Financial Modeling for Risk Management

Financial Modeling For Risk Management Using Portfolio
School of management studies, Chintech Page 1
CHAPTER 1
INTRODUCTION

1.1 INTRODUCTION TO THE STUDY
Capital market is now going through a turbulent state. The downturn in global
economy is having a significant impact on the performance of capital market. The recent
volatility in capital market and the complex state of the financial market has added to the
concerns of both retail and institutional investors.
In the present uncertain state of capital market, the concerns of the investors are of
twofold: how to ensure adequate return on their investment and how to control the risk
associated with their investment. In such a situation financial modelling for risk management
is the key to achieving investment objective of the investor. It involves structuring the
investment portfolio in a scientific way in order to ensure superior performance. This requires
application of portfolio optimization algorithms.
Portfolio optimization techniques, not only ensures superior returns on the investment
portfolio, but also ensures efficient diversification resulting in superior risk reduction. In an
uncertain state, as is now, the importance of financial modelling techniques involving the use
of portfolio optimization techniques cannot be over emphasized as poor investment decisions
can seriously undermine the long term welfare and wealth accumulation of the investors.
The Project entitled “Financial Modelling for Risk management using Portfolio”
examines the use of Sharpe’s optimization models in and superior portfolio performance. The
study examines the effectiveness of Sharpe’s Optimization Model.
1.2 SCOPE AND SIGNIFICANCE OF THE STUDY
The enormous growth in over the last twenty years in India has created a number of
new investors in capital market. One of the major concerns of the investors now is how to
ensure superior performance of their investment ensuring at the same time protection of their
wealth. As investors are now operating in a complex and uncertain investment environment,
poor investment decisions can seriously undermine the long term welfare and wealth
accumulation of the investors.
Under this complex and uncertain investment environment, financial modelling for
risk management assumes more significance. The study examines how portfolio optimization
models can improve the performance of portfolios and help investors to achieve their
investment objectives.

1.3. RESEARCH PROBLEM
The recent downturn in global economy is having a profound impact on Indian
Capital Market. The recent high volatility of the capital market due to the turmoil of the
global financial market has increased the concern of the investors. Investors are now realizing
the importance of efficient asset allocations in achieving their investment objectives under
present uncertain and complex investment environment. Efficient asset allocation can be
achieved only through application of superior portfolio optimization techniques. The present
study examines the use of the portfolio optimization algorithms in ensuring superior asset
allocation and superior portfolio performance. “Financial modelling for risk management
using portfolio” is helps to select optimal portfolio for investment and ensure maximum
return to the investors
1.4 OBJECTIVES OF THE STUDY
The objective of the study is to examine the application of financial modelling in
portfolio management and Risk management using portfolio. The specific objectives of the
study are stated below:
Major objective
To study the application of Sharpe’s portfolio optimization models and portfolio
diversification in Risk management.
Minor Objectives;
1. To construct optimal portfolios by using Sharpe’s portfolio optimization models and
to examine the effectiveness of Sharpe’s portfolio optimization in improving portfolio
performance.
2. To evaluate the Sharpe ratio, Treynor’s ratio, & Jensen measure of the optimal
portfolios constructed to get an insight into the portfolio performance evaluation process.
3. To study the role of VaR matrices by using Monte Carlo simulation method in
portfolio risk management.

1.5 RESEARCH METHODOLOGY
RESEARCH DESIGN
The research design is the conceptual structure within which research will be
conducted. Design includes an outline of what the researcher will do from writing the
hypothesis and its operational implications of the final analysis of the data. The type of
research is analytical.
1.5.1 TYPE OF DATA USED
The source of data is secondary in nature. The closing price of securities and closing
values of BSE SENSX index are the fundamental data for the study. The nature of data is
secondary. The main source of information is websites of stock exchanges. References are
also made to technical papers on the subject, Newspapers, Magazines, financial journals,
monecontrol.com, and indiainfoline.com.
1.5.2 CRITERIA OF SELECTION OF STOCK
Twelve securities of leading companies are selected on the following basis
• Securities included in the BSE listing are only selected on the basis that the alpha
value of the share should be positive.
• As far as possible, securities are selected from different sectors.
1.5.3 PERIOD OF STUDY
The study was conducted for a period of 60 days extending from 1st April 2013 to
31st May 2013.
1.5.4 TOOLS FOR ANALYSIS
The collected data has been analyzed using basic statistical tools like regression
analysis, correlation analysis, mathematical modelling, and optimization techniques. Ratios
and charts are also used for better exposition.

1.6 LIMITATIONS
 Researcher is limited with resources like specialized computer softwares for
constructing portfolio. Researcher uses only excel sheet for calculations
 Data considered is only for past 3 year period.
 Data is of secondary in nature.
 Only twelve securities are selected for the study.
1.7 CHAPTERIZATION:
Chapter I Introduction – deals with importance of the study,
Statement of problem, objectives of the study and the
scope of the study along with methodology.
Chapter II Theoretical frame work of portfolio optimization and
Literature review of project
Chapter III Industry and organization Profile; – contained a brief
detailing of capital market and about the organization
JRG securities Ltd.
Chapter IV Data Analysis;- include calculations and analysis of
collected data. It includes security analysis, portfolio
analysis, portfolio evaluation etc.
Chapter V Findings, Suggestions and Conclusions

CHAPTER 2
THEORETICAL FRAME WORK

THEORETICAL PERSPECTIVE
CONCEPTUAL FRAMEWORK OF THE STUDY
SECURITY ANALYSIS
PORT FOLIO
SELECTION
PORTFOLIO
OPTIMISATION
PORTFOLIO
EVLUATION
PORTFOLIO
MANAGEMENT
UNSYSTEMATIC RISKSYSTEMATIC RISK
RETURNRISK
SHARPE
OPTIMISATION
OPTIMISED PORTFOLIO
SHARPE RATIO
TREYNOR
RATIO
VALUE AT RISK
JENSEN ALPHA

PORTFOLIO MANAGEMENT
Portfolio is a collection of assets .Creation of portfolio helps to reduce risk without
sacrificing returns. It is rare to find investors investing in a single security, instead of this they
tend to invest in a group of securities. Such a group of securities is called a portfolio.
Portfolio management deals with the analysis of individual securities as well as with
the theory and practice of optimally combining securities in to portfolio. An investor is faced
with problems in choosing the securities among the large number of securities. His choice
depends upon risk return returns characteristics of individual securities. Another problem is
how much to invest in each security. The risk return characteristics of a portfolio differ from
those of individual securities combining to form a portfolio. The investor tries to choose the
optimal portfolio taking in to consideration the risk return characteristics of all possible
portfolios. Portfolio management is a complex process which tries to make investment
activity more rewarding and less risky.
Portfolio management process consist of the following five process,
1. Security analysis
2. Portfolio analysis
3. Portfolio selection
4. Portfolio revision
5. Portfolio evaluation
The success of portfolio management depends on how effectively each phase s carried
out.
1. SECURITY ANALYSIS
Security analysis is the initial phase of the portfolio management process. This step
consists of examining the risk return characteristics of individual securities. For the purpose
of analysis twelve securities are selected and the return, risk and risk adjusted rate of return
are determined. There are two alternative approaches to security analysis they are
fundamental analysis and technical analysis. They are based on different premises and follow
different techniques. Fundamental analysis concentrates on fundamental factors affecting the

company such as the EPS of the company, the dividend pay-out ratio, competition faced by
the company, market share .quality management, etc According to this approach the share
price of this company is determined by these fundamental factors. The fundament analysts
works out the true worth or intrinsic values of a security based on its fundamentals and then
compares this value with the current market price. If the current market price is higher than
the intrinsic value the share is said to be overpriced. Fundamental analysis helps to identify
fundamentally strong companies whose shares are worthy to be included in the investor’s
portfolio.
Technical analysis concentrates on price movements and ignores the fundamental s of
shares. The technical analyst believes that the share price movements are systematic and
exhibit certain consistent patterns .He therefore studies past movements in the prices of
shares to identify trends and patterns .He then tries to predict the future price movement s.
The current market is compared with the future predicted price to determine the extent of
mispricing.
More recent approach to security analysis is the efficient market hypothesis. This
hypothesis holds that share movements are random and not systematic. According to this
approach it is possible for an investor to earn normal returns by randomly choosing securities
of a given risk level.
2. PORTFOLIO ANALYSIS
Portfolio analysis phase of portfolio management consist of identifying the range of
portfolios that can be constituted from a given set of securities and calculating their return
and risk for further analysis. It is better to invest in a group of securities rather than a single
security. Such a group of securities held together as an investment is known as a portfolio. A
rational investor attempts to find out the most efficient portfolio. The efficiency can be
evaluated only in terms of the expected return and risk of different portfolio.
Security analysis provides the investor with a set of worthwhile or desirable
securities. From this set of securities an indefinitely large number of portfolios can be
constructed by choosing different set of securities and also by varying the proportion of
investment in each security. Each of these securities has its own risk return characteristics
which are not just the aggregate of individual security characteristics. The risk and return can

be measured and expressed quantitatively. Portfolio is being constructed using the following
formulas:
3. PORTFOLIO SELECTION
The proper goal of portfolio construction is to generate a portfolio that provides the
highest return at a given level of risk .A portfolio having this characteristic is known as
efficient portfolio. From this set of efficient portfolios, optimal portfolio has to be selected for
investment.
4. PORTFOLIO REVISION
Having constructed the optimal portfolio, the investor has to constantly monitor the
portfolio to ensure that it continues to be optimal. Portfolio revision involves changing the
existing mix of securities. The main objective of portfolio revision is to ensure the optimality
of the revised portfolio. Portfolio revision is not a causal process of portfolio management,
portfolio revision is as important as portfolio analysis and selection.
Portfolio revision may also be necessitated by some investor related changes such as
availability of additional fund, changes in risk attitude, need of cash for other alternative use
etc. portfolio revision has to be done scientifically and objectively so as to ensure the
optimality of the revised portfolio.
5. PORTFOLIO EVALUATION
The objective of constructing and revising it periodically is to earn maximum returns
with minimum risk. Portfolio evaluation is the process which is concerned with assessing the
performance of the portfolio over a selected period of time in terms of return and risk. It
provides mechanism for identifying weakness in the investment process for improving these
deficient areas. It provides a feedback mechanism for improving the entire portfolio
management process
TOOLS FOR PORTFOLIO EVALUATION
 SHARPE RATIO
The performance measured developed by William Sharpe is referred to as the Sharpe
ratio. It is the ratio of the reward or risk premium to the variability of return or risk as

measured by the standard deviation of return. The formula for calculating Sharpe ratio may
be stated as
Sharpe ratio (SR) = (portfolio Return – Risk free rate of return)
Portfolio standard deviation
=
𝑅𝑝−𝑅𝑓
𝜎𝑝
Where
Rp=realized return on the portfolio
Rf=Risk free rate of return
σp=Standard deviation of portfolio return
 TREYNOR RATIO
The performance measure developed by Jack Treynor is referred to as Treynor ratio
or reward to volatility ratio. It is the ratio of the reward or risk premium to the volatility of
return as measured by the portfolio beta. The formula for calculating Treynor ratio may be
stated as
Treynor ratio= (Portfolio Return- Risk free rate of return)/Portfolio beta
=
𝑅𝑝−𝑅𝑓
𝛽
Where
Rp=realized return on the portfolio
Rf=Risk free rate of return
βp=Portfolio beta
Both the measures are relative measures of performance because they relate the return
to the risk involved. However they differ in the measure of risk used for the purpose. Sharpe
uses the total risk as measured by standard deviation, while treynor employs the systematic
risk as measured by the beta coefficient in a fully diversified portfolio all the unsystematic

risk would be diversified away and the relevant measure of risk would be the beta coefficient.
For such a portfolio Treynor ratio would be the appropriate measure of performance
evaluation .For a portfolio that is not so well diversified , the Sharpe ratio using the the total
risk measure would be the appropriate performance measure.
 JENSEN RATIO
Another type of risk adjusted performance has been developed by the Michael Jensen
and is referred to a Jensen ratio. This ratio measures the differential between actual return
earned on a portfolio given its level of risk. The CAPM model is used to to calculate the
expected return on a portfolio. The difference between the return that a portfolio should earn
for a given level of risk
Jensen Measure (αp)=Rp-E(Rp)
Where,
Rp- Realized return of the portfolio
E(Rp)-Expected return of the portfolio
E(Rp)=Rf+βp(Rm-Rf)
βp-Beta of portfolio
Rm-Market return
Rf-Risk free rate of return
The difference between the return actually earned on a portfolio and the return
expected from the portfolio is a measure of the excess return.
The differential return is calculated as follows
αp= Rp- E(Rp)
Where
αp=Differential return earned
Rp= actual return earned on the portfolio

