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- 1. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 1 CHAPTER 1 INTRODUCTION
- 2. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 2 1.1 INTRODUCTION TO THE STUDY Capital market is now going through a turbulent state. The downturn in global economy is having a significant impact on the performance of capital market. The recent volatility in capital market and the complex state of the financial market has added to the concerns of both retail and institutional investors. In the present uncertain state of capital market, the concerns of the investors are of twofold: how to ensure adequate return on their investment and how to control the risk associated with their investment. In such a situation financial modelling for risk management is the key to achieving investment objective of the investor. It involves structuring the investment portfolio in a scientific way in order to ensure superior performance. This requires application of portfolio optimization algorithms. Portfolio optimization techniques, not only ensures superior returns on the investment portfolio, but also ensures efficient diversification resulting in superior risk reduction. In an uncertain state, as is now, the importance of financial modelling techniques involving the use of portfolio optimization techniques cannot be over emphasized as poor investment decisions can seriously undermine the long term welfare and wealth accumulation of the investors. The Project entitled “Financial Modelling for Risk management using Portfolio” examines the use of Sharpe’s optimization models in and superior portfolio performance. The study examines the effectiveness of Sharpe’s Optimization Model. 1.2 SCOPE AND SIGNIFICANCE OF THE STUDY The enormous growth in over the last twenty years in India has created a number of new investors in capital market. One of the major concerns of the investors now is how to ensure superior performance of their investment ensuring at the same time protection of their wealth. As investors are now operating in a complex and uncertain investment environment, poor investment decisions can seriously undermine the long term welfare and wealth accumulation of the investors. Under this complex and uncertain investment environment, financial modelling for risk management assumes more significance. The study examines how portfolio optimization models can improve the performance of portfolios and help investors to achieve their investment objectives.
- 3. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 3 1.3. RESEARCH PROBLEM The recent downturn in global economy is having a profound impact on Indian Capital Market. The recent high volatility of the capital market due to the turmoil of the global financial market has increased the concern of the investors. Investors are now realizing the importance of efficient asset allocations in achieving their investment objectives under present uncertain and complex investment environment. Efficient asset allocation can be achieved only through application of superior portfolio optimization techniques. The present study examines the use of the portfolio optimization algorithms in ensuring superior asset allocation and superior portfolio performance. “Financial modelling for risk management using portfolio” is helps to select optimal portfolio for investment and ensure maximum return to the investors 1.4 OBJECTIVES OF THE STUDY The objective of the study is to examine the application of financial modelling in portfolio management and Risk management using portfolio. The specific objectives of the study are stated below: Major objective To study the application of Sharpe’s portfolio optimization models and portfolio diversification in Risk management. Minor Objectives; 1. To construct optimal portfolios by using Sharpe’s portfolio optimization models and to examine the effectiveness of Sharpe’s portfolio optimization in improving portfolio performance. 2. To evaluate the Sharpe ratio, Treynor’s ratio, & Jensen measure of the optimal portfolios constructed to get an insight into the portfolio performance evaluation process. 3. To study the role of VaR matrices by using Monte Carlo simulation method in portfolio risk management.
- 4. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 4 1.5 RESEARCH METHODOLOGY RESEARCH DESIGN The research design is the conceptual structure within which research will be conducted. Design includes an outline of what the researcher will do from writing the hypothesis and its operational implications of the final analysis of the data. The type of research is analytical. 1.5.1 TYPE OF DATA USED The source of data is secondary in nature. The closing price of securities and closing values of BSE SENSX index are the fundamental data for the study. The nature of data is secondary. The main source of information is websites of stock exchanges. References are also made to technical papers on the subject, Newspapers, Magazines, financial journals, monecontrol.com, and indiainfoline.com. 1.5.2 CRITERIA OF SELECTION OF STOCK Twelve securities of leading companies are selected on the following basis • Securities included in the BSE listing are only selected on the basis that the alpha value of the share should be positive. • As far as possible, securities are selected from different sectors. 1.5.3 PERIOD OF STUDY The study was conducted for a period of 60 days extending from 1st April 2013 to 31st May 2013. 1.5.4 TOOLS FOR ANALYSIS The collected data has been analyzed using basic statistical tools like regression analysis, correlation analysis, mathematical modelling, and optimization techniques. Ratios and charts are also used for better exposition.
