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Master of Business Administration

MBA Semester 3

Name: Rahul Sharma

Roll No.: 520961340

Subject: Security Analysis &

Portfolio Management

Subject code: MF0001

Learning Centre: 01822

Assignment No: Set 1

and 2

Sign :

Submitted by: Rahul Sharma

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Dated : 4th Dec, 2010

Assignment No: Set 1

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, technicalanalysts 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 theyare 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, someof which are mathematical transformations of price, often including up anf

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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/callratios 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 patternidentification and interpretation.

Technical analysis is frequently contrasted with fundamental analysis, the

study ofeconomic 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 thanexternal 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

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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, the stock makes a

relative high equal to the most recent relative high. In this a techniciansees 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 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 thesurveys report extreme investor sentiment. Surveys that show

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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 ofcontrarian 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 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 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 reflect the knowledge and expectations of all investors.

The bottom line is that an investor should not be able to beat the marketsince there is no way for him/her to know something about a stock that

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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-strongand 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 availableinformation, 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

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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 notefficient. 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 areindependent. 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 theseare 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, 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,

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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 theseries 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 findany 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.

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 thestandard model with a drift and (5) for the standard model with drift and

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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 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 nullhypothesis of unit root is convincingly rejected, as the test statistic is more

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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 consistentsuggesting 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 ofthe 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 resultssupport 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 BSEsuggesting that the changes in settlement system may not significantly

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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 marketsmay 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 theincome.

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 toinvestors.

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

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(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.

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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 be10%.

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)

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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 bond certificate)

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 bond certificate)

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

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 riskIn 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.

Example

Examples of systematic risk include uncertainty about generaleconomic conditions, such as GNP, interest rates or inflation.

For example, consider an individual investor who purchases $10,000

ofstock 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, theinvestors would incur similar losses, due to systematic risk.

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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 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 canbe 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.

Example

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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: systematic risk and unsystematic risk:

CAPM is not perfect:-

The model assumes that either asset returns are (jointly)normally distributed random variables or that investorsemploy a quadratic form of utility. It is however frequentlyobserved that returns in equity and other markets are notnormally distributed. As a result, large swings (3 to 6 standard

deviations from the mean) occur in the market morefrequently than the normal distribution assumption wouldexpect.

The model assumes that the variance of returns is anadequate measurement of risk. This might be justified underthe assumption of normally distributed returns, but for generalreturn distributions other risk measures (like coherent riskmeasures) will likely reflect the investors' preferences moreadequately. Indeed risk in financial investments is not variancein itself, rather it is the probability of losing: it is asymmetric innature.

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

The model assumes that the probability beliefs of investorsmatch the true distribution of returns. A different possibility is

that investors' expectations are biased, causing market pricesto be informationally inefficient. This possibility is studied inthe field of behavioral finance, which uses psychologicalassumptions to provide alternatives to the CAPM such as theoverconfidence-based asset pricing model of Kent Daniel,David Hirshleifer, and Avanidhar Subrahmanyam (2001).

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

The model assumes that given a certain expected returninvestors will prefer lower risk (lower variance) to higher riskand conversely given a certain level of risk will prefer higherreturns to lower ones. It does not allow for investors who willaccept lower returns for higher risk. Casino gamblers clearly

pay for risk, and it is possible that some stock traders will payfor risk as well. The model assumes that there are no taxes or transaction

costs, although this assumption may be relaxed with morecomplicated versions of the model.

The market portfolio consists of all assets in all markets, whereeach asset is weighted by its market capitalization. Thisassumes no preference between markets and assets forindividual investors, and that investors choose assets solely asa function of their risk-return profile. It also assumes that allassets 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 (includingworks of art, real estate, human capital...) In practice, such amarket portfolio is unobservable and people usually substitutea stock index as a proxy for the true market portfolio.Unfortunately, it has been shown that this substitution is notinnocuous and can lead to false inferences as to the validity ofthe CAPM, and it has been said that due to the inobservabilityof the true market portfolio, the CAPM might not be empiricallytestable. This was presented in greater depth in a paper byRichard Roll in 1977, and is generally referred to as Roll'scritique.

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The model assumes just two dates, so that there is noopportunity to consume and rebalance portfolios repeatedlyover time. The basic insights of the model are extended andgeneralized in the intertemporal CAPM (ICAPM) of RobertMerton, 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 withportfolios that are held by individual investors: humans tend tohave fragmented portfolios or, rather, multiple portfolios: foreach 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; incommon 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 similarassets (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 sameprice.

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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 simultaneouslyto 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'.[note 1]

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:

and

where Vt 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.

