MF0010 – Security Analysis and Portfolio Management

Master of Business Administration- MBA Semester 3MF0010 – Security Analysis and Portfolio Management - 4 Credits

(Book ID: B1035)Assignment Set- 1

Q. 1 It is very often observed that retail investors enter the market when index is very high and exit when index is very low (comparatively speaking). Describe qualities of a savvy investor. Also throw light upon mistakes committed while managing investments.

Ans: Qualities of a Savvy Investor:

Smart investors have a plan for investing, and they stick to it: It is very easy to be tempted by a tip about a hot stock that is reported in all the financial papers. But this is not the way that smart investors make money. They look at their goals, time frame and knowledge of the markets to chart a plan that suits their needs. For example, if they are 40 years old and have twenty years until retirement, they implement a 20-year investment plan. They gather as much information as they can and then invest in assets that are appropriate for their plans, that they know about and that they are comfortable with. If they don’t understand a particular type of security, they will not buy it. They only buy securities that they have researched or that someone they trust has recommended. They stay with their investment plan.Smart investors invest consistently: To succeed year after year, they know that they must keep their money constantly growing. They generally use two methods to do this. First, they invest a part of their funds in securities with a growth potential (like stock and mutual funds). Second, they keep adding to their investment principal regularly.Smart investors are patient: It often takes time for a good investment to show results. Smart investors understand this, and therefore do not get excited about the daily ups and downs of the market. They understand that success is a long-term affair and therefore patience is required. They don’t jump in and out of investments in an effort to time the market. They don’t expect instant growth; they are not disappointed by temporary setbacks in the market.Smart investors are not emotionally tied to their investment positions: They know that to be successful, they must not be emotional towards their investment. No matter how attractive an investment looks or how badly an investment has performed recently, selling at the right time is just as important as buying. If an investment has consistently lost money, they don’t try to wait to recoup their losses. They know that it is necessary to cut losses and move ahead. Similarly, if an investment has appreciated phenomenally, successful investors know how to protect their gains. They are aware that no investment will move up forever, and they are able to sell it when the time is right.

Common Mistakes in Investment Management:When investment mistakes happen, money is lost. Mistakes can occur for a variety of

reasons, but they generally happen because of the clouding of the investor’s judgment by the influence of emotions, due to the misunderstanding of basic investment principles, or due to misconceptions about how securities react to varying economic, political, and fear-driven circumstances. The investor should always keep a calm, cool and rational head, and avoid these common investment mistakes:

· Not having a clearly-defined investment plan. A well-thought out investment plan does not need frequent adjustments, and there is no place in a well-managed plan for speculations and “hot picks”. Investment decisions should be made with an investment plan in mind. Investing is a goal-oriented activity that should include considerations of time, risk-tolerance, and future income.· Investors become bored with their plan or the rate of growth too quickly, change direction frequently, and make drastic rather than measured adjustments. Investing should always be regarded as a long-term activity and the investor should have this in mind before adjusting his portfolio.

· Investors tend to fall in love with securities that rise in price and forget to book their profits. Profits that are not realized are just book profits; they may disappear when the market goes down, While one should not be in a hurry to realize his profits, it is also true that he must not become so blinded by the beauty of unrealized gain that he forgets the basics of prudent investing. The investor may have the “unwilling-to-pay-the-taxes” problem little realizing that the investment may ultimately end up as a realized loss on the tax return.· Investors often overdose themselves on information, leading to “paralysis by analysis”. Such investors are likely to become confused and indecisive. Neither of these is good news for the health of an investment portfolio. Aggravating this problem for the investor is his inability to distinguish between genuine research and sales pitch of the sale side analyst. A narrow focus on information which has a bearing on the investment is a much more productive means of fact-finding.· Investors are constantly in search of a shortcut or gimmick that will provide them instant success with a minimum of effort; i.e. the “get-rich-quick pick” syndrome. Consequently, they buy every new product or service that comes along and catches their fancy. Their portfolios become a mixture of Mutual Funds, Index Funds, hedge funds, commodities, options, etc. that does not fit their investment plan.

Q.2 Explain the significance of index in general and stock market index in particular. What is risk involved in derivative products?

Ans: An index is a statistical indicator providing a representation of the value of the securities which constitute it. Indexes often serve as barometers for a given market or industry and benchmarks against which financial or economic performance is measured. A stock index reflects the price movement of shares while a bond index captures the manner in which bond prices go up and down.

For more than hundred years, people have tracked the market’s daily ups and downs using various indices of overall market performance. There are currently thousands of indices calculated by various information providers. Internationally, the best known indices are provided by Dow Jones & Co, S & P, Morgan Stanley Capital Markets (MSCI), Lehman Brothers (bond indices). Dow Jones alone currently publishes more than 3,000 indices. Some of the well-known indices are Dow Jones Industrial Average (DJIA), Standard & Poor’s 500 Index (S&P 500), Nasdaq Composite, Nasdaq 100, Financial Times-Stock Exchange 100 (FTSE 100), Nikkei 225 Stock Average, Hang Seng Index, Deutscher Aktienindex (DAX). In India the best known indices are Sensex and Nifty.

SENSEX: Sensex is the stock market index for BSE. It was first compiled in 1986. It is made of 30 stocks representing a sample of large, liquid and representative companies. The base year of SENSEX is 1978-79 and the base value is 100.

NIFTY: Nifty is the stock market index for NSE. S&P CNX Nifty is a 50 stock index accounting for 23 sectors of the economy. The base period selected for Nifty is the close of prices on November 3, 1995, which marked the completion of one-year of operations of NSE’s capital market segment. The base value of index was set at 1000.

Financial Derivatives: Derivatives are financial instruments that have no intrinsic value, but derive their value from something else. They hedge the risk of owning things that are subject to unexpected price fluctuations, e.g. foreign currencies, commodities (like wheat), stocks and bonds. The term ‘derivative’ indicates that it has no independent value, i.e. its value is entirely ‘derived’ from the value of the cash asset; e.g., price of a stock option depends on the underlying stock price and the price of currency future depends on the price of the underlying currency.

A derivative contract or product, or simply ‘derivative’, is to be distinguished from the underlying cash asset, i.e. the asset bought/sold in the cash market on normal delivery terms. The price of the cash instrument is referred to as the ‘underlying’ price. Examples of cash

instruments include actual shares in a company, commodities (crude oil, wheat), foreign exchange, etc. There are two types of derivative securities that are of interest to most investors- futures and options. Future contract is an agreement entered between two parties to buy or sell an asset at a future date for an agreed price. An Option is the right but not the obligation of the holder, to buy or sell underlying asset by a certain date at a certain price.