- 5. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 5 1.6 LIMITATIONS Researcher is limited with resources like specialized computer softwares for constructing portfolio. Researcher uses only excel sheet for calculations Data considered is only for past 3 year period. Data is of secondary in nature. Only twelve securities are selected for the study. 1.7 CHAPTERIZATION: Chapter I Introduction – deals with importance of the study, Statement of problem, objectives of the study and the scope of the study along with methodology. Chapter II Theoretical frame work of portfolio optimization and Literature review of project Chapter III Industry and organization Profile; – contained a brief detailing of capital market and about the organization JRG securities Ltd. Chapter IV Data Analysis;- include calculations and analysis of collected data. It includes security analysis, portfolio analysis, portfolio evaluation etc. Chapter V Findings, Suggestions and Conclusions
- 6. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 6 CHAPTER 2 THEORETICAL FRAME WORK
- 7. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 7 THEORETICAL PERSPECTIVE CONCEPTUAL FRAMEWORK OF THE STUDY SECURITY ANALYSIS PORT FOLIO SELECTION PORTFOLIO OPTIMISATION PORTFOLIO EVLUATION PORTFOLIO MANAGEMENT UNSYSTEMATIC RISKSYSTEMATIC RISK RETURNRISK SHARPE OPTIMISATION OPTIMISED PORTFOLIO SHARPE RATIO TREYNOR RATIO VALUE AT RISK JENSEN ALPHA
- 8. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 8 PORTFOLIO MANAGEMENT Portfolio is a collection of assets .Creation of portfolio helps to reduce risk without sacrificing returns. It is rare to find investors investing in a single security, instead of this they tend to invest in a group of securities. Such a group of securities is called a portfolio. Portfolio management deals with the analysis of individual securities as well as with the theory and practice of optimally combining securities in to portfolio. An investor is faced with problems in choosing the securities among the large number of securities. His choice depends upon risk return returns characteristics of individual securities. Another problem is how much to invest in each security. The risk return characteristics of a portfolio differ from those of individual securities combining to form a portfolio. The investor tries to choose the optimal portfolio taking in to consideration the risk return characteristics of all possible portfolios. Portfolio management is a complex process which tries to make investment activity more rewarding and less risky. Portfolio management process consist of the following five process, 1. Security analysis 2. Portfolio analysis 3. Portfolio selection 4. Portfolio revision 5. Portfolio evaluation The success of portfolio management depends on how effectively each phase s carried out. 1. SECURITY ANALYSIS Security analysis is the initial phase of the portfolio management process. This step consists of examining the risk return characteristics of individual securities. For the purpose of analysis twelve securities are selected and the return, risk and risk adjusted rate of return are determined. There are two alternative approaches to security analysis they are fundamental analysis and technical analysis. They are based on different premises and follow different techniques. Fundamental analysis concentrates on fundamental factors affecting the
- 9. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 9 company such as the EPS of the company, the dividend pay-out ratio, competition faced by the company, market share .quality management, etc According to this approach the share price of this company is determined by these fundamental factors. The fundament analysts works out the true worth or intrinsic values of a security based on its fundamentals and then compares this value with the current market price. If the current market price is higher than the intrinsic value the share is said to be overpriced. Fundamental analysis helps to identify fundamentally strong companies whose shares are worthy to be included in the investor’s portfolio. Technical analysis concentrates on price movements and ignores the fundamental s of shares. The technical analyst believes that the share price movements are systematic and exhibit certain consistent patterns .He therefore studies past movements in the prices of shares to identify trends and patterns .He then tries to predict the future price movement s. The current market is compared with the future predicted price to determine the extent of mispricing. More recent approach to security analysis is the efficient market hypothesis. This hypothesis holds that share movements are random and not systematic. According to this approach it is possible for an investor to earn normal returns by randomly choosing securities of a given risk level. 2. PORTFOLIO ANALYSIS Portfolio analysis phase of portfolio management consist of identifying the range of portfolios that can be constituted from a given set of securities and calculating their return and risk for further analysis. It is better to invest in a group of securities rather than a single security. Such a group of securities held together as an investment is known as a portfolio. A rational investor attempts to find out the most efficient portfolio. The efficiency can be evaluated only in terms of the expected return and risk of different portfolio. Security analysis provides the investor with a set of worthwhile or desirable securities. From this set of securities an indefinitely large number of portfolios can be constructed by choosing different set of securities and also by varying the proportion of investment in each security. Each of these securities has its own risk return characteristics which are not just the aggregate of individual security characteristics. The risk and return can
- 10. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 10 be measured and expressed quantitatively. Portfolio is being constructed using the following formulas: 3. PORTFOLIO SELECTION The proper goal of portfolio construction is to generate a portfolio that provides the highest return at a given level of risk .A portfolio having this characteristic is known as efficient portfolio. From this set of efficient portfolios, optimal portfolio has to be selected for investment. 4. PORTFOLIO REVISION Having constructed the optimal portfolio, the investor has to constantly monitor the portfolio to ensure that it continues to be optimal. Portfolio revision involves changing the existing mix of securities. The main objective of portfolio revision is to ensure the optimality of the revised portfolio. Portfolio revision is not a causal process of portfolio management, portfolio revision is as important as portfolio analysis and selection. Portfolio revision may also be necessitated by some investor related changes such as availability of additional fund, changes in risk attitude, need of cash for other alternative use etc. portfolio revision has to be done scientifically and objectively so as to ensure the optimality of the revised portfolio. 5. PORTFOLIO EVALUATION The objective of constructing and revising it periodically is to earn maximum returns with minimum risk. Portfolio evaluation is the process which is concerned with assessing the performance of the portfolio over a selected period of time in terms of return and risk. It provides mechanism for identifying weakness in the investment process for improving these deficient areas. It provides a feedback mechanism for improving the entire portfolio management process TOOLS FOR PORTFOLIO EVALUATION SHARPE RATIO The performance measured developed by William Sharpe is referred to as the Sharpe ratio. It is the ratio of the reward or risk premium to the variability of return or risk as
- 11. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 11 measured by the standard deviation of return. The formula for calculating Sharpe ratio may be stated as Sharpe ratio (SR) = (portfolio Return – Risk free rate of return) Portfolio standard deviation = 𝑅𝑝−𝑅𝑓 𝜎𝑝 Where Rp=realized return on the portfolio Rf=Risk free rate of return σp=Standard deviation of portfolio return TREYNOR RATIO The performance measure developed by Jack Treynor is referred to as Treynor ratio or reward to volatility ratio. It is the ratio of the reward or risk premium to the volatility of return as measured by the portfolio beta. The formula for calculating Treynor ratio may be stated as Treynor ratio= (Portfolio Return- Risk free rate of return)/Portfolio beta = 𝑅𝑝−𝑅𝑓 𝛽 Where Rp=realized return on the portfolio Rf=Risk free rate of return βp=Portfolio beta Both the measures are relative measures of performance because they relate the return to the risk involved. However they differ in the measure of risk used for the purpose. Sharpe uses the total risk as measured by standard deviation, while treynor employs the systematic risk as measured by the beta coefficient in a fully diversified portfolio all the unsystematic
