Major Project MBA

FINANCIAL MODELLING FOR PORTFOLIO SELECTION AND RISK MANAGEMENT

Submitted in the partial fulfillment of the requirements for the a ward of degree of o f M ASTER ASTER OF OF BUSI BUSI NESS NESS ADM I NI STRATI TRATI ON

SUBMITTED BY ARUN K T (CUALMGT004)

UNDER THE GUIDANCE OF Dr. B. JOHNSON READER DCMS UNIVERSITY OF CALICUT

DEPARTMENT OF COMMERCE AND MANAGEMENT STUDIES UNIVERSITY OF CALICUT 2011-13

DEPARTMENT OF COMMERCE AND MANAGEMENT STUDIES UNIVERSITY OF CALICUT

Dr.E K Satheesh

Calicut University

Associate Professor

Malappuram District

& Head of the Department

Kerala State – 673635 673635 CERTIFICATE

This is to certify that Mr. Arun K T , the student of this department conducted the study entitled “

Financial Modelling for Portfolio Selection and Risk Management

”

submitted for the partial

requirement of degree of Master of Business Administration at Department of Commerce and Management Studies, University of Calicut is a bonafide record of work done by him under the Professor, DCMS, University of Calicut . guidance of Dr. B Johnson, Professor,

Place: CU Campus Date:

Dr.E K Satheesh

DEPARTMENT OF COMMERCE AND MANAGEMENT STUDIES UNIVERSITY OF CALICUT

Dr. B.Johnson

Calicut University

Reader

Malappuram District

DCMS

Kerala State -673635

CERTIFICATE This is to certify that Mr. Arun K T is a bonafide student of the Department of Commerce and Management Studies, University of Calicut . This report entitled

“

Financial Modelling for

Portfolio Selection and Risk Management Management is an authentic record of the project work done by him ”

under my supervision in partial fulfillment of the requirements for the award of the degree of Master of Business Administration, University of Calicut. Place: CU Campus Date:

Dr. B. Johnson

DECLARATION

I, Arun K T, student of MBA 4th semester, Department of Commerce and Management Studies, University Of Calicut ,hereby declare that the project report entitled Financial Modelling “

for Portfolio Selection and Risk Management submitted to University of Calicut for the partial ”

fulfillment of Master of Business Administration is a record of original work done by me under the guidance of Dr. B. Johnson, Reader, DCMS, University of Calicut during the academic year 2011-2013. The empirical findings in this report are based on data collected by me, while studying and preparing this project report.

Date

:

Place: CU Campus

Arun K T

ACKNOWLEDGEMENTS First of all, I express our heartfelt gratitude to God, the almighty, without whose blessings I would not have completed this endeavor in time. I express my sincere and cordial gratitude to my guide, Dr. B Johnson, Reader, Department of Commerce and Management Studies, University Of Calicut, for his profound inspiration, valuable insights, continuous support and assistance throughout the study. I feel great delight in expressing my earnest thankfulness to Dr.E K Satheesh, Head, Department of Commerce and Management Studies, University Of Calicut, for providing all necessary help and guidance throughout the project. I am also indebted to Dr. K P Rajendran, visiting faculty, Department of Commerce and Management Studies, University of Calicut for his support and guidance for this project work. I am indebted to all my faculty members in the Department of Commerce and Management Studies, University of Calicut for their timely suggestions and guidance for this project work. I would like to extend my sincere gratitude to Mr.Thomas George, Faculty ,Cochin Stock Exchage Ltd. for providing me with all necessary aids to complete the tasks. Special thanks must go to my parents and friends for their zealous prayers and muse that strengthened our efforts to do this research work in time. The success of this project is the result of cooperation from different people. I would like to take this opportunity to express my ardent gratitude to all those people for the whole- hearted contribution made to this project that can never be forgotten ARUN K T

TABLE OF CONTENTS 1

CHAPTER 1: INTRODUCTION

1.1.1 Research problem

2

1.1.2 Significance of the study

3

1.1.3 Scope of the study

3

1.1.4 Objectives of the study

4

1.1.5 Research Methodology

4

1.1.6Sources of data

4

1.1.7 Tools for data collection

5

1.1.8 Sampling Plan

5

1.1.9 Tools for analysis

5

1.1.10 Variables of the study

9

1.1.11 Period of study

9

1.1.12 Conceptual model of the study

10

1.1.14 Limitations

10

1.2 Literature Review

11

CHAPTER 2: INDIAN CAPITAL MARKET-AN OVERVIEW

31

CHAPTER 3: COCHIN STOCK EXCHANGE LTD-A PROFILE

45

CHAPTER 4: DATA ANALYSIS

PART 1

53

CHAPTER 5: DATA ANALYSIS

PART 2

95

CHAPTER 6: FINDINGS, SUGGESTIONS & CONCLUSION

117

BLIOGRAPHY CHAPTER 6: ANNEXURE

123

LIST OF TABLES Table No.

Table 4.1

Details

Return of Securities

Page No 55

Table 4.2

Risk of Securities

56

Table 4.3

Beta of Securities

58

Table 4.4

Alpha of the Securities

60

Table 4.5

Systematic risk of Securities.

62

Table 4.6

Unsystematic risk/residual variance of Securities.

63

Table 4.7.1

Ranks of Securities based on excess return to beta.

64

Table 4.7.2

Calculation of cut-off point.

65

Table 4.8.1

Calculation of optimal portfolio

65

Table 4.8.2

Optimal portfolio

66

Table 4.9.1

Portfolio alpha in optimal portfolio

66

Table 4.9.2

Portfolio beta in optimal portfolio

67

Table 4.9.4

Optimal portfolio return , risk ,alpha ,beta , residual, variance

68

Table 4.9.5

Benefit of diversification.

68

Table 4.10.1

Portfolio alpha in equal weight

71

Table 4.10.2

Portfolio beta in equal weight

71

Table.4.10.3

Portfolio residual variance in equal weight

72

Table.4.10.4

Benefit of diversification in equal weight.

73

Table.4.11.1

Calculation of weight based on PE ratio

74

Table.4.11.2

Portfolio alpha based on PE ratio.

74

Table.4.11.3

Portfolio beta based on PE ratio.

75

Table 4.11.4

Portfolio residual variance based on PE ratio

75

Table 4.11.5

Benefit of diversification in based on PE ratio.

76

Table 4.12.1

Calculation of weight based on risk adjusted rate of return

77

Table 4.12.2

Portfolio alpha based on risk adjusted rate of return.

77

Table 4.12.3

Portfolio beta based on risk adjusted rate of return.

78

Table 4.12.4

Portfolio residual variance based on risk adjusted rate of return.

78

Table 4.12.5

Benefit of diversification in based on risk adjusted rate of return.

80

Table 4:13.1

Sharpe ratio of the portfolios.

82

Table 4.13.2

Treynor ratio of portfolios.

83

Table 4.13.3

Jensen measure of portfolios.

85

Table 4.14.1.1

Portfolio value for Mont Carlo Simulation.

88

Table 4.14.1.2

Changes in the total value of portfolio.

89

Table 4.14.2.1

Changes in total value of portfolio in Back testing.

92

Table 4.14.3.1

Variance Co-variance matrix.

93

Table 4.14.3.2

Portfolio PE weights

93

Table 5.1

Gender of the respondents.

96

Table 5.2

Age group of the respondents.

97

Table 5.3

Qualification of the respondents.

98

Table 5.4

Occupation of the respondents.

99

Table 5.5

Annual income of the respondents.

100

Table 5.6

Investment experience of the respondents.

101

Table 5.7

Investment preference of the respondents

102

Table 5.8

Sector Preference of the respondents

103

Table 5.9

Type of Analysis used by the respondents for investing

104

Table 5.10

Investment Objective of the respondents.

105

Table 5.11

Preferred rate of growth.

106

Table 5.12

Investment in stock market securities.

107

Table 5.13

Whether the respondents have financial advisor or not.

108

Table 5.14

Level of Knowledge of the respondents in Portfolio Management.

109

Table 5.15

Technique used by the respondents to balance risk and return.

110

Table 5.16

Technique used by the respondents for portfolio diversification.

111

Table 5.17

Familiarity of the respondents with the Financial Modelling.

112

Table 5.18

Portfolio evaluation techniques used by respondents.

113

Table 5.19

Awareness of VAR concepts among the respondents.

114

Table 5.20

Methods for measuring VAR used by the respondents

115

Table 5.22

Qualification and awareness of the investors.

116

Table 5.23

Chi-Square Tests

117

LIST OF FIGURES Figure No

Details

Page No

Fig.1.1.12

Conceptual Model

17

Fig.1.2

Efficient frontier.

21

Fig.3.1

Organisational Structre.

47

Fig.4.1

Return of Securities

55

Fig.4.2

Risk of Securities

56

Fig.4.3

Beta of Securities

58

Fig.4.4

Alpha of the Securities

60

Fig.4.5

Systematic risk of Securities.

62

Fig.4.6

Unsystematic risk/residual variance of Securities.

63

Fig.4:13.1

Sharpe ratio of the portfolios.

82

Fig.4.13.2

Treynor ratio of portfolios.

83

Fig.4.13.3

Jensen measure of portfolios.

85

Fig.5.1

Gender of the respondents.

96

Fig.5.2

Age group of the respondents.

97

Fig.5.3

Qualification of the respondents.

98

Fig.5.4

Occupation of the respondents.

99

Fig.5.5

Annual income of the respondents.

100

Fig.5.6

Investment experience of the respondents.

101

Fig.5.7

Investment preference of the respondents

102

Fig.5.8

Sector Preference of the respondents

103

Fig.5.9

Type of Analysis used by the respondents for investing

104

Fig.5.10

Investment Objective of the respondents.

105

Fig.5.11

Preferred rate of growth.

106

Fig.5.12

Investment in stock market securities.

107

Fig.5.13

Whether the respondents have financial advisor or not.

108

Fig.5.14 Fig.5.15 Fig.5.16

Level of Knowledge of the respondents in Portfolio Management. Technique used by the respondents to balance risk and return. Technique used by the respondents for portfolio diversification.

109 110 111

Fig.5.17

Familiarity of the respondents with the Financial Modelling.

112

Fig.5.18

Portfolio evaluation techniques used by respondents.

113

Fig.5.19

Awareness of VAR concepts among the respondents.

114

Fig.5.20

Methods for measuring VAR used by the respondents

115

CHAPTER 1 INTRODUCTION

Financial modelling for portfolio selection and risk management

Financial health plays a pivotal role in the overall well-being of an economy, organization, or individual. This can certainly be assessed qualitatively, but in order to make comparisons both vertically and horizontally, it makes sense to quantify this notion with the use of numbers and statistics. Therefore, it is vitally important to have standards and means to manage, monitor, maintain, and grow wealth. Even though there is lot of improvements happening day by day in financial and investment management area, the individual investors who are the main part of stock market are much concerned about the aspects like portfolio selection and risk management. Their intention is to maximize return by minimizing risk associated with their investment .So there are mainly two basic problems any individual investor is concerned. They are formation of an optimal portfolio and efficient management of its risk. The development of quantitative finance and financial modeling is helping both the investors and portfolio managers in improving the efficiency of their portfolio and effectiveness of risk management tools. Financial models are used to predict financial performance. It is the task of building an abstract model of a financial decision making situation. It normally involves application of quantitative and analytical techniques to build a statistical or mathematical model for explaining an investment situation and for explaining a financial process or product. A financial model can be compared to a prototype for a machine. Financial modeling is extensively used in investment management and corporate finance. It includes the application of various financial models in solving various problems in finance. The study titled

“Financial modeling for portfolio selection and risk management” is an attempt

to find out the application of different financial models for portfolio selection and management of risk. William Sharpe optimization model is used for finding out the optimal portfolio. Different Value at Risk measures like Monte Carlo simulation and Variance – Covariance method is used for studying the role of financial models in risk management.


1.1.1: RESEARCH PROBLEM

Today’s Financial Market is more complex and uncertain due to introduction of new processes and innovative products. Financial modeling strategies are effective analytical methods for making scientific and efficient investment decisions in such complex and volatile market. The three main problems faced by investors in managing their investment are 1. How to obtain superior performance performance of portfolio by striking a trade-off between risk & return 2.

How to identify under-priced securities for making investment decision.

3. How to manage the risk associated with the portfolio. Because of volatility and complexity of capital market traditional methods based on intuitive investment decisions fails to achieve this purpose. Investors have to use financial models for striking an optimal trade-off between risk and retur n. The study mainly focuses on studying the effectiveness of financial models in portfolio optimization, portfolio risk management. 1.1.2: SIGNIFICANCE OF THE STUDY

Every investment decision is based on an efficient risk-return trade-off. Increased complexity of financial instruments and the economic conditions such as recession, boom, etc makes it difficult for any investment manager to plan his investments. The study recognizes the importance of in generating an optimal portfolio for making right investment decision and devising superior strategy for risk management.

1.1.3: SCOPE OF THE STUDY

The study entitled “Financial Modelling and Risk Management” focuses on how effectively an investor can apply Financial Modelling in Portfolio Selection,Optimization and Portfolio Risk Management. The study also tries to study to Value at Risk risk management techniques using Montecarlo Simulation, Backtesting and Variance covariance model. The scope of the study is also limited to Indian Stock Market and Indian Derivative Securiti es Market.


1.1.4: OBJECTIVES

Broad objective of the study is to review the different financial models for portfolio selection & portfolio risk management. Specific objectives of the study are:

To study the application of Sharpe’s opti mization model in portfolio selection and optimization



To study the role of VaR matrics by using variance- covariance method and Monte Carlo simulation method in portfolio risk management.



To perform a back test in order to determine the reliability of the VaR model so developed.



To evaluate the awareness of Financial Modelling techniques among the investors.

1.1.5: RESEARCH METHODOLOGY Research design

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 to the final analysis of the data. The study is based on analytical type of research.

1.1.6: SOURCES OF DATA

Primary data and secondary data were collected in order to fulfill the purpose of the research. Primary data The primary data required for the study were collected from the respondents through questionnaire and personal interviews. Secondary data The main source of information is from the website Historical data of closing price of the

selected equities are collected from websites of the exchange. Data is also collected from newspapers, magazines and journals. Five years historical data was analyzed for doing this research.


1.1.7: TOOLS FOR DATA COLLECTION The research instrument mainly used for the data collection was questionnaire. Personal interview was another tool. 1.1.8: SAMPLING PLAN

The sampling method used for the research was purposive sampling. The research was done according to the ease of accessibility and proximity to the researcher. a. Sampling unit The sampling unit used by the researcher includes investors investing in Indian stock market. b. Sample size The sample size taken for the study was 30. c. Contact Method Direct contact method was used for the study. Questionnaires were circulated among the sample respondents. Criteria for selection of stocks

Ten securities which included in the CNX NIFTY are only selected on the base that they represent major stocks in the capital market. 1.1.9: TOOLS FOR ANALYSIS

The data collected has been analysed using basic statistical tools like standard deviation, mean etc.

Important Terms and Formula’s used 

Portfolio construction construction 

R i= (Today’s price- yesterday’s price)*100

Yesterday’s price 

Return (R i) = (PE -PB) *100 PB



Alpha = Stock Return – (Beta (Beta x Market Return)



Alpha (αi) =R i-βi*R m




Beta (β) =

NΣxy-ΣxΣy NΣx²-(Σx) ²





Risk (σ²) =Σ(xi-x)² N

Residual variance (σ²ei) = σ i²- βi ² * σ² m n



Portfolio alpha (αp) = Σ ωi αi i=1 n



Portfolio beta (βp) = Σ ωi βi i=1 n



Portfolio residual variance (σ²ei) = Σ ωi² σ² i=1



Portfolio return = Portfolio alpha+ (Portfolio beta * Market return)



R p= αp+ (βp*R m)



Portfolio risk, ( σ²p) = β

n

² p

σ²m+ Σ ωi ² σ²ei i=1

Cut off point n

σ²m Σ ((R i - R f) x βi)/ σ²ei i =1 Ci = n

1+ σ²m Σ βi²)/ σ²ei i=1

Proportion of fund invested in each security Zi Xi = n Σ Zi i=1

Financial modelling for portfolio selection and risk management Markowitz model

Portfolio return (R p)=X1R 1+X2R 2+X3R 3 Portfolio Risk (σ ² p)

σp2= σ12 X1 2+ σ2 2 X2 2+ σ3 2 X3 2+2 X1 X2 COV12+2 X2 X3 COV 23+2X1X3 COV13 R p=Portfolio Return

σp2=Portfolio Variance X1 = Proportion of funds invested in first security R 1=Return of first security X2= Proportion of funds invested in second security R 2= Return of second security X3= Proportion of funds invested in third security R 3= Return of second security

COV12=Covariance between the return of first and second securities COV 23 = Covariance between the return of second and third securities COV13 = Covariance between the return of first and third securities

TANGENCY PORTFOLIO:

A

=

MMULT (MMULT (TRANSPOSE (ONES), MINVERSE (VARIANCE CO-VARIANCE MATRIX)), ONES)

B

=

MMULT (MMULT (TRANSPOSE (ONES), MINVERSE (VARIANCE CO-VARIANCE MATRIX)), 1+ E®)

C.

=

MMULT (MMULT (TRANSPOSE (1+ E®), MINVERSE (VARIANCE CO-VARIANCE MATRIX)), 1+ E®)

DELTA :

A x C. - B2

GAMMA:

1 / (B-A x R.)

RISK =

SQRT (MMULT (MMULT (TRANSPOSE (OPTIMAL COMBINATION OF RISKY ASSETS), VARIANCE CO-VAR MATRIX), OPTIMAL COMBINATION OF RISKY ASSETS))

RETURN:

MMULT (TRANSPOSE (OPTIMAL COMBINATION OF RISKY ASSETS), 1+E®)-1


Portfolio evaluation: 

Sharpe ratio Sharpe ratio (SR ) = Portfolio return-Risk free rate of return Portfolio Standard deviation =

R p-R f

σp Where R p- realized return on the portfolio R f - Risk free rate of return

σp- Standard deviation of portfolio return 

Treynor ratio Treynor ratio =

R p-R f

βp Where R p - realized return on the portfolio R f - Risk free rate of return

βp - Portfolio beta 

Jensen measure Jensen measure (αp) = R p -E(R p)

Where, R p - Realized return of the portfolio E (R p) – Expected return of the portfolio E (R p) = R f + βp(R m – R f ):-Where,

βp - Beta of portfolio R m - Market Return R f - Risk free rate of return


Value at Risk

At 95% confidence level VaR = portfolio value x 1.65 σ

At 99% confidence level VaR = portfolio value x 2.33 σ

Monte Carlo Simulation

∂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 Є = Random drawing from a standardized normal distribution σ = Volatility of stock price or standard deviation of the expected return ∂ t = A small time interval

1.1.10: VARIABLES OF THE STUDY 

Return



Risk



Awareness



Optimization



Stock Price

1.1.11: PERIOD OF STUDY

The study was conducted for a period of 45 days extending from April 1 st to May 15 2013


1.1.12: CONCEPTUAL MODEL OF THE STUDY Fig.No:1.1.12

1.1.3: LIMITATIONS 

Duration of the study is limited to the period of one month .So in depth study is not possible.



Only four portfolio were constructed



The conclusion cannot be conclusive as market is unpredictable



Data considered is only for past 5 year period




Value at Risk estimate the market risk, based on the past data



Security beta is assumed to be static

1.2: LITERATURE REVIEW 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

Financial modelling for portfolio selection and risk management The success of portfolio management depends on how effectively each phase is 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 ten 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 investors’ 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 are compared with the future predicted price to determine the extend of mis pricing.

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

Financial modelling for portfolio selection and risk management 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.

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 ti me in terms of return and risk. It pro vides 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

Financial modelling for portfolio selection and risk management Portfolio Theory Portfolio theory is concerned with the risk-reducing role played by individual assets in an investment portfolio of several assets. The benefits of diversification were first formalized in 1952 by Harry Markowitz, who later was awarded the Nobel prize in economics for his work. Portfolio Theory is today a corner stone of modern financial theory, as well as a widely used tool for managing risk-return tradeoffs in investment portfolios.

Means and standard deviations of Total Return

The return and risk of an asset are commonly measured in terms of the mean and standard deviation of total return, where total return represents income plus capital gains or losses. The mean is the return one expects to obtain on average; standard deviation is a measure of dispersion. The mean and standard deviation of return for a given asset can be computed from historical returns. In that case, however, they are merely summary descriptors of past performance, and may or may not reflect the probability distribution of future returns.

Portfolio selection Optimal Portfolio selection using Sharpe’s optimization model 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.

Formation of optimal portfolio

The inclusion of any security in the portfolio 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 Govt. 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

Financial modelling for portfolio selection and risk management Excess return to beta ratio= (R i-R f )/βi

Where R i

= the expected return on security ‘I’

R f

= 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 (R i-R f) /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 (R i-R f) /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 (R i-R f) /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

N

σ2m∑ (R I-R F) βi/ σ2ei i=1

Ci

=

N

1+

σ2m ∑ βi2/ σ2ei i=1

4. The cumulated values of C i 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:

Financial modelling for portfolio selection and risk management Zi Xi

=

N

∑ Zi i=1

Where

βi Zi =

σi

(RI-RF) βi

- C*

Xi = weight on each security

Βi=Beta of each security σi=Risk of security R i=return of each security Rf =Risk free rate of return C*= cut off rate

The Markowitz Portfolio Theory

(Concept of Expected Risk and Expected Rates of Return) Creating an optimum portfolio doesn't involve simply finding the best risk vs. return situations, but considering varying relationships between different asset classes. In the early 1960s, there was much contemplation among investment industr y professionals about risk and its implications on selecting specific securities and other types of assets when constructing an optimum portfolio. Yet, there were also no effective means or models of measuring risk available at the time. By the same token, it was very clear that to construct the

optimum portfolio, capable of meeting an investor’s investment objectives within the constraints of his or her chosen investment horizon, was not going to be possible without adequate and quantifiable measures of risk. Prompted by this largely unmet need, Harry M. Markowitz introduced the preliminary portfolio model in a paper titled Portfolio Selection, which he had published in the 1952 Journal of Finance. Markowitz was further credited with the formulation of two terms critical to the development of the portfolio theory: the expected rate of return and the expected risk measure. Note that almost four decades after publishing Portfolio Selection, Markowitz shared a Nobel Prize with Merton Miller and William Sharpe for his contribution to the development of what has become known as the capital market theory.


Investor Behavior Assumptions The Markowitz Portfolio Theory relies on a number of assumptions regarding investor behavior;

such is that investors will always seek “the second opinion.” When presented with a spectrum of alternatives, investors will consider all expected rates of return over a specified holding period. Furthermore, investors are very much interested to know the estimated risk level of all securities contained within a portfolio. In fact, we could say that their investment decisions are solely based on these two variables: the levels of expected return and the expected risk. Notably, for any given risk level, investors will always rather go for portfolios with higher expected returns than for those with lower returns. Alternatively, for any given expected return level, investors are likely to prefer portfolios with less risk than those with more risk. Based on these assumptions, most of which are pretty much common sense, when comparing a single security or a portfolio of securities, only securities or portfolios with the highest expected return at the same or lower risk level are considered as efficient.

The Efficient Frontier

The Markowitz Portfolio Theory also examines the curve called the efficient frontier. The idea behind this curve is a graphic presentation of a set of portfolios that offer the maximum rate of return for any given level of risk. Alternatively, the efficient frontier identifies portfolios that offer the minimum risk for any given level of return. The Markowitz efficient investor will seek his or hers optimum portfolio somewhere along the efficient frontier curve, depending on their individual perception of the return-risk relationship. Each portfolio on the curve will either have a higher rate of return for the same or lower risk, or lower risk for an equal or better rate of return when compared to portfolios or securities that are not on the efficient frontier. Because portfolios enjoy benefits of diversification due to imperfectly correlated assets contained within them, the efficient frontier is really made up of portfolios rather than individual securities

or assets. The two potential exemptions would be the efficient frontier curve’s end points, at the beginning of which could be the asset with the lowest risk and at the end of which could be the asset with the highest return. What Harry Markowitz started back in the early 1960s was continued through the development of the capital market theory, whose final product, the capital asset pricing model (CAPM), allowed a Markowitz efficient investor to estimate the required rate of return for any risky security or asset.