E(Rp)=Expected return
DIVERSIFICATION
If one holds, say, equal amount of risky assets that are not perfectly correlated, the
portfolio expected return will be the average of the expected returns of the asset in the
portfolio. However the portfolio standard deviation will be, less than the average of the
standard deviation of the assets in the portfolio.
The power of this statement may be explained by imagining two assets with the same
expected return and the same standard deviation of the return. by holding both assets in a
portfolio, one obtain the same expected return as either one of them, but a standard deviation
that is lower than any one of them individually. Thus diversification leads to a reduction in
risk without any sacrifice in expected return.
RISK AND RETURN
While making a decision regarding investment and financing, the investor seeks to
achieve right balance between risks and return in order to optimize the value. Return and risk
go together in investment. Everything an investor does is tied directly or indirectly to return
and risk. The concept of return and risk is explained below.
RISK
Risk is the potential for variability in return. The expected return is the uncertain
future return that an investor expects to get from his investments. The realized return on
contrary is the certain return that an investor has actually obtained from his investment from
the end of the holiday period. The risk arises where there is a possibility of variation between
expectations and realizations with regard to an investment.
Element of Risk.
The essence of risk is an investment is the variation in its returns. This variation in
returns is caused by a number of factors. These factors which produce variation in the return
from an investment constitute the element of risk.
Total risk = Systematic Risk + Unsystematic Risk.

Systematic Risk
The impact of economic, political and social changes is system-wide and that portion
of total variability in security return caused by such system- wide factor is referred to as
systematic risk. Systematic risk is further sub divided into:
1. Interest rate risk: Interest rate risk is a type of systematic risk that particularly affects
securities like bond and debentures. The risk caused as the variation in bond prices caused
due to the variation in interest rate is known as interest rate risk.
2. Market risk: Market risk is a type of systematic risks that affect the shares. Market risk is
the increased variability of investor returns due to the alternating movement of share market.
3. Purchasing power risk: It refers to the variation in investor return caused by inflation.
Inflation causes a variation in the purchasing power of the returns from an investment. This is
known as purchasing power risk and its impact is uniformly felt on all securities in the market
and as such, is a systematic risk.
Unsystematic Risk
The return from a security may vary because of certain factors affecting only the
company issuing such securities. When variability of returns occurs because of such firm-
specific factors it is known as unsystematic risk. The unsystematic risk or unique risk
affecting specific securities arises from two sources.
• The operating environment of the company
• The financing pattern adopted by the company
These two types of unsystematic risk are referred to as business risk and financial risk
1. Business risk: Business risk is thus a function of the operating conditions faced by a
company and is the variability in operating conditions of the company.
2. Financial risk: Financial risk is a function of financial leverage which is the use of debt in
the capital structure. The variability in EPS due to the presence of debt in capital structure of
a company is referred to as financial risk.

MEASUREMENT OF RISK
Expected Returns
The expected return of the investment is the probability weighted average of all the
possible returns.
Ri = α¡+ β¡ Rm
Measurement of Systematic Risk
The systematic risk of a security is measured by a statistical measure called Beta
βi = rim σi σm
σ²m
RETURN
Return is a motivating force, inspiring the investor in the form of rewards, for
undertaking the investment. The importance of return in any investment decision can be trace
to the following factors:
 It enables the investor to compare alternative investment in terms of what they have to
offer the investor.
 Measurement of historical (past) return enables the investor to assess how well they
have done.
 Measurement of historical returns also helps in estimation of future returns.
Components of Return
Return is basically made up of two components:
 The periodic cash receipt or income on the investment in the form of interest,
dividend etc.The term yield is often used in connection with this component of return.
Yield refers to the income derived from a security in relation to its price, usually its
purchase price.
 The appreciation (depreciation) in the price of the asset, is referred to as capital
gain(loss).this is the difference between the purchase price and the price at which the
asset can be, or is, sold.

OPTIMAL PORTFOLIO SELECTION
The objective of every rational investor is to maximize his returns and minimize the
risk. Diversification is the method adopted for reducing risk. It essentially results in the
construction of portfolios. The proper goal of portfolio construction would be to generate a
portfolio that provides the highest return and the lowest risk. Such a portfolio would be
known as the optimal portfolio. The process of finding the optimal portfolio is described as
portfolio selection.
PORTFOLIO OPTIMIZATION
Portfolio optimization is a part of portfolio selection. Portfolio optimization helps to
maximize the returns with minimum risk.
OPTIMAL PORTFOLIO SELECTION USING SHARPE’S OPTIMIZATION
MODEL
The Sharpe’s optimization model was developed by researcher William Sharpe.
Sharpe had provided a model for the selection of appropriate securities in a portfolio. In this
model, the ranking criteria are used to order the stocks for selecting the optimal portfolio. The
Sharpe optimization model uses excess return to beta as the performance measure of
individual securities so as to include in the portfolio Sharpe had provided a model for the
selection of appropriate securities to be included in a portfolio. The selection of any stock is
directly related to its excess return beta ratio.
FORMATION OF OPTIMAL PORTFOLIO
The inclusion of any security in the portfolio is directly related to its excess return to
beta ratio. Excess return is the difference between the expected return on the stock and the
risk free rate of interest such as rate of return on Government securities. The excess return-to-
beta ratio measures the additional return on a stock (excess return over the risk free rate) per
unit of non –diversifiable risk. This ratio gets easy interpretation and acceptance because this
ratio gives relationship between potential reward risks. The numerator of this ratio gives the
extra return over the risk- free rate and the denominator give the non-diversifiable risk.

Excess return to beta ratio= (Ri-Rf)/βi
Where
Ri = the expected return on security i
Rf = the return on risk less asset
βi = the expected change in the ratio of return on stock I associated with a 1% change in
the market return
If the stock ranked by excess return –to – beta (from highest to lowest), ranking
represents the desirability of a stock inclusion in the portfolio. This implies that if a particular
stock with a specific ratio of (Ri-Rf)/βi included in the optimal portfolio, all stocks with
higher ratio will also be included. On the other hand, if a stock with a particular (Ri-Rf)/βi is
excluded from an optimal portfolio; all stocks with a lower ratio will be excluded. The
number of stocks included in the optimal portfolio depends on a unique cut off rate which
ensures that all stocks with higher (Ri-Rf)/βi will be included and all stocks with lower ratios
should be excluded. Cut off rate is denoted by “C*”
The steps for finding out the stocks to be included in the optimal portfolio are given
below
1. Find out the “excess return to beta” ratio for each stock under consideration
2. Rank them from the highest to lowest.
3. Proceed to calculate Ci for all stocks according to the ranked order using the
following formula
Ci= (𝜎²𝑚
(𝐑𝐢 − 𝐑𝐟)/𝛔²𝐞𝐢)/(𝟏 + 𝛔 𝟐
𝐦 (𝛃 𝐢 𝟐
/𝛔²𝐞𝐢))𝐧
𝐢=𝟎
βi =Beta of each security
σi =Risk of security
Ri =Return of each security
Rf =Risk free rate of return

Ci= Cut off rate
σ2m=Variance of the market index
σ2ei = Unsystematic Risk
4. The cumulated values of Ci starts declining after a particular Ci and that point is taken
as the cut-off point and that stock ratio is the cut –off ratio C*
CONSTRUCTING THE OPTIMAL PORTFOLIO
Once the cut-off rate is determined the next step is calculating the proportion to be
invested in each security. The proportion invested in each security is:
𝑿𝒊 = 𝒁𝒊/ 𝒁𝒊
𝒏
𝒊=𝟏
Where
𝒁𝒊 =
𝜷𝒊
𝝈 𝟐 𝒆𝒊
𝑹𝒊 − 𝑹𝒇
𝜷𝒊
− 𝑪 ∗
Zi =weight on each security
βi =Beta of each security
σ²ei =Unsystematic risk of security
Ri =return of each security
Rf =Risk free rate of return
C* = cut off rate
SINGLE INDEX MODEL
The basic notion underling the single index model is that all stocks are attracted by
movements in the stock market. Casual observation of share prices reveals that when the
market moves up (as measured by any of the widely used stock market indices), prices of
most of the shares tends to increase. When the market goes down, the price of most shares

tend to decline. This suggests that one reason why security returns might be correlated and
there is co-movement between securities, is because of a common response to market
changes. this co-movement of stocks with a market index may be studied with the help of a
simple linear regression analysis, taking the returns on an individual security as the depended
variable(Ri) and the returns on the market index (Rm)as the independent variable.
The return of individual securities may be expressed as:
𝑹𝒊 = 𝜶𝒊 + 𝜷𝒊(𝑹𝒎 + 𝒆𝒊)
Where,
α¡ is the component of security i's return that is independent of the market performance.
Rm is the rate of return on the market index.
β¡ is the constant that measures the expected change in Ri given a change in Rm.
e¡ is the error term representing the random or residual return.
Sharpe’s Optimal Portfolio
Sharpe has provided a model for the selection of the appropriate securities in the
portfolio. The selection of any stock is directly related to its excess return – beta ratio.
=
𝑹𝒊 − 𝑹𝒇
𝜷𝒊
where,
Ri – the expected return of the stock i.
Rf – Risk free return
βi - the expected change in the rate of return on the stock i, associated with one unit
change in the market return.
A fund allocated with the highest possible Sharpe ratio is said to be Sharpe optimal.
To find the Sharpe optimal portfolio, consider the plot on the investment opportunity set of
risk return possibilities for a portfolio. The slope of a straight line drawn from the risk-free

rate to a portfolio gives the Sharpe ratio for that portfolio. Hence, the portfolio on the line
with the steepest slope is the Sharpe optimal portfolio.
Ranking of the stock are done on the basis of their excess return to beta. Portfolio
manager would like to include stock with the highest ratio .The selection of the stocks
depends on a unique cut-off rate such that all stock higher ratio of Ri – Rf / βi are included
and stock within lower ratio are left off. The cut-off point is denoted by C*.Sharpe optimal
portfolio is one of the efficient portfolios on the Markowitz efficient frontier.
PORTFOLIO EVALUATION:
The optimized portfolios are being evaluated using the following tools.
i. Sharpe ratio
ii. Treynor ratio
iii. Jensen Measure
VALUE AT RISK
Risk management attempts to provide financial predictability for a company. Every
day firms face financial risks. Interest and exchange rate volatility, default on loans, and
changes in credit rating are some examples. These risks can be sorted into two categories-
credit risk and market risk. Credit risk includes all risks associated with the credit of specific
participants, such as potential default or changes in credit rating.
Market risk refers to risks affecting broad sectors of the economy, such as an increase
in interest rates, currency devaluation, or a decline in commodities prices, like aluminum and
oil. Financial analysts use a number of innovations to calculate and hedge against these kinds
of risk. One innovation that has been receiving immense attention is Value at Risk.
Value at Risk is a summary statistic that quantifies the exposure of an asset or
portfolio to market risk, or the risk that a position declines in value with adverse market price
changes. Measuring risk using VaR allows managers to statements regarding the expected
losses for a certain period.