There are two types Options: a call option is a contract that gives the owner the right, but not obligation to buy the underlying asset by a specified date at a specified price while a  put option is a contract that gives the owner the right, but not obligation to sell the underlying asset by a specified date at a specified price.

Options and futures contracts are important to investors because they provide a way for investors to manage portfolio risk. Investors incur the risk of adverse currency price movements if they invest in foreign securities, or they incur the risk that interest rates will adversely affect their fixed-income securities (like bonds). Options and futures contracts can be used to limit some, or all, of these risks, thereby providing risk-control (hedging) possibilities. For example, if you are holding Reliance shares, you can hedge against falling share price by purchasing a put option on the Reliance shares.

Speculators can use derivatives to bet on the direction of future stock prices, interest rates, exchange rates, and commodity prices. In many cases, these transactions produce high returns if you guess right, but large losses if you guess wrong. Here, derivatives can increase risk.

Q.3 What do you understand by industry (give examples)? What is importance of industry life cycle? Is it possible to asses the intrinsic value of security?

Ans: Industry refers to the production of an economic good (either material or a service) within an economy. There are four key industrial economic sectors: the primary sector, largely raw material extraction industries such as mining and farming; the secondary sector, involving refining, construction, and manufacturing; the tertiary sector, which deals with services (such as law and medicine) and distribution of manufactured goods; and the quaternary sector, a relatively new type of knowledge industry focusing on technological research, design and development such as computer programming, and biochemistry. A fifth, quinary, sector has been proposed encompassing nonprofit activities. The economy is also broadly separated into public sector and private sector, with industry generally categorized as private. Industries are also any business or manufacturing.

Many times it is more important to be in the right industry than in the right stock. While the individual company is still important, its industry group is likely to exert just as much, if not more, influence on the share price. Industries as a whole tend to react differently towards different economic cycles. Other factors being equal, companies from similar industries tend to respond alike towards certain economic conditions; when the share prices move, they usually move as groups.

Industries are not only affected by the varying economic cycles; they are also influenced by industry-specific news, such as new product launches, enactment of economic legislation related to the industry or new rules framed by the regulatory body that is regulating the industry. The factors that the industry analysis considers to assess the potential of an industry include the industry structure, overall growth rate, market size, importance to the economy, competition, supply-demand relationships, product quality, cost elements, government regulation, business cycle exposure, etc.

Importance of Industry life cycle:

Most industries go through fairly well-defined life cycle stages that affect the growth of companies in that industry, competition climate, the types of profit margins, and overall stability of the market. The industry life cycle has a major effect on the earnings per share and rates of return offered by the industry. As a result, the ability to recognize the industry life cycle stage is a valuable asset for any investor.

Many observers believe that industries evolve through at least three stages: the pioneering stage, the expansion stage, and the stabilization stage. The concept of an industry life cycle can apply to industries or product lines within industries. Each of the three stages is described briefly below:

1. Pioneering stage: During this stage, rapid growth in demand occurs. Although a number of companies within a growing industry fail at this stage as a result of strong competitive pressures, many experience rapid growth in sales and earnings, possibly at an increasing rate. Investor risk in an unproven company is high, but so are expected returns if the company succeeds.

2. Expansion stage: During this stage, the survivors from the pioneering stage are identifiable. The survivors continue to grow and prosper, but the rate of growth is more moderate than before. During the expansion stage, industries improve their products and sometimes lower their prices. The companies competing in an expanding industry are more stable and, consequently, attract considerable investment capital. This is because investors are more willing to invest in these industries as they have proven their potential and reduced their risk of failure. Toward the later period of this stage, dividends often become payable, further enhancing the attractiveness of these companies to a number of investors.

3. Stabilization stage (or maturity stage): During this stage, growth begins to be moderate. Sales may still be increasing, but at a much slower rate than before. Products become more standardized and less innovative, the marketplace is full of competitors, and costs are stable rather than decreasing through efficiency moves. Industries at this stage continue to move along but without significant growth. Stagnation may occur for a considerable period of time.

The three-part classification of industry life cycle described above helps investors to assess the growth potential of different companies in an industry. The pioneering stage may offer the highest potential returns, but it also poses the greatest risk. Investors interested primarily in capital gains should avoid the maturity stage. Companies at this stage may have relatively high dividend payouts because they have fewer growth prospects. On the other hand, these companies often offer stability in earnings and dividend growth. It is the expansion stage that is probably of most interest to investors. Industries that have survived the pioneering stage often offer good opportunities, since the demand for their products and services is growing more rapidly than the economy as a whole. Growth is rapid but orderly, which is an appealing characteristic to the investors.

Intrinsic value refers to the value of a security which is intrinsic to or contained in the security itself. It is also frequently called fundamental value. It is ordinarily calculated by summing the future income generated by the asset, and discounting it to the present value.

The intrinsic value for an in-the-money option is calculated as the absolute value of the difference between the current price (S) of the underlying and the strike price (K) of the option, floored to zero.

For a call option

IVcall = max{0,S − K}

while for a put option

IVput = max{0,K − S}

For example, if the strike price for a call option is Rs.1 and the price of the underlying is

Rs.1.20, then the option has an intrinsic value of Rs.0.20.

The total value of an option is the sum of its intrinsic value and its time value.

Q. 4 Is there any logic behind technical analysis? Explain meaning and basic tenets of technical analysis.

Ans: In finance, technical analysis is a security analysis discipline for forecasting the direction of prices through the study of past market data, primarily price and volume While fundamental analysts examine earnings, dividends, new products, research and the like, technical analysts examine what investors fear or think about those developments and whether or not investors have the where with all to back up their opinions; these two concepts are called psych (psychology) and supply/demand. In the M = P/E equation, technicians assess M, the multiple investors do/may pay - if they have the money - for the fundamentals they envision. Technicians employ many techniques, one of which is the use of charts. Using charts, technical analysts seek to identify price patterns and trends in financial markets and attempt to exploit those patterns. Technicians use various methods and tools, the study of price charts is but one.Supply/demand indicators monitor investors' liquidity; margin levels, short interest, cash in brokerage accounts, etc., in an attempt to determine whether they have any money left. Other indicators monitor the state of psych - are investors bullish or bearish? - and are they willing to spend money to back up their beliefs. A spent-out bull cannot move the market higher, and a well heeled bear won't!; investors need to know which they are facing. In the end, stock prices are only what investors think; therefore determining what they think is every bit as critical as an earnings estimate.Technicians using charts search for archetypal price chart patterns, such as the well-known head and shoulders or double top/bottom reversal patterns, study indicators, moving averages, and look for forms such as lines of support, resistance, channels, and more obscure formations such as flags, pennants, balance days and cup and handle patterns.Technical analysts also widely use market indicators of many sorts, some of which are mathematical transformations of price, often including up anf down volume, advance/decline data and other inputs. These indicators are used to help access whether an asset is trending, and if it is, its probability of its direction and of continuation. Technicians also look for relationships between price/volume indices and market indicators. Examples include the relative strength index, and MACD. Other avenues of study include correlations between changes in options (implied volatility) and put/call ratios with price. Also important are sentiment indicators such as Put/Call ratios, bull/bear ratios, short interest and Implied Volatility, etc.There are many techniques in technical analysis. Adherents of different techniques (for example, candlestick charting, Dow Theory, and Elliott wave theory) may ignore the other approaches, yet many traders combine elements from more than one technique. Some technical analysts use subjective judgment to decide which pattern(s) a particular instrument reflects at a given time, and what the interpretation of that pattern should be. Others employ a strictly mechanical or systematic approach to pattern identification and interpretation.Technical analysis is frequently contrasted with fundamental analysis, the study of economic factors that influence the way investors price financial markets. Technical analysis holds that prices already reflect all such trends before investors are aware of them. Uncovering those trends is what technical indicators are designed to do, imperfect as they may be. Fundamental indicators are subject to the same limitations, naturally. Some traders use technical or fundamental analysis exclusively, while others use both types to make trading decisions which conceivably is the most rational approach.Users of technical analysis are often called technicians or market technicians. Some prefer the term technical market analyst or simply market analyst. An older term, chartist, is sometimes