The capital asset pricing model

The capital asset pricing model was developed in mid – 1960’s

by three researchers William

Sharpe, John Lintner and Jan Mossin independently. This model is also known as Sharpe-LinterMossin Capital Asset Pricing Model.

The Capital Asset Pricing Model or CAPM is really an extension of the Portfolio theory of Markowitz. The portfolio theory is a description of how rational investors should build efficient portfolios and select the optimal portfolio. The Capital Asset Pricing Model derives the relationship between the expected return and risk of individual securities and portfolios in the capital markets if everyone behaves in the way the portfolio theory suggested.

Fundamental Notions of Portfolio theory

Return and risk are two important characteristic of every investment. Investors place their investment decisions on the expected return and risk of investments. Risk is measured by the variability in return.

Investors attempt to reduce the variability of returns through diversification of investment. This results in the creation of a portfolio. With a given set of securities, any number of portfolios may be created by altering the proportion of funds invested in each security. Among these portfolios some dominate others or some are more efficient than the vast majority of portfolios because of lower risk or higher returns. Investors identify this efficient set of portfolios. CAPM decomposes a portfolio's risk into systematic and specific risk. Systematic risk is the risk of holding the market portfolio. As the market moves, each individual asset is more or less affected. To the extent that any asset participates in such general market moves, that asset entails systematic risk. Specific risk is the risk which is unique to an individual asset. It represents the component of an asset's return which is uncorrelated with general market moves. According to CAPM, the marketplace compensates investors for taking systematic risk but not for taking specific risk. This is because specific risk can be diversified away. When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk, but through diversification, the investor's net exposure is just the systematic risk of the market portfolio

Financial modelling for portfolio selection and risk management Systematic risk can be measured using beta. According to CAPM, the expected return of a stock equals the risk-free rate plus the portfolio's beta multiplied by the expected excess return of the market portfolio Capital asset pricing model An estimation of the CAPM and the Security Market Line (purple) for the Dow Jones Industrial Average over the last 3 years for monthly data. The Capital Asset Pricing Model (CAPM) is used in finance to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already welldiversified portfolio, given that asset's non-diversifiable risk. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systemic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. The model was introduced by Jack Treynor, William Sharpe, John Lintner and Jan Mossin independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe received the Nobel Memorial Prize in Economics (jointly with Markowitz and Merton Miller) for this contribution to the field of financial economics.

Asset pricing Once the expected return, E ( Ri), is calculated using CAPM, the future cash flows of the asset can be discounted to their present value using this rate ( E ( Ri)), to establish the correct price for the asset. In theory, therefore, an asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate. If the observed price is higher than the valuation, then the asset is overvalued (and undervalued when the observed price is below the CAPM valuation). Alternatively, one can "solve for the discount rate" for the observed price given a particular valuation model and compare that discount rate with the CAPM rate. If the discount rate in the model is lower than the CAPM rate then the asset is overvalued (and undervalued for a too high discount rate).

Financial modelling for portfolio selection and risk management Asset-specific required return The CAPM returns the asset-appropriate required return or discount rate - i.e. the rate at which future cash flows produced by the asset should be discounted given that asset's relative riskiness. Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average. Thus a more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate. The CAPM is consistent with intuition - investors (should) require a higher return for holding a more risky asset. Since beta reflects asset-specific sensitivity to non-diversifiable, i.e. market risk, the market as a whole, by definition, has a beta of one. Stock market indices are frequently used as local proxies for the market - and in that case (by definition) have a beta of one. An investor in a large, diversified portfolio (such as a mutual fund) therefore expects performance in line with the market.

Risk and diversification

The risk of a portfolio comprises systematic risk, also known as diversifiable risk, and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk. Systematic risk refers to the risk common to all securities - i.e. market risk. Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio (specific risks "average out"). The same is not possible for systematic risk within one market. Depending on the market, a portfolio of approximately 30-40 securities in developed markets such as UK or US will render the portfolio sufficiently diversified to limit exposure to systemic risk only. In developing markets a larger number is required, due to the higher asset volatilities. A rational investor should not take on any diversifiable risk, as only non-diversifiable risks are rewarded within the scope of this model. Therefore, the required return on an asset, that is, the return that compensates for risk taken, must be linked to its riskiness in a portfolio context - i.e. its contribution to overall portfolio riskiness - as opposed to its "stand alone riskiness." In the CAPM context, portfolio risk is represented by higher variance i.e. less predictability. In other

Financial modelling for portfolio selection and risk management words the beta of the portfolio is the defining factor in rewarding the systematic exposure taken by an investor. The efficient frontier Fig.No:1.2

The (Markowitz) efficient frontier

The CAPM assumes that the risk-return profile of a portfolio can be optimized - an optimal portfolio displays the lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above (assuming that any asset is infinitely divisible). All such optimal portfolios, i.e., one for each level of return, comprise the efficient frontier. Because the unsystematic risk is diversifiable, the total risk of a portfolio can be viewed as beta. The market portfolio An investor might choose to invest a proportion of his or her wealth in a portfolio of risky assets with the remainder in cash - earning interest at the risk free rate (or indeed may borrow money to fund his or her purchase of risky assets in which case there is a negative cash weighting). Here,

Financial modelling for portfolio selection and risk management the ratio of risky assets to risk free asset does not determine overall return - this relationship is clearly linear. It is thus possible to achieve a particular return in one of two ways: 1.

By investing all of one's wealth in a risky portfolio,

2.

or by investing a proportion in a risky portfolio and the remainder in cash (either

borrowed or invested). For a given level of return, however, only one of these portfolios will be optimal (in the sense of lowest risk). Since the risk free asset is, by definition, uncorrelated with any other asset, option 2 will generally have the lower variance and hence be the more efficient of the two. This relationship also holds for portfolios along the efficient frontier: a higher return portfolio plus cash is more efficient than a lower return portfolio alone for that lower level of return. For a given risk free rate, there is only one optimal portfolio which can be combined with cash to achieve the lowest level of risk for any possible return. This is the market portfolio. Assumptions of CAPM All Investors: 

Aim to maximize utilities.



Are rational risk-averse.



Are price takers i.e. they cannot influence prices.



Can lend and borrow unlimited under the risk free rate of interest.



Securities are all highly divisible into small parcels.



No transaction or taxation costs incurred.

Capital market line & security market line The efficient frontier represents the efficient set of portfolios. The line formed by the action of all investors mixing the market portfolio with the risk free assets is known as the Capital market line. All efficient portfolios of all investors will lie along this CML. CML does not describe the risk return relationship of inefficient portfolios. The CAPM specifies the relationship between expected return and risk of all securities and all portfolios, whether efficient or inefficient.


SML gives the relationship between expected return and beta value (β) of a security. Beta value is a measure of the

security’s sensitivity to changes in the market return. Beta value greater than

one indicates higher sensitivity to changes in the market changes, whereas beta value less than one indicates lower sensitivity to market changes. When the beta value equals to one it indicates that security moves at the same rate and in the same direction as the market. Pricing securities with CAPM

The CAPM can also be used for evaluating the pricing of securities. It provides a frame work for assessing whether a security is underpriced, overpriced or correctly priced. According to CAPM each security is expected to provide a return commensurate with its level of risk. A security may be offering more returns than expected returns, making it more attractive. Another security may be offering less return than the expected return, making it less attractive. Shortcomings of CAPM 

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



The model assumes that the variance of returns is an adequate measurement of risk. This might be justified under the assumption of normally distributed returns, but for general return distributions other risk measures (like coherent risk measures) will likely reflect the investors' preferences more adequately.



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



The model assumes that given a certain expected return investors will prefer lower risk (lower variance) to higher risk and conversely given a certain level of risk will prefer

Financial modelling for portfolio selection and risk management higher returns to lower ones. It does not allow for investors who will accept lower returns for higher risk. Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well. 

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



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



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



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

Tools for portfolio evaluation 

Sharpe ratio

The performance measured developed by William Sharpe is referred to as the Sharpe ratio or the reward to variability 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 )=

R p-R f

σp Where R p=realized return on the portfolio R f =Risk free rate of return

=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=

R p-R f

Βp 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 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 .The difference between the return actually earned on a portfolio and the return expected from the portfolio is a measure of the excess return.

Financial modelling for portfolio selection and risk management Using the CAPM model the expected return of the portfolio can be calculated as follows

E(Rp) =Expected portfolio return R f =Risk free rate R m= Return on market index

Βp=Systematic risk of the portfolio The differential return is calculated as follows:

αp= Rp- E(Rp) Where

αp =Differential return earned R p= actual return earned on the portfolio E (Rp) =Expected return

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 Ri sk.

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








Variance Covariance model



Historical Simulation Method


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

Financial modelling for portfolio selection and risk management 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 ℓn * ST T

SO

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.

∂s = μS∂t + σSЄ√∂ t Where

∂s = Change in the stock price for one day S = Price of stock today

μ = Expected return for period T ε = Random number ∂ t = a small time interval

Financial modelling for portfolio selection and risk management For our analysis ∂ t = 1 day

The expected return μ

μ

= 1 ℓn * ST T

SO

ST = Stock price at time T SO = Stock price at time Zero

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 5 th worst outcome and 1-day VaR at 95% is the 25 th worst outcome.

 Variance Covariance model This model is termed as correlation models. It is based on J.P.Morgan’s Risk Metrics and Modern Portfolio Theory (MPT).Using this, expected return or standard deviation can be explained as function of volatility of return of each security in the portfolio and the covariance between each securities position.

These are less flexible models which require normal probability distribution, using equation based on Markowitz model. Inputs of data required are the variance and covariance of individual assets in the portfolio. The equation gives a value of portfolio variance and whose square root is

Financial modelling for portfolio selection and risk management the standard deviation of the portfolio .The VaR in this model is the multiple of standard deviation depending on the required confidence level. At 95% confidence level, the VaR equals to standard deviation. This method is used only to the portfolios that conform to normal distribution.



Historical Simulation Method This method is similar to the delta Normal method in that it also uses historical data of

asset returns and the exposure to these risk factors. The difference is that this return does not represent an actual portfolio but rather reconstructs the history of a hypothetical portfolio using the current position .both the methods would generate the same VAR if asset returns are all normally distributed This is also relatively simple .the drawback to this is that only one sample path is used for simulation, which may not adequately represent future distributions.

Back Testing

Statistically perverse nature of the asset returns compel risk managers to perform back testing. In back testing, the performance of VaR estimates of extreme losses with respect to realized losses is examined. That is, it allows the risk manager to determine whether VaR methods employed are adequate. Through back testing, the reasons for increase in actual losses than those predicted by VaR can be found out.

Sometimes, the composition of the portfolio can drive actual losses beyond VaR.If selling an asset in one day can be only accomplished only by accepting a large price- discount; the value change caused by an adverse set of price changes should reflect this. Accordingly, bid prices should be used for the computation of VaR, particularly if the risk manager believes that parts of the portfolio will be liquidated after adverse price movements. For this reason, institutions will often adjust their VaR for the liquidity of their positions.


CHAPTER 2 INDIAN CAPITAL MARKET-AN OVERVIEW


Stock exchanges are intricacy inter-woven in the fabric of a nation's economic life. The history of Indian capital markets spans back 200 years, around the end of the 18th century. It was at this time that India was under the rule of the East India Company. In 1860-61 the American Civil War broke out and cotton supply from United States of Europe was stopped; thus, the 'Share Mania' in India begun. The number of brokers increased to about 200 to 250. However, at the end of the American Civil War, 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 The capital market of India initially developed around Mumbai; with around 200 to 250 securities brokers participating in active trade during the second half of the 19th century. . In 1887, an indenture was executed and the Bombay Stock Exchange (BSE) was formally established as a society named Native Share and Stock Brokers Association. The effects of Industrial Revolution began to be felt in India by the dawn of 20 th century. After Independence, the Indian Government gave priority to infrastructure development considering the urgency of proceeding with large scale industrial development,. Accordingly, Industrial Finance Corporation was formed in 1948with the objective of providing financial assistance to the industrial sector. In 1955, Industrial Credit and Investment Corporation of India (ICICI) were set up for providing the capital market with underwriting facility. Establishment of Life Insurance Corporation in 1956 was another landmark in the field of institutionalization of the capital market. Apart from the insurance business it also invested in government securities. An important development in company law took place when the government of India promulgated the Companies Act, 1956 based on the recommendations of the company law committee. This was the largest statute ever passed by the Parliament. Unit Trust of India (UTI) was formed in 1964 for providing facilities of equity investment for small investors thereby supplementing the efforts of institutions engaged in mobilizing the savings of the community. Mutual fund scheme was first introduced in Indian by UTI in 1964. Industrial Development Bank

Financial modelling for portfolio selection and risk management of India (IDBI) was also formed in 1964 as a subsidiary of Reserve bank of India (RBI) to provide long term financial assistance to medium and large scale industries. As the apex development bank of the country, IDBI has been vested with the responsibility of strengthening the resources off the financial institutions including banks. The passing of Foreign Exchange Regulation Act, 1973 limited the shareholding of foreign firms to 40%, if they were to be recognized as Indian companies. For diluting their share holdings, many multinational companies offered shares to the public at attractive rates. During 1980s, debentures emerged as a powerful device for mobilizing funds in the capital market. Also, many public sector undertakings came out with bonds. There was also an impressive growth in the secondary market as ten stock exchanges were established in mideighties. Moreover, several instruments like convertible debentures and mutual fund schemes were offered to meet the expectations of emerging investors. During eighties, however, many stock exchanges were established: Cochin Stock Exchange (1980), Uttar Pradesh Stock Exchange Association Limited (at Kanpur, 1982), and Pune Stock Exchange Limited (1982), Ludhiana Stock Exchange Association Limited (1983), Gauhati Stock Exchange Limited (1984), Kanara Stock Exchange Limited (at Mangalore, 1985), Magadh Stock Exchange Association (at Patna, 1986), Jaipur Stock Exchange Limited (1989), Bhubaneswar Stock Exchange Association Limited (1989), Saurashtra Kutch Stock Exchange Limited (at Rajkot, 1989), Vadodara Stock Exchange Limited (at Baroda, 1990) and recently established exchanges - Coimbatore and Meerut. Thus, at present, there are totally twenty one recognized stock exchanges in India excluding the Over The Counter Exchange of India Limited (OTCEI) and the National Stock Exchange of India Limited (NSEIL). The Indian stock markets till date have remained stagnant due to the rigid economic controls. It was only in 1991, after the liberalization process that the India securities market witnessed a flurry of IPOs serially. The market saw many new companies spanning across different industry segments and business began to flourish . The launch of the NSE (National Stock Exchange) and the OTCEI (Over the Counter Exchange of India) in the mid-1990s helped in regulating a smooth and transparent form of securities trading. The stock market however received a dubbing in 1995-1996 onwards because of the sudden erosion of the saving of the investors. The investor lost confidence in the securities market and therefore the public issues dried up , thus ending of a golden era of public issues . However the resource mobilization continued to grow this time through other channels like bonds,

mutual

funds

and

considerably

through

private

placements.

Financial modelling for portfolio selection and risk management The regulatory body for the Indian capital markets was the SEBI (Securities and Exchange Board of India). Another sea change that the security market has witnessed is the introduction of demat trading in India. Now we have one of the best demat trading in the world, and almost 100% trading at the bourses take place in demat mode only.The capital markets in India experienced turbulence after which the SEBI came into prominence. The market loopholes had to be bridged by taking drastic measures. 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 out standings pay carry over charges (can tango 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 ,which prevailed in the Indian stock exchanges, resulted in much functional inefficiency such as absence of liquidity ,lack of transparency, undue delay in settlement of transactions, fraudulent practices etc. with the objective of providing more

efficient services to investors, the country’s first electronic which facilitates ringless,scripless

Financial modelling for portfolio selection and risk management trading was set up in 1992with the name Over the Counter Exchange Of India. It was sponsored

by the country’s premier financial institutions such as Unit Trust of India (UTI), Industrial Credit and Investment Corporation of India (ICICI), Industrial Development Bank of India (IDBI) ,SBI Capital Markets, Industrial Finance Corporation of India (IFCI), General Insurance Corporation (GIC) and its subsidiaries and Canbank Financial services. The exchange was set up to aid enterprising promoters in raising finance for new projects in a cost effective manner and to provide investors with a transparent and efficient mode of trading. The OTCEI has many novel features. It introduced screen based trading for the first time in the Indian stock market. Trading takes place through a network of computers of over the counter dealers located at several places, linked to a central OTC computer using tele communication links. All the activities of the OTC trading process are fully computerized. Moreover, OTCEI is a national exchange having a country wide reach. OTCEI has an exclusive listing in any other stock exchanges. For being listed in OTCEI the companies have to be sponsored by members of OTCEI. It was the first exchange in the country to introduce the practice of market making that is dealers in securities providing two way quotes (bid prices and offer prices of securities) Compared to the traditional Exchanges, OTC Exchange network has the following advantages: 

OTCEI has widely dispersed trading mechanism across the country which provides greater liquidity and lesser risk of intermediary charges.



Greater transparency and accuracy of prices is obtained due to the screen-based scrip less trading.



Since the exact price of the transaction is shown on the computer screen, the investor gets to know the exact price at which s/he is trading.



Faster settlement and transfer process compared to other exchanges.



In the case of an OTC issue (new issue), the allotment procedure is completed in a month and trading commences after a month of the issue closure, whereas it takes a longer period for the same with respect to other exchanges.


NATIONAL STOCK EXCHANGE (NSE):-

With the liberalization of the Indian economy, it was found inevitable to lift the Indian stock market trading system on par with the international standards. On the basis of the recommendations of high powered Pherwani Committee, the National Stock Exchange was incorporated in 1992 by Industrial Development Bank of India, Industrial Credit and Investment Corporation of India, Industrial Finance Corporation of India, all Insurance Corporations, selected commercial banks and others. The National Stock Exchange of India Limited has genesis in the report of the High Powered Study Group on Establishment of New Stock Exchanges. It recommended promotion of a National Stock Exchange by financial institutions (FIs) to provide access to investors from all across the country on an equal footing. Based on the recommendations, NSE was promoted by leading Financial Institutions at the behest of the Government of India and was incorporated in November 1992 as a tax-paying company unlike other stock exchanges in the country. On its recognition as a stock exchange under the Securities Contracts (Regulation) Act, 1956 in April 1993, NSE commenced operations in the Wholesale Debt Market (WDM) segment in june 1994. The following years witnessed rapid development of Indian capital market with introduction of internet trading, Exchange traded funds (ETF), stock derivatives and the first volatility index

India VIX in April2008, by NSE.

August 2008 saw introduction of Currency derivatives in India with the launch of Currency Futures in USD INR by NSE. Interest Rate Futures was introduced for the first time in India by NSE on 31st August 2009, exactly after one year of the launch of Currency Futures. The National Stock Exchange (NSE) is India's leading stock exchange covering various cities and towns across the country. NSE was set up by leading institutions to provide a modern, fully automated screen-based trading system with national reach. The Exchange has brought about unparalleled transparency, speed & efficiency, safety and market integrity. It has set up facilities that serve as a model for the securities industry in terms of systems, practices and procedures. NSE has played a catalytic role in reforming the Indian securities market in terms of microstructure, market practices and trading volumes. The market today uses state-of-art information technology to provide an efficient and transparent trading, clearing and settlement

Financial modelling for portfolio selection and risk management mechanism, and has witnessed several innovations in products & services viz. demutualization of stock exchange governance, screen based trading, compression of settlement cycles, dematerialization and electronic transfer of securities, securities lending and borrowing, professionalization of trading members, fine-tuned risk management systems, emergence of clearing corporations to assume counterparty risks, market of debt and derivative instruments and intensive use of information technology. STOCK MARKET:-

A stock market is a market for the trading of shares, debentures, derivatives and other instruments of different companies listed on different Stock Exchanges. Although common, the term 'the stock market' is a somewhat abstract concept for the mechanism that enables the trading of company stocks. It is also used to describe the totality of all stocks, especially within a country, for example in the phrase "the stock market was up today", or in the term "stock market bubble".It is distinct from a stock exchange, which is an entity (a corporation or a mutual organization) in the business of bringing buyers and sellers of stocks together. Trading:-

Participants in the stock market range from small individual stock investor to large hedge fund traders. Their orders usually end up with a professional at a stock exchange, who executes an order. Most stocks are traded on exchanges, which are places where buyers and sellers meet and decide on a price. Some exchanges are physical locations where transactions are carried out on a transaction floor, by a method known as open outcry. This type of auction is used in stock exchanges and commodity exchanges where traders may enter "verbal" bids and offers simultaneously. The other type of exchange is a virtual kind, composed of a network of computers where trades are made electronically via traders at computer terminals. Actual traders are based on an auction market paradigm where a potential buyer bids a specific price for a stock and a potential seller quotes a specific price for the stock. (Buying or selling at market means one will accept any bid or ask price for the stock.) When the bid and ask prices match, a sale takes place on a first come first serve basis if there are multiple bidders or askers at a given price. The purpose of a stock exchange is to facilitate the exchange of securities between buyers and sellers, thus providing a marketplace (virtual or real). Just imagine how difficult it would be to sell the shares (and what a disadvantage one would be at with respect to the buyer) if one had to call around trying to locate a buyer, as when selling a house. Really, a stock exchange is

Financial modelling for portfolio selection and risk management nothing more than a super-sophisticated farmers' market providing a meeting place for buyers and sellers. The New York Stock Exchange is a physical exchange, where much of the trading is done face-to-face on a trading floor. This is also referred to as a "listed" exchange (because only stocks listed within the exchange may be traded). The NASDAQ is a virtual (listed) exchange, where all of the trading is done by computers. The process is similar to the above, in that the seller provides an asking price and the buyer provides a bidding price. However, buyers and sellers are electronically matched. One or more NASDAQ market makers will always provide a bid and ask price at which they will always purchase or sell 'their' stock. Major Participants in the Indian Stock Market:-

There are 23 stock exchanges in India. Among them two are national level stock exchanges namely Bombay Stock Exchange (BSE) and National Stock Exchange of India (NSE). The rest 21 are Regional Stock Exchanges (RSE). Even though there are 23 stock Exchanges in India, increase in turnover took place mostly in the large exchanges at the expense of smaller ones. Bombay Stock Exchange:

A very common name for all traders in the stock market, BSE, stands for Bombay Stock

Exchange. The Bombay Stock Exchange, established in 1875, as “The Native Share and Stock Brokers Association” is the oldest i n Asia, even older than the Tokyo Stock Exchange, founded in 1878 until the establishment of National Stock Exchange; it was considered the premier stock exchange and trend setter in the country. Among the 23 stock exchanges recognized by the Government of India under the Securities Contract (Regulation) Act, 1956, it was the first one to be recognized and the only one that has been granted the privilege of permanent registration. In 1994, the Bombay Stock Exchange faced competition for the first time when National Stock Exchange was formed with completely automated trading system. It rose to the challenges of technology and in 1995, put the automated trading programming and trans ferred over 5000 scrips from floor to screen. The Bombay On-Line Trading (BOLT) network has been expanded to centers outside Mumbai. Market returns on equity shares as well as volatility in prices are measured through share price indices. In India, Bombay Stock Exchange 30 shares Sensitive Index (BSE SENSEX) is one of the popular benchmarks of share prices.