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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 itsbookkeeping 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 havemade a mistake by offering or posting incorrect odds. As

http://en.wikipedia.org/wiki/New_York_Stock_Exchangehttp://en.wikipedia.org/wiki/New_York_Stock_Exchangehttp://en.wikipedia.org/wiki/Chicago_Mercantile_Exchangehttp://en.wikipedia.org/wiki/Futures_contracthttp://en.wikipedia.org/wiki/Futures_contracthttp://en.wikipedia.org/wiki/Industrializationhttp://en.wikipedia.org/wiki/People's_Republic_of_Chinahttp://en.wikipedia.org/wiki/Indiahttp://en.wikipedia.org/wiki/Philippineshttp://en.wikipedia.org/wiki/Offshoringhttp://en.wikipedia.org/wiki/Arbitrage_bettinghttp://en.wikipedia.org/wiki/Internethttp://en.wikipedia.org/wiki/Bookmakershttp://en.wikipedia.org/wiki/Customerhttp://en.wikipedia.org/wiki/Dutch_bookhttp://en.wikipedia.org/wiki/New_York_Stock_Exchangehttp://en.wikipedia.org/wiki/New_York_Stock_Exchangehttp://en.wikipedia.org/wiki/Chicago_Mercantile_Exchangehttp://en.wikipedia.org/wiki/Futures_contracthttp://en.wikipedia.org/wiki/Futures_contracthttp://en.wikipedia.org/wiki/Industrializationhttp://en.wikipedia.org/wiki/People's_Republic_of_Chinahttp://en.wikipedia.org/wiki/Indiahttp://en.wikipedia.org/wiki/Philippineshttp://en.wikipedia.org/wiki/Offshoringhttp://en.wikipedia.org/wiki/Arbitrage_bettinghttp://en.wikipedia.org/wiki/Internethttp://en.wikipedia.org/wiki/Bookmakershttp://en.wikipedia.org/wiki/Customerhttp://en.wikipedia.org/wiki/Dutch_book

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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 Fundsallow 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 anyremaining 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.

http://en.wikipedia.org/wiki/Exchange-traded_fundhttp://en.wikipedia.org/wiki/Hedge_fundhttp://en.wikipedia.org/wiki/Security_(finance)http://en.wikipedia.org/wiki/Assethttp://en.wikipedia.org/wiki/Derivative_(finance)http://en.wikipedia.org/wiki/Hedge_(finance)http://en.wikipedia.org/wiki/Credit_default_swaphttp://en.wikipedia.org/wiki/Country_riskhttp://en.wikipedia.org/wiki/Exchange-traded_fundhttp://en.wikipedia.org/wiki/Hedge_fundhttp://en.wikipedia.org/wiki/Security_(finance)http://en.wikipedia.org/wiki/Assethttp://en.wikipedia.org/wiki/Derivative_(finance)http://en.wikipedia.org/wiki/Hedge_(finance)http://en.wikipedia.org/wiki/Credit_default_swaphttp://en.wikipedia.org/wiki/Country_risk

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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 portfolio

o 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 risksof 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. 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 bemodeled as a linear function of various macro-economic factors or

FFFRR SSGDPGDPII ++++=

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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

E(rj) is thejth 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,

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

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 thelatter 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 ofmatrix singularity).

Using the APTIdentifying 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.

http://en.wikipedia.org/wiki/Risk_premiumhttp://en.wikipedia.org/wiki/Risk-free_ratehttp://en.wikipedia.org/wiki/Linearhttp://en.wikipedia.org/wiki/Perfect_competitionhttp://en.wikipedia.org/wiki/Matrix_singularityhttp://en.wikipedia.org/wiki/Linear_regressionhttp://en.wikipedia.org/wiki/Linear_regressionhttp://en.wikipedia.org/wiki/Risk_premiumhttp://en.wikipedia.org/wiki/Risk-free_ratehttp://en.wikipedia.org/wiki/Linearhttp://en.wikipedia.org/wiki/Perfect_competitionhttp://en.wikipedia.org/wiki/Matrix_singularityhttp://en.wikipedia.org/wiki/Linear_regressionhttp://en.wikipedia.org/wiki/Linear_regression

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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

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:

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 atlow frequency (e.g. monthly) and often with significant estimation

errors. Market indices are sometimes derived by means offactor

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; : : : ; nwhere rj is the rate of return on asset (or portfolio) j, F1 denotes thefactors value, bj0and bj1 are parameters, and "j denotes an unobserved random error.It is assumed thatE[j l 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:

http://en.wikipedia.org/wiki/Empiricalhttp://en.wikipedia.org/wiki/A_priori_and_a_posteriori_(philosophy)http://en.wikipedia.org/wiki/Stephen_Ross_(economist)http://en.wikipedia.org/wiki/Inflationhttp://en.wikipedia.org/wiki/GNPhttp://en.wikipedia.org/wiki/Yield_curvehttp://en.wikipedia.org/wiki/Factor_analysishttp://en.wikipedia.org/wiki/Factor_analysishttp://en.wikipedia.org/wiki/S%26P_500http://en.wikipedia.org/wiki/NYSE_Composite_Indexhttp://en.wikipedia.org/wiki/NYSE_Composite_Indexhttp://en.wikipedia.org/wiki/Exchange_ratehttp://en.wikipedia.org/wiki/Empiricalhttp://en.wikipedia.org/wiki/A_priori_and_a_posteriori_(philosophy)http://en.wikipedia.org/wiki/Stephen_Ross_(economist)http://en.wikipedia.org/wiki/Inflationhttp://en.wikipedia.org/wiki/GNPhttp://en.wikipedia.org/wiki/Yield_curvehttp://en.wikipedia.org/wiki/Factor_analysishttp://en.wikipedia.org/wiki/Factor_analysishttp://en.wikipedia.org/wiki/S%26P_500http://en.wikipedia.org/wiki/NYSE_Composite_Indexhttp://en.wikipedia.org/wiki/NYSE_Composite_Indexhttp://en.wikipedia.org/wiki/Exchange_rate

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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.