used, but as the discipline has expanded and modernized, the use of the term chartist has become less popular, as it is only one aspect of technical analysis.PrinciplesTechnicians say that a market's price reflects all relevant information, so their analysis looks at the history of a security's trading pattern rather than external drivers such as economic, fundamental and news events. Price action also tends to repeat itself because investors collectively tend toward patterned behavior – hence technicians' focus on identifiable trends and conditions.Market action discounts everythingBased on the premise that all relevant information is already reflected by prices - a dubious concept in that much is unknown at any point - technical analysts believe it is important to understand what investors think of that information, known and perceived; studies such as by Cutler, Poterba, and Summers titled "What Moves Stock Prices?" do not cover this aspect of investing.Prices move in trendsTechnical analysts believe that prices trend directionally, i.e., up, down, or sideways (flat) or some combination. The basic definition of a price trend was originally put forward by Dow Theory.An example of a security that had an apparent trend is AOL from November 2001 through August 2002. A technical analyst or trend follower recognizing this trend would look for opportunities to sell this security. AOL consistently moves downward in price. Each time the stock rose, sellers would enter the market and sell the stock; hence the "zig-zag" movement in the price. The series of "lower highs" and "lower lows" is a tell tale sign of a stock in a down trend. In other words, each time the stock moved lower, it fell below its previous relative low price. Each time the stock moved higher, it could not reach the level of its previous relative high price.Note that the sequence of lower lows and lower highs did not begin until August. Then AOL makes a low price that doesn't pierce the relative low set earlier in the month. Later in the same month, the stock makes a relative high equal to the most recent relative high. In this a technician sees strong indications that the down trend is at least pausing and possibly ending, and would likely stop actively selling the stock at that point.History tends to repeat itselfTechnical analysts believe that investors collectively repeat the behavior of the investors that preceded them. "Everyone wants in on the next Microsoft," "If this stock ever gets to $50 again, I will buy it," "This company's technology will revolutionize its industry, therefore this stock will skyrocket" – these are all examples of investor sentiment repeating itself. To a technician, the emotions in the market may be irrational, but they exist. Because investor behavior repeats itself so often, technicians believe that recognizable (and predictable) price patterns will develop on a chart.Technical analysis is not limited to charting, but it always considers price trends. For example, many technicians monitor surveys of investor sentiment. These surveys gauge the attitude of market participants, specifically whether they are bearish or bullish. Technicians use these surveys to help determine whether a trend will continue or if a reversal could develop; they are most likely to anticipate a change when the surveys report extreme investor sentiment. Surveys that show overwhelming bullishness, for example, are evidence that an uptrend may reverse – the premise being that if most investors are bullish they have already bought the market (anticipating higher prices). And because most investors are bullish and invested, one assumes that few buyers remain. This leaves more potential sellers than buyers, despite the bullish sentiment. This suggests that prices will trend down, and is an example of contrarian trading.

Q.5 Explain role played by efficient market in economy. Apply the parameters of efficient market to Indian stock markets and find out whether they are efficient.

Ans: In finance, the efficient-market hypothesis (EMH) asserts that financial markets are "informationally efficient". That is, one cannot consistently achieve returns in excess of average market returns on a risk-adjusted basis, given the information publicly available at the time the investment is made.

There are three major versions of the hypothesis: "weak", "semi-strong", and "strong". Weak EMH claims that prices on traded assets (e.g., stocks, bonds, or property) already reflect all past publicly available information. Semi-strong EMH claims both that prices reflect all publicly available information and that prices instantly change to reflect new public information. Strong EMH additionally claims that prices instantly reflect even hidden or "insider" information. There is evidence for and against the weak and semi-strong EMHs, while there is powerful evidence against strong EMH.

The validity of the hypothesis has been questioned by critics who blame the belief in rational markets for much of the financial crisis of 2007–2010. Defenders of the EMH caution that conflating market stability with the EMH is unwarranted; when publicly available information is unstable, the market can be just as unstable.

The (now largely discredited) theory that all market participants receive and act on all of the relevant information as soon as it becomes available. If this were strictly true, no investment strategy would be better than a coin toss. Proponents of the efficient market theory believe that there is perfect information in the stock market. This means that whatever information is available about a stock to one investor is available to all investors (except, of course, insider information, but insider trading is illegal). Since everyone has the same information about a stock, the price of a stock should reflect the knowledge and expectations of all investors. The bottom line is that an investor should not be able to beat the market since there is no way for him/her to know something about a stock that isn't already reflected in the stock's price. Proponents of this theory do not try to pick stocks that are going to be winners; instead, they simply try to match the market's performance. However, there is ample evidence to dispute the basic claims of this theory, and most investors don't believe it.