- 12. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 12 risk would be diversified away and the relevant measure of risk would be the beta coefficient. For such a portfolio Treynor ratio would be the appropriate measure of performance evaluation .For a portfolio that is not so well diversified , the Sharpe ratio using the the total risk measure would be the appropriate performance measure. JENSEN RATIO Another type of risk adjusted performance has been developed by the Michael Jensen and is referred to a Jensen ratio. This ratio measures the differential between actual return earned on a portfolio given its level of risk. The CAPM model is used to to calculate the expected return on a portfolio. The difference between the return that a portfolio should earn for a given level of risk Jensen Measure (αp)=Rp-E(Rp) Where, Rp- Realized return of the portfolio E(Rp)-Expected return of the portfolio E(Rp)=Rf+βp(Rm-Rf) βp-Beta of portfolio Rm-Market return Rf-Risk free rate of return The difference between the return actually earned on a portfolio and the return expected from the portfolio is a measure of the excess return. The differential return is calculated as follows αp= Rp- E(Rp) Where αp=Differential return earned Rp= actual return earned on the portfolio
- 13. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 13 E(Rp)=Expected return DIVERSIFICATION If one holds, say, equal amount of risky assets that are not perfectly correlated, the portfolio expected return will be the average of the expected returns of the asset in the portfolio. However the portfolio standard deviation will be, less than the average of the standard deviation of the assets in the portfolio. The power of this statement may be explained by imagining two assets with the same expected return and the same standard deviation of the return. by holding both assets in a portfolio, one obtain the same expected return as either one of them, but a standard deviation that is lower than any one of them individually. Thus diversification leads to a reduction in risk without any sacrifice in expected return. RISK AND RETURN While making a decision regarding investment and financing, the investor seeks to achieve right balance between risks and return in order to optimize the value. Return and risk go together in investment. Everything an investor does is tied directly or indirectly to return and risk. The concept of return and risk is explained below. RISK Risk is the potential for variability in return. The expected return is the uncertain future return that an investor expects to get from his investments. The realized return on contrary is the certain return that an investor has actually obtained from his investment from the end of the holiday period. The risk arises where there is a possibility of variation between expectations and realizations with regard to an investment. Element of Risk. The essence of risk is an investment is the variation in its returns. This variation in returns is caused by a number of factors. These factors which produce variation in the return from an investment constitute the element of risk. Total risk = Systematic Risk + Unsystematic Risk.
- 14. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 14 Systematic Risk The impact of economic, political and social changes is system-wide and that portion of total variability in security return caused by such system- wide factor is referred to as systematic risk. Systematic risk is further sub divided into: 1. Interest rate risk: Interest rate risk is a type of systematic risk that particularly affects securities like bond and debentures. The risk caused as the variation in bond prices caused due to the variation in interest rate is known as interest rate risk. 2. Market risk: Market risk is a type of systematic risks that affect the shares. Market risk is the increased variability of investor returns due to the alternating movement of share market. 3. Purchasing power risk: It refers to the variation in investor return caused by inflation. Inflation causes a variation in the purchasing power of the returns from an investment. This is known as purchasing power risk and its impact is uniformly felt on all securities in the market and as such, is a systematic risk. Unsystematic Risk The return from a security may vary because of certain factors affecting only the company issuing such securities. When variability of returns occurs because of such firm- specific factors it is known as unsystematic risk. The unsystematic risk or unique risk affecting specific securities arises from two sources. • The operating environment of the company • The financing pattern adopted by the company These two types of unsystematic risk are referred to as business risk and financial risk 1. Business risk: Business risk is thus a function of the operating conditions faced by a company and is the variability in operating conditions of the company. 2. Financial risk: Financial risk is a function of financial leverage which is the use of debt in the capital structure. The variability in EPS due to the presence of debt in capital structure of a company is referred to as financial risk.
- 15. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 15 MEASUREMENT OF RISK Expected Returns The expected return of the investment is the probability weighted average of all the possible returns. Ri = α¡+ β¡ Rm Measurement of Systematic Risk The systematic risk of a security is measured by a statistical measure called Beta βi = rim σi σm σ²m RETURN Return is a motivating force, inspiring the investor in the form of rewards, for undertaking the investment. The importance of return in any investment decision can be trace to the following factors: It enables the investor to compare alternative investment in terms of what they have to offer the investor. Measurement of historical (past) return enables the investor to assess how well they have done. Measurement of historical returns also helps in estimation of future returns. Components of Return Return is basically made up of two components: The periodic cash receipt or income on the investment in the form of interest, dividend etc.The term yield is often used in connection with this component of return. Yield refers to the income derived from a security in relation to its price, usually its purchase price. The appreciation (depreciation) in the price of the asset, is referred to as capital gain(loss).this is the difference between the purchase price and the price at which the asset can be, or is, sold.
- 16. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 16 OPTIMAL PORTFOLIO SELECTION The objective of every rational investor is to maximize his returns and minimize the risk. Diversification is the method adopted for reducing risk. It essentially results in the construction of portfolios. The proper goal of portfolio construction would be to generate a portfolio that provides the highest return and the lowest risk. Such a portfolio would be known as the optimal portfolio. The process of finding the optimal portfolio is described as portfolio selection. PORTFOLIO OPTIMIZATION Portfolio optimization is a part of portfolio selection. Portfolio optimization helps to maximize the returns with minimum risk. OPTIMAL PORTFOLIO SELECTION USING SHARPE’S OPTIMIZATION MODEL The Sharpe’s optimization model was developed by researcher William Sharpe. Sharpe had provided a model for the selection of appropriate securities in a portfolio. In this model, the ranking criteria are used to order the stocks for selecting the optimal portfolio. The Sharpe optimization model uses excess return to beta as the performance measure of individual securities so as to include in the portfolio Sharpe had provided a model for the selection of appropriate securities to be included in a portfolio. The selection of any stock is directly related to its excess return beta ratio. FORMATION OF OPTIMAL PORTFOLIO The inclusion of any security in the portfolio is directly related to its excess return to beta ratio. Excess return is the difference between the expected return on the stock and the risk free rate of interest such as rate of return on Government securities. The excess return-to- beta ratio measures the additional return on a stock (excess return over the risk free rate) per unit of non –diversifiable risk. This ratio gets easy interpretation and acceptance because this ratio gives relationship between potential reward risks. The numerator of this ratio gives the extra return over the risk- free rate and the denominator give the non-diversifiable risk.
