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Assignment Set- 1 (30 Marks)

Q. 1

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 forforms 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.

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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.

Principles

Technicians 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 everything

Based 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 trends

Technical 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, thestock 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 itself

Technical 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

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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.2

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 EMHclaims 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 20072010. 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

relevantinformation 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

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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 informationinstantaneously. 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 testto 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

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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 andappropriate 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) anddifferent 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, Gupand 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, t 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 = ut-1 + vt where vt ~ N(0,2v).

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 rth order.

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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 t, t*,

t** = 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, is the

change in the index and t 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 = 1 in:

against the one-sided alternative < 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

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nature of Indias 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

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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 thecontrary 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. 3

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

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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).

y 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).

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

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

y 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). Overthe 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

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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%

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Assignment Set- 2 (30 Marks)

Q.1 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 w orking

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 thr ough diversification.

Whereas this type of risk affects a broad range of securities, unsystematic risk affects a veryspecific 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.

Example

Examples 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 inste ad, 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, thecontribution 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.

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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 risk

By 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 ri sk.

Example

On 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: sy stematic risk and

unsystematic risk:

Systematic Risk; m

Nonsystematic Risk; I

n

W

Total risk; U

risk icunsystemattheis

risk systematictheis

where

becomes

m

m R R

U R R

!

!

I

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CAPM is not perfect:-

y The model assumes that either asset returns are (jointly) normally

distributedrandom 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.

y 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.

y 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).

y 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).

y 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 EMHwrong indeed, this possibility makes volatility arbitrage a strategy for reliably

beating the market).

y 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.

y The model assumes that there are no taxes or transaction costs, although this

assumption may be relaxed with more complicated versions of the model.

y The market portfolio consists of all assets in all markets, where each asset is

weighted by its market capitalization. This assumes no preference between marketsand 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.

y 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

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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.

y 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.

y 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. 2

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, anarbitrage 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 (IPA: /rbtrr/)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 arbitrage

Arbitrage 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).

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Arbitrage is

¡ t 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 simu£

¤ an ¥ ously to avoid

e ¦ posure 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 e ¦ ecuted the prices in the market may have moved. Missing one of the legs of

the trade (and subse § uently having to trade it soon after at a worse price ̈ is called

'e ¦ ecution risk' or more specifically 'leg risk'.[note 1]

In the simplest e¦ ample, any good sold in one market should sell for the same price in

another. Traders may, for e ¦ ample, 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 e ¦ ample

ignores the cost of transport, storage, risk, and other factors. "True" arbitrage re§ uires that

there be no market risk involved. Where securities are traded on more than one e ¦ change,

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 ©

and

whereV t means a portfolio at time t.

Ex

pl

s

y Suppose that the e change rates (after taking out the f ees for making the e change

in London are £5 = $10 = ¥1000 and the e change 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 e change

arbitrages, such as the spot-forward arbitrage (see interest rate parity are much

more common.

y One e ample 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 diff erences 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 diff erences that would not be profitable if taken

individually.

y Economists use the term "global labor arbitrage" to ref er 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 re uisite level of political and

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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.)

y Sports arbitrage numerous internetbookmakers 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.

y 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 sellingof 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.

y 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

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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

y APT applies to well diversified portfolios and not necessarily to individual stocks.

y With APT it is possible for some individual stocks to be mispriced - not lie on the

SML.

y APT is more general in that it gets to an expected return and beta relationship

without the assumption of the market portfolio.

y APT can be extended to multifactor models.

y Both the CAPM and APT are risk-based models. There are alternatives.

y Empirical methods are based less on theory and more on looking for some

regularities in the historical record.

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

o Value portfolio

o Growth portfolio

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

as:

y 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.

y The CAPM can be viewed as a special case of the APT.

y Empirical models try to capture the relations between returns and stock attributes

that can be measured directly from the data without appeal to theory.

y 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.

y 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.

S S GDP GDP I I !

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Q. 3

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.

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 model

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

where

y E (r j ) is the j th asset's expected return,

y F k is a systematic factor (assumed to have mean zero),

y b j k is the sensitivity of the j th asset to factor k , also called factor loading,

y and j 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

y RPk is the risk premium of the factor,

y 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 numberof factors may never surpass the total number of assets (in order to avoid the problem of

matrix singularity).

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Using the APT

Identifying the factors

As 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 resul t, this issue is essentiallyempirical 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 movements

2. 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 required

4. 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:

y surprises in inflation;

y surprises in GNP as indicated by an industrial production index;

y surprises in investor confidence due to changes in default premium in corporate

bonds;

y 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:

y

short term interest rates;y the difference in long-term and short-term interest rates;

y a diversified stock index such as the S&P 500 or NYSE Composite Index;

y oil prices

y gold or other precious metal prices

y Currency exchange rates

Single factor model

r j = b j0 + b j1F1 + j; j = 1; 2; : : : ; n

wherer j is the rate of return on asset (or portfolio) j, F 1 denotes the factors value, b j0

and b j1 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 of

the factor, is zero.

APT prediction, single factor model:

The weight 1 is interpreted as the risk premium associated with the factor, that is, the risk

premium corresponds to the source of the systematic risk.

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