Financial modelling for portfolio selection and risk management BSE Vision: -

The vision of the Bombay Stock Exchange is to "Emerge as the premier Indian stock exchange by establishing global benchmarks." Regional Stock Exchanges (RSE) 

Ahmedabad Stock Exchange



Bangalore Stock Exchange



Bhubaneshwar Stock Exchange



Calcutta Stock Exchange



Cochin Stock Exchange



Coimbatore Stock Exchange



Delhi Stock Exchange



Guwahati Stock Exchange



Jaipur Stock Exchange



Ludhiana Stock Exchange



Madhya Pradesh Stock Exchange



Madras Stock Exchange



Magadh Stock Exchange



Mangalore Stock Exchange



Meerut Stock Exchange



OTC Exchange Of India



Pune Stock Exchange



Saurashtra Kutch Stock Exchange



Uttar Pradesh Stock Exchange

The Regional Stock Exchanges started clustering from the year 1894, when the first RSE, the Ahmedabad Stock Exchange (ASE) was established. In the year 1908, the second in the series, Calcutta Stock Exchange (CSE) came into existence. During the early sixties, there were only few recognized RSEs in India namely Calcutta, Madras, Ahmedabad, Delhi, Hyderabad and Indore. The number remained unchanged for the next two decades. 1980s was the turning point and many RSEs were incorporated. The latest is Coimbatore Stock Exchange and Meerut Stock Exchange.

Financial modelling for portfolio selection and risk management Financial Market:

Financial market is the market where financial securities like stocks and bonds and commodities like valuable metals are exchanged at efficient market prices. Here by efficient market prices we mean the unbiased price that reflects belief at collective speculation of all investors about the future prospect. Markets work by placing many interested buyers and sellers in one "place", thus making it easier for them to find each other. The trading of stock and bonds in the Financial Market can take place directly between buyers and sellers or by the medium of stock exchange .Financial markets can be domestic or international. Financial market is constituted mainly with money markets and capital markets. It also include other markets like bond market, stock market, commodity market, derivative ma rket, futures market, insurance market, foreign exchange market etc.. The financial instruments that have short or medium term maturity periods are dealt in the money market whereas the financial instruments that have long term maturity periods are dealt in the capital market. Here we are mainly focusing on money market and capital market as they are the major constituents in the financial market system. Money Market

Money market is the market for short term financial assets with maturities of one year or less. Treasury bills, commercial bills, commercial papers,etc. are the short term securities traded in the money market . these instruments being close substitutes for money ,the market for their trading is known as money market. Money market is the main source of working capital funds for business and industry. It provides a mechanism for evening out short term surpluses and deficits. The short term requirements of borrowers can be met by the creation of money market securities, which can be purchased by lenders with short term surpluses to park their funds for short durations. In India, the money market has a narrow base with limited number of participants who are mostly financial institutions. Capital Market

Capital market is the market segment where securities with maturity than one year are bought and sold. The market where investment funds like bonds, equities and mortgages are traded is known as the capital market. The primal role of the capital market is to channelize investments from investors who have surplus funds to the ones who are running a deficit. The

Financial modelling for portfolio selection and risk management instruments that are traded in the capital markets are equity instruments, credit market instruments, insurance instruments, foreign exchange instruments, hybrid instruments and derivative Capital markets may be classified as primary markets and secondary markets. In primary markets, new stock or bond issues are sold to investors via a mechanism known as underwriting. In the secondary markets, existing securities are sold and bought among investors or traders, usually on a securities exchange, over-the-counter, or elsewhere. Primary Market:

The market mechanism for buying and selling of new issues of securities is known as primary market. This market is also known as new issue market as it deals in new issues of securities. Companies, governments or public sector institutions can obtain funding through the sale of a new stock or bond issue. The process of selling new issues to investors is called underwriting. In the case of a new stock issue, this sale is an initial public offering (IPO). Secondary Market:-

The secondary market deals with securities which have already been issued and are owned by investors, both individual and institutional. These may be traded between investors. The buying and selling of securities already issued and outstanding takes place in stock exchanges. Hence, stock exchanges constitute the secondary market in securities. For the general investor, the secondary market provides an efficient platform for trading of his securities. For the management of the company, Secondary equity markets serve as a monitoring and control conduit — by facilitating value-enhancing control activities, enabling implementation of incentive-based management contracts, and aggregating information (via price discovery) that guides management decision. The main financial products dealt in secondary market includes: Equity:

The ownership interest in a company of holders of its common and preferred

stock. The various kinds of equity shares are as fol lows – 

Equity Shares: An equity share, commonly referred to as ordinary share also represents

the form of fractional ownership in which a shareholder, as a fractional owner, undertakes the maximum entrepreneurial risk associated with a business venture. The holders of such shares are members of the company and have voting rights. A company may issue such shares with differential rights as to voting, payment of dividend, etc.

Financial modelling for portfolio selection and risk management 

Rights Issue/ Rights Shares: The issue of new securities to existing shareholders at a

ratio to those already held. 

Bonus Shares: Shares issued by the companies to their shareholders free of cost by

capitalization of accumulated reserves from the profits earned in the earlier years. 

Preferred Stock/ Preference shares: Owners of these kinds of shares are entitled to a

fixed dividend or dividend calculated at a fixed rate to be paid regularly before dividend can be paid in respect of equity share. They also enjoy priority over the equity shareholders in payment of surplus. But in the event of liquidation, their claims rank

below the claims of the company’s creditors, bondholder s / debenture holders. 

Cumulative Preference Shares:

A type of preference shares on which dividend

accumulates if remains unpaid. All arrears of preference dividend have to be paid out before paying dividend on equity shares. 

Cumulative Convertible Preference Shares: A type of preference shares where the

dividend payable on the same accumulates, if not paid. After a specified date, these shares will be converted into equity capital of the company. 

Participating Preference Share: The right of certain preference shareholders to

participate in profits after a specified fixed dividend contracted for is paid. Participation right is linked with the quantum of dividend paid on the equity shares over and above a particular specified level. Security Receipts: Security receipt means a receipt or other security, issued by a securitization

company or reconstruction company to any qualified institutional buyer pursuant to a scheme, evidencing the purchase or acquisition by the holder thereof, of an undivided right, title or interest in the financial asset involved in securitization. Government securities (G-Secs): These are sovereign (credit risk-free) coupon bearing

instruments which are issued by the Reserve Bank of India on behalf of Government of India, in lieu of the Central Government's market borrowing programme. These securities have a fixed coupon that is paid on specific dates on half-yearly basis. These securities are available in wide range of maturity dates, from short date (less than one year) to long date (up to twenty years). Debentures: Bonds issued by a company bearing a fixed rate of interest usually payable half

yearly on specific dates and principal amount repayable on particular date on redemption of the debentures. Debentures are normally secured/ charged against the asset of the company in favor of debenture holder. Bond: A negotiable certificate evidencing indebtedness. It is normally unsecured. A debt security

is generally issued by a company, municipality or government agency. A bond investor lends

Financial modelling for portfolio selection and risk management money to the issuer and in exchange, the issuer promises to repay the loan amount on a specified maturity date. The issuer usually pays the bond holder periodic interest payments over the life of the loan. The various types of Bonds are as follows; 

Zero Coupon Bond: Bond issued at a discount and repaid at a face value. No periodic

interest is paid. The difference between the issue price and redemption price represents the return to the holder. The buyer of these bonds receives only one payment, at the maturity of the bond. 

Convertible Bond: A bond giving the investor the option to convert the bond into equity

at a fixed conversion price. Commercial Paper: A short term promise to repay a fixed amount that is placed on the market

either directly or through a specialized intermediary. It is usually issued by companies with a high credit standing in the form of a promissory note redeemable at par to the holder on maturity

and therefore, doesn’t require any guarantee. Commercial paper is a money market instrument issued normally for tenure of 90 days. Treasury Bills: Short-term (up to 91 days) bearer discount security issued by the Government

as a means of financing its cash requirements. Future of the capital market

In the liberalized economic environment, the capital market is all set to play a highly critical role in the process of economic development. The Indian capital market has to arrange funds to meet the financial needs of both domestic and foreign resources. What is more critical is that the changed environment is characterized by cutthroat competition. Ability of enterprises to mobilize funds at cheap cost will determine their competitiveness vis-à-vis their rivals.


CONCLUSION:

Over the last few years, there has been a rapid change in the Indian securities market especially in the secondary market. Advanced technology and online-based transactions have modernized the stock exchanges. In terms of the number of companies listed and total market capitalization, the Indian equity ma rket

is considered large relative to the country’s stage of economic

development. The debt market, however, is almost nonexistent in India even though there has been a large volume of Government bonds traded. Banks and financial institutions have been holding a substantial part of these bonds as statutory liquidity requirement. Securities market development has to be supported by overall macroeconomic and financial sector environments. If an investor has a clear understanding of the India financial market, then formulating investing strategies and tips would be easier. Unless stock markets provide professionalized service, small investors and foreign investors will not be interested in capital market operations. And capital market being one of the major source of long-term finance for industrial projects, India cannot afford to damage the capital market path. Further liberalization of interest rates, reduced fiscal deficits, fully market-based issuance of Government securities and a more competitive banking sector will help in the development of a sounder and a more e fficient capital market in India.


CHAPTER 3 COCHIN STOCK EXCHANGE LTDPROFILE


COCHIN STOCK EXCHANGE LTD. is one of the premier Stock Exchanges in India, established in the year 1978. The exchange had a humble beginning with just 5 companies listed in 1978 -79, and had only 14 members. Today the Exchange has more than 508 members and 240 listed companies. In 1980 the Exchange computerized its offices. In order to keep pace with the changing scenario in the capital market, CSE took various steps including trading in dematerialized shares. CSE introduced the facility for computerized trading - "Cochin Online Trading (COLT)" on March 17, 1997. CSE was one of the promoters of the "Interconnected Stock Exchange of India (ISE)". The objective was to consolidate the small, fragmented and less liquid markets into a national level integrated liquid market. With the enforcement of efficient margin system and surveillance, CSE has successfully prevented defaults. Introduction of fast track system made CSE the stock exchange with the shortest settlement cycle in the country at that time. By the dawn of the new century, the regional exchanges faced a serious challenge from the NSE & BSE. To face this challenge CSE promoted a 100% subsidiary called the "Cochin Stock Brokers Ltd. (CSBL)" and started trading in the National Stock Exchange (NSE) and Bombay Stock Exchange (BSE). CSBL is the first subsidiary of a stock exchange to get membership in both NSE & BSE. CSBL also became a depository participant in the Central Depository Services Ltd. The CSE has been playing a vital role in the economic development of the country in general, and Kerala in particular and striving hard to achieve the following goals: 

Providing investors with high level of liquidity whereby the cost and time involved in the entry into and exit from the market are minimized.



Bringing in high tech solutions and make all operations absolutely transparent.



Building infrastructure for capital market by turning CSE into a financial super market.



Serve the investors of the region.



Professional stock broking and investment management.



Imparting Capital Market knowledge to all intermediaries on a continuous basis

The Cochin Stock Exchange is directly under the control and supervision of Securities & Exchange Board of India (the SEBI), and is today a demutualized entity in accordance with the Cochin Stock Exchange (Demutualization) Scheme, 2005 approved and notified by SEBI on 29th of August 2005. Demutualization essentially means de-linking and separation of ownership and trading rights and restructuring the Board in accordance with the provisions of the

Financial modelling for portfolio selection and risk management scheme. The Exchange has been demutualised and the notification thereof published in the Gazette

MANAGEMENT OF CSE LTD

The policy decisions of the CSE are taken by the Board of Directors. The Board is constituted with 12 members of whom less than one-fourth are elected from amongst the trading member of CSE, another one fourth are Public Interest Directors selected by SEBI from the panel submitted by the Exchange and the remaining are Shareholder Directors. The Board appoints the Executive Director who functions as an ex-officio member of the Board and takes charge of the administration of the Exchange. Fig.No:3.1 Organisation Structure

Management - Board of Directors

The Exchange is professionally managed, under the overall direction of the Board of Directors.

The

Board consists of eminent

professionals from fields

such

as

judiciary,

administration and management, who are known as Public Representative Directors. The composition of the Board is such that 75% of the total strength of the Board consists of

Financial modelling for portfolio selection and risk management Public Representative Directors and Govt. And SEBI nominee Directors and the balance 25% are represented by the Brokers of the Exchange. DEPARTMENTS Legal:-

Guided by the Officer-Legal, the Legal Department is primarily responsible for advising the management of the merits and demerits of legal issues involving the Exchange. The department consistently monitors the compliance parameters in terms of the Companies Act, SEBI Act, Securities Contracts Regulation Act and other related statutes. Listing Guidelines and related criteria stipulated by SEBI, and the rules, regulations, directives and circulars issued by SEBI with regard to trading in the Capital Market are consistently scrutinized and necessary directions are given to the concerned departments to ensure strict and continued compliance. Relevant developments are brought to the notice of the members and the investing public. Officer-Legal is the Compliance Officer as per the provisions of SEBI regulations and also functions as Secretary to the Board of Directors. Other major activities undertaken by the department relate to Investor Grievance Service, Arbitration and Resolution of issues pertaining to declared defaulters.

Systems:-

The Systems Department is the heart of the various operations of CSE. The department provides the necessary technical support for screen based trading and the computerized functioning of all the other departments. The activities of the department include: 

Developments of software needed for the functions of the exchange.



Maintenance of Multex software, which enables online trading with NSE and BSE.



Maintenance of an effective network of computers for the smooth functioning of the exchange.



Providing the necessary services to the Settlement and Surveillance Depart ments.



The support for maintenance of depository participants’ accounts with the CSBL DP.

Membership:-

The Membership Department screens applications from prospective members to ensure that they are eligible to be members of the Exchange as per provisions of the Securities Contracts

Regulation Act. It is also verified whether they are ‘Fit and Proper’ persons eligible to be members as per the SEBI (Criteria for Fit and Proper persons) Regulation 2004. The eligible

Financial modelling for portfolio selection and risk management applications are processed and forwarded to SEBI for the purpose of obtaining registration with SEBI. The department continuously follows up the status of the applications with SEBI and provides necessary data if any required by SEBI. The members are informed of their fee liability as and when information in this regard is obtained from SEBI. The Membership Department also assists SEBI by ensuring proper delivery of notices and letters issued by SEBI to the concerned members. The changes in status and constitution of the Brokers are sent for approval to the Governing Board of the Exchange and thereafter to SEBI and Members are given necessary directions wherever required. Change in address and contact information are updated in the Finance and Accounting System and SEBI intimated. Settlement:-

Settlement Department is a key department of the Exchange, dealing with cash and securities. It assists the brokers in settling the matters related to their pay-in and payout, recovery of dues and settling issues related to bad deliveries. This department is headed by a Deputy Manager assisted by two Senior Officers who take care of the operations involved in the settlement activities in CSE. The Exchange follows the T+2 settlement system.

Listing:-

The Listing Department guides prospective companies desirous of being listed on the Exchange by providing the knowledge base and information on the statutory requirements that have to be complied with. The major functions undertaken by the department include post-listing monitoring and compliance with the listing agreement, monitoring the listing agreements and reviewing the provisions of listing agreement from time to time with specific reference to SEBI Regulations/Circulars that are in force. The department also ensures diligence in scrutinizing listing applications and adhering to the Listing Norms.

Compliance Monitoring is carried out with specific emphasis on the following clauses in the Listing Agreement. 

Clauses 15/16 - Short/non intimation of BC/RD



Clause 19 – Intimation of Board Meeting including advance notice wherever required



Clause 20- Outcome of Board Meeting



Clause 24 – In-principle approvals



Clause 31 – Annual Reports

Financial modelling for portfolio selection and risk management 

Clause 32 – Name Change, Cash Flow, Consolidated Financial Statement, Related Party Disclosures etc.



Clause 35 – Quarterly submission of Shareholding Pattern.



Clause 36 – Material Price sensitive Information



Clause 40 - Continuous Listing requirements



Clause 41 – Financial Results and Limited Review Reports



Clause 47 – Appointment of Compliance Officer The department also performs the processing of the documents submitted by companies

on new listings/additional listings and provides them with the listing approval/trading permission and also ensures that listing fee/processing fee is paid at the stipulated time. Marketing:-

The Marketing Department interacts with the brokers of the exchange trading both within the state and outside and collects their opinions and suggestions. These are brought to the notice of the Committee constituted for the purpose and decisions of the committee are placed for approval of the Governing Board of the Exchange .The efforts are aimed at improving the quality and efficiency of the service offered. In addition, the department conducts extensive surveys and campaigns in remote areas and where necessary organizes awareness programmes about capital markets. Experts with sufficient experience in the trade brief the participants and address their queries. Talk shows and interviews are conducted on television channels, clippings are displayed in theatres all with a view to increase public awareness and motivate their interest in the Capital Markets .The marketing wing also coordinates the off campus programmes of the CSE Institute and organizes regular classes at authorized centers after verifying the availability of suitable infrastructure and facilities. Finance:-

The Finance Department controls the financial transactions of the Exchange and is the life line of the organization. The department is headed by a Finance Officer. The activities of the department include:

Fund Management



Interaction with bankers



Maintaining general accounts of the Exchange



Preparation of various financial statements.



Maintaining payrolls and cash register.

Financial modelling for portfolio selection and risk management 

Coordinating accounting transactions of different branches and departments.



Taxation



Budgeting and Expense research.



Maintenance of internal control system.



Liaison with external and internal auditors



Annual Report Generation

Procedure for Acquiring Membership

Transactions pertaining to the Capital market can be carried out only through a broker or a sub-broker registered with SEBI. A Broker is a member of a recognized Stock Exchange permitted to trade on the Screen Based Trading System of different Exchanges. A Member has to be qualified for membership of a recognized Stock Exchange as per the provisions of Section 8 of the Securities Contracts Regulation Act. In addition eligibility as per the stipulations in the SEBI (Criteria for fit and proper persons) Regulation 2004 is also a pre-requisite. Trading Membership Selection Committee has been constituted by the Governing Board and entrusted with the specific responsibility of screening applications for admission to trading membership of the Exchange. Persons admitted as trading Members of Exchange are required to maintain the Base Minimum Capital as may specified by SEBI from time to time irrespective of whether they choose to exercise their right to trade or not. At present the Base Minimum Capital required to be maintained is Rs. 2 lakhs. In addition, annual subscription and contribution to the Investor Protection Fund has to be paid by Members. Individuals – Rs. 2,520/- and Corporates Rs. 6,120/- One time admission fee as may be prescribed by the Governing Board will also have to be remitted.

Investor Grievance Services at CSE Ltd

The Cochin Stock Exchange remains committed to the protection of investor interests. The complaints received from the investors are taken up with the companies/brokers concerned and wherever necessary with the enforcement authorities for redress. Resolution of complaints proceeds in two phases:1. At the preliminary stage when the Exchange receives a complaint, the concerned

broker/company is requested to settle the same. A copy of the complaint is sent to the concerned broker/company. 2. If the issue is still not resolved, it is referred to the Grievance Committee constituted by

the Exchange. Notice is issued to both parties. Opportunity to adduce evidence and privilege of


detailed and fair hearing is given to the parties’ .After weighing the evidence/documen ts on record and taking into consideration the arguments raised, a decision is given on merits which are communicated to the parties. If the concerned broker/company does not comply with the decision, the matter is referred to the Board Of Directors which initiates necessary action to ensure compliance. Complaints again st D efaul ter s: -

All claims and complaints against a trading member who is declared a defaulter is dealt with by the Committee for Settlement of Claims against Defaulters. Tenable claims are adjudged on merits after verification of records and a report is submitted to the Board Of Directors for taking the final decision. It may however be noted that belated claims will not be entertained.

Claims against Defaulter by a Trading Member:-

Within such time of the declaration of a defaulter every trading member carrying on business on the Exchange shall, be required to compare with the Committee for Settlement of Claims Against Defaulters his accounts with the defaulter / deemed defaulter, as provided in the Rules and Procedure, or furnish a statement of such accounts with the defaulter / deemed defaulter in such form or form as the Committee for Settlement of Claims Against Defaulters may prescribe or render a certificate that he has no such account.

Claims against Defaulter by Investors/Clients:-

Within the time frame decided by the Executive Director, on the declaration of defaulter / deemed defaulter, every person who had a transaction / dealing with the defaulter / deemed defaulter in relation to and/ or in connection with the stock broking business, and has to recover any amount and / or securities, shall be required to lodge a claim in the prescribed form, together with supporting papers / proof as may be specifie d in the Notice published in the daily newspaper by the Exchange /Clearing Corporation.


CHAPTER 4 DATA ANALYSIS PART I


Security analysis:

Security analysis is the initial phase of the portfolio management process. This step consists of examining the risk return characteristics of invidual securities. For the purpose of analysis ten securities are selected and the return, risk and risk adjusted rate of return are determined.

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 8.1%


4.1:Return of the Securities

The Table No: 4.1 shows the corresponding returns of the securities and the graphical representation of the same is given below. TABLE No: 4.1 Showing the Return of Securities COMPANY RETURN(%) RANK AMBUJACEMENT 15.37 14 ASIANPAINTS 32.25 2 BHARATIAIRTEL 18.59 7 CIPLA 15.50 13 HCL 33.74 1 HDFC 23.27 6 HUL 17.53 10 ITC 15.70 11 LUPINLTD 26.79 5 M&M 18.59 8 MARUTHI 15.58 12 MINDTREE 29.25 4 ONGC 9.86 15 SUNTVLTD 17.20 9 YESBANK 32.23 3 Source: Computed from Secondary data. Fig.No:4.1 Showing Return of Securities

From the above table and chart it can be seen that the security HCL is giving maximum return of 33.74% and ONGC has minimum return of 9.86%.


4.2:Risk of the Securities

The Table No:4.2 shows the corresponding risk of the securities and the graphical representation of the same is given below. TABLE No: 4.2 Showing the Risk of Securities COMPANY AMBUJACEMENT ASIANPAINTS BHARATIAIRTEL CIPLA HCL HDFC HUL ITC LUPINLTD M&M MARUTHI MINDTREE ONGC SUNTVLTD

YESBANK Source: Computed from secondary data

RISK(%) 39.94 26.82 48.82 29.19 45.49 34.01 27.50 36.50 48.39 48.82 35.85 44.30 34.06 49.07

50.50

Fig No: 4.2 Showing Return of Securities

From the above table and chart it can be seen that the security YES BANK is having maximum risk of 50.50%)and ASIAN PAINTS is having minimum risk of 26.82(%)


BETA

The beta value indicates the measure of systematic risk of security. Beta describes the relationship between the stock return and market index return. Beta of security may be positive or negative. If beta is one, one percent change in the market index return causes exactly one percent changes in the stock return. It indicates that the stock moves in tandem with the market. If the portfolio is efficient, the beta measures the systematic risk efficiently.

N∑XY-∑X∑Y

βi

=

N

= Number of Observation =750

Y

= Current Stock Price – Yesterday’s Stock Price

N∑X2-(∑X) 2

Yesterday’s Stock Price X

×

= Current Market Index- Yesterday’s Market Index

Yesterday’s Market Index

×100

100


4.3:Beta of the securities. The Table No: 4.3 shows the beta of the securities. The graphical representation of the same is given below. TABLE No: 4.3 Showing the Beta of Securities COMPANY AMBUJACEMENT ASIANPAINTS BHARATIAIRTEL CIPLA HCL HDFC HUL ITC LUPINLTD M&M MARUTHI MINDTREE ONGC SUNTVLTD

∑Y

∑X

76.16 159.85 92.14 76.80 167.24 115.31 86.87 77.80 132.77 92.14 77.21 144.99 48.88 85.24 YESBANK 159.72 Source: Computed from secondary data.