- 17. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 17 Excess return to beta ratio= (Ri-Rf)/βi Where Ri = the expected return on security i Rf = the return on risk less asset βi = the expected change in the ratio of return on stock I associated with a 1% change in the market return If the stock ranked by excess return –to – beta (from highest to lowest), ranking represents the desirability of a stock inclusion in the portfolio. This implies that if a particular stock with a specific ratio of (Ri-Rf)/βi included in the optimal portfolio, all stocks with higher ratio will also be included. On the other hand, if a stock with a particular (Ri-Rf)/βi is excluded from an optimal portfolio; all stocks with a lower ratio will be excluded. The number of stocks included in the optimal portfolio depends on a unique cut off rate which ensures that all stocks with higher (Ri-Rf)/βi will be included and all stocks with lower ratios should be excluded. Cut off rate is denoted by “C*” The steps for finding out the stocks to be included in the optimal portfolio are given below 1. Find out the “excess return to beta” ratio for each stock under consideration 2. Rank them from the highest to lowest. 3. Proceed to calculate Ci for all stocks according to the ranked order using the following formula Ci= (𝜎²𝑚 (𝐑𝐢 − 𝐑𝐟)/𝛔²𝐞𝐢)/(𝟏 + 𝛔 𝟐 𝐦 (𝛃 𝐢 𝟐 /𝛔²𝐞𝐢))𝐧 𝐢=𝟎 βi =Beta of each security σi =Risk of security Ri =Return of each security Rf =Risk free rate of return
- 18. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 18 Ci= Cut off rate σ2m=Variance of the market index σ2ei = Unsystematic Risk 4. The cumulated values of Ci starts declining after a particular Ci and that point is taken as the cut-off point and that stock ratio is the cut –off ratio C* CONSTRUCTING THE OPTIMAL PORTFOLIO Once the cut-off rate is determined the next step is calculating the proportion to be invested in each security. The proportion invested in each security is: 𝑿𝒊 = 𝒁𝒊/ 𝒁𝒊 𝒏 𝒊=𝟏 Where 𝒁𝒊 = 𝜷𝒊 𝝈 𝟐 𝒆𝒊 𝑹𝒊 − 𝑹𝒇 𝜷𝒊 − 𝑪 ∗ Zi =weight on each security βi =Beta of each security σ²ei =Unsystematic risk of security Ri =return of each security Rf =Risk free rate of return C* = cut off rate SINGLE INDEX MODEL The basic notion underling the single index model is that all stocks are attracted by movements in the stock market. Casual observation of share prices reveals that when the market moves up (as measured by any of the widely used stock market indices), prices of most of the shares tends to increase. When the market goes down, the price of most shares
- 19. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 19 tend to decline. This suggests that one reason why security returns might be correlated and there is co-movement between securities, is because of a common response to market changes. this co-movement of stocks with a market index may be studied with the help of a simple linear regression analysis, taking the returns on an individual security as the depended variable(Ri) and the returns on the market index (Rm)as the independent variable. The return of individual securities may be expressed as: 𝑹𝒊 = 𝜶𝒊 + 𝜷𝒊(𝑹𝒎 + 𝒆𝒊) Where, α¡ is the component of security i's return that is independent of the market performance. Rm is the rate of return on the market index. β¡ is the constant that measures the expected change in Ri given a change in Rm. e¡ is the error term representing the random or residual return. Sharpe’s Optimal Portfolio Sharpe has provided a model for the selection of the appropriate securities in the portfolio. The selection of any stock is directly related to its excess return – beta ratio. = 𝑹𝒊 − 𝑹𝒇 𝜷𝒊 where, Ri – the expected return of the stock i. Rf – Risk free return βi - the expected change in the rate of return on the stock i, associated with one unit change in the market return. A fund allocated with the highest possible Sharpe ratio is said to be Sharpe optimal. To find the Sharpe optimal portfolio, consider the plot on the investment opportunity set of risk return possibilities for a portfolio. The slope of a straight line drawn from the risk-free
- 20. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 20 rate to a portfolio gives the Sharpe ratio for that portfolio. Hence, the portfolio on the line with the steepest slope is the Sharpe optimal portfolio. Ranking of the stock are done on the basis of their excess return to beta. Portfolio manager would like to include stock with the highest ratio .The selection of the stocks depends on a unique cut-off rate such that all stock higher ratio of Ri – Rf / βi are included and stock within lower ratio are left off. The cut-off point is denoted by C*.Sharpe optimal portfolio is one of the efficient portfolios on the Markowitz efficient frontier. PORTFOLIO EVALUATION: The optimized portfolios are being evaluated using the following tools. i. Sharpe ratio ii. Treynor ratio iii. Jensen Measure VALUE AT RISK Risk management attempts to provide financial predictability for a company. Every day firms face financial risks. Interest and exchange rate volatility, default on loans, and changes in credit rating are some examples. These risks can be sorted into two categories- credit risk and market risk. Credit risk includes all risks associated with the credit of specific participants, such as potential default or changes in credit rating. Market risk refers to risks affecting broad sectors of the economy, such as an increase in interest rates, currency devaluation, or a decline in commodities prices, like aluminum and oil. Financial analysts use a number of innovations to calculate and hedge against these kinds of risk. One innovation that has been receiving immense attention is Value at Risk. Value at Risk is a summary statistic that quantifies the exposure of an asset or portfolio to market risk, or the risk that a position declines in value with adverse market price changes. Measuring risk using VaR allows managers to statements regarding the expected losses for a certain period.
