversified portfolios from which unsystematic risk has been essentially eliminated.
c)       Business and Financial Risk Variability: When businesses investigate opportunities, if the business mix and financing differ from the current business, then other required return calculations, like weighted average cost of capital (WACC) cannot be used. However, CAPM can.
d)      Determination of firm’s required return: To develop this overall cost of capital, the manager must have an estimate of the cost of equity capital. To calculate a cost of equity, some managers estimate the firm’s beta (often from historical data) and use the CAPM to determine the firm’s required return on equity.
e)      Public utility: The CAPM can also be used by the regulations of public utilities. Utilities rates can be set so that all costs, including costs of debt and equity capital, are covered by rates charged to consumers. In determining the cost of equity for the public utility, the CAPM can be used to estimate directly the cost of equity for the utility in question. The procedure is like that followed for any other firm. The beta and risk-free and market rates of return are estimated, and the CAPM is used to determine a cost of equity.
f)       Useful tool for investment managers: Investment practitioners have been more enthusiastic and creative in adapting the CAPM for their uses. The CAPM has been used to select securities, construct portfolios, and are forecastle considered under-valued, that is, attractive candidates for purchase.
g)      Most reliable and effective tool: Furthermore, in the opinion of most experts it is a more reliable and effective method of calculating risk than other models such as the Dividend Growth Model as CAPM takes into account a company's level of systematic risk against the stock market as a whole; this is a benefit as it allows for a company to compare itself to the market.
Or
(b) Discuss the limitation of factors models? In what way two factors model is better than one factor model? Justify.
Ans: In portfolio management computation of expected return, risk and covariance for every security included in the portfolio is crucial process and it proves a bit difficult too. Factor models relatively make the process easier as security return is assumed to be in correlation with one factor(s) or other(s). Factor models captured macro economic factors that systematically influence prices of securities. Any aspect of a security’s return unexplained by the factor model is taken as security specific. Factor models are otherwise known as index models. Securities return when assumed to be related to return on a market index, such model is called as market index model. Similar to return on market index, other factors to which security returns stand related can be modeled and used to estimate returns as securities. Similarly portfolio returns as related to identified factors can be found and used in portfolio management. And this will ease the problem of computing returns. One factor (say Market Return, Growth rate of gross Domestic Product or Inflation rate), two factors (any two of macro economic factors) and multi-factors models can be through of.
Limitations of factor models
a)      Problems in listing of various factors: The model requires listing of factors that have impact on the stock under consideration. Finding and listing all factors can be a difficult task and there is a risk that some or the other factor being ignored. Also risk of accidental correlations may exist which may cause a factor to become substantial impact provider or vice versa.
b)      Expected return of various factors: The expected returns for each of these factors will have to be arrived at, which depending on the nature of the factor, may or may not be easily available always.
c)       Difficult to measure Sensitivities of factors: The model requires calculating sensitivities of each factor which again can be a tedious task and may not be practically possible.
d)      Change in factors from time to time: The factors that affect the stock price for a particular stock may change over a period of time. Moreover, the sensitivities associated may also undergo shifts which need to be continuously monitored making it very difficult to calculate and maintain.
e)      Existence of arbitrage is essential: The APT model will prevail only if there is a opportunity of arbitrage. If arbitrage opportunity is not available, then this model does not prevail.
f)       Uncertain size or sign of factors: APT makes no statement about the size of sign of the factors.
g)      Unrealistic assumption: It is based on some assumptions which are not practical.
CAPM is based on single factor model and APT is based on multiple factor model. Multiple factor model is better than CAPM due the following reasons:
a)      APT model is a multi-factor model. So, the expected return is calculated taking into account various factors and their sensitivities that might affect the stock price movement. Thus it allows selection of factors that affect the stock price largely and specifically.
b)      APT model is based on arbitrage free pricing or market equilibrium assumptions which to a certain extent result in fair expectation of the rate of return on the risky asset.
c)       APT based multi factor model places emphasis on covariance between asset returns and exogenous factors unlike CAPM. CAPM places emphasis on covariance between asset returns and endogenous factors.
d)      APT model works better in multi period cases as against CAPM which is suitable for single period cases only.
e)      APT can be applied to cost of capital and capital budgeting decisions.
f)       The APT model does not require any assumption about the empirical distribution of the asset returns unlike CAPM which assumes that stock returns follow a normal distribution and thus APT a less restrictive model.