To arrive at a VaR measure for a given portfolio, a firm must generate a probability
distribution of possible changes in the value of some portfolio over a specific time or “risk
horizon” .J.P.Morgan Chairman Dennis Weatherstone introduced this concept.
Different approaches for calculating VaR
VaR can be calculated in many ways. As a result, firms using different calculating
methods can arrive at different Value at Risk numbers for the same portfolio. There are
advantages and disadvantages in each method of calculating VaR
 Monte Carlo Simulation
 Variance Covariance model
 Historical Simulation Method
Monte Carlo Simulation
For applying Monte Carlo simulation technique, security prices are assumed to be a
random variable. It is also assumed that the stock market is efficient in the weak form (which
is true for Indian Market).Since stock price is a random variable; the stock price movement is
a stochastic process.
The Wiener process, which is a particular type of Markov stochastic process, best
defines the stock price movement. The mathematical model which defines the stock price
movements under Wiener process is given by the following mathematical relation:
∂s = μS∂t + σSЄ√∂ t
Where,
∂s = change in the stock price for a small change in time interval ∂ t
S= stock price at time t
μ = expected rate of return per unit of time
ε = Random drawing from a standardized normal distribution
σ = Volatility of stock price or standard deviation of the expected return
∂ t = A small time interval

The stock price after a small time interval ∂ t would be
ST = S+∂s
Since the period considered is very small, a logo normal return or continuously
compounded return would be more appropriate. So the expected return μ for period T is
defined as
𝝁 =
𝟏
𝑻
𝓵𝐧 ∗ (𝐒𝐭/𝐒𝟎)
Where
ST = Stock price at time T
SO = Stock price at time Zero
ℓn = Natural logarithm
T =Time interval in years
Following steps are involved in Monte Carlo Simulation to calculate one-day VaR for a
portfolio.
1. Determining the expected return and standard deviation of the return for the stock (μ
and σ).These are assumed to be constant.
2. Value the portfolio today.(in our case 31.4.2008) in the usual way by using current
value of the stock price .
3. Sample once from the multivariate normal probability distribution to determine the
value of ε (for the purpose we have used a random number generator to obtain the random
number ε with the computer by using Microsoft Excel)
4. Determine the change in value of the security and the new value of the security using
the relation.
For our analysis ∂ t = 1 day
5. Revalue the portfolio at the end of the day in the usual way.

6. Subtract the value calculated in step 2 from the value in steps to determine a sample
change in portfolio value ∂P.
7. Repeat steps (3) to (6) many times (in our case 500 times) to build up a probability
distribution for ∂P.
We have repeated the steps to obtain 500 sample values for ∂P. The VaR is calculated
at 99%and95% confidence level.
The 500 simulated values of changes in portfolio values so obtained are then sorted in
ascending order.1-day VaR at 99% is the 5th worst outcome and 1-day VaR at 95% is the
25th worst outcome.
LITERATURE REVIEW
Investment risk management in Tehran Stock Exchange (TSE) using technique of
Monte Carlo Simulation (MCS) is a paper presented by Darush Farid, (Department of
Economics, Management and Accounting, Yazd University, Yazd, Iran),Alireza Rajabipoor
Meybodi, (Department of Business Management, Meybod University – Payam E Noor
(PNU), Yazd-Meybod, Yazd, Iran), Seyed Heydar Mirfakhraddiny, (Department of
Economics, Management and Accounting, Yazd University, Yazd, Iran) with the purpose to
identify how to manage risk by the use of “value at risk (VaR) concept” with Monte Carlo
Simulation (MCS) technique in stock exchanges. The paper specifies which equity stocks
have been more affected on VaR in set of portfolio and which equity stocks are lesser
affected. In addition, the main result which is derived by the research shows that if there is a
loss at future, what is max the loss at the level confidence which could be imposed by
investors. Thus, the paper suggests how the investors can invest their capital so that they
would minimize their loss and maximize their profit.
Risk-return optimization with different risk-aggregation strategies is a journal presented
by Stan Uryasev, Ursula A Theiler and Gaia Serraino tells new methods of integrated risk
modelling play an important role in determining the efficiency of bank portfolio
management. The purpose of this paper is to suggest a systematic approach for risk strategies
formulation based on risk-return optimized portfolios, which applies different methodologies
of risk measurement in the context of actual regulatory requirements. The authors find
evidence that risk aggregation in Internal Capital Adequacy Assessment Process (ICAAP)

should be based on risk-adjusted aggregation approaches, resulting in an efficient use of
economic capital. By using different values of confidence level in VaR and CVaR, deviation,
it is possible to obtain optimal portfolios with similar properties. Before deciding to insert
constraints on VaR or CVaR, one should analyze properties of the dataset on which
computation are based, with particular focus on the model for the tails of the distribution, as
none of them is “better” than the other.

CHAPTER 3
INDUSTRY AND ORGANIZATION PROFILE

INTRODUCTION
Capital Market Evolution
Indian Stock Markets are one of the oldest in Asia. Its history dates back to nearly 200
years ago. The earliest records of security dealings in India are meager and obscure. The East
India Company was the dominant institution in those days and business in its loan securities
used to be transacted towards the close of the eighteenth century. By 1830's business on
corporate stocks and shares in Bank and Cotton presses took place in Bombay. Though the
trading list was broader in 1839, there were only half a dozen brokers recognized by banks
and merchants during 1840 and 1850.
The 1850's witnessed a rapid development of commercial enterprise and brokerage
business attracted many men into the field and by 1860 the number of brokers increased into
60.In 1860-61 the number of brokers increased to about 200 to 250. In 1865, a disastrous
slump began (for example, Bank of Bombay Share which had touched Rs 2850 could only be
sold at Rs. 87).
At the end of the American Civil War, the brokers who thrived out of Civil War in
1874, found a place in a street (now appropriately called as Dalal Street) where they would
conveniently assemble and transact business. In 1887, they formally established in Bombay,
the "Native Share and Stock Brokers' Association" (which is alternatively known as “The
Stock Exchange "). In 1895, the Stock Exchange acquired a premise in the same street and it
was inaugurated in 1899. Thus, the Stock Exchange at Bombay was consolidated.
Indian Stock Exchanges - An Umbrella Growth
The Second World War broke out in 1939. It gave a sharp boom which was followed
by a slump. But, in 1943, the situation changed radically, when India was fully mobilized as a
supply base. On account of the restrictive controls on cotton, bullion, seeds and other
commodities, those dealing in them found in the stock market as the only outlet for their
activities. They were anxious to join the trade and their number was swelled by numerous
others. Many new associations were constituted for the purpose and Stock Exchanges in all
parts of the country were floated.
The Uttar Pradesh Stock Exchange Limited (1940), Nagpur Stock Exchange Limited
(1940) and Hyderabad Stock Exchange Limited (1944) were incorporated. In Delhi two stock

exchanges - Delhi Stock and Share Brokers' Association Limited and the Delhi Stocks and
Shares Exchange Limited - were floated and later in June 1947, amalgamated into the Delhi
Stock Exchange Association Limited.
Trading Pattern of the Indian Stock Market
Trading in Indian stock exchanges is limited to listed securities of public limited
companies. They are broadly divided into two categories, namely, specified securities
(forward list) and non-specified securities (cash list). Equity shares of dividend paying,
growth-oriented companies with a paid-up capital of at least Rs.50 million and a market
capitalization of at least Rs.100 million and having more than 20,000 shareholders are,
normally, put in the specified group and the balance in non-specified group.
Two types of transactions can be carried out on the Indian stock exchanges: (a) spot
delivery transactions "for delivery and payment within the time or on the date stipulated
when entering into the contract which shall not be more than 14 days following the date of
the contract and (b) forward transactions "delivery and payment can be extended by further
period of 14 days each so that the overall period does not exceed 90 days from the date of the
contract". The latter is permitted only in the case of specified shares. The brokers who carry
over the outstandings pay carry over charges (cantango or backwardation) which are usually
determined by the rates of interest prevailing. A member broker in an Indian stock exchange
can act as an agent, buy and sell securities for his clients on a commission basis and also can
act as a trader or dealer as a principal, buy and sell securities on his own account and risk, in
contrast with the practice prevailing on New York and London Stock Exchanges, where a
member can act as a jobber or a broker only.
The nature of trading on Indian Stock Exchanges are that of age old conventional
style of face-to-face trading with bids and offers being made by open outcry. However, there
is a great amount of effort to modernize the Indian stock exchanges in the very recent times.
Over The Counter Exchange of India (OTCEI)
The traditional trading mechanism prevailed in the Indian stock markets gave way to
many functional inefficiencies, such as, absence of liquidity, lack of transparency, unduly
long settlement periods and benami transactions, which affected the small investors to a great
extent.