- 21. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 21 To arrive at a VaR measure for a given portfolio, a firm must generate a probability distribution of possible changes in the value of some portfolio over a specific time or “risk horizon” .J.P.Morgan Chairman Dennis Weatherstone introduced this concept. Different approaches for calculating VaR VaR can be calculated in many ways. As a result, firms using different calculating methods can arrive at different Value at Risk numbers for the same portfolio. There are advantages and disadvantages in each method of calculating VaR Monte Carlo Simulation Variance Covariance model Historical Simulation Method Monte Carlo Simulation For applying Monte Carlo simulation technique, security prices are assumed to be a random variable. It is also assumed that the stock market is efficient in the weak form (which is true for Indian Market).Since stock price is a random variable; the stock price movement is a stochastic process. The Wiener process, which is a particular type of Markov stochastic process, best defines the stock price movement. The mathematical model which defines the stock price movements under Wiener process is given by the following mathematical relation: ∂s = μS∂t + σSЄ√∂ t Where, ∂s = change in the stock price for a small change in time interval ∂ t S= stock price at time t μ = expected rate of return per unit of time ε = Random drawing from a standardized normal distribution σ = Volatility of stock price or standard deviation of the expected return ∂ t = A small time interval
- 22. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 22 The stock price after a small time interval ∂ t would be ST = S+∂s Since the period considered is very small, a logo normal return or continuously compounded return would be more appropriate. So the expected return μ for period T is defined as 𝝁 = 𝟏 𝑻 𝓵𝐧 ∗ (𝐒𝐭/𝐒𝟎) Where ST = Stock price at time T SO = Stock price at time Zero ℓn = Natural logarithm T =Time interval in years Following steps are involved in Monte Carlo Simulation to calculate one-day VaR for a portfolio. 1. Determining the expected return and standard deviation of the return for the stock (μ and σ).These are assumed to be constant. 2. Value the portfolio today.(in our case 31.4.2008) in the usual way by using current value of the stock price . 3. Sample once from the multivariate normal probability distribution to determine the value of ε (for the purpose we have used a random number generator to obtain the random number ε with the computer by using Microsoft Excel) 4. Determine the change in value of the security and the new value of the security using the relation. For our analysis ∂ t = 1 day 5. Revalue the portfolio at the end of the day in the usual way.
- 23. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 23 6. Subtract the value calculated in step 2 from the value in steps to determine a sample change in portfolio value ∂P. 7. Repeat steps (3) to (6) many times (in our case 500 times) to build up a probability distribution for ∂P. We have repeated the steps to obtain 500 sample values for ∂P. The VaR is calculated at 99%and95% confidence level. The 500 simulated values of changes in portfolio values so obtained are then sorted in ascending order.1-day VaR at 99% is the 5th worst outcome and 1-day VaR at 95% is the 25th worst outcome. LITERATURE REVIEW Investment risk management in Tehran Stock Exchange (TSE) using technique of Monte Carlo Simulation (MCS) is a paper presented by Darush Farid, (Department of Economics, Management and Accounting, Yazd University, Yazd, Iran),Alireza Rajabipoor Meybodi, (Department of Business Management, Meybod University – Payam E Noor (PNU), Yazd-Meybod, Yazd, Iran), Seyed Heydar Mirfakhraddiny, (Department of Economics, Management and Accounting, Yazd University, Yazd, Iran) with the purpose to identify how to manage risk by the use of “value at risk (VaR) concept” with Monte Carlo Simulation (MCS) technique in stock exchanges. The paper specifies which equity stocks have been more affected on VaR in set of portfolio and which equity stocks are lesser affected. In addition, the main result which is derived by the research shows that if there is a loss at future, what is max the loss at the level confidence which could be imposed by investors. Thus, the paper suggests how the investors can invest their capital so that they would minimize their loss and maximize their profit. Risk-return optimization with different risk-aggregation strategies is a journal presented by Stan Uryasev, Ursula A Theiler and Gaia Serraino tells new methods of integrated risk modelling play an important role in determining the efficiency of bank portfolio management. The purpose of this paper is to suggest a systematic approach for risk strategies formulation based on risk-return optimized portfolios, which applies different methodologies of risk measurement in the context of actual regulatory requirements. The authors find evidence that risk aggregation in Internal Capital Adequacy Assessment Process (ICAAP)
- 24. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 24 should be based on risk-adjusted aggregation approaches, resulting in an efficient use of economic capital. By using different values of confidence level in VaR and CVaR, deviation, it is possible to obtain optimal portfolios with similar properties. Before deciding to insert constraints on VaR or CVaR, one should analyze properties of the dataset on which computation are based, with particular focus on the model for the tails of the distribution, as none of them is “better” than the other.