36.06 36.06 36.06 36.06 36.06 36.06 36.06 36.06 36.06 36.06 36.06 36.06 36.06 36.06 36.06

∑X2

∑XY

(∑X)2

3527.56 3527.56 3527.56 3527.56 3527.56 3527.56 3527.56 3527.56 3527.56 3527.56 3527.56 3527.56 3527.56 3527.56 3527.56

2976.32 988.80 3755.48 1764.90 3618.89 3370.87 1480.64 1993.14 1564.20 3755.48 2559.31 1638.63 2814.77 2654.71 4671.52

1300.476 1300.476 1300.476 1300.476 1300.476 1300.476 1300.476 1300.476 1300.476 1300.476 1300.476 1300.476 1300.476 1300.476 1300.476

BETA(β) 0.84 0.28 1.06 0.50 1.02 0.95 0.42 0.56 0.44 1.06 0.73 0.46 0.80 0.75 1.32

Fig. No: 4.3 Showing Beta of Securities

From the above table and graph it can be seen that YES BANK has the maximum beta value, which means maximum sensitivity to market (1.32). The minimum sensitivity to market is for ASIAN PAINTS (0.28).


ALPHA

The alpha value indicates the extra return earn by the stock over and above the market return. Alpha measures the unsystematic risk of security. Return of stock = Alpha + (Beta ×Market Return per Year) R i

=

αi+ (βi×R m)

=

R i-( βi×R m)

So

Alpha (αi) Where,

αi

- Alpha of the security

R i

- return of the security

βi

- Beta of the security

R m

- Return of the market


4.4: Alpha of the securities. The Table No: 4.4 shows the alpha of the securities. The graphical representation of the same is given below. TABLE No: 4.4 Showing the Alpha of Securities COMPANY R i AMBUJACEMENT 15.37 ASIANPAINTS 32.25 BHARATIAIRTEL 18.59 CIPLA 15.50 HCL 33.74 HDFC 23.27 HUL 17.53 ITC 15.70 LUPINLTD 26.79 M&M 18.59 MARUTHI 15.58 MINDTREE 29.25 ONGC 9.86 SUNTVLTD 17.20 YESBANK 32.23

βI 0.84 0.28 1.06 0.50 1.02 0.95 0.42 0.56 0.44 1.06 0.73 0.46 0.80 0.75 1.32

R m 7.27 7.27 7.27 7.27 7.27 7.27 7.27 7.27 7.27 7.27 7.27 7.27 7.27 7.27 7.27

ALPHA(αi) 9.23 30.23 10.85 11.86 26.29 16.32 14.48 11.59 23.57 10.85 10.31 25.89 4.06 11.73 22.61

Fig No: 4.4 Showing Alpha of Securities

ASIAN PAINTS has the maximum Alpha 30.23 indicating that it has maximum extra return and ONGC has the minimum Alpha 4.06 which indicate its earning is below market return.


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 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 index model:

Systematic risk =β12*2 m 2 2* 2 Unsystematic risk =  -β  m 1


4.5: Systematic risk of the securities

The Table No: 4.5 shows the systematic risk of the securities. The graphical representation of the same is given below. TABLE No: 4.5 Showing the Systematic Risk of Securities

COMPANY βi2 σi2 AMBUJACEMENT 0.71 1595.54 ASIANPAINTS 0.08 719.11 BHARATIAIRTEL 1.13 2383.77 CIPLA 0.25 852.11 HCL 1.05 2069.39 HDFC 0.91 1156.39 HUL 0.18 755.99 ITC 0.32 1332.03 LUPINLTD 0.20 2341.89 M&M 1.13 2383.77 MARUTHI 0.53 1284.87 MINDTREE 0.21 1962.88 ONGC 0.64 1159.83 SUNTVLTD 0.57 2407.79 YESBANK 1.75 2550.71 Source: Computed from secondary data.

σm2 712.14 712.14 712.14 712.14 712.14 712.14 712.14 712.14 712.14 712.14 712.14 712.14 712.14 712.14 712.14

Systematic Risk(βi2 x σm2) 506.51 55.46 806.46 177.92 747.92 649.37 125.11 226.97 139.42 806.46 374.42 152.97 453.23 402.81 1247.17

Fig No: 4.5 Showing Systematic Risk of Securities

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 YESBANK has the maximum systematic risk 1247.17% and ASIANPAINTS has minimum systematic risk 55.46%.


4.6: Unsystematic risk of the securities The Table No: 4.6 shows the unsystematic risk of the securiti es. The graphical representation of the same is given below. TABLE No: 4.6 Showing the unsystematic Risk/residual variance of Securities

Unsystematic Risk(σei2)=σi2(βi2*σm2)

COMPANY βi2 σi2 σm2 AMBUJACEMENT 0.71 1595.54 712.14 ASIANPAINTS 0.08 719.11 712.14 BHARATIAIRTEL 1.13 2383.77 712.14 CIPLA 0.25 852.11 712.14 HCL 1.05 2069.39 712.14 HDFC 0.91 1156.39 712.14 HUL 0.18 755.99 712.14 ITC 0.32 1332.03 712.14 LUPINLTD 0.20 2341.89 712.14 M&M 1.13 2383.77 712.14 MARUTHI 0.53 1284.87 712.14 MINDTREE 0.21 1962.88 712.14 ONGC 0.64 1159.83 712.14 SUNTVLTD 0.57 2407.79 712.14 YESBANK 1.75 2550.71 712.14 Source: Computed from secondary data. Fig No: 4.6 Showing Unsystematic Risk/Residual Variance

1089.03 663.64 1577.30 674.19 1321.46 507.02 630.88 1105.07 2202.48 1577.30 910.45 1809.91 706.60 2004.98 1303.54

From the above table and chart shows LUPIN LTD has maximum residual variance or unsystematic risk 2202.48 and HDFC has minimum unsystematic risk 507.02.


CONSTRUCTION OF PORTFOLIO USING SHARPE’S MODEL

After the decomposing the risk of the securities it is required to construct the optimal portfolio. For the construction of optimal portfolio first the best stocks from the current 15 stocks need to be selected. This can be done by first ranking the stocks based on excess return to beta .Then a cut-off point is determined. This cut-off point is taken as the basis for selecting the stock. After That Sharpe’s optimization model is used to determine the weights for each security and hence the portfolio is formed.

4.7: Ranking of Securities The Table No: 4.7.1 shows the computation for ranking the securities by finding the excess return on beta.

TABLE: 4.7.1 Showing ranks of securities based on excess return to beta

Sl.No:

Security name

Mean return Ri

Rf

Excess return beta Ri-Rf

Beta

β

Excess return to beta Ri-Rf/βi

RANK

1 AMBUJACEMENT

15.37

8.1

7.2665427

0.84

8.650646071

14

2 ASIANPAINTS

32.25

8.1 24.15407754

0.28

86.26456264

1

3 BHARATIAIRTEL

18.59

8.1 10.49079027

1.06

9.896971952

13

4 CIPLA

15.50

8.1

7.39694599

0.5

14.79389198

8

5 HCL

33.74

8.1 25.64452304

1.02

25.14168925

4

6 HDFC

23.27

8.1 15.16633789

0.95

15.9645662

7

7 HUL

17.53

8.1

9.42763104

0.42

22.44674057

5

8 ITC

15.70

8.1 7.599091749

0.56

13.56980669

9

9 LUPINLTD

26.79

8.1 18.68898194

0.44

42.47495896

3

18.59 15.58 29.25 9.86 17.20

8.1 8.1 8.1 8.1 8.1

10.49079027 7.478317992 21.15469397 1.762090632 9.09950262

1.06 0.73 0.46 0.8 0.75

9.896971952 10.24427122 45.98846515 2.20261329 12.13267016

12 11 2 15 10

8.1 24.12741325

1.32

18.27834337

6

10 11 12 13 14

M&M MARUTHI MINDTREE ONGC SUNTVLTD

15 YESBANK 32.23 Source: Computed from secondary data.


Calculation of cut off point The Table No: 4.7.2 shows the calculation for finding the cut-off point.

TABLE: 4.7.2 Showing Calculation of cut off point Sl.No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

COMPANY ASIANPAINTS MINDTREE LUPINLTD HCL HUL YESBANK HDFC CIPLA ITC SUNTVLTD MARUTHI BHARATIAIRTEL M&M AMBUJACEMENT ONGC

σ²ei

Σ(RiRf)*βi/σ²ei Rf)*βi/σ²ei βi²/σ²ei (Ri-

719.11 1962.88 2341.89 2069.39 755.99 2550.71 1156.39 852.11 1332.03 2407.79 1284.87 2383.77 2383.77 1595.54 1159.83

0.009 0.005 0.004 0.013 0.005 0.012 0.012 0.004 0.003 0.003 0.004 0.005 0.005 0.004 0.001

0.009 0.014 0.018 0.031 0.036 0.048 0.061 0.065 0.068 0.071 0.075 0.080 0.085 0.088 0.090

Σβi²/σ²ei

0.000109024 0.000109024 0.000107801 0.000216825 8.26682E-05 0.000299494 0.000502757 0.000802251 0.000233336 0.001035587 0.000683104 0.001718691 0.000780447 0.002499138 0.000293391 0.002792529 0.00023543 0.003027958 0.000233617 0.003261575 0.000414751 0.003676327 0.000471355 0.004147682 0.000471355 0.004619037 0.000442232 0.005061269 0.000551806 0.005613075

Source:Computed from secondary data.

From the calculation shown in the table it can be seen that the cut off value is 15.55. 4.8.1: Optimal Portfolio The Table No: 4.8.1 shows the calculation for optimization model.

obtaining optimal portfolio by using Sharpe’s

TABLE: 4.8.1 Showing calculation of optimal portfolio

COMPANY σ²ei (Ri-Rf)/βi ASIANPAINTS 719.11 86.26 MINDTREE 1962.88 45.99 LUPINLTD 2341.89 42.47 HCL 2069.39 25.14 HUL 755.99 22.45 YESBANK 2550.71 18.28 HDFC 1156.39 15.96 Source: Computed from secondary data.

C* Zi 0.74 15.55 0.32 15.55 0.24 15.55 0.22 15.55 0.11 15.55 0.07 15.55 0.01 15.55

∑Zi 1.70 1.70 1.70 1.70 1.70 1.70 1.70

Xi 0.43 0.19 0.14 0.13 0.06 0.04 0.01

Ci 6.22 8.86 10.49 13.83 14.65 15.45 15.55 15.50 15.39 15.23 14.82 14.41 14.05 13.68 12.78


TABLE: 4.8.2 Showing optimal portfolio

Sl.No

COMPANY PROPOTION 1 ASIANPAINTS 0.43 2 MINDTREE 0.19 3 LUPINLTD 0.14 4 HCL 0.13 5 HUL 0.06 6 YESBANK 0.04 7 HDFC 0.01 Source: Computed from secondary data. 4.9:Return and Risk of optimal portfolio

In order to determine the effectiveness of optimization, the return and risk of the optimal portfolio are determined.

The Table No: 4.9.1 shows the calculation for obtaining the alpha of the portfolio. TABLE: 4.9.1 Shows portfolio alpha in optimal portfolio

COMPANY WEIGHT(ωI) ALPHA(αi) ASIANPAINTS 0.43 30.23 MINDTREE 0.19 25.89 LUPINLTD 0.14 23.57 HCL 0.13 26.29 HUL 0.06 14.48 YESBANK 0.04 22.61 HDFC 0.01 16.32 TOTAL 1.00 Source: Computed from secondary data.

n

Portfolio alpha = Σ ωiαi i=1 = 26.58

ALPHA*WEIGHT(αIωI) 13.1083261 4.804989058 3.389463848 3.321486146 0.896023331 0.946829668 0.111044348 26.58

Financial modelling for portfolio selection and risk management The Table No: 4.9.2 shows the calculation for obtaining the beta of the portfolio. For that weight of each stock is multiplied with its corresponding beta.

TABLE: 4.9.2 Shows portfolio beta in optimal portfolio

Sl.No

COMPANY ASIANPAINTS MINDTREE LUPINLTD HCL HUL YESBANK HDFC

WEIGHT(ωI)

1 2 3 4 5 6 7 TOTAL Source: Computed from secondary data.

BETA(βi)

0.43 0.19 0.14 0.13 0.06 0.04 0.01 1.00

BETA*WEIGHT(βiωI) 0.28 0.46 0.44 1.02 0.42 1.32 0.95

0.12 0.09 0.06 0.13 0.03 0.06 0.01 0.49

n

Portfolio Beta=Σ ωiβi =0.49 i=1

TABLE: 4.9.3 Shows portfolio residual variance in optimal portfolio

COMPANY WEIGHT(ωi) ASIANPAINTS 0.43 MINDTREE 0.19 LUPINLTD 0.14 HCL 0.13 HUL 0.06 YESBANK 0.04 HDFC 0.01 TOTAL 1.00 Source:Computed from secondary data.

RESIDUAL

ω

VARIANCE (σ²ei)

2 i

0.19 0.03 0.02 0.02 0.00 0.00 0.00

719.11 1962.88 2341.89 2069.39 755.99 2550.71 1156.39 26.58

ωi2 *σ²ei 135.25 67.64 48.42 33.02 2.89 4.47 0.05 291.76

Financial modelling for portfolio selection and risk management n

Portfolio residual variance=Σωi2σ2ei i=1 =291.76

MEASURING PORTFOLIO RETURN AND RISK PORTFOLIOS RETURN (R P)

PORTFOLIO RETURN= PORTFOLIOALPHA+(PORTFOLIOBETA×MARKET RETURN)

R P

=αP+ (βp×R m)

αP

= 26.58

βp

= 0.49

R m

=7.27

R P

= 26.58+(0.49 X 7.27) = 30.14

PORTFOLIO RISK (σ 2P) Portfolio risk (σ p) = β σ = 0.49 βp2 2

σ2m

= 712.14

Σωi2σ2ei

= 221.76

σ2p

= 462.74

σp

= 21.51

n

Σwi2σ2ei

2 2 p m+


TABLE: 4.9.4 Shows optimal portfolio Return, Risk, Alpha, Beta, Residual variance Portfolio

Return

Risk

Optimal

30.14

21.51

Alpha

Beta

Residual variance

0.49

291.76

26.54

Source: Computed from secondary data

The Table No: 4.9.4 illustrates the benefit that have been achieved due to di versification of the portfolio

Risk Class Systematic Risk Unsystematic Risk

TABLE: 4.9.5 Shows Benefit of Diversification Total for Benefit of securities Portfolio Diversification 8438.93 170.98 8267.95

3117.42 11556.35 Total Risk Source: Computed from secondary data

291.76 462.74

2825.66 11093.61

% of risk reduction 97.97

90.64 96.00


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 based on the proportion of investment in different securities for the three portfolios under consideration are: 1. Equal investment in each security 2. Investment in each security in proportion to the P/E multiple of each security. 3. Investment in each security in proportion to the risk adjusted rate of return of the security. The return and risk of these portfolios are determined for the purpose of evaluation of the performance of these portfolios


4.10:1st PORTFOLIO ( By giving equal weight to each security.)

First portfolio is constructed by giving equal weights to the six securities and then the portfolio alpha, portfolio beta and weighted residual variance are calculated to arrive at portfolio return and risk. The Table No: 4.10.1 shows the calculation for obtaining the portfolio alpha. Portfolio alpha can be obtained by multiplying weight of each security by its corresponding alpha. TABLE: 4.10.1 Shows portfolio alpha in equal weight COMPANY ASIANPAINTS

MINDTREE LUPINLTD HCL HUL YESBANK HDFC

WEIGHT(ωI) ALPHA(αi) ALPHA*WEIGHT(αIωI) 0.14

30.23

4.32

0.14 0.14 0.14 0.14 0.14 0.14

25.89 23.57 26.29 14.48 22.61 16.32

3.70 3.37 3.76 2.07 3.23 2.33

TOTAL 1.00 Source: Computed from secondary data n Portfolio alpha = Σ ωiαi i=1

22.77

=22.77 The Table No: 4.10.2 shows the calculation for obtaining the portfolio beta. Portfolio beta can be obtained by multiplying weight of each security by its corresponding alpha. TABLE: 4.10.2 Shows portfolio beta in equal weight COMPANY WEIGHT(ωI) ASIANPAINTS 0.14 MINDTREE 0.14 LUPINLTD 0.14 HCL 0.14 HUL 0.14 YESBANK 0.14 HDFC 0.14 TOTAL 1.00 Source: Computed from secondary data

BETA(βi) BETA*WEIGHT(βiωI) 0.28 0.46 0.44 1.02 0.42 1.32 0.95

0.04 0.07 0.06 0.15 0.06 0.19 0.14 0.70

Financial modelling for portfolio selection and risk management n

Portfolio Beta=Σ ωiβi =0.70 i=1 TABLE: 4.10.3 Shows portfolio residual variance in equal weight


WEIGHT(ωi) 0.14 0.14 0.14 0.14 0.14 0.14 0.14

ωi2 0.02 0.02 0.02 0.02 0.02 0.02 0.02

TOTAL 1.00 Source: Computed from secondary data

RESIDUAL VARIANCE (σ²ei) 719.11 1962.88 2341.89 2069.39 755.99 2550.71 1156.39 26.58

n

Portfolio residual variance=Σ ωi 2*σ 2ei i=1 =235.84

MEASURING PORTFOLIO RETURN AND RISK PORTFOLIOS RETURN (R P) Portfolio Return= Portfolio Alpha + (Portfolio Beta × Market return) R P

=αP+ (βp×R m)

Where,

αP

= 22.77

βp

= 0.70

R m

=7.27

R P

=22.77+ (0.70 x 7.27) = 27.85

ωi2 *σ²ei 14.68 40.06 47.79 42.23 15.43 52.06 23.60 235.84


PORTFOLIO RISK (σ P2) Portfolio risk (σ

n 2 2 2 2 p m+ i ei i=1

=β σ

2 p )

Σω σ

Where,

βp2

= 0.49

σ2m

= 712.14

Σωi2σ2ei

= 235.84

σ2p

= 583.37

σp

= 24.15

The Table No: 4.10.4 illustrates the benefit that have been achiev ed due to diversification of the portfolio TABLE: 4.10.4 Shows Benefit of diversification


Total for securities 8438.93

3117.42 11556.35 Total Risk Source: Computed from secondary data

Portfolio 347.53

235.84 583.37

Benefit of Diversification 8091.41

% of risk reduction 95.88

2881.58 10972.98

92.43 94.95


4.11:2nd PORTFOLIO (BASED ON PE Ratio)

Second portfolio is constructed on the basis on PE Ratio of the six securities and then the portfolio alpha, portfolio beta and weighted residual variance are calculated to arrive at portfolio return and risk The Table No: 4.11.1 shows the calculation of the weight based on the PE ratio of the securities. TABLE: 4.11.1 Shows the calculation of weight based on PE ratio

COMPANY ASIANPAINTS MINDTREE LUPINLTD HCL HUL YESBANK HDFC TOTAL

P/E RATIO

WEIGHT(ωI)

40.58 15.80 32.19 13.96 78.00 14.30 89.08 283.91

0.14 0.06 0.11 0.05 0.27 0.05 0.31 1.00

The Table No: 4.11.2 shows the calculation for obtaining the portfolio alpha. Portfolio alpha can be obtained by multiplying weight of each security by its corresponding alpha. TABLE: 4.11.2 SHOWS PORTFOLIO ALPHA COMPANY

ASIANPAINTS MINDTREE LUPINLTD HCL HUL YESBANK HDFC TOTAL

WEIGHT(ωI) ALPHA(αi) 0.14 0.06 0.11 0.05 0.27 0.05 0.31 1.00

Source: Computed from secondary data n Portfolio alpha =Σ ωiαi i=1 =19.96

30.23 25.89 23.57 26.29 14.48 22.61 16.32

ALPHA*WEIGHT(αIωI) 4.32 1.44 2.67 1.29 3.98 1.14 5.12 19.96


The Table No: 4.11.3 shows the calculation for obtaining the portfolio beta. Portfolio beta can be obtained by multiplying weight of each security by its corresponding beta.

TABLE: 4.11.3 SHOWS PORTFOLIO BETA COMPANY ASIANPAINTS MINDTREE LUPINLTD HCL HUL YESBANK HDFC

WEIGHT(ωI) BETA(βi)

0.14 0.06 0.11 0.05 0.27 0.05 0.31 TOTAL 1.00 Source: Computed from secondary data

BETA*WEIGHT(βiωI)

0.28 0.46 0.44 1.02 0.42 1.32 0.95

0.04 0.03 0.05 0.05 0.12 0.07 0.30 0.65

n

Portfolio Beta = Σ ωiβi = 0.65 i=1

TABLE: 4.11.4 SHOWS PORTFOLIO RESIDUAL VARIANCE


WEIGHT(ωi)

ωi2

0.14 0.06 0.11 0.05 0.27 0.05 0.31

0.02 0.00 0.01 0.00 0.08 0.00 0.10

TOTAL 1.00 Source: Computed from secondary data n

Portfolio residual variance=Σ ωi2σ2ei i=1 =233.25

RESIDUAL VARIANCE (σ²ei) 719.11 1962.88 2341.89 2069.39 755.99 2550.71 1156.39 26.58

ωi2 *σ²ei 14.69 6.08 30.11 5.00 57.06 6.47 113.84 233.25


MEASURING PORTFOLIO RETURN AND RISK PORTFOLIO RETURN (R P)

PORTFOLIO RETURN RETURN)

= PORTFOLIO ALPHA + (PORTFOLIO BETA×MARKET

R P

=αP+ (βp×R m)

αP

= 19.96

βp

= 0.65

R m

=7.27

R P

= 19.96+ (0.65*7.27) = 24.65

PORTFOLIO RISK (σ 2P) Portfolio risk (σ

2

p)

n 2 2 2 2 p m+ i ei i=1

=β σ

βp2

= 0.42

σm2

= 712.14

Σwi2σ2ei

= 233.25

σ2p

= 530.1

σp

= 23.02

Σω σ

The Table No: illustrates the benefit that have been achieved due to diversification of the portfolio TABLE: 4.11.5 Benefit of diversification


Total for securities 8438.93 3117.42

11556.35 Total Risk Source: Computed from secondary data

Portfolio 296.83 233.25 530.08

Benefit of Diversification 8142.10 2884.17

% of risk reduction 96.48 92.52

11026.27

95.41


4.12:3rd PORTFOLIO BASED ON RISK ADJUSTED RATE OF RETURN)

Third portfolio is constructed on the basis on Risk Adjusted Rate of Return of the six 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. The Table No: 4.12.1 shows the calculation of the weight based on risk adjusted rate of return.

TABLE: 4.12.1 Shows calculation of weight based on risk adjusted rate of return

RETURN COMPANY (Ri) σ²ei ASIANPAINTS 719.11 32.25 MINDTREE 1962.88 29.25 LUPINLTD 2341.89 26.79 HCL 2069.39 33.74 HUL 755.99 17.53 YESBANK 2550.71 32.23 HDFC 1156.39 23.27 TOTAL Source: Computed from secondary data

Rf 8.10 8.10 8.10 8.10 8.10 8.10 8.10

(Ri-Rf)/σ 0.90 0.48 0.39 0.56 0.34 0.48 0.45 3.59

WEIGHT(ωI) 0.25 0.13 0.11 0.16 0.10 0.13 0.12

The Table No: 4.12.2 shows the calculation for obtaining the portfolio alpha. Portfolio alpha can be obtained by multiplying weight of each security by its corresponding alpha. TABLE: 4.12.2 Shows portfolio alpha in risk adjusted rate of return COMPANY ASIANPAINTS MINDTREE LUPINLTD HCL HUL YESBANK HDFC TOTAL

WEIGHT(ωI) 0.25 0.13 0.11 0.16 0.10 0.13 0.12 1.00

ALPHA(αi) ALPHA*WEIGHT(αIωI) 30.23 25.89 23.57 26.29 14.48 22.61 16.32

7.57 3.44 2.53 4.12 1.38 3.00 2.03 24.08


n Portfolio alpha =Σ ωiαi i=1

=24.08 The Table No: 4.12.3 shows the calculation for obtaining the portfolio beta. Portfolio beta can be obtained by multiplying weight of each security by its corresponding beta.