To provide improved services to investors, the country's first ringless, scripless,
electronic stock exchange - OTCEI - was created in 1992 by country's premier financial
institutions - Unit Trust of India, Industrial Credit and Investment Corporation of India,
Industrial Development Bank of India, SBI Capital Markets, Industrial Finance Corporation
of India, General Insurance Corporation and its subsidiaries and CanBank Financial Services.
Trading at OTCEI is done over the centres spread across the country. Securities traded
on the OTCEI are classified into:
• Listed Securities - The shares and debentures of the companies listed on the OTC can
be bought or sold at any OTC counter all over the country and they should not be
listed anywhere else
• Permitted Securities - Certain shares and debentures listed on other exchanges and
units of mutual funds are allowed to be traded
• Initiated debentures - Any equity holding at least one lakh debentures of particular
scrip can offer them for trading on the OTC.
The Indian Financial system is regulated and supervised by two government agencies
under the Ministry of Finance - They are:
• The Reserve Bank of India [RBI]
• The Securities Exchange Board of India [SEBI]
All parts of the financial system are interconnected with one another and the
jurisdictions of the RBI and the SEBI overlap in many fields.
• Securities and Exchange Board of India
• Stock Exchanges of India
Scope of Capital Market Research
We were next faced with another difficult question about what can be classified as a
work on capital markets. A variety of work in economics, accounting and finance would have
some linkages with capital markets. Works in corporate finance have strong linkages with
security markets. For our purpose therefore, we considered works falling into any of the
following categories as those belonging to the field of capital markets: valuation of stocks

and functioning of the stock markets; valuation of bonds, convertible debentures and market
for debt; new issues market and merchant banking; market efficiency; dividends, bonus &
rights issues and rates of return; and performance and regulations of mutual
Bombay Stock Exchange
Established in 1875, BSE Ltd. (formerly known as Bombay Stock Exchange Ltd.), is
Asia’s first Stock Exchange and one of India’s leading exchange groups. Over the past 137
years, BSE has facilitated the growth of the Indian corporate sector by providing it an
efficient capital-raising platform. Popularly known as BSE, the bourse was established as
"The Native Share & Stock Brokers' Association" in 1875. BSE is a corporatized and
demutualised entity, with a broad shareholder-base which includes two leading global
exchanges, Deutsche Bourse and Singapore Exchange as strategic partners. BSE provides an
efficient and transparent market for trading in equity, debt instruments, derivatives, mutual
funds. It also has a platform for trading in equities of small-and-medium enterprises (SME).
More than 5000 companies are listed on BSE making it world's No. 1 exchange in
terms of listed members. The companies listed on BSE Ltd command a total market
capitalization of USD 1.32 Trillion as of January 2013. It is also one of the world’s leading
exchanges (3rd largest in December 2012) for Index options trading (Source: World
Federation of Exchanges).
BSE also provides a host of other services to capital market participants including risk
management, clearing, settlement, market data services and education. It has a global reach
with customers around the world and a nation-wide presence. BSE systems and processes are
designed to safeguard market integrity, drive the growth of the Indian capital market and
stimulate innovation and competition across all market segments. BSE is the first exchange in
India and second in the world to obtain an ISO 9001:2000 certification. It is also the first
Exchange in the country and second in the world to receive Information Security
Management System Standard BS 7799-2-2002 certification for its On-Line trading System
(BOLT). It operates one of the most respected capital market educational institutes in the
country (the BSE Institute Ltd.). BSE also provides depository services through its Central
Depository Services Ltd. (CDSL) arm.BSE’s popular equity index - the S&P BSE SENSEX -
is India's most widely tracked stock market benchmark index. It is traded internationally on
the EUREX as well as leading exchanges of the BRCS nations (Brazil, Russia, China and
South Africa).

BSE has won several awards and recognitions that acknowledge the work done and
progress made like The Golden Peacock Global CSR Award for its initiatives in Corporate
Social Responsibility, NASSCOM - CNBC-TV18’s IT User Awards, 2010 in Financial
Services category, Skoch Virtual Corporation 2010 Award in the BSE StAR MF category and
Responsibility Award (CSR) by the World Council of Corporate Governance. Its recent
milestones include the launching of BRICSMART indices derivatives, BSE-SME Exchange
platform, S&P BSE GREENEX to promote investments in Green India
Vision
"Emerge as the premier Indian stock exchange with best-in-class global practice in
technology, products innovation and customer service."
Brand identity
Bombay Stock Exchange has now adopted only its initials as the new name (BSE),
positioning itself better position as a national multi-asset financial infrastructure institution.
BSE’s strategic shift in approach, attitude and business focus is reflected in its new tag line -
Experience the New.
With renewed zeal and focus on new business opportunities, product and service
innovation, upgrades in technology, increased investor and member focus, BSE is always
pushing the envelope on all fronts. The ambition is to continually improve and adopt new and
better ways of conducting our business.
As the first stock exchange in Asia and the pioneer of securities transaction business,
BSE prides itself on being at the forefront of bringing innovations to the Indian capital
markets while creating diverse investment opportunities for the investor community in India
throughout its long history.
BSE continues to undertake several initiatives to build on its strong brand, legacy and
market position to create value for its stakeholders and the financial system.
Product information
Equity
BSE Equities data is available in Real-time and as 1 minute snapshots Following data
is available in the feed for Equities.

 Level 1 Data contains the following information:
 BSE Scrip Code
 Open, High, Low and Last Traded Price
 Best Bid / Offer with Volume
 Traded Volume
 Level 2 Data contains the following information in addition to the level 1 data:
 Weighted Average Price
 Upper Circuit Limit and Lower Circuit Limit
 Turnover Value, Number of Trades, Trend
 Total Buy Quantity and Total Sell Quantity
Derivatives
BSE provides trading opportunities for Equity and Index Derivatives. The data related
to the trading of these instruments is available in the same format as the Equities data. BSE
currently has Index and Equity Futures contracts, Index and Equity Monthly Options
contracts and Index and Equity Weekly Options contracts. For the purpose of popularising
the Derivatives trading on BSE, currently Derivatives data is being provided free of charge
and without any reporting obligations for Real-time distributors.
Debt
BSE provides opportunities to trade in Debt instruments, both government as well as
corporate debt. The trade feeds for these instruments are available along with the BSE
equities feeds. In addition to the traded debt instruments, BSE also provides a facility to
report Over the Counter trades in Corporate Bonds on the Indian Corporate Debt Market
(ICDM). ICDM feeds are separately available for subscription. These feeds are provided
through the Internet in XML format.
Indices
BSE Indices are available through the feed in Real-time and as 1 minute snapshots.
All indices that are calculated on real-time are being provided in this feed. Open, High, Low
and Latest Value of the Indices are provided in the feed.

COMPANY PROFILE
JRG Securities Limited is headquarter in Kochi, in the state of Kerala in the southern
part of India. The Comp. took life as a partnership firm called JRG Associates, started by Mr.
Regi Jacob, Mr. Giby Mathew and Mr. Jiji Antony in 1992. The firm was converted into a
private limited company; JRG Associates Pvt. limited in 1994 with the inclusion of few of
their close relatives & associates on the board as financial investors, and became a member of
Cochin Stock Exchange. The Company initially focused on developing a client base in Kerala
& Tamil Nadu & established several operation centers across these states.
In 1999, the Comp. became a member of NSE & in the following years, began to
cultivate clients from Karnataka, Andhra Pradesh & Maharashtra. As the business developed,
JRG intensified its operational reach in the southern states. In August 2003, the company
changed its name to JRG Securities Pvt. Ltd. in order to accurately reflect the business focus
of the company. The following month, i.e. September 2003, the company was converted into
a public limited company and over the next two years began operations in commodities and
insurance broking and distribution of financial products. In March 2005, we become a
member of the BSE.
In April 2006, JRG Securities Limited, the flagship company of JRG Group, came out
with a Rs 14.50 crore public issue of 36,25,000 equity shares with a face value of Rs 10 at a
premium of Rs 30 per share. In July 2007, Baring India Private Equity Fund II Ltd (Baring
India) announced an investment of up to $35 million in JRG Securities Ltd. through a
preferential issue and warrants for a minimum 44.8 per cent stake in the company, subject to
the approvals from Securities and Exchange Board of India and shareholders among others.
Post the allotment, Baring India Partners will become the single largest share holder in the
company
VISION
JRG Securities Limited was born out of a vision to explore the immense investment
opportunities in the Indian financial market, to benefit the investors. The company is built on
the pillars of financial expertise, professionalism, exemplary ethics and a commitment to
provide ultimate customer satisfaction. JRG constantly strives to meet the changing market
needs and trends.

They cater efficiently to the diverse and complex needs of over 200,000 customers,
most of whom are individual traders, institutions and money managers. The vision of the JRG
Group is to be a Financial Super Market. It aims to provide all types of financial services to
its clients at one place to save them from going from place to place to meet their investment
needs.
Guiding Principles of JRG
 Serve the clients with the highest level of responsiveness and integrity.
 Place the client's interests and protection of their investment as the top priorities.
 Operate on predefined and constantly updated service standards. Be customer driven,
rather than deal drive.
 Adopt futuristic technology to gather vital information on real time basis to optimize
investor protection and investor returns.
 Set up most modern trading facilities for its clients at par with global standards.
Group of Companies
JRG Securities Ltd
JRG Wealth Management Ltd
JRG Insurance Broking Pvt. Ltd
JRG Metal & Commodities DMCC, Dubai
JRG Fin Corp Limited
Competitors
The major competitors of JRG securities are:
• Geojit Financial Services Limited
• Karvy Stock Broking Limited
• Olive Capital And Services Private Limited
• Mathew Chacko & Co

JRG’S Competitive advantage
• Member of NSE,BSE
• Member of the leading commodity exchanges NCDEX, NMCE, and MCX.
• Country wide network and presence
• Integrated V-sat and VPN network across India
• State of the art online Back office operations
• Exclusive NRI Services.
• Strong Research Division
• Training and Development opportunities.
• Risk management Services
• Strong and loyal clients
JRG’S Business strategy
The company’s business processes are empowered by knowledge and it creates
competitive edge over our competitors. JRG have charted our future growth plans after the
analysis of the financial services scenario. JRG derive our business prospects from the
following key considerations:
• Potential to add value in providing financial products
• Recognition and appreciation of global systems and processes as a differentiator
• Growth potential of the sector.
• Opportunities for various financial products and competitor activity
• Macro economic considerations.
JRG focus to empower our business processes and systems with latest and futuristic
technologies. And committed to adopt global best practices in technology for the increased
customer satisfaction and improving process efficiencies. JRG have set ambitious targets for
Insurance operations. JRG’s team of sales managers and financial advisors would set the

standard of operations and best practices. The JRG will open Branches across India with
greater velocity to cater to the invest needs of the customers.
Organizational Chart
Source: secondary data from the company JRG securities Ltd.
Services offered by JRG
JRG was set up in 1992 and at that time they were focusing only on broking service
sector. But, gradually their service portfolio was stretched from stock brokering to various
exchanges such as capital, commodity, and insurance and also in mutual funds.
• Stock Broking- Within the short period of time, JRG Securities Ltd. Has becomes
one of the leading broking houses in India. For supporting the stock broking functions, JRG
has a very active Research Department with highly qualified financial experts.
Back office staff Dealer Equities
Office
assistance
Dealer
commodities
State head
Territory manager
Branch manager
MD

• Commodity Broking- On June, 2003 JRG achieved its milestone by introducing
online commodity futures trading. Today, JRG offers online commodity future trading in
rubber, pepper, coconut oil, rice, wheat, gold, silver and 46other commodities.
• Insurance Broking- The JRG group of companies strengthens their services to the
public by adding general and life insurance services. JRG obtained license for extending
general and life insurance services of 24 Indian Insurance Companies to the public as the
insurance broker.
• Mutual funds and Bond services- Today more and more people are discovering
mutual funds as the better investment options. JRG has a strong mutual fund wing and they
use objective and quantitative measures to identify the best funds.
• Depository Services- JRG is a depository participant of National Securities
Depository Ltd. (NSDL). The main objective of depository system is to reduce risk by
minimizing the paper work involved in trading, settling and transferring securities.