Studies on Indian Stock Market Efficiency : The efficient market hypothesis is related to the random walk theory. The idea that asset prices may follow a random walk pattern was introduced by Bachelier in 1900. The random walk hypothesis is used to explain the successive price changes which are independent of each other. Fama (1991) classifies market efficiency into three forms - weak, semi-strong and strong. In its weak form efficiency, equity returns are not serially correlated and have a constant mean. If market is weak form efficient, current prices fully reflect all information contained in the historical prices of the asset and a trading rule based on the past prices can not be developed to identify miss-priced assets. Market is semi-strong efficient if stock prices reflect any new publicly available information instantaneously. There are no undervalued or overvalued securities and thus, trading rules are incapable of producing superior returns. When new information is released, it is fully incorporated into the price rather speedily. The strong form efficiency suggests that security prices reflect all available information, even private information. Insiders profit from trading on information not already incorporated into prices. Hence the strong form does not hold in a world with an uneven playing field. Studies testing market efficiency in emerging markets are few. Poshakwale (1996) showed that Indian stock market was weak form inefficient; he used daily BSE index data for the period 1987 to 1994. Barua (1987), Chan, Gup and Pan (1997) observed that the major Asian markets were weak form inefficient. Similar results were found by Dickinson and Muragu (1994) for Nairobi stock market; Cheung et al (1993) for Korea and Taiwan; and Ho and Cheung (1994) for Asian markets. On the other hand, Barnes (1986) showed a high degree of efficiency in Kuala Lumpur market. Groenewold and Kang (1993)

found Australian market semi-strong form efficient. Some of the recent studies, testing the random walk hypothesis (in effect testing for weak form efficiency in the markets) are; Korea (Ryoo and Smith, 2002; this study uses a variance ratio test and find the market to follow a random walk process if the price limits are relaxed during the period March 1988 to Dec 1988), China, (lee et al 2001; find that volatility is highly persistent and is predictable, authors use GARCH and EGARCH models in this study), Hong Kong (Cheung and Coutts 2001; authors use a variance ratio test in this study and find that Hang Seng index on the Hong Kong stock exchange follow a random walk), Slovenia (Dezlan, 2000), Spain (Regulez and Zarraga, 2002), Czech Republic (Hajek, 2002), Turkey (Buguk and Brorsen, 2003), Africa (Smith et al. 2002; Appiah-kusi and Menyah, 2003) and the Middle East (Abraham et al. 2002; this study uses variance ratio test and the runs test to test for random walk for the period 1992 to 1998 and find that these markets are not efficient).

METHODOLOGY & DATA:-To test historical market efficiency one can look at the pattern of short-term movements of the combined market returns and try to identify the principal process generating those returns. If the market is efficient, the model would fail to identify any pattern and it can be inferred that the returns have no pattern and follow a random walk process. In essence the assumption of random walk means that either the returns follow a random walk process or that the model used to identify the process is unable to identify the true return generating process. If a model is able to identify a pattern, then historical market data can be used to forecast future market prices, and the market is considered not efficient. There are a number of techniques available to determine patterns in time series data. Regression, exponential smoothing and decomposition approaches presume that the values of the time series being predicted are statistically independent from one period to the next. Some of these techniques are reviewed in the following section and appropriate techniques identified for use in this study.

Runs test (Bradley 1968) and LOMAC variance ratio test (Lo and MacKinlay 1988) are used to test the weak form efficiency and random walk hypothesis. Runs test determines if successive price changes are independent. It is non-parametric and does not require the returns to be normally distributed. The test observes the sequence of successive price changes with the same sign. The null hypothesis of randomness is determined by the same sign in price changes. The runs test only looks at the number of positive or negative changes and ignores the amount of change from mean. This is one of the major weaknesses of the test. LOMAC variance ratio test is commonly criticised on many issues and mainly on the selection of maximum order of serial correlation (Faust, 1992). Durbin-Watson test (Durbin and Watson 1951), the augmented Dickey-Fuller test (Dickey and Fuller 1979) and different variants of these are the most commonly used tests for the random walk hypothesis in recent years (Worthington and Higgs 2003; Kleiman, Payne and Sahu 2002; Chan, Gup and Pan 1997). Under the random walk hypothesis, a market is (weak form) efficient if most recent price has all available information and thus, the best forecaster of future price is the most recent price. In the most stringent version of the efficient market hypothesis, εt is random and stationary and also exhibits no autocorrelation, as disturbance term cannot possess any systematic forecast errors. In this study we have used returns and not prices for test of market efficiency as expected returns are more commonly used in asset pricing literature (Fama (1998). Returns in a market conforming to random walk are serially uncorrelated, corresponding to a random walk hypothesis with dependant but uncorrelated increments. Parametric serial correlations tests of independence and non-parametric runs tests can be used to test for serial dependence. Serial correlation coefficient test is a widely used procedure that tests the relationship between returns in the current period with those in the previous period. If no significant autocorrelation are found then the series are expected to follow a random walk. A

simple formal statistical test was introduced was Durbin and Watson (1951). Durbin-Watson (DW) is a test for first order autocorrelation. It only tests for the relationship between an error and its immediately preceding value. One way to motivate this test is to regress the error of time t with its previous value.

ut = ρut-1 + vt where vt ~ N(0,σ2v).

DW test can not detect some forms of residual autocorrelations, e.g. if corr(ut, ut-1) = 0 but corr(ut, ut-2) ≠ 0, DW as defined earlier will not find any autocorrelation. One possible way is to do it for all possible combinations but this is tedious and practically impossible to handle. The second-best alternative is to test for autocorrelation that would allow examination of the relationship between ut and several of its lagged values at the same time. The Breusch- Godfrey test is a more general test for autocorrelation for the lags of up to r‟th order.

Because of the abovementioned weaknesses of the DW test we do not use the DW test in our study. An alternative model which is more commonly used is Augmented Dickey Fuller test (ADF test). Three regression models (standard model, with drift and with drift and trend) are used in this study to test for unit root in the research, (Chan, Gup and Pan 1997; Brooks 2002). In this study we followed the test methodologies from Brooks (2002) with slight adjustments.

Where: St = the stock price u* and u** = the drift terms T = total number of observations εt, εt*, εt** = error terms that could be ARMA processes with time dependent variances.

Where St is the logarithm of the price index seen at time t, u is an arbitrary drift parameter, α is the change in the index and εt is a random disturbance term. Equation (3) is for the standard model; (4) for the standard model with a drift and (5) for the standard model with drift and trend. Augmented Dickey-Fuller (ADF) unit root test of nonstationarity is conducted in the form of the following regression equation. The objective of the test is to test the null hypothesis that θ = 1 in:

against the one-sided alternative θ < 1. Thus the hypotheses to be tested are:

H0: Series contains a unit root against H1: Series is stationary

In this study we calculate daily returns using daily index values for the Mumbai Stock Exchange (BSE) and National Stock Exchange (NSE) of India. The data is collected from the Datastream data terminal from Macquarie University. The time period for BSE is from 24th May 1991 to 26th May 2006 and for NSE 27th May to 26th May 2006. Stock exchanges are closed for trading on weekends and this may appear to be in contradiction with the basic time series requirement that observations be taken at a regularly spaced intervals. The requirement

however, is that the frequency be spaced in terms of the processes underlying the series. The underlying process of the series in this case is trading of stocks and generation of stock exchange index based on the stock trading, as such for this study the index values at the end of each business day is appropriate (French 1980). Table 1 presents the characteristics of two data sets used in this study. During the period covered in this study, the mean return of the NSE index is much lower than that of the BSE, similarly the variance of NSE is lower as compared with BSE index suggesting a lower risk and a lower average return at NSE as compared with BSE. It is relevant to note that NSE was established by the government of India to improve the market efficiency in Indian stock markets and to break the monopolistic position of the BSE. NSE index is a more diversified one as compared to the same of BSE. This can also be due to the unique nature of India‟s equity markets, the settlement system on BSE was intermittent (Badla system up until 2nd July 2001) and on NSE it was always cash.