6. Write notes on any two of the following:
a)      Sharpe model.
b)      Treynor’s model.
c)        Jansen model.
d)      Stock selection.

Ans: a)  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.
Example
Portfolio
Average return
S.D.
Risk Free Rate
A
15%
3%
9%
B
20%
8%
9%
SA  = (15 – 9)/3 = 2
SB  = (20 – 9)/8 = 1.375
Thus, portfolio A is ranked higher because its index i.e. 2.0 is higher as compare to B’s index i.e. 1.375. This is despite the fact that B has a higher return (20% >15%)
Advantages of Sharpe’s Ratio:
a) The main advantage of this ratio is that it is easy to calculate and it is used widely.
b) This index gives a measure of portfolios total risk and variability of returns in relation to the risk premium.
c) The Sharpe ratio also standardizes the relationship between risk and return and therefore can be used to compare different asset classes i.e., comparison of stocks with commodities.
d) An advantage of Sharpe ratio is that a beta estimate is not required.
Disadvantages of Sharpe ratio:
a) When risk free rate is known, it is very difficult to find the right expected return and standard deviation. In a stable market, it is very easy to predict expected return but in today’s dynamic market it is very difficult to predict future expected return.
b) This ratio is not appropriate when evaluating individual stocks because it uses total risk rather than systematic.
c) It is overstated if the return are smoothen and historical prices are used.
d) It can be manipulated by the fund managers if non-linear derivatives are used.
b) The Treynor Measure
Jack L. Treynor based his model on the concept of characteristic line. This line is the least square regression line relating the return to the risk and beta is the slope of the line. The slope of the line measures volatility. A steep slope means that the actual rate of return for the portfolio is highly sensitive to market performance whereas a gentle slope indicates that the actual rate of return for the portfolio is less sensitive to market fluctuations.
The Treynor index, also commonly known as the reward-to-volatility ratio, is a measure that quantifies return per unit of risk. This Index is a ratio of return generated by the fund over and above risk free rate of return, during a given period and systematic risk associated with it (beta). The portfolio beta is a measure of portfolio volatility, which is used as a proxy for overall risk – specifically risk that cannot be diversified. A beta of one indicates volatility on par with the broader market, usually an equity index. A beta of 0.5 means half the volatility of the market. Portfolios with twice the volatility of the market would be given a beta of 2. Symbolically, Treynor’s ratio can be represented as:
Treynor's Index (Tt) = (Rt – Rf)/Bt
Whereas,
Tt = Treynor’ measure of portfolio
Rt = Return of the portfolio
Rf = Risk free rate of return
Bt = Beta coefficient or volatility of the portfolio
All risk-averse investors would like to maximize this value. While a high and positive Treynor's Index shows a superior risk-adjusted performance of a fund, a low and negative Treynor's Index is an indication of unfavorable performance. Treynor ratios can be used in both an ex-ante and ex-post sense. The ex-ante form of the ratio uses expected values for all variables, while the ex-post variation uses realized values.
Graphically Treynor’s measure is depicted as:
Example
Portfolio
Return
Volatility
Risk free Rate
A
20%
5%
8%
B
24%
8%
8%
Treynor’s index has ranked portfolio A as the better performer because value is higher (2.4 > 2.0) despite the fact that portfolio B has a higher return (24% > 20%). It is due to the difference in volatility of two portfolios.
Advantages of Treynor’s ratio:
a) The main advantage to the Treynor Ratio is that it indicates the volatility a stock brings to an entire portfolio. 
b) The Treynor Ratio should be used only as a ranking mechanism for investments within the same sector.  In a situation where rate of return from various investments alternatives are same, investments with higher Treynor Ratios are less risky and better managed.
c) It is proper measure for diversified portfolio.
d) This method is easy to calculate and simple to understand.