CHAPTER 4
DATA ANALYSIS

INTRODUCTION TO DATA ANALYSIS &INTERPRETATION
ANALYSIS PART-1 SECURITY ANALYSIS
A rational investor makes investment decisions by evaluating the risk and return of a
security. A better evaluation strategy would be to determine the risk adjusted rate of return of
the security .an investor would also be interested in identifying mispriced securities in the
market in order to make buy, hold or sell decisions.
Security analysis consists of examining the risk-return characteristics of individual
securities. Security analysis also involves identifying mispriced securities by determining the
intrinsic value of the securities.
ASSUMPTIONS
 All stocks selected are included in BSE.
 Stocks are selected in such a way that Beta value is near to or more than 1.
 Stocks are selected from different sectors.
 Risk free rate is taken as 8.10%, which is rate of interest on 91 days T-Bill rate.
 Since specialized optimization software is not available& also manual computation
involved would be extensive, calculations are done in excel using different functions.
RISK AND RETURN OF SECURITIES:
The return of the securities is measured by the arithmetic mean of the security’s
return. The risk of the security is measured by the variance or standard deviation of its
securities. The risk adjusted rate of return of the security is the excess return per unit of risk,
the excess return being the difference between the security return and the risk free rate of
return. For our analysis the risk free return is taken as 8.10%

TABLE1: Showing the Return of Securities
SECURITIES RETURN(Ri %)
ACC 9.775434154
AIRTEL 3.755249102
CIPLA 6.409999744
MRF 23.05587277
BRITANIA 11.43700679
APOLLOTYRES 12.85362527
IOC 1.914868774
INFOSYS 6.235360781
JETAIR 16.60978579
BOSCH 22.915216
DABUR 20.75980261
BAJAJ AUTO 22.87184654
Source: Computed by the researcher Using Primary Data collected from BSE Ltd website
CHART 3: Showing Return of Securities
0
5
10
15
20
25
RETURN(Ri%)
RETURN(Ri %)
INFERENCE:
From the above table and chart it is clear that MRF has the maximum return (23.06%)
and INDIAN OIL CORPORATION has the minimum return (1.91%).

TABLE2: Showing the Risk of Securities
SECURITIES RISK (σi)
ACC 24.74421321
AIRTEL 31.42032496
CIPLA 22.92643112
MRF 30.75069892
IOC 27.9595705
INFOSYS 26.92425907
JETAIR 52.68658093
BOSCH 18.8487195
DABUR 22.2483177
Source: Computed by the researcher Using Primary Data collected from BSE Ltd website
CHART 4: Showing Risks of Securities
0
10
20
30
40
50
60
RISK (σi)
RISK (σ
INFERENCE:
From the above table and chart it is clear that JET AIR (52.68%) is having the
maximum total risk & BOSCH (18.85%) is having the minimum total risk.
BETA
The beta value indicates the measure of systematic risk of a security. Beta describes
the relationship between the stock return and market index return. Beta of a security may be
positive, negative, zero. The beta of an asset is the measure of the variability of that asset

relative to the variability of the market as a whole. Beta is an index of the systematic risk of
an asset
Βi=
𝑵 𝒙𝒚− 𝒙 𝒚
𝑵 𝒙
𝟐
− 𝒙 𝟐
N = Number of Observation =750
Y = (Current Stock Price – Yesterday’s Stock Price)*100
Yesterday’s Stock Price
X = Current Market Index- Yesterday’s Market Index ×100
Yesterday’s Market Index
TABLE 3: Showing Beta Values Of Securities
SECURITY βi
ACC 0.685184039
AIRTEL 0.802056364
CIPLA 0.46972998
MRF 0.833538788
IOC 0.447230221
INFOSYS 0.876494436
JETAIR 1.257658321
BOSCH 0.283724534
DABUR 0.350578089
Source: Computed by the researcher Using Primary Data collected from BSE Ltd

CHART 5: Showing Beta Value of Securitie
INFERENCE:
From the above table and graph it can be seen that JETAIR has the maximum beta
value, which means maximum sensitivity to market (1.26). The minimum sensitivity to
market is for BRITANIA (0.27).
ALPHA
The alpha value indicates the extra return earned by the stock over and above the
market return. Alpha measures the unsystematic risk of a security.
Return of stock = alpha + (Beta ×Market Return per Year)
Ri = αi+ (βi×Rm)
So
Alpha (αi) = Ri-( βi×Rm)
Where,
αi - Alpha of the security
Ri - return of the security
βi - Beta of the security
Rm - Return of the market
0
0.2
0.4
0.6
0.8
1
1.2
1.4
βi
βi

TABLE 4: Showing Alpha Value of Securities
SECURITY αi
ACC 0.029405585
AIRTEL 0.003670965
CIPLA 0.018992773
MRF 0.080427947
IOC 0.001330647
INFOSYS 0.012538027
JETAIR 0.048641814
BOSCH 0.087645832
DABUR 0.078078122
CHART 6: Showing Alpha Values of Securities
INFERENCE:
BOSCH has the maximum Alpha (0.08) indicating that it has maximum extra return
and INDIAN OIL CORPORATION has the minimum Alpha (0.001).
DECOMPOSITION OF TOTAL RISK OF SECURITIES
The total risk of security can be resolved in to two components; the systematic or
market risk, which cannot be diversified, and the unsystematic or specific risk, which can be
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
αi
αi

diversified by construction of the portfolio. An investor would be interested in knowing these
two risks of the security in order to plan his portfolio. For the purpose of the analysis the
systematic and unsystematic risk of the securities are measured by using Sharpe’s single
index model. According to Sharpe’s single index model:
Systematic risk = β
1
2

2
m
Unsystematic risk = 
2
- β
1
2

2
m
TABLE 5: Showing Systematic Risks of Securities
Security β¡ β¡² σᵐ σᵐ² β¡²·σᵐ²
ACC 0.685184039 0.469477167 17.06847467 291.3328274 136.7741106
AIRTEL 0.802056364 0.643294412 17.06847467 291.3328274 187.4127798
CIPLA 0.46972998 0.220646254 17.06847467 291.3328274 64.28149698
MRF 0.833538788 0.694786912 17.06847467 291.3328274 202.4142354
BRITANIA 0.279525438 0.07813447 17.06847467 291.3328274 22.76313613
APOLLOTYRES 1.173529896 1.377172418 17.06847467 291.3328274 401.2155342
IOC 0.447230221 0.20001487 17.06847467 291.3328274 58.27089766
INFOSYS 0.876494436 0.768242496 17.06847467 291.3328274 223.8142585
JETAIR 1.257658321 1.581704453 17.06847467 291.3328274 460.8024304
BOSCH 0.283724534 0.080499611 17.06847467 291.3328274 23.45217934
DABUR 0.350578089 0.122904997 17.06847467 291.3328274 35.8062602
BAJAJ AUTO 0.690437997 0.476704628 17.06847467 291.3328274 138.8797072
CHART 7: Showing Systematic Risks of Securities
0
50
100
150
200
250
300
350
400
450
500
β¡²·σᵐ²
β¡²·σᵐ²

INFERENCE:
Systematic risk or non-diversifiable risk is the component of the total risk, which
cannot be diversified. From the above table it is clear that JETAIR has the maximum
systematic risk (460.80) and BRITANIA has minimum systematic risk (22.76)
TABLE 6: Showing Unsystematic Risk or Residual Variance of Securities
Security σ¡ σ¡² β¡²·σᵐ² σei2 = σi² - βi².σm²
ACC 24.74421321 612.2760872 136.7741106 475.5019766
AIRTEL 31.42032496 987.2368205 187.4127798 799.8240407
CIPLA 22.92643112 525.6212437 64.28149698 461.3397467
MRF 30.75069892 945.6054838 202.4142354 743.1912484
BRITANIA 22.79374556 519.5548368 22.76313613 496.7917007
APOLLOTYRES 40.25893133 1620.781551 401.2155342 1219.566017
IOC 27.9595705 781.7375825 58.27089766 723.4666848
INFOSYS 26.92425907 724.9157265 223.8142585 501.101468
JETAIR 52.68658093 2775.87581 460.8024304 2315.07338
BOSCH 18.8487195 355.2742267 23.45217934 331.8220474
DABUR 22.2483177 494.9876407 35.8062602 459.1813805
BAJAJ AUTO 26.04673059 678.4321746 138.8797072 539.5524674
CHART 8: Showing Unsystematic Risk or Residual Variance of Securities
0
500
1000
1500
2000
2500
σei2 = σi² - βi².σm²

INFERENCE:
From the above table and chart it is clear that JETAIR has maximum residual variance
or unsystematic risk 2315.07 (%) ² and BOSCH has minimum unsystematic risk 331.82(%)²
TABLE 7: Showing Risks of Securities
Security σei² βi².σm² σi² = σei² + βi².σm²
ACC 475.5019766 136.7741106 612.2760872
AIRTEL 799.8240407 187.4127798 987.2368205
CIPLA 461.3397467 64.28149698 525.6212437
MRF 743.1912484 202.4142354 945.6054838
BRITANIA 496.7917007 22.76313613 519.5548368
APOLLOTYRES 1219.566017 401.2155342 1620.781551
IOC 723.4666848 58.27089766 781.7375825
INFOSYS 501.101468 223.8142585 724.9157265
JETAIR 2315.07338 460.8024304 2775.87581
BOSCH 331.8220474 23.45217934 355.2742267
DABUR 459.1813805 35.8062602 494.9876407
BAJAJ AUTO 539.5524674 138.8797072 678.4321746
CHART 9: Showing Risks of Securities
0
500
1000
1500
2000
2500
3000
σi² = σei² + βi².σm²
σi² = σei² + βi².σm²

INFERENCE:
TYPE OF RISK MAXIMAM MINIMUM
SYSTEMATIC RISK JETAIR BRITANIA
UNSYSTEMATIC RISK JETAIR BOSCH
TOTAL RISK JETAIR BOSCH
ANALYSIS PART -2 PORTFOLIO OPTIMIZATION
Portfolio optimization is one of the most important stages in the portfolio
management. Portfolio selection process involves identification of optimal portfolio. Optimal
portfolio is that portfolio for which return is maximum and risk is minimum. In order to
identify the optimal portfolio, Portfolio managers use different numerical algorithms known
as portfolio optimization models. This stage of the analysis focuses on the application of
different portfolio optimization models in deriving the optimal portfolio. Here researches uses
sharpe’s optimization model for building optimal portfolio.
The Sharpe’s optimization model uses excess return- to- beta ratio as the performance
measure of individual securities so as to include in optimal portfolio.