- 25. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 25 CHAPTER 3 INDUSTRY AND ORGANIZATION PROFILE
- 26. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 26 INTRODUCTION Capital Market Evolution Indian Stock Markets are one of the oldest in Asia. Its history dates back to nearly 200 years ago. The earliest records of security dealings in India are meager and obscure. The East India Company was the dominant institution in those days and business in its loan securities used to be transacted towards the close of the eighteenth century. By 1830's business on corporate stocks and shares in Bank and Cotton presses took place in Bombay. Though the trading list was broader in 1839, there were only half a dozen brokers recognized by banks and merchants during 1840 and 1850. The 1850's witnessed a rapid development of commercial enterprise and brokerage business attracted many men into the field and by 1860 the number of brokers increased into 60.In 1860-61 the number of brokers increased to about 200 to 250. In 1865, a disastrous slump began (for example, Bank of Bombay Share which had touched Rs 2850 could only be sold at Rs. 87). At the end of the American Civil War, the brokers who thrived out of Civil War in 1874, found a place in a street (now appropriately called as Dalal Street) where they would conveniently assemble and transact business. In 1887, they formally established in Bombay, the "Native Share and Stock Brokers' Association" (which is alternatively known as “The Stock Exchange "). In 1895, the Stock Exchange acquired a premise in the same street and it was inaugurated in 1899. Thus, the Stock Exchange at Bombay was consolidated. Indian Stock Exchanges - An Umbrella Growth The Second World War broke out in 1939. It gave a sharp boom which was followed by a slump. But, in 1943, the situation changed radically, when India was fully mobilized as a supply base. On account of the restrictive controls on cotton, bullion, seeds and other commodities, those dealing in them found in the stock market as the only outlet for their activities. They were anxious to join the trade and their number was swelled by numerous others. Many new associations were constituted for the purpose and Stock Exchanges in all parts of the country were floated. The Uttar Pradesh Stock Exchange Limited (1940), Nagpur Stock Exchange Limited (1940) and Hyderabad Stock Exchange Limited (1944) were incorporated. In Delhi two stock
- 27. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 27 exchanges - Delhi Stock and Share Brokers' Association Limited and the Delhi Stocks and Shares Exchange Limited - were floated and later in June 1947, amalgamated into the Delhi Stock Exchange Association Limited. Trading Pattern of the Indian Stock Market Trading in Indian stock exchanges is limited to listed securities of public limited companies. They are broadly divided into two categories, namely, specified securities (forward list) and non-specified securities (cash list). Equity shares of dividend paying, growth-oriented companies with a paid-up capital of at least Rs.50 million and a market capitalization of at least Rs.100 million and having more than 20,000 shareholders are, normally, put in the specified group and the balance in non-specified group. Two types of transactions can be carried out on the Indian stock exchanges: (a) spot delivery transactions "for delivery and payment within the time or on the date stipulated when entering into the contract which shall not be more than 14 days following the date of the contract and (b) forward transactions "delivery and payment can be extended by further period of 14 days each so that the overall period does not exceed 90 days from the date of the contract". The latter is permitted only in the case of specified shares. The brokers who carry over the outstandings pay carry over charges (cantango or backwardation) which are usually determined by the rates of interest prevailing. A member broker in an Indian stock exchange can act as an agent, buy and sell securities for his clients on a commission basis and also can act as a trader or dealer as a principal, buy and sell securities on his own account and risk, in contrast with the practice prevailing on New York and London Stock Exchanges, where a member can act as a jobber or a broker only. The nature of trading on Indian Stock Exchanges are that of age old conventional style of face-to-face trading with bids and offers being made by open outcry. However, there is a great amount of effort to modernize the Indian stock exchanges in the very recent times. Over The Counter Exchange of India (OTCEI) The traditional trading mechanism prevailed in the Indian stock markets gave way to many functional inefficiencies, such as, absence of liquidity, lack of transparency, unduly long settlement periods and benami transactions, which affected the small investors to a great extent.
- 28. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 28 To provide improved services to investors, the country's first ringless, scripless, electronic stock exchange - OTCEI - was created in 1992 by country's premier financial institutions - Unit Trust of India, Industrial Credit and Investment Corporation of India, Industrial Development Bank of India, SBI Capital Markets, Industrial Finance Corporation of India, General Insurance Corporation and its subsidiaries and CanBank Financial Services. Trading at OTCEI is done over the centres spread across the country. Securities traded on the OTCEI are classified into: • Listed Securities - The shares and debentures of the companies listed on the OTC can be bought or sold at any OTC counter all over the country and they should not be listed anywhere else • Permitted Securities - Certain shares and debentures listed on other exchanges and units of mutual funds are allowed to be traded • Initiated debentures - Any equity holding at least one lakh debentures of particular scrip can offer them for trading on the OTC. The Indian Financial system is regulated and supervised by two government agencies under the Ministry of Finance - They are: • The Reserve Bank of India [RBI] • The Securities Exchange Board of India [SEBI] All parts of the financial system are interconnected with one another and the jurisdictions of the RBI and the SEBI overlap in many fields. • Securities and Exchange Board of India • Stock Exchanges of India Scope of Capital Market Research We were next faced with another difficult question about what can be classified as a work on capital markets. A variety of work in economics, accounting and finance would have some linkages with capital markets. Works in corporate finance have strong linkages with security markets. For our purpose therefore, we considered works falling into any of the following categories as those belonging to the field of capital markets: valuation of stocks
- 29. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 29 and functioning of the stock markets; valuation of bonds, convertible debentures and market for debt; new issues market and merchant banking; market efficiency; dividends, bonus & rights issues and rates of return; and performance and regulations of mutual Bombay Stock Exchange Established in 1875, BSE Ltd. (formerly known as Bombay Stock Exchange Ltd.), is Asia’s first Stock Exchange and one of India’s leading exchange groups. Over the past 137 years, BSE has facilitated the growth of the Indian corporate sector by providing it an efficient capital-raising platform. Popularly known as BSE, the bourse was established as "The Native Share & Stock Brokers' Association" in 1875. BSE is a corporatized and demutualised entity, with a broad shareholder-base which includes two leading global exchanges, Deutsche Bourse and Singapore Exchange as strategic partners. BSE provides an efficient and transparent market for trading in equity, debt instruments, derivatives, mutual funds. It also has a platform for trading in equities of small-and-medium enterprises (SME). More than 5000 companies are listed on BSE making it world's No. 1 exchange in terms of listed members. The companies listed on BSE Ltd command a total market capitalization of USD 1.32 Trillion as of January 2013. It is also one of the world’s leading exchanges (3rd largest in December 2012) for Index options trading (Source: World Federation of Exchanges). BSE also provides a host of other services to capital market participants including risk management, clearing, settlement, market data services and education. It has a global reach with customers around the world and a nation-wide presence. BSE systems and processes are designed to safeguard market integrity, drive the growth of the Indian capital market and stimulate innovation and competition across all market segments. BSE is the first exchange in India and second in the world to obtain an ISO 9001:2000 certification. It is also the first Exchange in the country and second in the world to receive Information Security Management System Standard BS 7799-2-2002 certification for its On-Line trading System (BOLT). It operates one of the most respected capital market educational institutes in the country (the BSE Institute Ltd.). BSE also provides depository services through its Central Depository Services Ltd. (CDSL) arm.BSE’s popular equity index - the S&P BSE SENSEX - is India's most widely tracked stock market benchmark index. It is traded internationally on the EUREX as well as leading exchanges of the BRCS nations (Brazil, Russia, China and South Africa).