TABLE: 4.12.3 Shows portfolio beta in risk adjusted rate of return COMPANY ASIANPAINTS MINDTREE LUPINLTD HCL HUL YESBANK HDFC

WEIGHT(ωI)

BETA(βi) BETA*WEIGHT(βiωI)

0.25 0.13 0.11 0.16 0.10 0.13 0.12

0.28 0.46 0.44 1.02 0.42 1.32 0.95

0.07 0.06 0.05 0.16 0.04 0.18 0.12

TOTAL 1.00 Source: Computed from secondary data

n

Portfolio Beta= Σ i=1

0.67

wiβi =0.67

TABLE: 4.12.4 Shows portfolio residual variance in risk adjusted rate of return

COMPANY WEIGHT(ωi) ωi2 ASIANPAINTS 0.25 0.06 MINDTREE 0.13 0.02 LUPINLTD 0.11 0.01 HCL 0.16 0.02 HUL 0.10 0.01 YESBANK 0.13 0.02 HDFC 0.12 0.02 TOTAL 1.00 Source: Computed from secondary data

RESIDUAL VARIANCE

(σ²ei)

719.11 1962.88 2341.89 2069.39 755.99 2550.71 1156.39 26.58

ωi2 *σ²ei 45.15 34.63 27.03 50.89 6.88 45.05 17.80 227.43


n

Portfolio residual variance=Σ i=1

ωi 2 σ 2ei = 227.43

MEASURING PORTFOLIO RETURN AND RISK PORTFOLIOS RETURN (R P)

Portfolio Return

= Portfolio Alpha + (Portfolio Beta×Market Return)

R P

=αP+ (βp×R m)

αP

= 24.08

βp

= 0.67

R m

=7.27

R P

= 24.08+ (0.67*7.27) =28.96

PORTFOLIO RISK (σ P2) Portfolio risk (σ

2 p )

=β σ

2 2 p m+

n

Σ ω i2 σei2 i=1

βp2

= 0.45

σ 2m

= 712.14

Σ ωi2 σ2ei

= 204.74

σ 2p

= 548.87

σp

=23.43


The Table No: 4.12.5 illustrates the benefit that have been achiev ed due to diversification of the portfolio

TABLE: 4.12.5 Benefit of diversification Total for Risk Class securities 8438.93 Systematic Risk 3117.42 Unsystematic Risk 11556.35 Total Risk Source: Computed from secondary data

Portfolio 321.44 227.43 548.87

Benefit of Diversification 8117.50 2889.99 11007.49

% of risk reduction 96.19 92.70 95.25


4.13: 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 TREYNEOR ratio. The following three different evaluation processes is used .

  

SHARPE RATIO TREYNOR RATIO JENSEN MEASURE

4.13.1: SHARPE RATIO:

Sharpe Ratio (SR )

= R p – Rf

σP Where, R p

= is the realized return on the portfolio

R f

= is the risk free rate of return

σP

= is the standard deviation of portfolio return


The Table No 4.13.1 shows the calculation for obtaining the Sharpe ratio of the portfolios. TABLE: 4.13.1 Shows Sharpe Ratio of the portfolios PORTFOLIO Rp(%) Rf(%) OPTIMAL 30.14 8.10 1 27.85 8.10 2 24.66 8.10 3 28.96 8.10 Source: Computed from secondary data

σpi(%) 21.51 24.15 23.02 23.43

(Rp-Rf)/σp 1.02 0.82 0.72 0.89

Fig No: 4.13.1 Shows the Sharpe ratio of different portfolios

Optimal portfolio has highest Sharpe ratio (1.02) and PE ratio portfolio has lowest Sharpe ratio (0.72).


4.12.2: 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. Treynor Ratio

=

R p-R f

βp Where, R p

=Return of the portfolio

R f

=Risk free rate return

β p

=Standard deviation of portfolio

The Table No 4.13.2 shows the calculation for ob taining the Treynor’s ratio of the portfolios. TABLE: 4.13.2 Shows Treynor ratio of the portfolio

PORTFOLIO Rp(%) OPTIMAL 30.14 1 27.85 2 24.66 3 28.96 Source: Computed from secondary data

Rf(%) 8.10 8.10 8.10 8.10

βp

(Rp-

Rf)/βp

0.49 0.70 0.65 0.67

45.29 28.27 25.65 31.14

Fig No: 4.12.2 Shows the Treynor ratio of different portfolios

Optimal portfolio has highest Treynor ratio (45.29) and PE ratio portfolio has lowest Treynor ratio (25.65).


4.13.3: JENSEN’S MEASURE

In finance, Jensen's alpha is used to determine the excess return of a stock, other security, or portfolio over the security's required rate of return as determined by the Capital Asset Pricing Model. This model is used to adjust for the level of beta risk, so that riskier securities are expected to have higher returns. The measure was first used in the evaluation of mutual fund managers by Michael Jensen in the 1970's. It is mentioned as a measure of absolute performance because a definite standard is set and against that the performance is measured.

Where, Rp = Average return of portfolio R f = Riskless rate of interest

βp= Portfolio beta

R m= Average market return


The Table No: 4.13.3

shows the calculation for obtaining the Jensen’s measure of the portfolios.

The graphical representation of the same is given below. TABLE: 4.13.3 Shows Jensen measure of the portfolio

E(Rp)= PORTFOLIO Rp(%) Rf(%) OPTIMAL 30.14 8.10 1 27.85 8.10 2 24.66 8.10 3 28.96 8.10 Source: Computed from secondary data

Rf+βp(Rm-

Βp 0.49 0.70 0.65 0.67

Rm(%) 7.27 7.27 7.27 7.27

Rf)

7.70 7.52 7.56 7.54

RpE(Rp) 22.45 20.33 17.09 21.42

Fig No: 4.13.3

Optimal portfolio has highest Jensen alpha ( 22.45) and PE ratio portfolio has lowest Jensen alpha (17.09)


4.14: V VALUE A AT R R ISK

Every type of business involves some extent of risk. Risk can be minimized but can not be eliminated. The only way to totally eliminate the risk is by stopping the business itself .in the 1990 VaR concepts become more popular. It is latest concept in the field of risk management. VAR is a method of assessing risk using standard statistical techniques. Formally, it is the maximum loss over a target horizon such that there is a low, predetermined probability that the actual loss will be larger. VAR has a scientific basis and provides users with summary measure of market risk

METHODS FOR CALCULATING VaR

Various methods are possible to compute Value At Risk .these methods basically differ in terms of: 

Distributional assumptions for the risk factors (normal versus other distributions )



Linear vs Full valuation , where the former approximates the exposure to risk factors by a linear mode

Some important methods for measuring VaR are: 1. Monte Carlo Method 2. Variance Covariance Method 3. Historical Simulation Method


4.14.1:MONTE C CAR LO S 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 steps are involved in Monte Carlo simulation. 1. the data is collected on the movements of each securities for the past 500days before 1 st April 2013. 2. the daily returns of each security securit y for this 500days is calculated 3. This provides us 500 alternative scenarios for what can happen between today (1 st April 2013) and tomorrow. 4. the closing price of each security for each scenario

is then calculated by using the

formula Vp= V op(1+r) Simulated price = closing price × (1+(r/100)) r

=return of each day

5. the value of the portfolio and change in value of the portfolio is then determined for each scenario and then arranged in ascending order 6. the estimate of VaR is the portfolio loss at 1 st percentile point (5th item ) for 99% confidence level and 5th percentile point (25 th item) for 95% confidence level

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 today (31 st march 2008). 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


Here initial amount taken is Rs.7000000.The Table No shows the value of the portfolio on 1 st April 2013 for the Monte Carlo simulation.

TABLE: 4.14.1.1

Showing Portfolio Value on 1 st April 2013 (Today) For the Monte Carlo simulation

Closing Price 174.25 904.30 631.10 788.50 471.35 432.30 623.85

COMPANY ωi ASIANPAINTS 0.43 MINDTREE 0.19 LUPINLTD 0.14 HCL 0.13 HUL 0.06 YESBANK 0.04 HDFC 0.01 TOTAL 1.00 Source: Computed from secondary data

Total Value 3035833.92 3035833.92 1299396.33 1006541.62 884264.03 433153.95 293191.21 47618.95 7000000.00

No: of Shares 17422.29 1436.91 1594.90 1121.45 918.96 678.21 76.33

Actual No: 17422.00 1437.00 1595.00 1121.00 919.00 678.00 76.00

Actual Value 3035783.50 1299479.10 1006604.50 883908.50 433170.65 293099.40 47412.60 6999458.25


The Table No 4.14.1.2 shows possible values of portfolio sorted in ascending order. From here we get VAR at 99% and 95% confidence level. TABLE: 4.14.1.2 Showing Changes in Total Value of Portfolio (sorted in ascending order). Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Portfolio 7104535.15 7104535. 15 7007990.43 7023208.27 7023208. 27 6964696.47 7032340.33 7053401.26 7053401. 26 7096244.09 7096244. 09 6933708.56 7063724.04 7063724. 04 7000630.03 7065147.3 7061278.1 7085987.24 7085987.24 7060857.77 6892250.87 7089498.86 7089498.86 7010892.88 7010892.88 7083021.82 7083021.82 6937416.36 7010557.9 6983163.28 6984084.42 6934340.52 7078443.42 7078443.42 6888207.84 7116990.29 6907362.93 6994994.46 7076745.58 7076745.58 6997460.86 7193596.6 7084282.08 7084282.08 6923717.06 7176085.07 6937661.14 6944139.17

Change in value 105076.9 8532.18 23750.02 -34761.78 32882.08 53943.01 96785.84 -65749.69 64265.79 1171.78 65689.05 61819.85 86528.99 61399.52 -107207.38 90040.61 11434.63 83563.57 -62041.89 11099.65 -16294.97 -15373.83 -65117.73 78985.17 -111250.41 117532.04 -92095.32 -4463.79 77287.33 -1997.39 194138.35 84823.83 -75741.19 176626.82 -61797.11 -55319.08


Value at risk -344389.44 -220221.61 -212887.14 -208741.57 -191274.86 -186838.82 -183370.59 -181937.14 -180199.11 -168804.28 -151046.86 -147821.96 -147565.37 -145795.8 -145175.34 -142423.07 -142356.96 -140817.87 -138025.75 -135355.82 -133757.55 -126985.56 -126778.15 -124133.04 -123742.83 -123135.48 -121446.22 -120378.58 -119874.81 -119802.56 -118653.96 -116866.12 -116728.77 -116492.93 -115205.76 -115101.11

At 99% confidence level

At 95% confidence level


From the above table it is clear that:Value at Risk At 99% of confidence level =191274.86

At 99% confidence level the maximum daily loss or gain of the portfolio will be Rs 191274.86.; that is portfolio value will lie between 6808183.39 and 7190733.11 Value at Risk at 95% of confidence level =123742.83

At 95% confidence level the maximum daily loss or gain of the portfolio will be Rs. 123742.83; that is portfolio value will be lie between Rs. 6875715.42 and Rs.7123201.08


4.14.2: B BACK TESTING

In back testing risk management teams examines the performance of their VaR estimates of extreme losses with respect to realized losses. That is back testing allows the risk manager to determine whether the VaR methods employed are adequate. While in back testing, the risk manager must be aware that there will be periods in which actual losses will exceed those predicted by VaR. For example, the risk manager must realize that statistically, actual losses will exceed a 5% of VaR, 5% of the time. Here the VaR through Monte Carlo simulation method, from that Value at Risk At 99% of confidence level = -Rs.1817415.70

and Value at Risk at 95% of confidence

level=Rs.1336210.65 was found. For back testing past 250 days of data selected from before 1st April 2013 The detailed calculation for the change in the value of the portfolio for 250 days are shown in a separate table in Appendix no.4


The Table No: 4.14.2.1 shows values of portfolio sorted in ascending order. From here we get Back testing values in 99% and 95% confidence level. TABLE: 4.14.2.1

Showing Change in Total Value of the Portfolio (Sorted In Ascending Order) in Back Testing Sl.No

Change 1 -4251543.8 2 -2024189.35 3 -1817415.7 99% Confidence Interval 4 -1688437.1 5 -1633201.25 6 -1574157.1 7 -1568466.5 8 -1525137.4 9 -1461409.85 10 -1445007.35 11 -1391928.4 12 -1370060.35 13 -1336210.65 95% Confidence Interval 14 -1327271.15 15 -1257758.45 16 -1240362.85 17 -1219338.6 18 -1195918.95 19 -1190387.75 20 -1150599.2 21 -1121047.6 22 -1114543.8 23 -1104266.3 24 -1092375.1 25 -1006020.55 26 -981703.85 27 -980731.9 28 -900990.6 29 -875899.55 30 -849582.45 31 -795150.15 32 -788465.15 33 -770526.4 34 -767259.2 35 -767245.4 Source: Computed from secondary data


4.14.3:Variance-Covariance Model

The Table No: 4.13.3.1 shows the variance covariance matrix. From this matrix VAR can be calculated. TABLE: 4.14.3.1 Shows Variance co-variance matrix COMPANY

ASIANPAINTS

MINDTREE

LUPINLTD

1040.33

96.94

191.00

190.13

85.67

391.59

201.86

MINDTREE

96.94

855.84

169.97

565.40

133.72

442.61

272.62

LUPINLTD

191.00

169.97

717.65

362.02

145.96

485.67

312.89

HCL

190.13

565.40

362.02

1138.69

314.69

1016.64

677.08

HUL

85.67

133.72

145.96

314.69

307.22

755.38

277.02

YESBANK

391.59

442.61

485.67

1016.64

755.38

1038.61

960.40

HDFC

201.86

272.62

312.89

677.08

277.02

960.40

541.32

HCL

HUL

YESBANK

HDFC

ASIANPAINTS

HCL

HUL

YESBANK

HDFC

TABLE: 4.14.3.2 COMPANY

ASIANPAINTS

MINDTREE

LUPINLTD

0.14

0.06

0.11

Portfolio Weight(P/E)

0.05

0.27


Variance per year

=

0.0359

Standard deviation per year

=

0.1875

Standard deviation per day

=

0.01875(standard deviation per day/√250)

Daily volatility

=

0.01875

Value of portfolio

=

Rs.6999458.25

Value at Risk at 5% significant level.

VaR

=

Value of portfolio*1.65*σp

=

6999458.25 x 1.65 x 0.01875

= Rs.216545.70 At 5% significant level the maximum daily loss or gain of the portfolio will be Rs.216545.70 , that is portfolio value will lie between Rs. 6782912.51 and Rs.7216003.99.

0.05

0.31


Value at Risk at 25% significant level.

VaR

=

Value of portfolio*2.33*σ p

=

6999458.25 x 2.33 x 0.01875

= Rs.305788.83 At 25 % significant level the maximum daily loss or gain of the portfolio will be Rs.305788.83, that is portfolio value will lie between Rs. 6693669.418 and Rs. 7305247.08. .


CHAPTER 5 DATA ANALYSIS PART II


5.1: Gender of the respondents.

The Table No: 5.1 shows the gender of the respondents. The percentage analysis of the same is given below. TABLE: 5.1 Gender Male 26 Female 4 Total

30

Source: Primary Data

Fig No: 5.1

Majority of the respondents are male. Male respondents constitute 87%.


5.2: Age group of the respondents.

The Table No: 5.2 shows the age group of the respondents. The percentage analysis of the same is given below. TABLE: 5.2 Age Group Below 25 25-30 35-45 45-55 55 & Above

3 5 10 9 3

Total

30


Fig No: 5.2

Majority of the respondents are in the age group 35-55 i.e. about 63%.


5.3: Qualification of the respondents.

The Table No: 5.3 shows the qualification of the respondents. The percentage analysis of the same is given below. TABLE: 5.3 Qualification Graduate 8 Post graduate 10 Professional 12 Total 30


Fig No: 5.3

About 40% of the respondents have professional qualification, 33% are post graduates And the rest are graduates.


5.4: Occupation of the respondents.

The Table No: 5.4 shows the occupation of the respondents. The percentage analysis of the same is given below. TABLE: 5.4 Occupation Entrepreneurs Business Professional Others Total

2 6 14 8 30


Fig No: 5.4

About 46% of the respondents are professionals and 27% of the respondents are doing business.


5.5: Annual Income of the respondents.

The Table No: 5.5 shows the income range of the respondents. The percentage analysis of the same is given below. TABLE: 5.5 Annual Income Below 2 lakh 2-5 lakhs 5-10 lakhs Above 10 lakhs

2 8 16 4

Total

30


Fig No: 5.5

About 53% of the respondents are in the income range 5-10 lakhs,27% in the range 2-5 lakhs 13% in the range above 10 lakhs and the rest are below 2 lakhs range.


5.6:Investment experience of the respondents.

The Table No: 5.6 shows the investment experience of the respondents. The percentage analysis of the same is given below. TABLE: 5.6 Investment Experience Less than 1 2-5 years 5-10 years Above 10 years Total

2 6 15 7 30


Fig No: 5.6

About 50% of have investment experience of 5-10 years,23% in the range above 10 years range 20% in the range above 2-5 years and the rest are below 1 year range.


5.7: Investment preference of the respondents.

The Table No: 5.7 shows the investment preference of the respondents. The percentage analysis of the same is given below. TABLE: 5.7 Type of Investment Stock Bond Gold ETF Bank Deposit Mutual Fund Life Insurance Real Estate

Frequency

Total

25 5 24 3 26 5 16 8

30 30 30 30 30 30 30 30


Fig No: 5.7

From the above data it is clear that respondents are more interested in investing in stock gold and in bank deposits


5.8: Sector preference of the respondents while investing.

The Table No: 5.9 shows the sector preference of the respondents. The percentage analysis of the same is given below. TABLE: 5.8 Sector Government Private Foreign Diversify

5 4 2 19

Total

30


Fig No: 5.8

Majority of the respondents are interested to diversify their investment rather than putting their money in a single sector.


5.9:Type of analysis used by the respondents for investing.

The Table No: 5.10 shows the types of analysis used by the respondents. The percentage analysis of the same is given below. TABLE: 5.9 Type of Analysis Fundamental Technical

8 12

Both

9

None

1

Total

30


Fig No: 5.9

About 40 % of the respondents use technical analysis,27% use fundemental analysis and 30% use both.


5.10:Investment objective of the respondents.

The Table No: shows the investment objective of the respondents. The percentage anal ysis of the same is given below. TABLE: 5.10 Investment Objective Income & Capital Preservation Long-term growth Short term growth Safety Liquidity

10 7 6 4 3

Total

30


Fig No: 5.10

About 34 % of the respondent’s objective is Income & Capital Preservation,23 % of the respondents objective is long-term growth,20% of respondents aim short-term growth,13% aims at the saftey of their investment and rest 10% aims at short-term growth.


5.11: Preferred rate of growth of investment by the respondents The Table No: preferred rate of growth of investments by the respondents. The percentage analysis of the same is given below. TABLE: 5.11 Preferred Investment Growth Steadily

10

Average Rate Fast

16 4

Total

30

Source: Primary Data Fig No: 5.11

About 53 % of the respondents preferres investment to grow at an average rate,34% at a steady rate and the rest at a fast rate.


5.12: Percentage of investment in stock market securities by the respondents The Table No: 5.13 percentage of investments in stock market securitie s by the respondents. The percentage analysis of the same is given below. TABLE: 5.12 Investment in Stock Market Securities 0-15% 15-30% 30-50% More than 50% Total

13 14 2 1 30


Fig No: 5.12

About 47% of the respondents is investing about 15-30% in stock market securities,43% in 0-15% investment range,7% in 30-50% range and rest 3% in more than 50% range.


5.13:Whether the respondents have a financial advisor or not. The Table No: 5.14 percentage of respondents having financial advisor.The percentage analysis of the same is given below. TABLE: 5.13 Whether there is Financial Advisor Yes No

7 23

Total

30


Fig No: 5.13

About 77% of the respondents does not have a financial advisor and the rest 23% has financial advisor.


5.14:Level of Knowledge of the respondents in Portfolio Management The Table No: 5.15 level of knowledge of the respondents in portfolio management. The percentage analysis of the same is given below. TABLE: 5.14 Knowledge in Portfolio Management Expert 5 High 10 Moderate 8 Basic 6 No 1 Total 30


Fig No: 5.14

About 33% has high level of knowledge,27% Moderate,17% expert,20% basic and 3% no knwoledge.


5.15: Technique used by the respondents to balance risk and return. The Table No: 5.16 technique used by the respondents to balance risk and return. The percentage analysis of the same is given below. TABLE: 5.15 Balance Risk/Return Portfolio Optimization Portfolio Diversification Both Total

8 7 15 30


Fig No: 5.15

About 50% respondents use both portfolio diversification and optimization,27% uses portfolio diversification and rest uses portfolio optimisation


5.16: Technique used by the respondents for portfolio diversification The Table No: 5.16 technique used by the respondents for portfolio diversification. The percentage analysis of the same is given below. TABLE: 5.16 Technique Used For Portfolio diversification Investing in different Securities 23 Including more securities to portfolio 7 Total 30


Fig No: 5.16

About 77% respondents diversifies by investing in different securities and the rest by Including more securities to portfolio.


5.17: Familiarity of the respondents with Financial modeling. The Table No: 5.17 the familiarity of the respondents with financial modeling techniques. The percentage analysis of the same is given below. TABLE: 5.17 Familiarity with Financial Modelling Yes No Total

Frequency 9 21 30


Fig.No:5.17

About 70% respondents are not familiar with financial modelling techniques.


5.18: Portfolio evaluation techniques used by respondents.

The Table No: 5.18 the familiarity of the respondents with financial modeling techniques. The percentage analysis of the same is given below. TABLE: 5.18 Technique Used for evaluation of Portfolio Sharpe 25 30 Treynor 22 30 Jenson 20 30 Information

5

30


Fig No: 5.18

From the above data it is clear that Sharpe ,Teynor ratios are the most used for portfolio evaluation.


5.19: Awareness of VAR Concepts among the respondents. The Table No: 5.19 shows the awareness of VAR concepts among the respondents. The percentage analysis of the same is given below. TABLE:5.19 Awareness of VAR Concepts Yes No Total


Fig No:5.19

Only 40% of the respondents are aware of VAR Concepts.

12 18 30


5.20: Methods for measuring VAR used by the respondents

The Table No: 5.20 shows the techniques used by respondents to measure VAR. The percentage analysis of the same is given below. TABLE: 5.20 Method used for measuring VAR Monte-Carlo Simulation Historical Simulation Backtest Others Source: Primary Data

6 5 4 2

30 30 30 30

Fig No: 5.20

From the above data it is clear that Monte-Carlo Simulation and Historical Simulation are the two most used techiques by the respondents to measur VAR.


5.21: Qualification of the investors and their awareness towards Financial modeling techniques

Table No:5.21 shows the qualification of the investors and their level of awareness towards Financial Modeling Techniques.

TABLE NO:5.21

Qualification Graduate Postgraduate Professional Awareness Yes No Total

Total

0

0

9

9

8

10

3

21

8

10

12

30

Ho : There is no relation between the qualification of the investors and their level of awareness towards Financial Modelling techniques.

H1 : There is no relation between the qualification of the investors and their level of awareness towards Financial Modelling techniques.