CONSRUCTION OF OPTIMAL PORTFOLIO USING SHARPE’S OPTIMIZATION
MODEL
TABLE 8(a): SHOWING CALCULATION OF CUT OFF POINT
Security name
Mean
return
Ri
Excess return
beta
Ri-Rf Beta
β
Unsystematic
risk
σ²ei
Excess return
to beta
Ri-Rf/βi
ACC 9.77543415 1.675434154 0.68518404 475.5019766 2.445232315 8
AIRTEL 3.7552491 -4.344750898 0.80205636 799.8240407 -5.417014427 11
CIPLA 6.40999974 -1.690000256 0.46972998 461.3397467 -3.597812209 10
MRF 23.0558728 14.95587277 0.83353879 743.1912484 17.94262364 4
BRITANIA 11.4370068 3.337006785 0.27952544 496.7917007 11.93811488 5
APOLLOTYRES 12.8536253 4.753625271 1.1735299 1219.566017 4.050706578 7
IOC 1.91486877 -6.185131226 0.44723022 723.4666848 -13.82985975 12
INFOSYS 6.23536078 -1.864639219 0.87649444 501.101468 -2.127382836 9
JETAIR 16.6097858 8.509785788 1.25765832 2315.07338 6.766373381 6
BOSCH 22.915216 14.815216 0.28372453 331.8220474 52.21690133 1
DABUR 20.7598026 12.65980261 0.35057809 459.1813805 36.11122027 2
BAJAJ AUTO 22.8718465 14.77184654 0.690438 539.5524674 21.39489223 3
TABLE 8(b): SHOWING CALCULATION OF CUT OFF POINT (CONTINUED)
RANK SECURITY (Ri-Rf) βi σ²ei (Ri-Rf)*βi (Ri-Rf)*βi/σ²ei
1 BOSCH 14.815216 0.28372453 331.82205 4.20344026 0.012667755
2 DABUR 12.65980261 0.35057809 459.18138 4.43824941 0.009665569
3 BAJAJ AUTO 14.77184654 0.690438 539.55247 10.1990441 0.018902785
4 MRF 14.95587277 0.83353879 743.19125 12.4663001 0.016774014
5 BRITANIA 3.337006785 0.27952544 496.7917 0.93277828 0.001877604
6 JETAIR 8.509785788 1.25765832 2315.0734 10.7024029 0.004622922
7 APOLLOTYRES 4.753625271 1.1735299 1219.566 5.57852137 0.004574186
8 ACC 1.675434154 0.68518404 475.50198 1.14798074 0.00241425
9 INFOSYS -1.86463922 0.87649444 501.10147 -1.6343459 -0.003261507
10 CIPLA -1.69000026 0.46972998 461.33975 -0.7938438 -0.001720736
11 AIRTEL -4.3447509 0.80205636 799.82404 -3.4847351 -0.004356877
12 IOC -6.18513123 0.44723022 723.46668 -2.7661776 -0.003823504

TABLE 8(c): SHOWING CALCULATION OF CUT OFF POINT (CONTINUED)
SECURITY σ²ei (Ri-Rf)*βi/σ²ei
∑(Ri-
Rf)*βi/σ²ei β¡ βi²/σ²ei ∑βi²/σ²ei
BOSCH 331.8220474 0.012667755 0.012667755 0.2837245 0.000243 0.000243
DABUR 459.1813805 0.009665569 0.022333324 0.3505781 0.000268 0.00051
BAJAJ AUTO 539.5524674 0.018902785 0.041236108 0.690438 0.000884 0.001394
MRF 743.1912484 0.016774014 0.058010122 0.8335388 0.000935 0.002329
BRITANIA 496.7917007 0.001877604 0.059887726 0.2795254 0.000157 0.002486
JETAIR 2315.07338 0.004622922 0.064510648 1.2576583 0.000683 0.003169
APOLLOTYRES 1219.566017 0.004574186 0.069084834 1.1735299 0.001129 0.004298
ACC 475.5019766 0.00241425 0.071499084 0.685184 0.000987 0.005286
INFOSYS 501.101468 -0.003261507 0.068237577 0.8764944 0.001533 0.006819
CIPLA 461.3397467 -0.001720736 0.066516841 0.46973 0.000478 0.007297
AIRTEL 799.8240407 -0.004356877 0.062159964 0.8020564 0.000804 0.008101
IOC 723.4666848 -0.003823504 0.05833646 0.4472302 0.000276 0.008378
TABLE 8(d) SHOWING CONTINUTATION OF CUT OFF POINT
C*={[σ²m∑(Ri-Rf)βi/σ²ei]/[1+σ²m∑β²i/σ²ei]}
SECURITY σ²m ∑(Ri-Rf)*βi/σ²ei ∑βi²/σ²ei cut off point Ci
BOSCH 291.332827 0.012667755 0.000242599 3.446915206
DABUR 291.332827 0.022333324 0.00051026 5.664388211
BAJAJ AUTO 291.332827 0.041236108 0.001393778 8.544079477
MRF 291.332827 0.058010122 0.002328648 10.06919442
BRITANIA 291.332827 0.059887726 0.002485926 10.1188597
JETAIR 291.332827 0.064510648 0.003169146 9.771902957
APOLLOTYRES 291.332827 0.069084834 0.004298378 8.936220974
ACC 291.332827 0.071499084 0.005285707 8.201122034
INFOSYS 291.332827 0.068237577 0.006818815 6.656470487
CIPLA 291.332827 0.066516841 0.007297088 6.199384481
AIRTEL 291.332827 0.062159964 0.008101383 5.389335455
IOC 291.332827 0.05833646 0.00837785 4.939435272
TABLE 9: SHOWING CALCULATION OF OPTIMAL PORTFOLIO
SECURITY βi σ²ei βi/σ²ei (Ri-Rf)/βi
CUT OFF
POINT Ci Xi
BOSCH 0.283725 331.822 0.000855 52.21690133 3.44691521 0.457019
DABUR 0.350578 459.1814 0.000763 36.11122027 5.66438821 0.254761
BAJAJ AUTO 0.690438 539.5525 0.00128 21.39489223 8.54407948 0.180224
MRF 0.833539 743.1912 0.001122 17.94262364 10.0691944 0.096779
BRITANIA 0.279525 496.7917 0.000563 11.93811488 10.1188597 0.011218
1

TABLE 10: SHOWING OPTIMAL PORT FOLIO
SECURITY WEIGHT(%)
BOSCH 45.70188656
DABUR 25.47607128
MRF 9.677852489
100
OPTIMAL PORTFOLIO
TABLE 11(a): SHOWS PORTFOLIO ALPHA FOR OPTIMAL PORTFOLIO
SECURITY αi Xi Xi*αi
BOSCH 21.9114579 0.457018866 10.01394963
DABUR 19.51953061 0.254760713 4.972809531
BAJAJ AUTO 20.42922123 0.180223508 3.681825925
MRF 20.10698676 0.096778525 1.945924519
BRITANIA 10.44810422 0.011218388 0.11721089
Total 92.41530072 1 20.7317205
Portfolio alpha = 20.73 %
TABLE 11(b): SHOWS PORTFOLIO BETA FOR OPTIMAL PORTFOLIO
SECURITY βi Xi Xi*βi
BOSCH 0.283724534 0.45701887 0.129667465
DABUR 0.350578089 0.25476071 0.089313524
BAJAJ AUTO 0.690437997 0.18022351 0.124433158
MRF 0.833538788 0.09677852 0.080668654
BRITANIA 0.279525438 0.01121839 0.003135825
Total 2.437804847 1 0.427218626
Portfolio beta = 0.43

TABLE 11(c): SHOWS PORTFOLIO RESIDUAL VARIANCE FOR OPTIMAL
PORTFOLIO
SECURITY σ²ei wi wi² wi²*σ²ei
BOSCH 331.8220474 0.4570189 0.20886624 69.3064245
DABUR 459.1813805 0.2547607 0.06490302 29.8022587
BAJAJ AUTO 539.5524674 0.1802235 0.03248051 17.5249409
MRF 743.1912484 0.0967785 0.00936608 6.96079083
BRITANIA 496.7917007 0.0112184 0.00012585 0.06252235
Total 2570.538844 1 0.31574171 123.656937
Portfolio Residual variance = 123.66(%) ²
TABLE 11(d): SHOWS PORTFOLIO RISK, RETURN, ALPHA, BETA, AND RESIDUAL
VARIANCE FOR OPTIMAL PORTFOLIO
PORTFOLIO RETURN (Rp) σ²p αp Βp σei² Σp
OPTIMAL PF 22.24 176.83 20.73 0.43 123.66 13.3
MEASURING PORTFOLIO RETURN AND RISK
PORTFOLIO RETURN (RP)
PORTFOLIO RETURN = PORTFOLIO ALPHA + (PORTFOLIO BETA×MARKET
RETURN)
RP = αP+ (βp×Rm)
αP = 20.73
βp = 0.43
Rm = 3.54
RP = 20.73+ (0.43* 3.54) = 22.24%

PORTFOLIO RISK (σP2)
Portfolio risk (σp2) = 𝛽𝑝²𝜎𝑚² + 𝑤𝑖²𝜎𝑖𝑒²𝑛
𝑖=1
βp2 = 0.183
σm2 = 291.31
∑wi2σie2 = 123.66
σp2 = 176.83(%)²
σp = 13.30
TABLE 11(e): SHOWS BENEFIT OF DIVERSIFICATION
RISK CLASS
TOTAL RISK OF
SECURITIES
(%)²
PORTFOLIO
RISK (%)²
BENEFIT OF
DIVERSIFICATION
(%)²
RISK REDUCTION
(%)
UN SYS RISK 9066.41 123.65 8942.76 98.63
SYS RISK 1955.88 53.17 1902.71 97.25
TOTAL RISK 11022.30 176.83 10845.47 98.40
Effectiveness of Optimization
To examine the effectiveness of optimization, three different portfolios are
constructed with the securities included in the optimal portfolio. The criteria used for
construction of these portfolios are:
1. Equal investment in each security (We name it as Portfolio Gamma, Г).
2. Investment in each security in random proportion (We name it as Portfolio Pi, Π)

3. Investment in each security in proportion to the P/E multiple of each security (We
name it as Portfolio Omega, Ω)
The return and risk of these portfolios are determined for the purpose of evaluation of
the performance of these portfolios.
Thereafter the performance of these portfolios was measured by using Sharpe Ratio,
Treynor Ratio and Jensen Measure. The performance of these portfolios was then compared
with that of the optimal portfolio. In all the performance measures, the optimal portfolio came
out to be the best, thereby confirming its optimality. The analysis is shown below:
PORTFOLIO BASED ON EQUAL WEIGHT (PORTFOLIO GAMMA, Г)
The first portfolio is constructed by giving equal weights to the five securities and
then the portfolio alpha, portfolio beta and weighted residual variance are calculated to arrive
at portfolio return and risk
TABLE 12(a): SHOWS PORTFOLIO ALPHA IN EQUAL WEIGHT
Security ALPHA
(αi) WEIGHT(Wi) ALPHA x WEIGHT
(αiWi)
BOSCH 21.9114579 0.2 4.38229158
DABUR 19.51953061 0.2 3.903906121
BAJAJ AUTO 20.42922123 0.2 4.085844246
MRF 20.10698676 0.2 4.021397353
BRITANIA 10.44810422 0.2 2.089620843
1 18.48306014
Portfolio alpha =18.48 %
TABLE 12(b): SHOWS PORTFOLIO BETA IN EQUAL WEIGHT
Security BETA
(βi) WEIGHT(Wi) BETA x WEIGHT
(βiWi)
BOSCH 0.283724534 0.2 0.056744907
DABUR 0.350578089 0.2 0.070115618
BAJAJ AUTO 0.690437997 0.2 0.138087599
MRF 0.833538788 0.2 0.166707758
BRITANIA 0.279525438 0.2 0.055905088
1 0.487560969
Portfolio beta =0.49