RESULTS:- This study conducts a test of random walk for the BSE and NSE markets in India, using stock market indexes for the Indian markets. It employs unit root tests (augmented Dickey-Fuller (ADF)). We perform ADF test with intercept and no trend and with an intercept and trend. We further test the series using the Phillips-Perron tests and the KPSS tests for a confirmatory data analysis. In case of BSE and NSE markets, the null hypothesis of unit root is convincingly rejected, as the test statistic is more negative than the critical value, suggesting that these markets do not show characteristics of random walk and as such are not efficient in the weak form. We also test using Phillip-Perron test and KPSS test for confirmatory data analysis and find the series to be stationary. Results are presented in Table 2. For both BSE and NSE markets, the results are statistically significant and the results of all the three tests are consistent suggesting these markets are not weak form efficient.

Results of the study suggest that the markets are not weak form efficient. DW test, which is a test for serial correlations, has been used in the past but the explanatory power of the DW can be questioned on the basis that the DW only looks at the serial correlations on one lags as such may not be appropriate test for the daily data. Current literature in the area of market efficiency uses unit root and test of stationarity. This notion of market efficiency has an important bearing for the fund managers and investment bankers and more specifically the investors who are seeking to diversify their portfolios internationally. One of the criticisms of the supporters of the international diversification into emerging markets is that the emerging markets are not efficient and as such the investor may not be able to achieve the full potential benefits of the international diversification.

CONCLUSIONS & IMPLICATIONS:- This paper examines the weak form efficiency in two of the Indian stock exchanges which represent the majority of the equity market in India. We employ three different tests ADF, PP and the KPSS tests and find similar results. The results of these tests find that these markets are not weak form efficient. These results support the common notion that the equity markets in the emerging economies are not efficient and to some degree can also explain the less optimal allocation of portfolios into these markets. Since the results of the two tests are contradictory, it is difficult to draw conclusions for practical implications or for policy from the study. It is important to note that the BSE moved to a system of rolling settlement with effect from 2nd July 2006 from the previously used „Badla‟ system. The „Badla‟ system was a complex system of forward settlement which was not transparent and was not accessible to many market participants. The results of the NSE are similar (NSE had a cash settlement system from the beginning) to BSE suggesting that the changes in settlement system may not significantly impact the results. On the contrary a conflicting viewpoint is that the results of these markets may have been influenced by volatility spillovers, as such the results may be significantly different if the changes in the settlement system are incorporated in the analysis. The research in the area of volatility spillover has argued that the volatility is transferred across markets (Brailsford, 1996), as such the results of these markets may be interpreted cautiously. For future research, using a computationally more efficient model like generalized autoregressive conditional heteroskesdasticity (GARCH) could help to clear this.

Q. 6 What do you understand by yield? Explain the concept of YTM with the help of example

Ans: In finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return. Yield applies to various stated rates of return on stocks (common and preferred, and convertible), fixed income instruments (bonds, notes, bills, strips, zero coupon), and some other investment type insurance products (e.g. annuities).The term is used in different situations to mean different things. It can be calculated as a ratio or as an internal rate of return (IRR). It may be used to state the owner's total return, or just a portion of income, or exceed the income.Because of these differences, the yields from different uses should never be compared as if they were equal. This page is mainly a series of links to other pages with increased details.

The income return on an investment. This refers to the interest or dividends received from a security and is usually expressed annually as a percentage based on the investment's cost, its current market value or its face value. This seemingly simple term, without a qualifier, can be rather confusing to investors. For example, there are two stock dividend yields. If you buy a stock for $30 (cost basis) and its current price and annual dividend is $33 and $1, respectively, the "cost yield" will be 3.3% ($1/$30) and the "current yield" will be 3% ($1/$33).Bonds have four yields: coupon (the bond interest rate fixed at issuance), current (the bond interest rate as a percentage of the current price of the bond), and yield to maturity (an estimate of what an investor will receive if the bond is held to its maturity date). Non-taxable municipal bonds will have a tax-equivalent (TE) yield determined by the investor's tax bracket.Mutual fund yields are an annual percentage measure of income (dividends and interest) earned by the fund's portfolio, net of the fund's expenses. In addition, the "SEC yield" is an indicator of the percentage yield on a fund based on a 30-day period.

Yield To Maturity (YTM)

The Yield to maturity (YTM) or redemption yield of a bond or other fixed-interest security, such as gilts, is the internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule. Yield to maturity is actually an estimation of future return, as the rate at which coupon payments can be reinvested when received is unknown.[1] It enables investors to compare the merits of different financial instruments. The YTM is often given in terms of Annual Percentage Rate (A.P.R.), but more usually market convention is followed: in a number of major markets the convention is to quote yields semi-annually (see compound interest: thus, for example, an annual effective yield of 10.25% would be quoted as 5.00%, because 1.05 x 1.05 = 1.1025).

The yield is usually quoted without making any allowance for tax paid by the investor on the return, and is then known as "gross redemption yield". It also does not make any allowance for the dealing costs incurred by the purchaser (or seller).

If the yield to maturity for a bond is less than the bond's coupon rate, then the (clean) market value of the bond is greater than the par value (and vice versa).

If a bond's coupon rate is less than its YTM, then the bond is selling at a discount.

If a bond's coupon rate is more than its YTM, then the bond is selling at a premium.

If a bond's coupon rate is equal to its YTM, then the bond is selling at par.

concept used to determine the rate of return an investor will receive if a long-term, interest-bearing investment, such as a bond, is held to its maturity date . It takes into account purchase price, redemption value, time to maturity, coupon yield, and the time between interest payments. Recognizing time value of money, it is the discount rate at which the present value of all future payments would equal the present price of the bond, also known as Internal Rate of Return It is implicitly assumed that coupons are reinvested at the YTM rate. YTM can be approximated using a bond value table (also called a bond yield table) or can be determined using a programmable calculator equipped for bond mathematics calculations.

Example

Consider a 30-year zero-coupon bond with a face value of $100. If the bond is priced at an

annual YTM of 10%, it will cost $5.73 today (the present value of this cash flow, 100/(1.1)30 =

5.73). Over the coming 30 years, the price will advance to $100, and the annualized return will

be 10%.