TABLE NO:5.23 Chi-Square Tests

Value

Asymp. Sig. (2-sided)

df

19.286a

2

.000

Likelihood Ratio

23.156

2

.000

Linear-by-Linear Association

14.386

1

.000

N of Valid Cases

30

Pearson Chi-Square

Since the table value is greater than the computed value. Ho is rejected,ie; there is a relation Between the qualification of the investors and their level of awareness towards the Financial Modelling techniques.


CHAPTER 6 FINDINGS, SUGGESTIONS AND CONCLUSION


6.1:FINDINGS SECUR ITY A ANALYSIS Return of Securities: 

HCL has the maximum return (33.74%) ONGC has the minimum return

(9.86%) Beta Value of the Securities: 

YES BANK has the maximum beta value, which means maximum sensitivity to

market (1.32). The minimum sensitivity to market is for ASIAN PAINTS (0.28).

Alpha Value of the Securities: 

ASIAN PAINTS has the maximum Alpha (30.23) indicating that it has

maximum extra return and ONGC has the minimum Alpha (4.06) which indicate its earning is below market return Risk of Securities:

i.

Systematic Risk Of Securities: 

YES BANK has the maximum systematic risk (1247.17%) and ASIAN PAINTS

has minimum systematic risk (55.46 %) ii.

Unsystematic Risk of Securities: 

LUPIN LTD has maximum residual variance or unsystematic risk (2202.48) and HDFC has minimum unsystematic risk (507.02)

ii.

Risk Of Securities: 

YES BANK has maximum risk (50.50 %) and ASIANPAINTS has minimum

risk (26.82%) PORTFOLIO ANALYSIS 

Portfolio return:

The return of optimal portfolio is highest with return (28.96%) and the return of 2 nd portfolio based on PE ratio has the least return of (24.65) 

Portfolio risk:

The risk of equal weight portfolio is highest with risk (24.15) and the risk of 2nd portfolio based on PE ratio has the least risk (23.02)


Portfolio evaluation:

The portfolio is tested for optimality by comparing its performance against the four other portfolios

using Sharpe’s ratio, Treynor ratio and Jensen ratio Tangency. In all cases except the

performance of the optimal portfolio is found to be superior

VALUE AT RISK: Monte Carlo simulation:

Value at Risk At 99% of confidence level =191274.86 At 99% confidence level the maximum daily loss or gain of the portfolio will be Rs. 191274.86.; that is portfolio value will lie between 6808183.39 and 7190733.11 Value at Risk at 95% of confidence level =123742.83 At 95% confidence level the maximum daily loss or gain of the portfolio will be Rs. 123742.83; that is portfolio value will be lie between Rs. 6875715.42 and 7123201.08 Back testing:

The back test result shows at 5 % level significant day loss is stipulated by 5% historical simulation value, at the same time 1% level significant day loss not stipulated but it very near to 1% level of confidence Variance covariance model





At 5% significant level the maximum daily loss or gain of the portfolio will be Rs.216545.70 , that is portfolio value will lie between Rs. 6782912.51 and Rs.7216003.99. At 25 % significant level the maximum daily loss or gain of the portfolio will be Rs.305788.83, that is portfolio value will lie between Rs. 6693669.418 and Rs. 7305247.08.

. FINDINGS FROM PRIMARY DATA 

Most of the investors are not aware of Financial Modelling techniques.



Most of the investors are not aware of VaR technique’s for risk management.



Qualification of the investors do affect their level of awareness of investors towards Financial Modelling techniques. It can be observed those who are professionally qualified are more aware of Financial Modelling techniques.


6.2: SUGGESTIONS 

The investor should calculate the cost and benefit of each risk management strategy with the conditions prevailing in the market while he is opting a risk reduction



Even though the investor can use any type of models for optimization and risk management, he has to consider the present state of securities market before his investment.



Most o of the iinvestor s a ar e n not a awar e o of these ttechniques tthey sshould iim pr ove ttheir k nowledge.


CONCLUSION Financial modelling is the task of building an abstract model of a financial decision making situation.

In Today’s complex and dynamic investment environment it is necessary for any

investment manager to device and apply different kind of financial modeling strategies. Due to the increased volatility and upswings in the capital market, every investment manager must be careful regarding his investment decisions. Increased complexity of financial instruments and the economic conditions such as recession, boom, etc. makes it difficult for any investment manager to plan his investments. In these conditions, financial modeling strategies will help him to effectively manage his assets. Every investment decision is based on an efficient risk-return trade-off. Modern financial management offers different kind of financial models which will enable an investment manager to strike an optimal balance between risk and return. A portfolio is not a simple aggregation of a random group of securities. It is a combination of carefully selected securities, combined in a specific way so as to reduce the risk of investment to

the minimum. A good portfolio selection through Sharpe’s optimization model & Markowitz theory along with VaR techniques like Monte Carlo Simulation and variance covariance method will assist an individual investor to select a good portfolio which maximizes his return by keeping his portfolio risk at a minimum level.


BIBLIOGRAPHY 

David A. Dubofsky and Thomas W, Miller J R., Derivates Valuation and Risk Management,Oxford University Press.



Ederington,W. T.(1979),The Hedging Performance of the New Futures Market , The Journal of Finance



Punithavathy Pandian,Security Analysis and Portfolio Management ,Vikas Publishing House Pvt. Ltd.



Dr.Krishna Swami O.R, Research Methods,Himalaya Publishing House.



Kevin S, Portfolio Management , Pearson Education

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ANNEXURE

FINANCIAL MODELLING FOR PORTFOLIO SELECTION AND RISK MANAGEMENT QUESTIONNAIRE INSTRUCTIONS  

Read all the questions carefully and put tick mark on appropriate box. All the information collected is only for academic purpose and will be kept confidential.

1. Name (optional):__________________ 2. Gender:

Male

Female

3. Age group: Below 25

25-35yrs

45-55yrs

35-45 yrs

55 & Above

4. Qualification: Undergraduate

Graduate

Postgraduate

Professional

5. Occupation: Entrepreneur

Business

Professional

Others

6. Annual income: Below 2 lakh

2 - 5 lakhs

5-10 lakhs

Above 10 lakhs

7. How many years of Investment experience do you have? Less than 1 year

2-5 years

5-10

More than 10 years

8. What type of investments do you have? Please tick all appropriate Stock

Bond

Mutual fund

Life insurance

ETF

Gold Real estate

Bank deposit

9. Which sector do you prefer invest your money? Private sector

Government sector

Foreign sector

Diversify

Public sector

10. Which type of analysis do you use for taking investment decisions? Fundemental Analysis

Technical Analysis

Both

None 11.What is your investment objective? Income and capital preservation

Long term growth

Short term growth

Liquidity

Safety

12. At what rate do you want your investment to grow? Steadily

Average rate

Fast

13. What percentage of your income do you invest in stock market securities? 0-15%

15-30%

30-50%

More than 50%

14. Do you believe that investment in selected sectors is a successful strategy for maximizing returns and minimizing risks? Yes

No

15. Do you have a financial advisor? Yes

No

16.What is your knowledge regarding portfolio management? Expert knowledge Basic knowledge

High knowledge No knowledge

Moderate knowledge

17.Which technique would you use to balance the risk and return of the investment? Portfolio optimization

Portfolio diversification

Both

18.Which technique would you use for portfolio diversification? Investing in different securities Including more securities in portfolio 19. Are you familiar with financial modeling techniques? Yes No 20. Which of the following techniques you use for evaluation of portfolio? Sharpe’ ratio Treynor’s ratio Jenson’s ratio Information ratio 21. Are you aware of VAR concepts in the field of risk management? Yes No 22. .If yes which method is used by you for measuring VAR? Monte-Carlo Simulation Historical Simulation Others