- 30. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 30 BSE has won several awards and recognitions that acknowledge the work done and progress made like The Golden Peacock Global CSR Award for its initiatives in Corporate Social Responsibility, NASSCOM - CNBC-TV18’s IT User Awards, 2010 in Financial Services category, Skoch Virtual Corporation 2010 Award in the BSE StAR MF category and Responsibility Award (CSR) by the World Council of Corporate Governance. Its recent milestones include the launching of BRICSMART indices derivatives, BSE-SME Exchange platform, S&P BSE GREENEX to promote investments in Green India Vision "Emerge as the premier Indian stock exchange with best-in-class global practice in technology, products innovation and customer service." Brand identity Bombay Stock Exchange has now adopted only its initials as the new name (BSE), positioning itself better position as a national multi-asset financial infrastructure institution. BSE’s strategic shift in approach, attitude and business focus is reflected in its new tag line - Experience the New. With renewed zeal and focus on new business opportunities, product and service innovation, upgrades in technology, increased investor and member focus, BSE is always pushing the envelope on all fronts. The ambition is to continually improve and adopt new and better ways of conducting our business. As the first stock exchange in Asia and the pioneer of securities transaction business, BSE prides itself on being at the forefront of bringing innovations to the Indian capital markets while creating diverse investment opportunities for the investor community in India throughout its long history. BSE continues to undertake several initiatives to build on its strong brand, legacy and market position to create value for its stakeholders and the financial system. Product information Equity BSE Equities data is available in Real-time and as 1 minute snapshots Following data is available in the feed for Equities.
- 31. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 31 Level 1 Data contains the following information: BSE Scrip Code Open, High, Low and Last Traded Price Best Bid / Offer with Volume Traded Volume Level 2 Data contains the following information in addition to the level 1 data: Weighted Average Price Upper Circuit Limit and Lower Circuit Limit Turnover Value, Number of Trades, Trend Total Buy Quantity and Total Sell Quantity Derivatives BSE provides trading opportunities for Equity and Index Derivatives. The data related to the trading of these instruments is available in the same format as the Equities data. BSE currently has Index and Equity Futures contracts, Index and Equity Monthly Options contracts and Index and Equity Weekly Options contracts. For the purpose of popularising the Derivatives trading on BSE, currently Derivatives data is being provided free of charge and without any reporting obligations for Real-time distributors. Debt BSE provides opportunities to trade in Debt instruments, both government as well as corporate debt. The trade feeds for these instruments are available along with the BSE equities feeds. In addition to the traded debt instruments, BSE also provides a facility to report Over the Counter trades in Corporate Bonds on the Indian Corporate Debt Market (ICDM). ICDM feeds are separately available for subscription. These feeds are provided through the Internet in XML format. Indices BSE Indices are available through the feed in Real-time and as 1 minute snapshots. All indices that are calculated on real-time are being provided in this feed. Open, High, Low and Latest Value of the Indices are provided in the feed.
- 32. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 32 COMPANY PROFILE JRG Securities Limited is headquarter in Kochi, in the state of Kerala in the southern part of India. The Comp. took life as a partnership firm called JRG Associates, started by Mr. Regi Jacob, Mr. Giby Mathew and Mr. Jiji Antony in 1992. The firm was converted into a private limited company; JRG Associates Pvt. limited in 1994 with the inclusion of few of their close relatives & associates on the board as financial investors, and became a member of Cochin Stock Exchange. The Company initially focused on developing a client base in Kerala & Tamil Nadu & established several operation centers across these states. In 1999, the Comp. became a member of NSE & in the following years, began to cultivate clients from Karnataka, Andhra Pradesh & Maharashtra. As the business developed, JRG intensified its operational reach in the southern states. In August 2003, the company changed its name to JRG Securities Pvt. Ltd. in order to accurately reflect the business focus of the company. The following month, i.e. September 2003, the company was converted into a public limited company and over the next two years began operations in commodities and insurance broking and distribution of financial products. In March 2005, we become a member of the BSE. In April 2006, JRG Securities Limited, the flagship company of JRG Group, came out with a Rs 14.50 crore public issue of 36,25,000 equity shares with a face value of Rs 10 at a premium of Rs 30 per share. In July 2007, Baring India Private Equity Fund II Ltd (Baring India) announced an investment of up to $35 million in JRG Securities Ltd. through a preferential issue and warrants for a minimum 44.8 per cent stake in the company, subject to the approvals from Securities and Exchange Board of India and shareholders among others. Post the allotment, Baring India Partners will become the single largest share holder in the company VISION JRG Securities Limited was born out of a vision to explore the immense investment opportunities in the Indian financial market, to benefit the investors. The company is built on the pillars of financial expertise, professionalism, exemplary ethics and a commitment to provide ultimate customer satisfaction. JRG constantly strives to meet the changing market needs and trends.