What happens in the meantime? Suppose that over the first 10 years of the holding period,

interest rates decline, and the yield-to-maturity on the bond falls to 7%. With 20 years

remaining to maturity, the price of the bond will be 100/1.0720, or $25.84. Even though the

yield-to-maturity for the remaining life of the bond is just 7%, and the yield-to-maturity

bargained for when the bond was purchased was only 10%, the return earned over the first 10

years is 16.25%. This can be found by evaluating (1+i) from the equation (1+i)10 =

(25.842/5.731), giving 1.1625.

Over the remaining 20 years of the bond, the annual rate earned is not 16.25%, but rather 7%.

This can be found by evaluating (1+i) from the equation (1+i)20 = 100/25.84, giving 1.07.

Over the entire 30 year holding period, the original $5.73 invested increased to $100, so 10%

per annum was earned, irrespective of any interest rate changes in between.

Here is another example:

You buy ABC Company bond which matures in 1 year and has a 5% interest rate (coupon) and

has a par value of $100. You pay $90 for the bond.

The current yield is 5.56% ((5/90)*100).

If you hold the bond until maturity, ABC Company will pay you $5 as interest and $100 for the

matured bond.

Now for your $90 investment you made $105 and your yield to maturity is 16.67% [= (105/90)-

1] or [=(105-90)/90]

sum total of the annual effective rate of return earned by an owner of a bond if that bond is

held until its maturity date. This effective return includes the current income generated by the

bond as well as any difference in the face value of the bond and the bond's purchase price.

The relationship of YTM and the bond's coupon rate is as follows: (1) if the purchase price of

the bond is greater than the face value of the bond (purchase made at a premium), the YTM is

lower than the coupon rate (rate printed on bond certificate); (2) if the purchase price of the

bond is less than the face value of the bond (purchase made at a discount), the YTM is higher

than the coupon rate; and (3) if the purchase price of the bond is equal to the face value of the

bond, the YTM is equal to the coupon rate. The equation for the computation of the YTM is as

follows:

YTM

=

I +(FVOB - CVOB)

n(FVOB + CVOB)

2

I = Interest rate paid annually (in dollars) by the bond (coupon rate of the bond)

where: FVOB = face value of bond (amount printed on bondcertificate)

CVOB = current value of bond (market value of bond)

n = number of years until bond reaches maturity date. For example, assume the following:

I = 8% coupon rate of the bond (rate printed on bondcertificate)

FVOB = $1000 printed on bond certificate

CVOB = $980 market value

n = 30

then:

YTM =

$80 + ($1000 - $980)

30($1000 + $980)

2

= 8.15%

Master of Business Administration- MBA Semester 3MF0010 – Security Analysis and Portfolio Management - 4 Credits

(Book ID: B1035)Assignment Set- 2

Q. 1 Explain basic steps involved in PM. What is difference between PM and a Mutual Fund? What are various types of risk associated with PM?

Ans:

Q. 2 Explain with the help of example how is it possible to reduce risk associated with portfolio with the help of diversification. Which risk are still bound to persist?

Ans:

Q.3 With the help of examples explain what is systematic (also called systemic) and unsystematic risk? All said and done CAPM is not perfect , do you agree?

Ans: Systematic risk: In finance, systematic risk, sometimes called market risk, aggregate risk, or undiversifiable risk, is the risk associated with aggregate market returns.Systematic risk should not be confused with systemic risk, the risk of loss from some catastrophic event that collapses the entire financial system.It is the risk which is due to the factors which are beyond the control of the people working in the market and that's why risk free rate of return in used to just compensate this type of risk in market. Interest rates, recession and wars all represent sources of systematic risk because they affect the entire market and cannot be avoided through diversification. Whereas this type of risk affects a broad range of securities, unsystematic risk affects a very specific group of securities or an individual security. Systematic risk can be mitigated only by being hedged. Even a portfolio of well-diversified assets cannot escape all risk. 

ExampleExamples of systematic risk include uncertainty about general economic conditions, such as GNP, interest rates or inflation. For example, consider an individual investor who purchases $10,000 of stock in 10 biotechnology companies. If unforeseen events cause a catastrophic setback and one or two companies' stock prices drop, the investor incurs a loss. On the other hand, an investor who purchases $100,000 in a single biotechnology company would incur ten times the loss from such an event. The second investor's portfolio has more unsystematic risk than the diversified portfolio. Finally, if the setback were to affect the entire industry instead, the investors would incur similar losses, due to systematic risk.Systematic risk is essentially dependent on macroeconomic factors such as inflation, interest rates and so on. It may also derive from the structure and dynamics of the market.

Systematic risk and portfolio management

Given diversified holdings of assets, an investor's exposure to unsystematic risk from any particular asset is small and uncorrelated with the rest of the portfolio. Hence, the contribution of unsystematic risk to the riskiness of the portfolio as a whole may become negligible.In the capital asset pricing model, the rate of return required for an asset in market equilibrium depends on the systematic risk associated with returns on the asset, that is, on the covariance of the returns on the asset and the aggregate returns to the market.Lenders to small numbers of borrowers (or kinds of borrowers) face unsystematic risk of default. Their loss due to default is credit risk, the unsystematic portion of which is concentration risk.

Unsystematic riskBy contrast, unsystematic risk, sometimes called specific risk, idiosyncratic risk, residual risk, or diversifiable risk, is the company-specific or industry-specific risk in a portfolio, which is uncorrelated with aggregate market returns.Unsystematic risk can be mitigated through diversification, and systematic risk can not be. This is the risk other than systematic risk and which is due to the factors which are controllable by the people working in market and market risk premium is used to compensate this type of risk. Total Risk = Systematic risk + Unsystematic Risk The risk that is specific to an industry or firm. Examples of unsystematic risk include losses caused by labor problems, nationalization of assets, or weather conditions. This type of risk can be reduced by assembling a portfolio with significant diversification so that a single event affects only a limited number of the assets. Company- or industry-specific risk as opposed to overall market risk; unsystematic risk can be reduced through diversification. As the saying goes, “Don't put all of your eggs in one basket.” Also known as specific risk, diversifiable risk, and residual risk.

ExampleOn the other hand, announcements specific to a company, such as a gold mining company striking gold, are examples of unsystematic risk.

Risk: Systematic and Unsystematic

We can break down the risk, U, of holding a stock into two components: systematic risk and unsystematic risk:

Systematic Risk; m

Nonsystematic Risk;

n

Total risk; U

riskicunsystemattheis

risksystematictheis

where

becomes

ε

m

εmRR

URR

++=

+=

CAPM is not perfect:-

The model assumes that either asset returns are (jointly) normally distributed random variables or that investors employ a quadratic form of utility. It is however frequently observed that returns in equity and other markets are not normally distributed. As a result, large swings (3 to 6 standard deviations from the mean) occur in the market more frequently than the normal distribution assumption would expect.