TABLE 12(c): SHOWS PORTFOLIO RESIDUAL VARIANCE IN EQUAL WEIGHT
Security RESIDUAL VARIANCE
(σαi) WEIGHT(Wi) Wi² Wi²*σei²
BOSCH 331.8220474 0.2 0.04 13.2728819
DABUR 459.1813805 0.2 0.04 18.36725522
BAJAJ AUTO 539.5524674 0.2 0.04 21.5820987
MRF 743.1912484 0.2 0.04 29.72764994
BRITANIA 496.7917007 0.2 0.04 19.87166803
2570.538844 1 0.2 102.8215538
Source Table 12: Computed by the researcher
Portfolio residual variance =102.82 (%)²
MEASURING 1ST PORTFOLIO RETURN AND RISK
RETURN)
RP = αP+ (βp×Rm)
αP = 18.48
βp = 0.49
Rm = 3.54
RP = 18.48+ (0.49*3.54) = 20.21 %
𝑖=1
βp2 = 0.24
σm2 = 291.33
∑wi2σie2 = 102.82
σp2 = 172.08 (%)²
σp = 13.12%

TABLE 12(d): SHOWS BENEFIT OF DIVERSIFICATION
RISK CLASS
TOTAL RISK OF
SECURITIES
(%)²
PORTFOLIO
RISK (%)²
BENEFIT OF
DIVERSIFICATION
(%)²
RISK
REDUCTION
(%)
UN SYS RISK 9066.41 102.82 8963.59 98.87
SYS RISK 1955.88 69.25 1886.63 96.45
TOTAL RISK 11022.30 172.08 10850.22 98.44
Source Table 12(d): Computed by the researcher
PORTFOLIO 2 BASED ON RANDOM WEIGHT (PORTFOLIO PI, Π)
Third portfolio is constructed on the basis on Random weight of the seven securities
and then the portfolio alpha, portfolio beta and weighted residual variance are calculated to
arrive at portfolio return and risk. For this purpose the risk free rate return is taken as 8.1%.
TABLE 13(a): SHOWS PORTFOLIO ALPHA IN RANDOM WEIGHT
Security ALPHA
(αi) random nor WEIGHT(Wi)
ALPHA x
WEIGHT
BOSCH 21.9114579 0.224100148 0.075943184 1.664025875
DABUR 19.5195306 0.881503146 0.29872428 5.830957726
BAJAJ AUTO 20.4292212 0.183002511 0.062015993 1.266938449
MRF 20.1069868 0.809161033 0.274208944 5.513515613
BRITANIA 10.4481042 0.853125356 0.289107599 3.020626319
1 17.29606398
Portfolio alpha = 17.30%
TABLE 13(b): SHOWS PORTFOLIO BETA IN RANDOM WEIGHT
Security BETA
(βi) WEIGHT(Wi)
BETA x
WEIGHT
(βiWi)
BOSCH 0.28372453 0.075943184 0.021546944
DABUR 0.35057809 0.29872428 0.104726187
BAJAJ AUTO 0.690438 0.062015993 0.042818198
MRF 0.83353879 0.274208944 0.228563791
BRITANIA 0.27952544 0.289107599 0.080812928
2.43780485 1 0.478468049

Portfolio beta = 0.48
TABLE 13(c): SHOWS PORTFOLIO RESIDUAL VARAINCE IN RANDOM WEIGHT
Security RESIDUAL VARIANCE
(σαi)WEIGHT(Wi) Wi² Wi²*σei²
BOSCH 331.8220474 0.075943184 0.005767367 1.913739582
DABUR 459.1813805 0.29872428 0.089236195 40.97559941
BAJAJ AUTO 539.5524674 0.062015993 0.003845983 2.075109854
MRF 743.1912484 0.274208944 0.075190545 55.8809551
BRITANIA 496.7917007 0.289107599 0.083583204 41.52344183
1 0.257623295 142.3688458
Source For Table 14: Computed by the researcher
Portfolio Residual variance = 142.37 (%) ²
MEASURING 2nD PORTFOLIO RETURN AND RISK
RETURN)
RP = αP+ (βp×Rm)
αP = 17.30
βp = 0.48
Rm = 3.54
RP = 17.30+ (0.48* 3.54) = 18.99%
𝑖=1
βp2 = 0.23
σm2 = 291.33
∑wi2σie2 = 142.37
σp2 = 209.06(%) ²

σp = 14.46%
RISK CLASS
TOTAL RISK
OF
SECURITIES
(%)²
PORTFOLIO
RISK (%)²
BENEFIT OF
DIVERSIFICATION
(%)²
RISK
REDUCTION (%)
UN SYS RISK 9066.41 142.37 8924.04 98.43
SYS RISK 1955.88 66.69 1889.19 96.60
TOTAL RISK 11022.30 209.06 10813.24 98.10
Source : Computed by the researcher Using Primary Data collected from BSE Ltd
PORTFOLIO 3 BASED ON PRICE EARNINGS RATIO (PORTFOLIO OMEGA, Ω)
Fourth portfolio is constructed on the basis on price earnings ratio of the five
securities and then the portfolio alpha, portfolio beta and weighted residual variance are
calculated to arrive at portfolio return and risk. For this purpose the risk free rate return is
taken as 8.1%.
TABLE 14(a): SHOWS PORTFOLIO ALPHA IN PRICE EARNINGS RATIO
Security ALPHA
(αi) P/E ratio weight Wi
alpha*weight
(Wi*ἀ¡)
BOSCH 21.9114579 32.19 0.230224574 5.044556071
DABUR 19.5195306 46.08 0.329566586 6.432985055
BAJAJ AUTO 20.4292212 17.5 0.125160921 2.556940148
MRF 20.1069868 9.32 0.066657131 1.340274043
BRITANIA 10.4481042 34.73 0.248390788 2.595212841
139.82 1 17.96996816
Portfolio alpha = 17.97%

TABLE 14(b): SHOWS PORTFOLIO BETA IN PRICE EARNINGS RATIO
Security P/E ratio BETA
(βi) WEIGHT(Wi)
BETA x WEIGHT
(βiWi)
BOSCH 32.19 0.2837245 0.23022457 0.06532036
DABUR 46.08 0.3505781 0.32956659 0.115538824
BAJAJ AUTO 17.5 0.690438 0.12516092 0.086415856
MRF 9.32 0.8335388 0.06665713 0.055561304
BRITANIA 34.73 0.2795254 0.24839079 0.069431544
139.82 1 0.392267887
Porfolio Beta =0.39
TABLE 14(c): SHOWS PORTFOLIO RESIDUAL VARIANCE IN PRICE EARNINGS
RATIO
Security
RESIDUAL
VARIANCE WEIGHT(Wi) Wi² Wi²*σei²
BOSCH 331.8220474 0.230224574 0.053003 17.58768
DABUR 459.1813805 0.329566586 0.108614 49.87359
BAJAJ AUTO 539.5524674 0.125160921 0.015665 8.452228
MRF 743.1912484 0.066657131 0.004443 3.302127
BRITANIA 496.7917007 0.248390788 0.061698 30.65105
1 0.243424 109.8667
Source: Computed by the researcher Using Secondary Data collected
Portfolio Residual variance = 109.87 (%) ²
MEASURING 3RD PORTFOLIO RETURN AND RISK
RETURN
RP = αP+ (βp×Rm)
αP = 17.97
βp = 0.39
Rm = 3.54

RP = 17.97+ (0.39*3.54 ) = 19.35%
𝑖=1
βp2 = 0.15
σm2 = 291.33
∑wi2σie2 = 109.87
σp2 = 154.70(%)²
σp = 12.44%
RISK CLASS
TOTAL RISK
OF
SECURITIES
(%)²
PORTFOLIO
RISK(%)²
BENEFIT OF
DIVERSIFICATION
(%)²
RISK
REDUCTION
(%)
UN SYS RISK 9066.41 109.87 8956.54 98.79
SYS RISK 1955.88 44.83 1911.05 97.71
TOTAL RISK 11022.30 154.69 10867.61 98.60

TABLE 15: SHOWS EFFECT OF DIVERSIFICATION
PORTFOLIO
RISK REDUCTION (%)
UNSYSTEMATIC
RISK(%)²
SYSTEMATIC
RISK(%)²
TOTAL
RISK(%)²
OPTIMAL
PORTFOLIO 123.66 53.17 176.83
PORTFOLIO
GAMMA, Г 102.82 69.25 172.08
PORTFOLIO PI,
Π 142.37 66.69 209.06
PORTFOLIO
OMEGA, Ω 109.86 44.82 154.69
INFERENCE:
From above table, it is also clear that diversification has resulted in considerable
reduction of not only unsystematic risk but also systematic risk.
OPTIMALITY TEST
The optimality of the optimal portfolio constructed with Sharpe’s Optimization Model
is tested by comparing its performance against the performance of other four portfolios. The
traditional performance evaluation measures like Sharpe ratio, Treynor ratio and Jensen
measure are used for this purpose. In all these measures, the optimal portfolio came out with
maximum value thereby validating its optimality.
PORTFOLIO EVALUATION
Portfolio evaluation is the process to determine the performance of the portfolio. The
best measure for evaluation of portfolio is the risk adjusted rate of return as determined by
SHARPE RATIO and TREYNOR RATIO and JENSEN MEASURE. The evaluation process
using these retios is discussed below:

TABLE 16: SHOWS SHARPE RATIO OF THE PORTFOLIOS
PORTFOLIO Rp(%) Rf(%) σpi(%) (Rp-Rf)/σp
OPTIMAL
PORTFOIO 68.26655599 8.1 29.6679969 2.03
PORTFOLIO
GAMMA, 1 20.20902598 8.1 13.11777193 0.92
PORTFOLIO
Pi, 2 18.98984088 8.1 14.45905106 0.75
PORTFOLIO
OMEGA , 3 19.35859648 8.1 12.43765437 0.91
Source: Computed by the researcher
CHARTNO 10 SHARPE RATIO OF PORTFOLIOS
INFERENCE:
Sharpe ratio is maximum for the optimal portfolio whereas minimum for Portfolio
PI,Π with random weights.
TREYNOR RATIO
Treynor ratio is also the ratio of excess return to risk. But here risk is defined as the
systematic risk or market risk on the assumption that the portfolio is well diversified.
0.00
0.50
1.00
1.50
2.00
2.50
OPTIMAL GAMMA Pi OMEGA
SHARPE RATIO
(Rp-Rf)/σp