Limitations of Treynor’s ratio:
a) It is only a ranking criterion. It does not consider any values or metrics calculated by means of the management of portfolios or investments.
b) A Treynor ratio is a backward-looking design. This ratio gives importance to how the portfolio behaved in pas. It is possible that a portfolio may perform differently in future from how it has done in the past.
c) Weakness of Treynor’s ratio is that it requires an estimate of beta, which can differ a lot depending on the source which in turn can lead to mis-measurement of risk adjusted return. Many investors accomplish that a beta cannot give a clear picture of risk involved with the investment.
d) It can be overstated if market neutral strategies are used and assets used in the portfolio are highly leveraged.
c) Jensen Model
Jensen's model proposes another risk adjusted performance measure. This measure was developed by Michael Jensen and is sometimes referred to as the Differential Return Method. This measure involves evaluation of the returns that the fund has generated vs. the returns actually expected out of the fund given the level of its systematic risk. The surplus between the two returns is called Alpha, which measures the performance of a fund compared with the actual returns over the period. Required return of a fund at a given level of risk (b) can be calculated as:
Rt – R = a + b (Rm – R)
Where, Rt = Portfolio Return
R = Risk less return
a = Intercept the graph that measures the forecasting ability of the portfolio manager.
b = Beta coefficient, a measure of systematic risk
Rm = Return of the market portfolio
Thus, Jensen’s equation involves two steps:
(i) First he calculates what the return of a given portfolio should be on the basis of b, Rm and R.
(ii) He compares the actual realised return of the portfolio with the calculated or predicted return. Greater the excess of realised return over the calculated return, better is the performance of the portfolio.
Limitation of this model is that it considers only systematic risk not the entire risk associated with the fund and an ordinary investor can not mitigate unsystematic risk, as his knowledge of market is primitive.
Graphic representation of Jensen’s model is a given in the following figure:
The figure shows three lines showing negative, neutral and positive values. The negative line shows that the management of the performed portfolio is inferior. The positive line shows that superior quality of management of funds. The neutral value shows that the performance of the fund is similar to the performance of the market portfolio.
A comparison between the three models shows that the intercept of the line is Sharpe and Treynor models is always at the origin, where as Jensen’s model it may be at the origin (a = 0), above the origin (a > 0) and even be below the origin indicating a negative value (a < 0). The risk adjusted measures have been criticized for using a market surrogate instead of the true market portfolio. These measures have been unable to statistically distinguish luck or change from skill except over very long period of time. Moreover, these models rely heavily on the validity of CAPM. If in estimating the measures the analyst assumes the wrong from of the CAPM in the market place, he will get based measure of performance, usually in favour of low risk portfolios.
Advantages of this model:
a) This model is very easy to interpret.
b) It helps to measure how much of the portfolio's rate of return is attributable to deliver above-average returns, adjusted for market risk. The higher the ratio, the better the risk adjusted returns.
c) Because it is estimated from a regression equation, it is possible to make statements about the statistical significance of the manager’s skill level.
d) It is flexible enough to allow for alternative models of risk and expected return than the CAPM.
Disadvantages of this model:
a) Weakness of Treynor’s ratio is that it requires an estimate of beta, which can differ a lot depending on the source which in turn can lead to mis-measurement of risk adjusted return. Many investors accomplish that a beta cannot give a clear picture of risk involved with the investment.
b) It does not consider the advantage of a diversified portfolio.
c) Jensen’s alpha doesn’t take the portfolio’s volatility and takes into account, only the expected return.
d) It will miss out on characteristics such as returns kurtosis and skewness, which are of great importance in determining whether you’ll go broke before you realize profits.
d) Stock Selection: Overall performance of the fund can be examined in terms of superior or inferior stock selection and the normal return associated with a given level of risk. Thus, Total Excess Return = Selecting + Risk. To earn average returns, the fund managers have to diversify. The market pays returns only on the basis of systematic risk. The level of diversification can be judged on the basis of the correlation between the portfolio returns and the returns for a market portfolio. A completely diversified portfolio is perfectly correlated with the market portfolio, which is in turn completely diversified. To earn the above average return, fund managers will generally have to forsake some diversification that will have its cost in terms of additional portfolio risk. Hence some additional return is needed for this additional diversification risk. Capital Market Line (CML) helps in determining the risk commensurate with the incurred risk.
7. (a) Calculate the full price of a 3 months (91 days) call and put options with exercise price of 120 for a stock quoting at Rs. 100. Assume interest rate of 10% and S.D. of 0.8.
Or
(b) Stock PQR is currently priced at Rs. 1010. A put option with exercise price of Rs. 980 is available for Rs. 42. What are the intrinsic value and time value?


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