The model assumes that the variance of returns is an adequate measurement of risk. This might be justified under the assumption of normally distributed returns, but for general return distributions other risk measures (like coherent risk measures) will likely reflect the investors' preferences more adequately. Indeed risk in financial investments is not variance in itself, rather it is the probability of losing: it is asymmetric in nature.

The model assumes that all investors have access to the same information and agree about the risk and expected return of all assets (homogeneous expectations assumption).

The model assumes that the probability beliefs of investors match the true distribution of returns. A different possibility is that investors' expectations are biased, causing market prices to be informationally inefficient. This possibility is studied in the field of behavioral finance, which uses psychological assumptions to provide alternatives to the CAPM such as the overconfidence-based asset pricing model of Kent Daniel, David Hirshleifer, and AvanidharSubrahmanyam (2001).

The model does not appear to adequately explain the variation in stock returns. Empirical studies show that low beta stocks may offer higher returns than the model would predict. Some data to this effect was presented as early as a 1969 conference in Buffalo, New York in a paper by Fischer Black, Michael Jensen, and Myron Scholes. Either that fact is itself rational (which saves the efficient-market hypothesis but makes CAPM wrong), or it is irrational (which saves CAPM, but makes the EMH wrong – indeed, this possibility makes volatility arbitrage a strategy for reliably beating the market).

The model assumes that given a certain expected return investors will prefer lower risk (lower variance) to higher risk and conversely given a certain level of risk will prefer higher returns to lower ones. It does not allow for investors who will accept lower returns for higher risk. Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well.

The model assumes that there are no taxes or transaction costs, although this assumption may be relaxed with more complicated versions of the model.

The market portfolio consists of all assets in all markets, where each asset is weighted by its market capitalization. This assumes no preference between markets and assets for individual investors, and that investors choose assets solely as a function of their risk-return profile. It also assumes that all assets are infinitely divisible as to the amount which may be held or transacted.

The market portfolio should in theory include all types of assets that are held by anyone as an investment (including works of art, real estate, human capital...) In practice, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio. Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that due to the inobservability of the true market portfolio, the CAPM might not be empirically testable. This was presented in greater depth in a paper by Richard Roll in 1977, and is generally referred to as Roll's critique.

The model assumes just two dates, so that there is no opportunity to consume and rebalance portfolios repeatedly over time. The basic insights of the model are extended and generalized in the intertemporal CAPM (ICAPM) of Robert Merton, and the consumption CAPM (CCAPM) of Douglas Breeden and Mark Rubinstein.

CAPM assumes that all investors will consider all of their assets and optimize one portfolio. This is in sharp contradiction with portfolios that are held by individual investors: humans tend to have fragmented portfolios or, rather, multiple portfolios: for each goal one portfolio.

Q. 4 What do you understand by arbitrage? Make a critical comparison between APT & CAPM.

Ans: In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit at zero cost.In principle and in academic use, an arbitrage is risk-free; in common use, as in statistical arbitrage, it may refer to expected profit, though losses may occur, and in practice, there are always risks in arbitrage, some minor (such as fluctuation of prices decreasing profit margins), some major (such as devaluation of a currency or derivative). In academic use, an arbitrage involves taking advantage of differences in price of a single asset or identical cash-flows; in common use, it is also used to refer to differences between similar assets (relative value or convergence trades), as in merger arbitrage.People who engage in arbitrage are called arbitrageurs—such as a bank or brokerage firm. The term is mainly applied to trading in financial instruments, such as bonds, stocks, derivatives, commodities and currencies.

Conditions for arbitrageArbitrage is possible when one of three conditions is met:

1. The same asset does not trade at the same price on all markets ("the law of one price").2. Two assets with identical cash flows do not trade at the same price.3. An asset with a known price in the future does not today trade at its future price

discounted at the risk-free interest rate (or, the asset does not have negligible costs of storage; as such, for example, this condition holds for grain but not for securities).

Arbitrage is not simply the act of buying a product in one market and selling it in another for a higher price at some later time. The transactions must occur simultaneously to avoid exposure to market risk, or the risk that prices may change on one market before both transactions are complete. In practical terms, this is generally only possible with securities and financial products which can be traded electronically, and even then, when each leg of the trade is executed the prices in the market may have moved. Missing one of the legs of the trade (and subsequently having to trade it soon after at a worse price) is called 'execution risk' or more specifically 'leg risk'. In the simplest example, any good sold in one market should sell for the same price in another. Traders may, for example, find that the price of wheat is lower in agricultural regions than in cities, purchase the good, and transport it to another region to sell at a higher price. This type of price arbitrage is the most common, but this simple example ignores the cost of transport, storage, risk, and other factors. "True" arbitrage requires that there be no market risk involved. Where securities are traded on more than one exchange, arbitrage occurs by simultaneously buying in one and selling on the other.See rational pricing, particularly arbitrage mechanics, for further discussion.Mathematically it is defined as follows:

andwhereVt means a portfolio at time t.

Examples Suppose that the exchange rates (after taking out the fees for making the exchange) in

London are £5 = $10 = ¥1000 and the exchange rates in Tokyo are ¥1000 = $12 = £6.

Converting ¥1000 to $12 in Tokyo and converting that $12 into ¥1200 in London, for a profit of ¥200, would be arbitrage. In reality, this "triangle arbitrage" is so simple that it almost never occurs. But more complicated foreign exchange arbitrages, such as the spot-forward arbitrage (see interest rate parity) are much more common.

One example of arbitrage involves the New York Stock Exchange and the Chicago Mercantile Exchange. When the price of a stock on the NYSE and its corresponding futures contract on the CME are out of sync, one can buy the less expensive one and sell it to the more expensive market. Because the differences between the prices are likely to be small (and not to last very long), this can only be done profitably with computers examining a large number of prices and automatically exercising a trade when the prices are far enough out of balance. The activity of other arbitrageurs can make this risky. Those with the fastest computers and the most expertise take advantage of series of small differences that would not be profitable if taken individually.

Economists use the term "global labor arbitrage" to refer to the tendency of manufacturing jobs to flow towards whichever country has the lowest wages per unit output at present and has reached the minimum requisite level of political and economic development to support industrialization. At present, many such jobs appear to be flowing towards China, though some which require command of English are going to India and the Philippines. In popular terms, this is referred to as offshoring. (Note that "offshoring" is not synonymous with "outsourcing", which means "to subcontract from an outside supplier or source", such as when a business outsources its bookkeeping to an accounting firm. Unlike offshoring, outsourcing always involves subcontracting jobs to a different company, and that company can be in the same country as the outsourcing company.)