TABLE 17: SHOWS TREYNOR RATIO OF THE PORTFOLIO
PORTFOLIO Rp(%) Rf(%) βp (Rp-Rf)/βp
OPTIMAL 68.27 8.10 0.98 61.65
GAMMA 20.21 8.10 0.49 24.84
Pi 18.99 8.10 0.48 22.76
OMEGA 19.36 8.10 0.39 28.70
CHART NO 11: TREYNOR RATIOS OF THE PORTFOLIOS
INFERENCE:
Treynor ratio is maximum for the optimal portfolio whereas minimum for Portfolio
Pi, with Random weights.
JENSEN ALPHA
Jensen Measure Gives Differential Return earned by a portfolio over and above the
expected return as mandated by capital asset pricing model. A positive alpha indicates
superior performance of the portfolio.
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
TERYNOR RATIO
(Rp-Rf)/βp

TABLE 18: SHOWS JENSEN ALPHA OF THE PORTFOLIOS
PORTFOLIO Rp(%) Rf(%) βp Rm(%)
E(Rp)=
Rf+βp(Rm-
Rf)
Rp-
E(Rp)
OPTIMAL 68.27 8.10 0.98 3.54 3.65 64.62
GAMMA 20.21 8.10 0.49 3.54 5.88 14.33
Pi 18.99 8.10 0.48 3.54 5.92 13.07
OMEGA 19.36 8.10 0.39 3.54 6.31 13.05
CHART NO 12: JENSEN ALPHA
INFERENCE:
Jensen alpha is maximum for the optimal portfolio whereas minimum for Portfolio
OMEGA, Ω with PE ratio weights.
Optimality Test for the Optimal Portfolio
The above analysis shows that all performance measures, namely, Sharpe Ratio,
Treynor Ratio and Jensen Measure, are maximum for Optimal Portfolio thereby proving the
optimality of the Optimal Portfolio.
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
JENSON MEASURE
Rp-E(Rp)

VALUE AT RISK
MONTE CARLO SIMULATION:
Under this method VaR for a portfolio is calculated using a one day time horizon at
95% and 99% confidence level for 500 days of data. The following tables show the
estimation of VaR using this method .the first table gives the value of the opening value of
the portfolio for 31st march 2013. Only part of the table containing the critical values of VaR
is shown in the following table. The detailed calculation for the change in the value of the
portfolio for 500 scenarios are shown in a separate table in Appendix no.1
TABLE 19: SHOWING PORTFOLIO VALUE ON 31ST MARCH 2013 FOR THE MONTE
CARLO SIMULATION
SECURITY WEIGHT(Xi)
CLOSING
PRICE
TOTAL
VALUE
NUMBER OF
SHARES
ACTUAL NUMBER
OF SHARES
ACTUAL
VALUE
BOSCH 0.45701887 9054.35 914037.7 100.950121 101 914489.4
DABUR 0.25476071 137.05 509521.4 3717.77764 3718 509551.9
BAJAJ AUTO 0.18022351 1794.9 360447 200.817325 201 360774.9
MRF 0.09677852 11992.6 193557 16.139707 16 191881.6
BRITANIA 0.01121839 524.3 22436.78 42.7937757 43 22544.9
1 2000000 4079 1999243
Source: calculated by researcher taking 20,00,000 as the size of lot

TABLE 20: SHOWING CHANGES IN TOTAL VALUE OF PORTFOLIO (SORTED IN
ASCENDING ORDER).
SLNO PORTFOLIOCHANGE IN VALUEVALUE AT RISK
1 2003801 4557.89 -42005.7
2 1988733 -10509.3 -41776.3
3 2008240 8997.4 -40911.6
4 1990446 -8797.1 -40431.4
5 1990285 -8957.16 -39647.1 At 99% confidence level
6 2021773 22530.35 -37115.8
7 2006973 7730.65 -36975.6
8 2017059 17816.63 -34972.2
9 1969070 -30173.1 -34054.1
10 2019442 20198.85 -33824.3
11 2007171 7928.32 -31134.8
12 2006385 7142.38 -30173.1
13 2034476 35233.34 -28577.7
14 2036307 37064.82 -28540.2
15 2009301 10057.99 -28523.9
16 2013397 14154.6 -27299.2
17 2008386 9143.01 -26941.6
18 1958811 -40431.4 -26790.4
19 1989160 -10083.1 -26511.4
20 1982344 -16898.3 -25885.2
21 2014891 15648.79 -25504.7
22 2007886 8643.49 -25378.2
23 2001835 2592.02 -25280.6
24 2000334 1091.67 -25125.5 At 95% confidence level
25 1965189 -34054.1 -24816.1
26 2038552 39308.89 -23960.2
27 2005652 6409.64 -22900.2
28 2031756 32513.34 -22714.1
29 1986444 -12798.3 -22506
30 1990699 -8544.14 -22427.6
31 2013936 14693.71 -21706.4
32 2019240 19997.57 -21231.2
33 1984821 -14422.1 -20996.4
34 2040799 41556.03 -20857.6
35 2009212 9969.69 -20838.4
36 1992501 -6741.57 -20547
37 1993785 -5457.82 -20315.4

INFERENCE:
From the above table it is clear that:-
Value at Risk At 99% of confidence level = -39647.14
At 99% confidence level the maximum daily loss or gain of the portfolio will be RS -
39647.14; that is portfolio value will lie between 1959595.51 and 2038889.79
Value at Risk at 95% of confidence level= -24816.15
At 95% confidence level the maximum daily loss or gain of the portfolio will be RS. -
24816.15; that is portfolio value will be lie between Rs.1974426.5 and 2024058.8

CHAPTER 5
FINDINGS, SUGGETIONS AND CONCLUSION

FINDINGS
SECURITY ANALYSIS
Return
MRF is giving the maximum return 23.06% and INDIAN OIL CORPORATION is
giving the minimum return 1.91%.
Total Risk
JET AIR has the maximum risk of 52.68% and BOSCH has the minimum risk of
18%.
Security Beta
The beta value is maximum for JETAIR (1.25) indicating the highest systematic risk
and the minimum beta is for BRITANIA (0.27) indicating the minimum systematic risk.
Security Alpha
The alpha value is maximum for BOSCH (0.087) i.e. it earns the maximum extra
return over market return. INDIAN OIL CORPORATION (0.0013) have the least alpha
value.
Systematic Risk
Systematic risk is maximum for JETAIR with variance (460.80) and minimum for
BRITANIA with variance(22.76)
Unsystematic Risk
Unsystematic risk is maximum for JETAIR with a variance of (2315.07)% and
minimum for BOSCH with a variance of (331.82%).
PORTFOLIO ANALYSIS
Portfolio Return and Risk
The return of optimal portfolio with Sharpe’s model is highest (68.27) and the return
of Portfolio Pi (with RANDOME weight proportion) is the minimum (18.99). Portfolio with

Random weight has the highest risk with a standard deviation of 14.46 % and Portfolio
Omega (Portfolio based on P/E ratio) has the lowest risk with a standard deviation of 12.44%.
Portfolio Alpha and Beta
Portfolio alpha is maximum for optimal portfolio with Sharpe’s Model (20.73) and
minimum for Portfolio Pi (with Random weight proportion) (17.29)
Portfolio beta is maximum for portfolio Pi (0.48) and is minimum for portfolio
Omega (PE ratio portfolio) (0.39)
Portfolio Optimization
An optimal portfolio is constructed by using Sharpe’s Optimization Models. The
findings are summarized below:
The return of optimal portfolio is 22.24%
The risk of optimal portfolio is 176.82%
The beta value of optimal portfolio is 0.43
The alpha value of optimal portfolio is 20.73%
The residual variance of optimal portfolio is 123.66(%)2
Sharpe Ratio = 2.03%
Treynor Ratio = 61.65%
Jensen Measure = 64.62%
The portfolio is tested for optimality by comparing its performance against the three
other portfolios using Sharpe’s ratio, Treynor ratio, and Jensen ratio. All performance
measures were highest for the optimal portfolio thereby proving its optimality.
Value at Risk
VaR is calculated using Monte Carlo Simulation method and the findings are below
Value at Risk At 99% of confidence level = -39647.14

Value at Risk at 95% of confidence level= -24816.15
that is portfolio value will lie between 1959595.51 and 2038889.79 at 99% of
confidence level and will be lie between Rs.1974426.5 and 2024058.8 at 95% of confidence
level
Benefit Of Diversification
From the calculations, we can find that diversification has resulted in considerable
reduction of not only unsystematic risk but also systematic risk to some extent.
SUGGESTIONS
An investor should neither make investment decisions on the basis of tips and rumors
nor adopt a naïve investment strategy, especially in a volatile market as we have now. A
naïve investment strategy based on tips and rumors might result in poor investment decisions
which might seriously undermine their long-term welfare and wealth accumulation.
Investors should make investment decisions on the basis of scientific and analytical
asset allocation techniques.
Financial modeling using portfolio is very helpful for risk reduction and optimal
portfolio construction also very efficient in risk diversification for securities. Investors should
make use of these portfolio optimization algorithms in order ensure efficient asset allocation
and superior portfolio performance.
Investors should clearly define their investment objectives and select appropriate asset
allocation techniques in order to achieve their investment objectives.
CONCLUSION
Scientific investment involves, investors clearly specifying their investment
objectives and developing an efficient asset allocation strategy to achieve those objectives.
One of the important investment objectives of a rational investor would be to maximize the
return on his investment while minimizing the risk associated with his investment. This
involves striking an optimal trade-off between risk and return. But achieving an optimal
trade-off between risk and return in a volatile and complex investment environment is a
difficult task and involves application of financial modeling and portfolio optimization

techniques. In such volatile and uncertain investment environment, applying native
investment strategies and making poor investment decisions will result in significant
investment losses to the investors. In a dynamic, uncertain and volatile investment
environment, investors should use superior asset allocation techniques by employing efficient
portfolio optimization models, in order to ensure superior performance of their investment
portfolio.
The objective of using a portfolio optimization technique is to ensure efficient asset
allocation. An efficient asset allocation would in turn ensure superior portfolio performance
by ensuring maximum return with minimum risk.
Portfolio optimization is a complex process. .It involves identification of optimal
portfolio from a domain of feasible and efficient set of portfolios. Different portfolio
optimization models are developed for identification of optimal portfolio. This study
examines the use of Sharpe’s optimization Model in ensuring efficient asset allocation.
The study has revealed the effectiveness of Sharpe’s portfolio optimization models in
ensuring superior portfolio performance. The optimization process has also resulted in
considerable reduction of risk by diversification.

BIBLIOGRAPHY
BOOKS
 Kevin S – Portfolio Management, Prentice Hall, New Delhi 2003
 Punithavathy Pandyan – Security Analysis and Portfolio Management, Vikas
Publishing House, New Delhi 2001
 Simon Benninga, Financial Modelling ,Sloan Institute Of management, MIT
publications,2008
WEBSITES
 http://www.bseindia.com
 www.money.rediff.com
 www.moneycontrol.com
 www.indiainfoline.com
 www.google.com
 www.wikipedia.com
 www.equitymaster.com
 www.emeraldinsight.com
2

Financial Modeling for Risk Management

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (20)

Andere mochten auch

Andere mochten auch (20)

Ähnlich wie Financial Modeling for Risk Management

Ähnlich wie Financial Modeling for Risk Management (20)

Kürzlich hochgeladen

Kürzlich hochgeladen (20)

Financial Modeling for Risk Management