Th ank you for your valu able time

Appendix No: 2 Monte Carlo Simulation ASIANPAINTS SLN

SIMULA

O

TED

MINDTREE SIMULA

VALUE

PRICE

TED

LUPINLTD SIMUL

VALUE

PRICE

ATED

HCL SIMULA

VALUE

PRICE

TED

HUL SIMUL

VALUE

PRICE

ATED

YESBANK SIMUL

VALUE

PRICE

ATED

HDFC BANK SIMUL

VALUE

PRICE

ATED

VALUE

PRICE

1

178.2

3104101.4

914.4

1313992.9

647.1

1032117.0

774.8

868541.7

473.7

435301.5

446.0

302409.5

632.5

48071.2

2

178.4

3108700.4

877.6

1261154.6

616.4

983134.5

786.5

881643.0

484.7

445395.5

414.6

281088.8

616.8

46873.6

3

173.2

3017884.3

932.7

1340263.1

627.5

1000904.5

796.1

892441.6

462.1

424676.4

442.4

299948.6

619.6

47089.7

4

170.6

2972352.2

944.2

1356836.8

624.7

996420.5

759.8

851758.5

478.4

439663.7

445.9

302346.0

596.3

45318.7

5

171.4

2985680.1

907.3

1303777.1

668.7

1066644.7

785.0

880023.6

474.2

435752.2

460.7

312387.1

632.6

48075.6

6

173.9

3029960.4

924.2

1328095.1

610.9

974441.4

839.4

940917.5

476.9

438231.1

434.6

294672.4

619.5

47083.5

7

180.8

3150318.8

917.4

1318325.7

616.1

982621.9

770.4

863634.0

482.2

443140.3

429.0

290895.3

622.5

47308.1

8

173.5

3022688.4

907.6

1304189.1

603.4

962422.5

775.8

869629.0

466.3

428544.8

440.5

298648.4

626.1

47586.3

9

175.6

3060031.1

908.6

1305697.4

630.5

1005667.5

813.0

911404.6

486.3

446933.7

421.8

286005.6

631.4

47984.0

10

172.4

3003493.2

918.9

1320492.2

642.2

1024330.9

764.8

857350.2

487.0

447528.7

441.1

299046.7

636.7

48388.0

11

176.7

3079029.5

874.9

1257164.3

674.2

1075301.6

803.8

901101.1

458.1

421006.2

420.9

285342.4

607.9

46202.2

12

179.9

3134597.6

916.6

1317197.2

599.2

955763.2

782.6

877303.8

480.0

441134.7

427.0

289529.7

602.0

45751.9

13

174.8

3044627.2

887.2

1274888.7

672.2

1072128.4

816.3

915039.9

474.1

435715.1

436.8

296156.1

624.1

47431.6

14

172.7

3009316.4

911.5

1309850.7

651.6

1039349.5

830.3

930727.1

466.3

428558.9

434.3

294449.2

639.6

48605.9

15

175.8

3062274.5

869.5

1249484.9

618.1

985885.0

728.2

816330.6

473.2

434867.3

437.5

296636.1

615.4

46772.4

16

171.8

2992934.8

955.3

1372720.9

657.8

1049201.3

820.2

919439.1

467.3

429439.1

411.9

279241.9

612.1

46521.8

17

173.8

3028696.8

918.8

1320327.8

645.2

1029030.3

761.7

853913.1

481.5

442461.3

427.9

290137.5

609.6

46326.0

18

174.9

3047206.3

922.9

1326238.5

654.5

1043883.4

806.8

904379.2

471.6

433414.6

414.5

281036.2

616.6

46863.7

19

172.7

3009312.0

892.2

1282162.2

621.4

991053.7

787.7

883001.6

459.2

422017.9

444.5

301401.5

637.7

48467.5

20

171.7

2991860.5

897.5

1289767.5

664.2

1059376.0

811.3

909510.2

466.0

428250.7

419.6

284472.8

622.6

47320.2

21

173.9

3029757.3

929.9

1336325.1

627.3

1000546.2

750.5

841290.6

479.0

440229.7

424.6

287896.8

620.0

47117.6

22

176.8

3080089.9

911.4

1309649.2

571.6

911625.3

798.7

895366.8

472.5

434203.8

449.9

305010.5

633.4

48138.8

23

173.4

3021212.0

884.3

1270667.5

610.0

972969.0

816.0

914758.9

449.7

413276.0

433.4

293843.2

626.5

47613.9

24

176.4

3072424.7

905.5

1301252.9

658.8

1050712.1

785.0

879944.4

482.2

443136.1

419.1

284121.8

616.5

46851.3

25

170.0

2961009.8

871.0

1251640.4

624.0

995216.6

809.8

907804.6

473.2

434877.6

427.2

289629.8

632.0

48029.0

26

176.1

3067643.8

929.0

1334911.0

644.7

1028334.1

825.3

925123.8

467.3

429486.3

418.5

283768.0

627.9

47723.3

27

175.4

3055484.8

898.7

1291410.3

561.5

895524.9

784.7

879650.1

485.1

445809.5

432.9

293473.5

605.4

46009.7

28

170.8

2976168.2

971.4

1395892.6

636.0

1014454.2

767.0

859808.0

459.0

421863.2

411.0

278629.1

633.9

48179.1

29

181.9

3168767.1

911.9

1310364.3

617.7

985152.0

755.2

846545.4

463.8

426189.7

434.5

294600.5

593.8

45126.6

30

174.0

3031334.2

925.4

1329811.2

622.3

992604.5

769.9

863060.7

476.6

437984.1

435.3

295133.0

625.4

47533.2

31

179.3

3123182.8

907.8

1304507.0

679.3

1083494.2

813.2

911641.0

477.9

439168.9

418.3

283602.9

631.6

47999.7

32

174.9

3046983.3

921.9

1324752.9

635.0

1012827.0

818.3

917361.6

476.6

438029.5

438.2

297080.3

621.7

47247.4

33

173.7

3026738.5

884.5

1271093.0

615.5

981691.5

765.5

858168.2

467.2

429322.5

456.1

309218.1

624.8

47485.2

34

179.4

3126237.4

918.1

1319247.2

641.7

1023433.4

821.1

920402.1

476.0

437466.8

446.1

302441.2

616.5

46857.0

35

169.7

2957127.5

935.0

1343635.5

630.0

1004897.5

780.0

874408.2

470.6

432493.8

409.6

277714.4

623.5

47384.1

36

175.3

3054136.4

898.9

1291763.3

593.1

946023.7

794.5

890627.8

454.9

418098.2

437.7

296779.0

614.6

46710.9

37

171.8

2992745.6

889.1

1277634.5

648.3

1034101.7

790.2

885772.5

467.3

429469.9

414.9

281316.7

638.8

48545.3

38

173.5

3023442.3

882.5

1268086.9

612.9

977540.4

793.9

889919.9

462.6

425125.8

449.4

304711.7

615.3

46761.4

39

172.7

3008381.3

908.7

1305784.6

643.1

1025807.1

752.4

843424.2

473.0

434700.1

414.4

280996.1

630.1

47886.7

40

176.1

3067480.3

943.8

1356285.1

591.8

943867.7

781.2

875760.3

463.0

425538.3

438.9

297559.1

631.6

48001.7

41

175.7

3061672.3

929.1

1335148.0

665.2

1061069.7

767.3

860166.3

481.7

442669.1

409.1

277375.6

603.7

45877.7

42

171.6

2989325.5

886.3

1273589.6

615.4

981485.7

821.8

921189.0

482.4

443321.1

437.2

296451.4

606.0

46057.0

43

177.6

3094391.1

903.2

1297954.9

675.3

1077076.0

767.9

860780.6

458.2

421122.7

423.1

286829.1

629.5

47839.8

44

171.6

2990353.8

918.6

1320092.0

614.2

979576.4

779.7

874061.2

470.3

432192.6

418.0

283385.3

619.2

47058.1

45

173.8

3027170.2

919.6

1321485.2

682.0

1087834.4

817.1

916013.0

465.6

427913.1

434.7

294743.1

620.9

47186.7

46

170.7

2973083.4

919.4

1321181.8

674.7

1076165.0

829.7

930066.4

463.5

425916.9

437.1

296368.6

618.7

47019.1

47

174.2

3034073.0

910.3

1308161.5

577.2

920563.2

785.1

880044.3

469.4

431338.7

433.3

293803.9

640.6

48683.1

48

175.2

3052516.3

919.6

1321480.8

638.7

1018698.2

789.3

884784.7

479.0

440242.8

449.0

304426.3

612.8

46573.7

49

175.9

3064789.8

880.8

1265738.1

602.8

961478.4

761.5

853653.2

456.2

419206.5

396.1

268548.5

623.5

47389.7

50

171.8

2993612.3

886.6

1274046.6

636.5

1015262.1

807.9

905629.7

468.2

430294.0

425.2

288310.5

649.4

49353.0

51

172.3

3002532.3

896.4

1288181.6

599.1

955634.2

797.9

894447.4

470.4

432284.9

431.0

292243.0

629.0

47804.3

52

176.3

3072042.1

903.4

1298245.8

586.5

935515.5

800.1

896945.6

460.6

423335.2

411.0

278677.7

630.4

47910.9

53

182.4

3178378.3

911.8

1310275.3

623.8

994932.7

756.5

848061.7

472.0

433802.6

458.8

311043.3

625.0

47501.7

54

175.8

3061934.0

900.5

1294083.5

610.3

973443.3

779.9

874273.2

468.9

430923.3

450.9

305705.5

634.9

48253.9

55

172.8

3011148.3

922.7

1325910.1

625.7

998040.9

745.3

835474.6

475.3

436792.1

450.9

305737.0

600.6

45642.7

56

170.5

2970310.2

934.7

1343173.0

643.0

1025599.0

783.4

878193.4

486.5

447125.1

426.7

289269.4

612.6

46558.2

57

169.5

2952882.6

924.9

1329033.3

621.2

990781.3

784.9

879903.2

473.2

434914.1

432.4

293166.7

628.2

47739.4

58

177.9

3099416.1

906.2

1302247.9

636.5

1015150.4

730.4

818755.2

471.5

433298.3

428.6

290580.3

621.4

47223.5

59

179.4

3125012.9

898.3

1290920.2

643.5

1026425.1

744.0

833970.8

463.0

425469.8

453.5

307479.4

623.7

47404.9

60

174.5

3040854.7

905.9

1301755.8

659.9

1052501.1

768.6

861648.9

477.7

439000.6

460.5

312197.7

618.0

46964.3

61

174.4

3037730.7

891.8

1281566.6

623.8

994981.4

775.9

869764.3

479.6

440721.0

410.1

278029.3

615.0

46743.5

62

178.8

3114632.2

927.6

1332947.7

628.2

1001929.1

766.0

858721.6

464.7

427029.2

435.9

295558.3

608.1

46218.5

63

175.7

3061156.9

884.9

1271625.6

659.3

1051567.9

780.2

874651.4

478.6

439851.1

424.2

287584.4

599.0

45522.7

64

175.8

3061944.8

867.4

1246413.9

634.9

1012692.0

789.7

885271.7

444.4

408426.9

450.2

305248.9

632.3

48053.3

65

170.7

2974303.5

929.5

1335709.1

674.5

1075759.1

762.5

854763.6

464.8

427127.3

453.6

307511.6

614.2

46677.3

66

173.6

3025057.8

887.4

1275258.1

574.9

916940.1

797.5

893990.6

471.2

433018.5

457.8

310387.1

622.9

47337.3

67

173.0

3013946.9

883.5

1269615.1

667.0

1063889.2

795.7

892010.2

473.5

435110.8

445.7

302204.3

628.6

47772.7

68

177.8

3098457.4

943.2

1355401.0

640.8

1022004.6

814.8

913338.9

460.2

422914.5

401.9

272457.0

610.2

46372.8

69

178.1

3102288.4

849.7

1220977.4

638.2

1017915.0

752.9

843981.0

474.1

435724.2

429.6

291239.6

631.0

47957.3

70

177.2

3086418.1

886.5

1273959.8

561.8

896140.4

814.9

913472.4

474.7

436220.2

437.1

296372.2

650.6

49448.3

71

172.9

3012406.8

896.6

1288361.9

619.3

987851.0

755.8

847256.6

463.6

426036.1

448.0

303717.1

612.4

46544.4

72

174.8

3045181.6

923.8

1327520.0

644.1

1027333.7

806.0

903511.5

468.6

430623.1

426.9

289444.9

615.6

46788.4

73

168.9

2942724.0

910.3

1308063.3

621.6

991470.0

786.1

881226.2

470.5

432425.0

430.4

291800.6

644.7

48994.6

74

175.1

3050771.6

860.6

1236709.4

666.0

1062204.3

790.3

885947.4

451.2

414620.1

434.5

294615.4

621.1

47204.5

75

169.2

2948585.1

885.4

1272257.6

638.1

1017838.1

785.8

880849.1

474.3

435871.4

452.6

306896.7

622.2

47286.9

76

171.1

2980428.2

886.2

1273498.4

668.5

1066333.6

798.5

895117.3

470.0

431889.4

431.4

292522.1

634.8

48244.4

77

175.9

3064038.8

863.5

1240864.1

659.8

1052451.5

783.6

878421.7

468.3

430388.4

457.2

309981.9

612.1

46516.4

78

171.6

2989958.6

925.4

1329757.8

634.1

1011357.4

797.0

893409.6

475.0

436541.3

433.9

294213.1

632.5

48067.1

79

171.3

2984510.4

906.4

1302429.5

583.3

930438.7

784.3

879255.0

466.0

428238.8

420.0

284786.4

623.4

47376.4

80

182.1

3173409.4

915.6

1315735.4

604.2

963772.7

780.0

874363.7

462.9

425422.7

416.2

282194.1

639.0

48566.7

81

176.7

3079156.4

907.6

1304196.7

672.5

1072703.2

763.2

855494.1

474.4

435939.2

443.0

300327.9

631.1

47961.5

82

174.3

3036375.1

902.2

1296456.8

624.7

996402.3

796.8

893160.1

458.0

420867.0

434.6

294661.0

621.6

47240.6

83

177.1

3084600.4

929.7

1335958.7

640.3

1021235.3

799.5

896255.7

453.7

416944.1

462.9

313823.1

602.5

45792.6

84

171.7

2991021.9

953.0

1369458.6

661.6

1055183.1

809.6

907551.4

467.8

429941.1

410.9

278593.1

600.8

45657.8

85

174.9

3047032.8

830.1

1192903.7

629.6

1004195.4

769.1

862205.8

459.8

422515.4

435.9

295570.9

635.0

48256.2

86

176.7

3078699.6

878.1

1261812.7

700.5

1117261.5

771.3

864673.7

456.2

419274.8

427.1

289586.8

607.4

46158.7

87

176.1

3068190.7

882.7

1268501.0

640.6

1021702.5

786.2

881377.5

468.4

430503.8

427.7

290009.5

634.3

48206.4

88

173.6

3024457.8

915.8

1315966.2

609.7

972411.9

788.6

884056.8

480.9

441924.6

448.8

304299.4

648.5

49285.4

89

174.3

3037367.6

924.1

1327894.7

632.9

1009467.0

809.6

907598.8

468.7

430776.1

413.4

280270.3

634.1

48195.1

90

177.5

3091726.6

905.4

1301116.0

661.6

1055188.7

755.1

846442.9

465.4

427744.0

415.4

281651.1

618.4

46998.0

91

176.0

3066332.5

879.3

1263549.4

646.9

1031816.4

761.4

853531.1

458.4

421260.8

425.9

288730.6

635.1

48267.2

92

174.5

3039441.2

866.3

1244819.4

621.5

991292.6

774.3

868021.6

471.3

433152.9

447.5

303396.4

609.7

46337.3

93

172.5

3006023.6

896.5

1288335.8

601.6

959628.4

789.3

884799.0

473.7

435295.5

429.8

291429.0

624.3

47443.1

94

167.7

2920985.6

883.4

1269439.9

636.5

1015295.2

765.5

858086.1

483.0

443866.7

431.1

292310.6

637.2

48427.3

95

172.6

3007177.2

941.3

1352617.2

669.1

1067171.2

790.3

885886.1

472.7

434414.4

426.4

289112.0

628.4

47757.3

96

173.7

3026521.3

907.2

1303692.3

619.6

988206.9

774.3

867999.2

479.0

440216.0

421.0

285464.6

623.8

47410.9

97

173.6

3024997.8

861.4

1237885.3

623.2

993967.6

783.9

878791.7

458.3

421210.9

422.7

286581.4

624.3

47449.2

98

174.0

3031058.5

936.1

1345156.5

621.9

991991.9

800.4

897271.4

466.3

428575.2

441.7

299501.1

609.0

46286.9

99

173.0

3013978.3

914.5

1314195.7

628.5

1002388.7

835.5

936589.0

471.0

432876.0

439.3

297855.3

636.9

48408.0

100

178.5

3110675.9

894.5

1285396.8

642.6

1024882.5

809.8

907773.2

474.8

436365.6

438.0

296968.7

645.5

49061.7

101

178.8

3114747.9

907.9

1304658.8

686.3

1094580.3

818.2

917210.2

471.3

433100.0

443.3

300575.9

629.9

47872.4

102

180.4

3143162.1

909.1

1306314.1

537.2

856868.0

801.5

898432.5

478.5

439731.6

439.7

298092.0

623.5

47389.6

103

170.7

2974553.4

934.3

1342574.9

630.8

1006136.7

783.1

877855.3

467.6

429678.8

442.9

300315.0

631.0

47956.9

104

176.9

3081768.2

921.5

1324210.6

613.2

978109.1

772.1

865530.5

469.7

431689.4

442.2

299800.0

626.9

47646.4

105

165.6

2885473.1

901.8

1295902.8

618.6

986711.8

805.3

902740.7

483.7

444482.1

437.4

296529.5

615.8

46800.4

106

173.1

3015923.9

899.0

1291862.5

597.5

953082.0

797.8

894290.2

463.3

425770.6

400.7

271663.2

619.2

47058.0

107

173.4

3021474.2

921.6

1324375.0

622.7

993144.8

785.3

880345.1

475.7

437147.8

427.7

289953.3

626.5

47615.4

108

174.5

3039609.1

921.3

1323847.4

655.4

1045287.5

770.1

863336.7

475.2

436748.0

440.1

298403.2

646.4

49125.8

109

175.7

3060480.7

894.1

1284848.6

629.4

1003901.5

795.5

891786.0

461.4

424062.3

435.6

295347.1

616.5

46854.4

110

177.0

3083071.6

888.5

1276798.7

723.3

1153690.4

738.1

827432.5

465.0

427302.6

425.1

288217.1

632.2

48050.8

111

179.9

3133675.8

888.1

1276174.5

651.7

1039515.6

814.3

912832.5

477.8

439083.0

415.4

281629.5

627.7

47706.2

112

171.3

2984000.7

940.8

1351964.3

663.2

1057854.7

789.2

884650.3

486.3

446922.6

456.1

309232.0

621.9

47261.2

113

176.0

3065909.3

876.3

1259290.8

638.8

1018809.3

771.0

864241.7

462.8

425288.6

401.8

272427.0

641.9

48781.3

114

169.5

2952517.9

911.2

1309394.6

602.0

960133.2

789.2

884640.0

474.5

436046.6

434.1

294305.3

622.6

47319.5

115

179.9

3135009.5

906.6

1302791.4

655.3

1045195.4

767.9

860775.2

472.0

433736.7

429.3

291047.1

644.1

48953.7

116

173.6

3024968.2

868.0

1247292.7

638.5

1018481.1

784.9

879854.8

461.0

423682.1

416.4

282316.8

608.2

46220.7

117

170.5

2970890.7

928.6

1334409.2

635.0

1012885.1

783.1

877847.7

475.3

436787.4

430.3

291736.7

631.4

47988.8

118

174.1

3032759.6

883.9

1270201.1

671.4

1070899.8

798.6

895209.5

482.6

443497.8

425.5

288500.9

624.7

47478.3

119

175.0

3048317.2

849.3

1220500.6

642.9

1025389.5

794.3

890430.3

465.4

427704.7

439.1

297738.2

649.7

49380.6

120

173.1

3016422.9

858.8

1234025.1

605.9

966456.4

754.6

845921.0

466.1

428330.4

413.1

280064.4

632.1

48038.9

121

170.6

2971818.2

901.0

1294767.4

650.1

1036926.5

776.1

870011.8

467.9

429992.2

471.6

319756.4

635.6

48307.5

122

175.0

3049687.6

901.6

1295544.0

630.2

1005129.2

790.1

885702.8

471.3

433100.8

437.0

296319.5

636.4

48367.6

123

171.6

2990210.7

921.8

1324619.2

607.8

969443.4

837.4

938711.5

484.7

445454.3

436.4

295867.5

615.1

46751.2

124

175.5

3057160.8

897.9

1290329.9

609.6

972305.0

749.3

839999.5

485.2

445899.9

435.7

295395.7

643.3

48889.4

125

177.9

3099199.5

883.4

1269410.4

664.9

1060465.5

811.8

909971.8

477.3

438635.8

417.0

282712.9

610.7

46415.8

126

175.9

3064424.9

927.6

1333012.7

603.9

963281.0

779.8

874128.5

468.7

430758.3

414.8

281226.8

622.9

47339.4

127

175.3

3053681.1

904.1

1299258.4

613.5

978537.7

772.9

866383.8

468.0

430071.8

420.3

284953.8

604.8

45964.0

128

175.9

3064534.3

893.4

1283862.8

650.8

1038035.6

794.9

891106.8

479.0

440238.6

428.8

290737.3

631.4

47986.1

129

175.3

3053581.1

898.8

1291575.0

666.4

1062962.4

776.3

870273.3

457.9

420783.1

418.5

283761.6

628.2

47744.7

130

172.0

2997088.1

897.9

1290262.8

653.4

1042183.8

772.2

865661.2

472.1

433872.8

417.7

283182.2

606.8

46117.8

131

176.9

3082712.6

942.1

1353741.5

653.0

1041572.7

765.6

858288.5

458.7

421515.8

440.3

298550.0

593.0

45065.8

132

173.5

3022416.8

894.8

1285777.0

658.1

1049649.9

797.4

893917.4

464.5

426916.7

432.0

292911.8

629.9

47871.4

133

171.8

2992324.2

911.4

1309729.6

631.5

1007320.1

777.0

871054.2

463.5

425923.9

425.9

288771.5

634.3

48209.9

134

172.1

2999055.4

917.3

1318132.8

621.2

990756.4

829.5

929864.2

465.1

427423.1

453.4

307423.5

603.0

45826.2

135

173.5

3022328.1

936.3

1345450.2

630.0

1004902.9

802.4

899543.3

469.4

431361.5

418.9

283988.9

602.7

45803.7

136

173.8

3027736.3

886.1

1273392.7

644.9

1028657.5

780.2

874565.6

472.1

433822.5

454.3

308036.2

599.1

45532.5

137

178.1

3103642.7

914.5

1314105.0

689.0

1098950.3

786.0

881120.5

468.1

430213.1

415.1

281463.1

635.1

48266.1

138

170.8

2975925.6

922.7

1325979.5

625.9

998330.0

810.9

909053.9

469.5

431514.9

442.1

299753.3

620.5

47155.5

139

169.5

2953107.1

886.3

1273601.0

597.1

952441.6

774.9

868612.9

478.8

440027.1

432.9

293522.9

649.2

49341.3

140

174.8

3045634.2

923.3

1326788.4

658.6

1050487.1

824.4

924204.2

484.3

445039.6

421.3

285672.4

638.8

48549.1

141

178.1

3102532.2

871.4

1252254.7

617.2

984373.6

773.5

867066.8

461.4

423990.9

438.6

297397.5

624.1

47433.0

142

172.0

2996041.8

925.2

1329520.0

585.7

934249.5

759.7

851679.2

470.9

432765.5

423.2

286935.1

630.1

47888.7

143

174.0

3032090.0

874.0

1255875.2

630.0

1004859.3

752.8

843935.9

475.6

437122.2

441.9

299640.3

621.3

47218.7

144

173.2

3017562.1

874.8

1257135.2

638.6

1018529.1

777.5

871618.2

455.2

418296.8

422.8

286635.9

639.4

48594.4

145

171.5

2988250.7

920.4

1322580.5

637.4

1016630.3

788.6

883981.0

468.4

430465.5

438.1

297030.8

617.5

46929.7

146

176.5

3074938.8

925.9

1330561.6

645.1

1028863.0

813.1

911482.8

471.5

433335.3

418.1

283501.0

617.2

46908.2

147

171.7

2991349.4

900.9

1294558.2

661.1

1054455.0

817.0

915901.4

469.0

431034.5

442.1

299767.3

621.4

47225.8

148

171.4

2985351.5

908.0

1304795.9

714.4

1139398.7

775.2

869054.5

475.1

436600.3

424.1

287509.1

621.5

47233.0

149

176.0

3066052.8

886.3

1273673.5

618.5

986437.8

768.8

861770.1

479.4

440528.6

424.8

288032.9

643.1

48875.9

150

171.9

2995285.3

904.9

1300319.3

594.5

948262.2

750.6

841423.8

465.7

427998.9

431.6

292642.6

636.2

48350.8

151

171.6

2989094.6

901.9

1296066.1

606.7

967739.6

784.2

879068.4

474.4

436002.4

419.4

284383.1

642.4

48822.0

152

177.1

3084929.8

902.0

1296219.6

622.3

992497.3

814.8

913392.8

482.8

443724.4

414.8

281257.1

626.6

47624.3

153

176.3

3070861.1

913.1

1312090.6

627.5

1000858.3

812.8

911197.4

479.0

440173.7

427.2

289649.0

628.0

47729.9

154

174.0

3032244.6

889.5

1278242.4

608.2

970109.6

750.2

841013.7

476.7

438125.7

431.5

292588.5

661.9

50302.5

155

178.3

3106460.7

873.8

1255657.8

624.2

995658.0

740.2

829751.6

467.6

429703.8

405.9

275221.1

623.9

47419.0

156

173.7

3026120.2

900.0

1293345.6

664.3

1059617.0

809.1

906992.2

475.5

436966.7

430.6

291953.9

620.5

47155.3

157

174.6

3041433.6

903.5

1298388.2

674.2

1075364.7

798.0

894515.6

469.1

431077.8

431.4

292474.1

628.3

47753.1

158

168.2

2930865.2

919.8

1321792.6

721.2

1150352.9

814.9

913483.2

473.2

434852.7

439.2

297763.0

623.9

47415.9

159

173.0

3013154.2

906.8

1303007.2

636.8

1015746.2

805.4

902811.0

480.0

441157.1

426.9

289406.2

630.5

47920.1

160

175.3

3054254.4

909.4

1306847.2

617.4

984780.8

762.0

854244.8

462.3

424814.8

450.2

305269.0

657.4

49961.6

161

175.9

3064584.4

923.6

1327234.3

617.3

984562.9

784.4

879339.9

471.4

433199.1

448.6

304183.2

630.3

47899.8

162

173.3

3018695.5

913.4

1312581.7

631.4

1007157.0

763.6

855961.9

476.6

437957.7

408.9

277224.8

619.9

47109.6

163

176.9

3081450.9

892.5

1282468.9

637.1

1016252.7

778.2

872390.4

463.8

426271.3

428.7

290632.6

615.2

46756.6

164

173.8

3027489.6

874.2

1256205.1

634.8

1012517.9

745.0

835138.7

466.0

428241.9

437.0

296292.5

636.6

48383.0

165

178.5

3110296.6

927.8

1333260.9

623.2

993996.8

782.6

877317.8

462.0

424597.9

426.6

289266.8

636.3

48359.8

166

174.3

3036661.2

886.8

1274304.0

622.4

992664.6

760.9

852954.1

472.3

434001.3

436.7

296113.8

623.5

47385.6

167

178.7

3113170.1

906.4

1302469.7

634.4

1011901.0

804.8

902187.3

461.9

424457.0

437.1

296324.4

639.5

48604.4

168

170.3

2966934.6

950.0

1365203.1

646.0

1030373.4

767.1

859906.4

468.1

430144.8

448.4

304005.2

628.6

47772.2

169

175.4

3054968.6

944.1

1356727.5

631.6

1007440.0

794.5

890652.3

458.2

421083.9

446.7

302894.5

621.9

47265.3

170

173.0

3013640.4

932.6

1340109.4

625.6

997807.9

769.0

862009.3

457.6

420580.1

459.9

311834.6

627.9

47717.6

171

176.6

3076076.2

912.6

1311353.7

638.1

1017827.5

740.5

830075.0

477.0

438353.8

439.5

298006.3

618.3

46991.9

172

175.5

3057589.4

911.0

1309044.4

611.7

975586.4

800.5

897395.2

465.9

428197.7

458.1

310618.0

606.2

46068.3

173

174.5

3039634.9

951.4

1367099.9

618.1

985912.7

801.0

897886.4

474.0

435563.0

413.6

280437.9

619.4

47077.9

174

172.2

3000255.5

895.8

1287272.9

602.6

961165.1

789.3

884857.5

473.0

434723.3

435.2

295046.9

628.9

47795.3

175

177.5

3092102.9

928.3

1333908.8

623.3

994140.5

799.8

896526.8

487.7

448191.8

420.0

284783.8

625.7

47549.6

176

176.7

3077934.2

907.4

1303895.8

699.5

1115734.3

766.1

858847.1

468.2

430287.9

421.7

285911.2

611.4

46469.0

177

170.0

2960879.6

921.8

1324598.0

621.1

990585.1

788.0

883366.6

469.3

431248.6

450.3

305277.1

636.7

48392.8

178

169.4

2951337.8

927.8

1333270.2

659.6

1052101.1

774.8

868594.0

471.0

432852.8

433.3

293745.4

606.9

46120.8

179

167.0

2908699.7

923.0

1326325.9

639.5

1020016.9

737.3

826568.0

471.1

432931.4

426.8

289359.4

654.8

49761.2

180

173.8

3028794.5

908.9

1306159.3

614.9

980716.4

813.5

911906.1

475.2

436708.1

412.4

279637.2

645.4

49046.8

181

173.3

3019469.5

895.9

1287455.1

620.9

990388.3

756.1

847543.3

479.5

440680.5

435.9

295546.4

618.9

47038.0

182

173.0

3013431.1

886.6

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190

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199

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204

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216

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280

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287

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289

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298

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350

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357

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364

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367

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369

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370

174.0

3031531.8

862.5

1239402.3

597.0

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918349.4

468.2

430309.3

440.7

298814.5

643.4

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371

174.7

3043672.7

892.0

1281859.6

669.5

1067889.8

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281672.8

621.8

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175.1

3051394.3

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1276127.6

620.0

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442.5

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612.6

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373

178.2

3103742.7

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418008.5

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297888.7

645.5

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374

175.1

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595.6

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486.5

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375

170.4

2969164.5

917.9

1319052.5

570.9

910653.9

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426139.3

466.6

316374.3

625.8

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376

174.7

3042776.6

909.4

1306868.6

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757.6

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377

170.6

2972910.7

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1315974.6

636.4

1015131.8

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378

169.5

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379

178.2

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380

176.2

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434604.8

416.6

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612.5

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381

175.0

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174.5

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384

173.2

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182.5

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387

173.5

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430.5

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388

177.9

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389

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3023050.5

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390

175.5

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899510.2

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176.7

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392

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397

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400

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403

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666.7

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440

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617.7

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441

173.1