Sports arbitrage – numerous internet bookmakers offer odds on the outcome of the same event. Any given bookmaker will weight their odds so that no one customer can cover all outcomes at a profit against their books. However, in order to remain competitive their margins are usually quite low. Different bookmakers may offer different odds on the same outcome of a given event; by taking the best odds offered by each bookmaker, a customer can under some circumstances cover all possible outcomes of the event and lock a small risk-free profit, known as a Dutch book. This profit would typically be between 1% and 5% but can be much higher. One problem with sports arbitrage is that bookmakers sometimes make mistakes and this can lead to an invocation of the 'palpable error' rule, which most bookmakers invoke when they have made a mistake by offering or posting incorrect odds. As bookmakers become more proficient, the odds of making an 'arb' usually last for less than an hour and typically only a few minutes. Furthermore, huge bets on one side of the market also alert the bookies to correct the market.

Exchange-traded fund arbitrage – Exchange Traded Funds allow authorized participants to exchange back and forth between shares in underlying securities held by the fund and shares in the fund itself, rather than allowing the buying and selling of shares in the ETF directly with the fund sponsor. ETFs trade in the open market, with prices set by market demand. An ETF may trade at a premium or discount to the value of the underlying assets. When a significant enough premium appears, an arbitrageur will buy the underlying securities, convert them to shares in the ETF, and sell them in the open market. When a discount appears, an arbitrageur will do the reverse. In this way, the arbitrageur makes a low-risk profit, while fulfilling a useful function in the ETF marketplace by keeping ETF prices in line with their underlying value.

Some types of hedge funds make use of a modified form of arbitrage to profit. Rather than exploiting price differences between identical assets, they will purchase and sell

securities, assets and derivatives with similar characteristics, and hedge any significant differences between the two assets. Any difference between the hedged positions represents any remaining risk (such as basis risk) plus profit; the belief is that there remains some difference which, even after hedging most risk, represents pure profit. For example, a fund may see that there is a substantial difference between U.S. dollar debt and local currency debt of a foreign country, and enter into a series of matching trades (including currency swaps) to arbitrage the difference, while simultaneously entering into credit default swaps to protect against country risk and other types of specific risk.

Comparison between APT & CAPM APT applies to well diversified portfolios and not necessarily to individual stocks. With APT it is possible for some individual stocks to be mispriced - not lie on the SML. APT is more general in that it gets to an expected return and beta relationship without

the assumption of the market portfolio. APT can be extended to multifactor models. Both the CAPM and APT are risk-based models. There are alternatives. Empirical methods are based less on theory and more on looking for some regularities

in the historical record. Be aware that correlation does not imply causality. Related to empirical methods is the practice of classifying portfolios by style e.g.

o Value portfolioo Growth portfolio

The APT assumes that stock returns are generated according to factor models such as:

As securities are added to the portfolio, the unsystematic risks of the individual securities offset each other. A fully diversified portfolio has no unsystematic risk.

The CAPM can be viewed as a special case of the APT. Empirical models try to capture the relations between returns and stock attributes that

can be measured directly from the data without appeal to theory. Difference in Methodology

CAPM is an equilibrium model and derived from individual portfolio optimization. APT is a statistical model which tries to capture sources of systematic risk.Relation

between sources determined by no Arbitrage condition. Difference in Application

APT difficult to identify appropriate factors. CAPM difficult to find good proxy for market returns. APT shows sensitivity to different sources. Important for hedging in portfolio

formation.CAPM is simpler to communicate, since everybody agrees upon.

Q. 5 Diversification is key to good investment. What are pros and cons of foreign investment?

Ans:

Q. 6 Explain in brief APT with single factor model.

Ans: Arbitrage pricing theory (APT), in finance, is a general theory of asset pricing, that has become influential in the pricing of stocks.

εFβFβFβRR SSGDPGDPII ++++=

APT holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly - the asset price should equal the expected end of period price discounted at the rate implied by model. If the price diverges, arbitrage should bring it back into line.The theory was initiated by the economist Stephen Ross in 1976.

The APT modelRisky asset returns are said to follow a factor structure if they can be expressed as:

where E(rj) is the jth asset's expected return, Fk is a systematic factor (assumed to have mean zero), bjk is the sensitivity of the jth asset to factor k, also called factor loading, andεj is the risky asset's idiosyncratic random shock with mean zero.

Idiosyncratic shocks are assumed to be uncorrelated across assets and uncorrelated with the factors.The APT states that if asset returns follow a factor structure then the following relation exists between expected returns and the factor sensitivities:

where RPk is the risk premium of the factor, rf is the risk-free rate,

That is, the expected return of an asset j is a linear function of the assets sensitivities to the n factors.Note that there are some assumptions and requirements that have to be fulfilled for the latter to be correct: There must be perfect competition in the market, and the total number of factors may never surpass the total number of assets (in order to avoid the problem of matrix singularity).

Using the APTIdentifying the factorsAs with the CAPM, the factor-specific Betas are found via a linear regression of historical security returns on the factor in question. Unlike the CAPM, the APT, however, does not itself reveal the identity of its priced factors - the number and nature of these factors is likely to change over time and between economies. As a result, this issue is essentially empirical in nature. Several a priori guidelines as to the characteristics required of potential factors are, however, suggested:

1. their impact on asset prices manifests in their unexpected movements2. they should represent undiversifiable influences (these are, clearly, more likely to be

macroeconomic rather than firm-specific in nature)3. timely and accurate information on these variables is required4. the relationship should be theoretically justifiable on economic grounds

Chen, Roll and Ross (1986) identified the following macro-economic factors as significant in explaining security returns:

surprises in inflation; surprises in GNP as indicated by an industrial production index; surprises in investor confidence due to changes in default premium in corporate bonds; surprise shifts in the yield curve.

As a practical matter, indices or spot or futures market prices may be used in place of macro-economic factors, which are reported at low frequency (e.g. monthly) and often with significant estimation errors. Market indices are sometimes derived by means of factor analysis. More direct "indices" that might be used are:

short term interest rates; the difference in long-term and short-term interest rates; a diversified stock index such as the S&P 500 or NYSE Composite Index; oil prices gold or other precious metal prices Currency exchange rates

Single factor modelrj = bj0 + bj1F1 + €j; j = 1; 2; : : : ; n whererj is the rate of return on asset (or portfolio) j, F1 denotes the factor’s value, bj0

and bj1 are parameters, and "j denotes an unobserved random error. It is assumed thatE[€jl F1] = 0, that is, the expected value of the random error, conditional upon the value ofthe factor, is zero.APT prediction, single factor model:

The weight λ1 is interpreted as the risk premium associated with the factor, that is, the riskpremium corresponds to the source of the systematic risk.