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435.7

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173.5

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610.3

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446

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447

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611.9

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458.8

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417.6

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628.7

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448

168.5

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601.6

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450

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452

177.6

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633.8

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453

177.4

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454

176.6

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633.4

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460

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616.5

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461

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413.3

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462

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465

176.5

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1279862.6

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946383.8

789.1

884555.0

470.8

432688.2

448.5

304108.1

618.6

47010.6

466

169.2

2948284.8

947.1

1361010.6

617.0

984143.7

797.9

894462.3

463.2

425702.8

435.2

295096.0

608.4

46236.6

467

173.1

3015772.5

889.3

1277937.0

619.1

987455.3

767.6

860528.1

476.5

437875.5

454.2

307948.0

640.1

48645.2

468

172.5

3005737.7

914.9

1314745.1

615.8

982254.2

749.1

839722.6

467.8

429885.9

438.9

297595.4

637.5

48448.9

469

171.3

2984758.7

896.8

1288704.6

649.2

1035478.7

764.4

856887.6

476.5

437923.4

425.8

288658.9

595.1

45231.1

470

175.7

3061812.8

913.5

1312700.6

621.6

991474.6

822.6

922164.1

464.8

427141.8

440.1

298389.6

650.9

49466.0

471

177.5

3092650.6

911.4

1309617.1

621.9

991998.2

767.7

860537.9

473.5

435192.3

418.1

283465.6

614.8

46722.4

472

178.2

3103805.5

917.8

1318809.8

661.1

1054488.1

754.6

845937.7

471.9

433707.1

444.5

301339.4

625.0

47498.9

473

170.1

2963999.2

892.2

1282126.0

621.0

990441.2

773.2

866765.2

473.7

435346.5

439.3

297834.8

628.2

47739.6

474

173.6

3023910.1

903.6

1298525.9

588.1

938015.2

812.8

911163.5

463.4

425865.9

444.8

301574.4

612.8

46574.8

475

168.7

2938884.7

886.8

1274288.8

680.4

1085179.7

844.8

947002.0

480.9

441959.8

421.0

285450.1

640.6

48687.4

476

176.5

3074829.7

903.1

1297760.4

625.3

997323.5

774.4

868109.6

480.7

441745.2

443.0

300341.1

615.8

46802.9

477

174.9

3047259.9

895.9

1287424.7

653.0

1041575.4

759.2

851117.7

479.4

440534.0

427.2

289617.7

623.7

47402.0

478

173.3

3020077.4

930.6

1337283.2

581.4

927382.2

761.7

853812.8

462.2

424724.6

428.9

290794.6

609.1

46289.6

479

175.5

3057157.7

939.9

1350587.5

598.8

955105.0

795.5

891733.0

472.0

433737.0

434.7

294693.2

628.4

47761.4

480

173.7

3026000.5

903.3

1298046.4

608.5

970592.0

789.6

885111.2

463.3

425788.8

417.0

282737.2

634.4

48217.8

481

173.0

3014801.2

900.5

1294029.7

634.5

1012045.8

782.3

876966.0

477.7

439024.8

420.2

284862.5

651.7

49529.8

482

174.2

3034903.3

857.4

1232022.2

608.8

971019.4

788.2

883617.2

481.3

442339.9

457.0

309818.3

647.7

49226.6

483

176.6

3077138.2

878.8

1262789.1

642.2

1024274.2

845.0

947260.1

472.4

434155.3

414.9

281303.4

620.5

47159.6

484

173.1

3015428.6

905.8

1301593.1

654.4

1043709.2

812.9

911240.2

462.6

425116.8

408.5

276954.1

618.4

46994.7

485

172.2

3000734.0

881.9

1267340.3

651.3

1038857.1

740.4

829953.3

469.2

431239.1

431.8

292763.3

626.0

47572.5

486

174.5

3040926.1

890.8

1280041.4

623.9

995128.2

737.6

826820.1

480.4

441479.3

422.2

286269.9

620.5

47157.0

487

171.5

2988099.3

929.5

1335646.3

667.4

1064541.8

790.6

886316.3

477.2

438588.0

455.2

308630.5

626.1

47585.3

488

170.2

2965062.1

876.0

1258820.2

574.2

915783.7

789.3

884788.6

478.4

439618.1

451.3

305981.9

624.6

47466.3

489

177.2

3087968.1

919.9

1321900.5

619.7

988370.4

762.0

854216.3

470.2

432124.4

433.3

293797.1

627.8

47716.2

490

167.5

2917819.6

881.4

1266570.5

632.9

1009423.8

798.1

894659.4

465.7

427994.7

424.9

288079.1

623.0

47345.8

491

173.7

3025564.5

912.2

1310791.5

640.7

1021925.7

789.7

885266.2

457.4

420339.4

433.0

293588.7

630.0

47876.4

492

175.7

3061510.1

918.8

1320379.2

621.9

991881.3

793.9

889942.3

477.3

438617.1

456.5

309478.8

629.1

47810.9

493

176.2

3069228.8

871.2

1251901.8

666.4

1062978.5

787.7

883022.5

476.6

437990.4

456.9

309762.0

642.3

48818.6

494

169.6

2955196.6

850.7

1222434.5

590.0

941113.0

809.5

907481.3

463.5

425971.9

433.1

293660.9

590.2

44858.4

495

178.3

3105785.6

902.5

1296852.5

606.4

967176.7

784.9

879838.9

469.7

431655.3

405.1

274652.0

643.3

48887.5

496

174.9

3046403.0

935.2

1343871.2

616.2

982896.9

720.9

808143.2

468.8

430790.9

440.3

298510.4

656.2

49874.0

497

176.4

3073511.1

917.3

1318162.9

640.3

1021238.3

806.4

903939.6

468.4

430425.2

447.5

303426.4

628.1

47736.9

498

172.0

2996396.3

914.3

1313789.1

658.0

1049542.1

805.3

902753.4

468.0

430101.6

436.0

295581.3

606.0

46058.9

499

180.1

3138561.1

866.2

1244698.3

658.5

1050367.9

774.5

868159.2

480.8

441883.3

426.8

289390.0

627.2

47666.6

500

167.1

2910636.7

912.9

1311851.5

613.9

979138.2

781.7

876230.9

476.7

438066.3

474.8

321903.5

626.0

47572.3

Appendix No:3 Back Test

PORTFOLIO VALUE Date

ASIANPAINTS

MINDTREE

LUPINLTD

HCL

HUL

YESBANK

HDFC

Change in Value

2-Apr-12

56854954.8

713686.05 713686.05

858827.8

561901.25

372792.35

252927.9 252927.9

40154.6

1622532.3

3-Apr-12

58475200.8

718571.85

852368

566553.4

371046.25

253741.5

40295.2

-569491.15

4-Apr-12

57902017

723026.55

852447.8 852447.8

570645.05

366864.8

253266.9

40017.8

-770526.4

9-Apr-12

57127609.1

727122

860422.8

558594.3

371735.5

252622.8

39653

-381499.85

10-Apr-12

56735614.1

723673.2

869354.8 869354.8

550411

381339.05

255978.9

39888.6

-343334.05

11-Apr-12

56392400.7

707075.85

886501

549290

382855.4

254792.4

40010.2

331459.55

12-Apr-12

56719934.3

713901.6

877090.5

554222.4

387082.8

251843.1

40310.4

789282.9

13-Apr-12

57511764.2

708297.3

897985

536902.95

390712.85

247775.1

40230.6

935436.3

16-Apr-12

58442970.1

702261.9

903009.3 903009.3

543460.8

387128.75

250012.5

40261

-419240.65

17-Apr-12

57984771.5

761178.9

884906

539032.85

388001.8

251673.6

40299

-287012.85

18-Apr-12

57686855.3

758879.7

882752.8 882752.8

554110.3

388599.15

250792.2

40861.4

327072.2

19-Apr-12

57995224.7

767573.55

880280.5

564367.45

391034.5

249334.5

42107.8

216718.35

20-Apr-12

58199062.1

783596.1

879802

566497.35

388737

247063.2

41883.6

2246091.25

23-Apr-12

60471762

782015.4

875415.8 875415.8

555511.55

383314.9

243266.4

41446.6

-149380.55

24-Apr-12

60314964

784817.55

860343

571934.2

386439.5

243673.2

41180.6

-663510.25

25-Apr-12

59623310.6

789559.65

883071.8

569019.6

385152.9

248181.9

41545.4

1015601.85

26-Apr-12

60663404

800911.95

864888.8

561564.95

381109.3

242486.7

41078

749448.75

27-Apr-12

61382932.6

832525.95

857631.5

572774.95

381752.6

236147.4

41127.4

421280.65

28-Apr-12

61814127.1

819736.65

859306.3

571093.45

383774.4

236825.4

41309.8

-317821.2

30-Apr-12

61443909.6

847255.2

881078

574008.05

383774.4

237096.6

41230

91793.15

2-May-12

61513597.6

864068.1

872544.8

581182.45

390575 390575

236384.7

41792.4

1229440.3

3-May-12

62781919.2

839136.15 839136.15

860263.3

577595.25

399535.25

229028.4 229028.4

42107.8

214703.35

4-May-12

62986627.7

834753.3

880838.8

575297.2

399673.1

226248.6

40850

514694.8

7-May-12

63492736.8

858104.55

879722.3

562629.9

395124.05

230214.9

40451

131129.1

8-May-12

63686992.1

835831.05

872385.3

536622.7

395951.15

223163.7

39166.6

928934.1

9-May-12

64613842.5

836118.45

869833.3 869833.3

545478.6

397513.45

217299

38961.4

-980731.9

10-May-12

63657374.7

838848.75

832829.3

550747.3

398156.75

221028

39330

-541578.2

11-May-12

63134714.7

833675.55

821425

547664.55

397053.95

223401

38801.8

1342246.2

14-May-12

64413489.5

866654.7

862336.8

543741.05

398708.15

216010.8 216010.8

38041.8

1246388.55

15-May-12

65646967.1

883108.35

857073.3

548112.95

397421.55

214756.5

37931.6

-261380.25

16-May-12

65408285.7

871253.1

863214

544693.9

393102.25

205806.9

37635.2

-1006020.55

17-May-12

64375161.1

892017.75

868876.3

543965.25

395124.05

204993.3

37832.8

79199.2

18-May-12

64479693.1

874127.1

854521.3

541891.4

397053.95

211841.1

38041.8

938248.85

21-May-12

65406543.5

876138.9

867201.5

537463.45

391677.8

218587.2 218587.2

37806.2

-1336210.65

22-May-12

64060694

877791.45

869354.8

546655.65

389518.15

218010.9

37183

-7630.45

23-May-12

64069405

872905.65

858987.3 858987.3

543404.75

392413

217434.6

37027.2

1255263.05

24-May-12

65328144.5

871756.05

851809.8

544469.7

390299.3

222384

37977.2

292829

25-May-12

65608638.7

890149.65

846307

546039.1

386761.15

223773.9

38000

1003101.35

28-May-12

66599950.5

888928.2

851331.3

551027.55

383636.55

229231.8

38665

358411.9

29-May-12

66944906.1

890940

848460.3

566497.35

382533.75

229469.1

38376.2

-449984.05

30-May-12

66490191.9

897693.9

843834.8

570813.2

388231.55

222384

38049.4

3602335.85

31-May-12

70063444.1

905597.4

864011.5 864011.5

565040.05

393332

223638.3

38471.2

-4251543.8

1-Jun-12

65851675.6

903585.6

858668.3

546039.1

385520.5

219231.3

37270.4

-1688437.1

4-Jun-12

64186132.4

889503

849975.5 849975.5

553605.85

378995.6

217671.9

37669.4

630224.75

5-Jun-12

64791546.9

903441.9

862017.8

555287.35

374308.7

219061.8

38114

1886104.45

6-Jun-12

66622599.1

913500.9

880599.5 880599.5

562854.1

386025.95

224790.9

39512.4

374926.7

7-Jun-12

67034629.4

876641.85 876641.85

874538.5

559435.05

389426.25

229265.7

40872.8

-383447.6

8-Jun-12

66644376.6

882030.6

869673.8

555567.6

394526.7

234215.1

40971.6

152717.3

11-Jun-12

66834276.4

887994.15

836497.8

540882.5

400821.85

232418.4

41188.2

819119.45

12-Jun-12

67663563.6

896688

814247.5

543404.75

397513.45

236011.8

41769.6

-78025.3

13-Jun-12

67556418.3

899059.05

822382

550186.8

411298.45

234655.8

41173

-152230.05

14-Jun-12

67433593.2

899130.9

822701

536678.75

405095.2

225129.9

40614.4

267974.85

15-Jun-12

67704505.3

881886.9

818394.5

544749.95

413044.55

226723.2

41613.8

-425526.65

18-Jun-12

67318608

868810.2

819989.5

526757.9

410287.55

220282.2

40656.2

413187.3

19-Jun-12

67703634.2

882964.65

830277.3 830277.3

529055.95

412814.8

219061.8

40770.2

21971.2

20-Jun-12

67685341.1

884904.6

839927

545646.75

418696.4

225435

40599.2

201690.9

21-Jun-12

67888307.4

874917.45

842000.5

540153.85

422877.85

232723.5

41260.4

-113458.75

22-Jun-12

67793357.5

869385

841123.3

529840.65

423015.7

230689.5

41370.6

-1461409.85

25-Jun-12

66342976

877144.8

832669.8

521096.85

422785.95

229909.8

40789.2

-849582.45

26-Jun-12

65489298

887563.05

837295.3

516668.9

414193.3

231469.2

41302.2

329172.3

27-Jun-12

65788085.3

913069.8

834663.5 834663.5

526589.75

415801.55

227028.3

41724

-462935.1

28-Jun-12

65315949.1

920973.3

850932.5

514595.05

415066.35

224824.8

41686

2470351.8

29-Jun-12

67746318.1

926577.6

856754.3 856754.3

534100.45

417685.5

230113.2

42829.8

625510.2

2-Jul-12

68314275.3

967316.55

867680

543068.45

410425.4

233503.2

43620.2

365029

3-Jul-12

68647035.5

1011001.35

856594.8

543180.55

405600.65

237740.7

43764.6

-1190387.75

4-Jul-12

67465823.9

1005900

857392.3

541947.45

402476.05

237062.7

43928

-1574157.1

5-Jul-12

65875195.3

999217.95 999217.95

861938

552036.45

405141.15

242452.8 242452.8

44391.6

-1195918.95

6-Jul-12

64713147.9

950791.05

871747.3

549794.45

409919.95

244859.7

44194

-552143.5

9-Jul-12

64173065.9

947198.55

870391.5

545814.9

407990.05

243910.5

43939.4

194825.55

10-Jul-12

64341188.2

955030.2

873581.5

558650.35

410241.6

243707.1

44737.4

-16945.65

11-Jul-12

64355125.8

940660.2

872146

552428.8

405646.6

239571.3

44612

480561.35

12-Jul-12

64865590.4

914363.1

880440

539425.2

407071.05

239774.7

44087.6

-227719.65

13-Jul-12

64605131.5

944180.85

884826.3

542115.6

405370.9

236791.5

44615.8

-265261.7

16-Jul-12

64338574.9

921619.95

910984.3

539593.35

405416.85

237300

44281.4

-517142.55

17-Jul-12

63811559.4

933259.65

908990.5

536678.75

408173.85

237639

44327

32097.25

18-Jul-12

63849887.8

928086.45

908033.5

533876.25

410149.7

238079.7

44612

-788465.15

19-Jul-12

63052831.3

925715.4

912340

537519.5

410471.35

240588.3

44794.4

1730401.25

20-Jul-12

64761929.5

952587.3

908113.3

537855.8

409919.95

239978.1

44277.6

-2024189.35

23-Jul-12

62763626.1

940588.35

909708.3

535613.8

407071.05

230316.6

43548

-568471.15

24-Jul-12

62140789.6

942025.35

927891.3

538976.8

437627.8

231062.4

43627.8

-643505.7

25-Jul-12

61470913.7

932469.3

934191.5

575689.55

426829.55

234621.9

43779.8

-1104266.3

26-Jul-12

60438660.2

898053.15

902052.3

573671.75

424440.15

234350.7

43000.8

657921.95

27-Jul-12

61083274.2

893526.6

903328.3

580341.7

426967.4

240283.2

44429.6

1279058.3

30-Jul-12

62310654.1

902651.55

941767.8

579332.8

428024.25

244147.8

44631

1173475.05

31-Jul-12

63456150.6

907034.4

958435.5

581294.55

429494.65

247605.6

44669

-254452.05

1-Aug-12

63188722.9

921763.65

950301

584993.85

432067.85

247809

44574

417879.1

2-Aug-12

63612948.6

921907.35

943681.8

588412.9

430505.55

246385.2

44270

1815334.15

3-Aug-12

65458809.5

909692.85

926455.8

585610.4

428805.4

249368.4

44703.2

-139213.2

6-Aug-12

65299398.2

913500.9

941767.8

586507.2

429494.65

247944.6

45619

-61923.35

7-Aug-12

65224483.6

916446.75

938179

594690.5

431838.1

251063.4

45607.6

-224548.4

8-Aug-12

65008450.8

905956.65

927971

602369.35

438500.85

248995.5

45516.4

331669

9-Aug-12

65333371.1

904160.4

929725.5

601640.7

448701.75

245876.7

45953.4

-638480.6

10-Aug-12

64694854.8

903154.5

926296.3

601752.8

457386.3

241740.9

45763.4

1030842.45

13-Aug-12

65727108.3

895682.1

928290

608590.9

450585.7

245368.2

46166.2

198544.25

14-Aug-12

65889132.9

925499.85

918640.3

617166.55

455732.1

247944.6

46219.4

-1240362.85

16-Aug-12

64669592.9

933547.05

886899.8

625574.05

454675.25

244080

45603.8

-558534.7

17-Aug-12

64087698.1

927511.65

909947.5

624789.35

462624.6

243639.3

45227.6

288595.7

21-Aug-12

64358610.2

934265.55

911702

625237.75

471998.4

242893.5

45326.4

84.50000001

22-Aug-12

64322895.1

966957.3

921351.8

620025.1

471309.15

242215.5

45364.4

162052.75

23-Aug-12

64461400

977088.15

922627.8

627031.35

478247.6

240351

45425.2

-386800.35

24-Aug-12

64052854.1

1004894.1

927891.3

624845.4

475996.05

233571

45318.8

-302463.5

27-Aug-12

63803719.5

967316.55

914014.8

626134.55

478844.95

227706.3

45170.6

1078968.05

28-Aug-12

64913500.9

938935.8

910505.8

624957.5

481647.9

227536.8

44790.6

-423169.6

29-Aug-12

64500599.5

934193.7

920873.3

613803.55

480223.45

224282.4

44729.8

-64032.35

30-Aug-12

64397809.7

949138.5

940172.8

612682.55

485875.3

223706.1

45288.4

-981703.85

31-Aug-12

63428275.4

946911.15

945994.5

610272.4

473376.9

222892.5

45246.6

193204.15

3-Sep-12

63607722

956467.2

938577.8

622771.55

473376.9

222384

44874.2

760486.7

4-Sep-12

64342930.4

956036.1

948785.8

629441.5

478844.95

225774

44847.6

-721784.45

5-Sep-12

63613819.7

973495.65

934590.3

630058.05

488172.8

219739.8

44999.6

920642.15

6-Sep-12

64465755.5

1004175.6

968165

637344.55

483807.55

221570.4

44699.4

1254007.4

7-Sep-12

65689651

1004247.45

971514.5

646817

495295.05

227130

44870.4

-175311.1

8-Sep-12

65471876

1032700.05

984992.3

643734.25

497133.05

228858.9

44919.8

-340203.9

10-Sep-12

65134760.3

1023575.1

999985.3

643117.7

491802.85

225841.8

44927.4

648907.5

11-Sep-12

65788085.3

1037729.55

982759.3

646760.95

488770.15

223638.3

45174.4

1268409.35

12-Sep-12

66994558.8

1074085.65

988979.8

652702.25

497179

228282.6

45539.2

47540.7

13-Sep-12

67065989

1069199.85

956601.3

658923.8

502738.95

229875.9

45539.2

844184

14-Sep-12

67970190.8

1039956.9

918002.3

653374.85

503657.95

241300.2

46569

-356885.95

17-Sep-12

67676630.1

999720.9

912499.5

636335.65

488770.15

255978.9

46230.8

261073.45

18-Sep-12

67954511

988153.05

904923.3

643061.65

489275.6

251300.7

46014.2

-66023.65

20-Sep-12

67871756.5

1001445.3

923824

636840.1

484772.5

246453

46124.4

891906.85

21-Sep-12

68757665.2

990595.95

930283.8

638801.85

486794.3

251470.2

47511.4

548669.75

24-Sep-12

69337817.8

987721.95

919996

626302.7

476087.95

255606

48260

-742768.05

25-Sep-12

68581703

975004.5

930124.3

633701.3

485599.6

254487.3

48404.4

-767245.4

26-Sep-12

67826459.3

958335.3

933314.3

637680.85

484175.15

253877.1

47937

-356132.05

27-Sep-12

67428366.6

951796.95

951018.8

654047.45

494192.25

258284.1

47940.8

1123572.9

28-Sep-12

68552085.6

950791.05

950540.3

647321.45

501636.15

259029.9

47815.4

105998.5

1-Oct-12

68636582.3

957401.25

956282.3

651469.15

498879.15

267267.6

47336.6

-535177.2

3-Oct-12

68086047.1

948491.85

953172

662903.35

510504.5

271844.1

47078.2

-643864.35

4-Oct-12

67492828

930601.2

923824

660325.05

510504.5

270115.2

47978.8

-1121047.6

5-Oct-12

66399597.5

932684.85

906199.3

642949.55

519602.6

266793

47302.4

1350693.3

8-Oct-12

67768966.7

945114.9

902052.3

626358.75

514685.95

261470.7

47173.2

67387.3

9-Oct-12

67799455.2

949713.3

917842.8

628600.75

522773.15

267267.6

47557

76893.7

10-Oct-12

67876112

964227

904285.3

633701.3

518224.1

266589.6

46964.2

-32067.85

11-Oct-12

67863916.6

949497.75

876213.3

646648.85

525070.65

269199.9

47488.6

110194.25

12-Oct-12

67928378

960562.65

903248.5

652029.65

528470.95

267572.7

47967.4

-421056.55

15-Oct-12

67490214.7

979459.2

895512.8

654327.7

531687.45

267776.1

48195.4

168538.05

16-Oct-12

67685341.1

973926.75

886102.3

655224.5

527735.75

259470.6

47910.4

391409.15

17-Oct-12

68099113.6

929667.15

911941.3

650796.55

526632.95

261233.4

47735.6

308403.45

18-Oct-12

68358701.4

948348.15

913616

673721

528976.4

263809.8

48351.2

-747748.45

19-Oct-12

67626977.4

939223.2

914573

678597.35

520659.45

259979.1

47766

859922.1

22-Oct-12

68453651.3

965807.7

908831

685099.15

523324.55

262419.9

48564

-345443.25

23-Oct-12

68123504.4

955389.45

897905.3

682352.7

524151.65

270759.3

48191.6

-230206.35

25-Oct-12

67878725.3

947845.2

913616

682969.25

518270.05

282183.6

48438.6

449092.85

26-Oct-12

68354345.9

945043.05

902929.5

682913.2

507471.8

280014

48423.4

143429.4

29-Oct-12

68495464.1

951868.8

901653.5

683810

501819.95

281268.3

48685.6

-767259.2

30-Oct-12

67735864.9

948491.85

902770

679774.4

506001.4

276251.1

48157.4

-291277.25

31-Oct-12

67444046.4

947342.25

903487.8

681568

502325.4

279064.8

48199.2

111200.85

1-Nov-12

67572969.2

937858.05

903328.3

681680.1

493916.55

279708.9

47773.6

464457.3

2-Nov-12

68003292.6

942815.7

924541.8

688518.2

489827

284793.9

47902.8

940384

5-Nov-12

68938854

942025.35

931240.8

688125.85

489827

283743

48260

2438412.9

6-Nov-12

71349187.7

967747.65

937939.8

682016.4

489689.15

285302.4

48605.8

468861.2

7-Nov-12

71786479.9

988512.3

938896.8

690704.15

491251.45

284861.7

48643.8

984411.05

8-Nov-12

72790858.2

975076.35

931320.5

693338.5

490148.65

284454.9

48564

-1114543.8

9-Nov-12

71679334.6

975076.35

932596.5

689078.7

486288.85

288251.7

48590.6

-434050.05

12-Nov-12

71249011.2

963149.25

933553.5

695020

486886.2

288048.3

49498.8

-85918.75

13-Nov-12

71137510.4

998571.3

931480

690311.8

486151

286048.2

49175.8

-1219338.6

15-Nov-12

69948458.9

974286

918640.3

695748.65

490562.2

283098.9

49115

-1150599.2

16-Nov-12

68835193.1

963867.75

919677

681287.75

478799

281675.1

48811

-1327271.15

19-Nov-12

67540738.5

949785.15

896230.5

690367.85

474801.35

280963.2

49153

-450033.7

20-Nov-12

67073828.9

951796.95

906199.3

687901.65

478063.8

284522.7

49692.6

1223087.85

21-Nov-12

68292497.8

953593.2

897985

692217.5

482107.4

286251.6

50441.2

847249.35

22-Nov-12

69131367.1

948851.1

900856

703203.3

481877.65

285336.3

50851.6

1514452.45

23-Nov-12

70630530.2

955964.25

893519

713460.45

487253.8

285166.8

50901

537760.45

26-Nov-12

71140994.8

966166.95

901414.3

717383.95

493870.6

284421

50304.4

765527.55

27-Nov-12

71846585.8

992176.65

916646.5

720690.9

497776.35

294489.3

51718

3432164.65

29-Nov-12

75259555.6

996918.75

922149.3

716094.8

503749.85

300591.3

53188.6

252765.45

30-Nov-12

75443357.7

1035214.8

942645

735936.5

494513.9

299845.5

53500.2

265008.65

3-Dec-12

75727336.3

1033346.7

934510.5

726239.85

493043.5

303337.2

52208.2

92983.75

4-Dec-12

75820544

1019838.9

947908.5

726632.2

490470.3

305540.7

52071.4

421155.25

5-Dec-12

76270902.7

999074.25

951178.3

716319

488678.25

305371.2

52637.6

-387092.85

6-Dec-12

75899814.1

985782

948546.5

701129.45

491894.75

317100.6

52801

-795150.15

7-Dec-12

75133246.1

975938.55

955245.5

688350.05

487667.35

308795.1

52675.6

68795.3

10-Dec-12

75190738.7

965089.2

963938.3

696533.35

491527.15

310218.9

52668

-258187.85

11-Dec-12

74918084.4

984704.25

958276

688686.35

500763.1

309507

52504.6

386001.8

12-Dec-12

75271751

1020844.8

967606.8

690872.3

486840.25

307879.8

52732.6

-209611.85

13-Dec-12

75081851.2

1004894.1

971913.3

696309.15

477650.25

303777.9

52519.8

-499997.2

14-Dec-12

74580097.6

996775.05

965373.8

707238.9

474801.35

312286.8

52345

-526410.3

17-Dec-12

74033046.8

1015599.75

956521.5

709536.95

480407.25

315981.9

51414

820107.65

18-Dec-12

74836201

1013085

972790.5

709312.75

482245.25

317609.1

51372.2

2365506.55

19-Dec-12

77176846.7

1016964.9

983875.8

719065.45

480591.05

318490.5

52288

248962.35

20-Dec-12

77426852.4

1011360.6

979808.5

716879.5

489551.3

320694

51938.4

-1568466.5

21-Dec-12

75893716.4

1026808.35

954687.3

706173.95

484450.85

311405.4

51376

98549.05

24-Dec-12

75977342

1015743.45

967606.8

713460.45

488632.3

312998.7

51383.6

1090340.2

26-Dec-12

77068830.3

1012366.5

977894.5

711218.45

481004.6

314490.3

51702.8

-1370060.35

27-Dec-12

75722980.8

1000223.85

979250.3

700961.3

476225.8

316117.5

51687.6

837006.9

28-Dec-12

76564463.4

994116.6

978532.5

702082.3

479809.9

313947.9

51501.4

641877.65

31-Dec-12

77223886.1

981255.45

979090.8

693562.7

482337.15

314625.9

51573.6

-134061.5

1-Jan-13

77058377.1

992967

980446.5

697430.15

487621.4

323406

52022

-875899.55

2-Jan-13

76168112.9

996056.55

980765.5

700905.25

487529.5

330762.3

52238.6

427968.2

3-Jan-13

76599307.4

997349.85

971115.8

701689.95

489229.65

333711.6

51934.6

100305.65

4-Jan-13

76691644

1003457.1

964177.5

710770.05

491389.3

331575.9

51630.6

-158671.4

7-Jan-13

76558365.7

997206.15

955086

703875.9

482842.6

337813.5

50783.2

12305.25

8-Jan-13

76554010.2

1006402.95

953730.3

711498.7

482934.5

338762.7

50939

-513077.6

9-Jan-13

76032221.3

1025658.75

944718.5

712787.85

477236.7

341847.6

50730

-26542.85

10-Jan-13

76006959.4

1023718.8

933154.8

719233.6

474755.4

349475.1

51360.8

-1092375.1

11-Jan-13

74905017.9

1054470.6

937381.5

722876.85

457753.9

337915.2

50866.8

1188502.75

14-Jan-13

76056612.1

1061655.6

923664.5

754208.8

464370.7

343407

50866.8

-900990.6

15-Jan-13

75142828.2

1064745.15

930124.3

744456.1

462900.3

357950.1

50790.8

-614540.05

16-Jan-13

74536542.6

1061368.2

924940.5

755329.8

459637.85

351237.9

50198

1014579

17-Jan-13

75493010.4

1070205.75

935547.3

789184

460005.45

355204.2

50676.8

-377664.1

18-Jan-13

75107113.1

1088024.55

938418.3

791033.65

450677.6

350526

50376.6

-329607.9

21-Jan-13

74703793.8

1138606.95

948466.8

801739.2

456972.75

346932.6

50049.8

2121853.75

22-Jan-13

76884157.1

1132212.3

933314.3

782065.65

441947.1

345034.2

49685

480030.65

23-Jan-13

77397235

1138247.7

933234.5

758244.4

422785.95

348797.1

49901.6

-665047.15

24-Jan-13

76745652.2

1124021.4

941448.8

746978.35

430827.2

344288.4

50182.8

47067.4

25-Jan-13

76756105.4

1124452.5

956122.8

763457.05

437903.5

341881.5

50543.8

-72983.3

28-Jan-13

76642862.4

1146223.05

949344

780888.6

432251.65

354966.9

50946.6

552620.6

29-Jan-13

77207335.2

1147588.2

952613.8

775619.9

430597.45

346763.1

49586.2

750447.6

30-Jan-13

77941672.5

1149384.45

955883.5

772369

438776.55

352560

49905.4

465401.85

31-Jan-13

78419035.3

1133361.9

963858.5

771248

435560.05

354017.7

48871.8

743064.6

1-Feb-13

79140306.1

1147947.45

972790.5

771191.95

427197.15

360933.3

48651.4

1711354.55

4-Feb-13

80889474.9

1139612.85

952294.8

764746.2

429264.9

355814.4

49164.4

-103839.4

5-Feb-13

80818915.8

1134870.75

948945.3

752303.1

424118.5

348424.2

48955.4

-255326.05

6-Feb-13

80561941.3

1139469.15

955883.5

751126.05

417455.75

346729.2

48602

-383862.75

7-Feb-13

80208274.7

1118201.55

949025

749668.75

419064

344356.2

48754

-1391928.4

8-Feb-13

78808417

1121794.05

952932.8

751294.2

416031.3

345542.7

49403.8

175842.55

11-Feb-13

78982637

1127757.6

948068

739299.5

423245.45

350322.6

49928.2

-375171.3

12-Feb-13

78564509

1128691.65

964975

760598.5

422740

354017.7

50555.2

-643446.35

13-Feb-13

77894633.1

1148378.55

947828.8

795181.35

418834.25

347305.5

50479.2

949797.25

14-Feb-13

78853714.2

1145217.15

941369

793948.25

426921.45

339983.1

51284.8

260946

Major Project MBA

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