- 33. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 33 They cater efficiently to the diverse and complex needs of over 200,000 customers, most of whom are individual traders, institutions and money managers. The vision of the JRG Group is to be a Financial Super Market. It aims to provide all types of financial services to its clients at one place to save them from going from place to place to meet their investment needs. Guiding Principles of JRG Serve the clients with the highest level of responsiveness and integrity. Place the client's interests and protection of their investment as the top priorities. Operate on predefined and constantly updated service standards. Be customer driven, rather than deal drive. Adopt futuristic technology to gather vital information on real time basis to optimize investor protection and investor returns. Set up most modern trading facilities for its clients at par with global standards. Group of Companies JRG Securities Ltd JRG Wealth Management Ltd JRG Insurance Broking Pvt. Ltd JRG Metal & Commodities DMCC, Dubai JRG Fin Corp Limited Competitors The major competitors of JRG securities are: • Geojit Financial Services Limited • Karvy Stock Broking Limited • Olive Capital And Services Private Limited • Mathew Chacko & Co
- 34. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 34 JRG’S Competitive advantage • Member of NSE,BSE • Member of the leading commodity exchanges NCDEX, NMCE, and MCX. • Country wide network and presence • Integrated V-sat and VPN network across India • State of the art online Back office operations • Exclusive NRI Services. • Strong Research Division • Training and Development opportunities. • Risk management Services • Strong and loyal clients JRG’S Business strategy The company’s business processes are empowered by knowledge and it creates competitive edge over our competitors. JRG have charted our future growth plans after the analysis of the financial services scenario. JRG derive our business prospects from the following key considerations: • Potential to add value in providing financial products • Recognition and appreciation of global systems and processes as a differentiator • Growth potential of the sector. • Opportunities for various financial products and competitor activity • Macro economic considerations. JRG focus to empower our business processes and systems with latest and futuristic technologies. And committed to adopt global best practices in technology for the increased customer satisfaction and improving process efficiencies. JRG have set ambitious targets for Insurance operations. JRG’s team of sales managers and financial advisors would set the
- 35. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 35 standard of operations and best practices. The JRG will open Branches across India with greater velocity to cater to the invest needs of the customers. Organizational Chart Source: secondary data from the company JRG securities Ltd. Services offered by JRG JRG was set up in 1992 and at that time they were focusing only on broking service sector. But, gradually their service portfolio was stretched from stock brokering to various exchanges such as capital, commodity, and insurance and also in mutual funds. • Stock Broking- Within the short period of time, JRG Securities Ltd. Has becomes one of the leading broking houses in India. For supporting the stock broking functions, JRG has a very active Research Department with highly qualified financial experts. Back office staff Dealer Equities Office assistance Dealer commodities State head Territory manager Branch manager MD
- 36. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 36 • Commodity Broking- On June, 2003 JRG achieved its milestone by introducing online commodity futures trading. Today, JRG offers online commodity future trading in rubber, pepper, coconut oil, rice, wheat, gold, silver and 46other commodities. • Insurance Broking- The JRG group of companies strengthens their services to the public by adding general and life insurance services. JRG obtained license for extending general and life insurance services of 24 Indian Insurance Companies to the public as the insurance broker. • Mutual funds and Bond services- Today more and more people are discovering mutual funds as the better investment options. JRG has a strong mutual fund wing and they use objective and quantitative measures to identify the best funds. • Depository Services- JRG is a depository participant of National Securities Depository Ltd. (NSDL). The main objective of depository system is to reduce risk by minimizing the paper work involved in trading, settling and transferring securities.
- 37. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 37 CHAPTER 4 DATA ANALYSIS
- 38. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 38 INTRODUCTION TO DATA ANALYSIS &INTERPRETATION ANALYSIS PART-1 SECURITY ANALYSIS A rational investor makes investment decisions by evaluating the risk and return of a security. A better evaluation strategy would be to determine the risk adjusted rate of return of the security .an investor would also be interested in identifying mispriced securities in the market in order to make buy, hold or sell decisions. Security analysis consists of examining the risk-return characteristics of individual securities. Security analysis also involves identifying mispriced securities by determining the intrinsic value of the securities. ASSUMPTIONS All stocks selected are included in BSE. Stocks are selected in such a way that Beta value is near to or more than 1. Stocks are selected from different sectors. Risk free rate is taken as 8.10%, which is rate of interest on 91 days T-Bill rate. Since specialized optimization software is not available& also manual computation involved would be extensive, calculations are done in excel using different functions. RISK AND RETURN OF SECURITIES: The return of the securities is measured by the arithmetic mean of the security’s return. The risk of the security is measured by the variance or standard deviation of its securities. The risk adjusted rate of return of the security is the excess return per unit of risk, the excess return being the difference between the security return and the risk free rate of return. For our analysis the risk free return is taken as 8.10%
- 39. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 39 TABLE1: Showing the Return of Securities SECURITIES RETURN(Ri %) ACC 9.775434154 AIRTEL 3.755249102 CIPLA 6.409999744 MRF 23.05587277 BRITANIA 11.43700679 APOLLOTYRES 12.85362527 IOC 1.914868774 INFOSYS 6.235360781 JETAIR 16.60978579 BOSCH 22.915216 DABUR 20.75980261 BAJAJ AUTO 22.87184654 Source: Computed by the researcher Using Primary Data collected from BSE Ltd website CHART 3: Showing Return of Securities 0 5 10 15 20 25 RETURN(Ri%) RETURN(Ri %) INFERENCE: From the above table and chart it is clear that MRF has the maximum return (23.06%) and INDIAN OIL CORPORATION has the minimum return (1.91%).
- 40. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 40 TABLE2: Showing the Risk of Securities SECURITIES RISK (σi) ACC 24.74421321 AIRTEL 31.42032496 CIPLA 22.92643112 MRF 30.75069892 BRITANIA 22.79374556 APOLLOTYRES 40.25893133 IOC 27.9595705 INFOSYS 26.92425907 JETAIR 52.68658093 BOSCH 18.8487195 DABUR 22.2483177 BAJAJ AUTO 26.04673059 Source: Computed by the researcher Using Primary Data collected from BSE Ltd website CHART 4: Showing Risks of Securities 0 10 20 30 40 50 60 RISK (σi) RISK (σ INFERENCE: From the above table and chart it is clear that JET AIR (52.68%) is having the maximum total risk & BOSCH (18.85%) is having the minimum total risk. BETA The beta value indicates the measure of systematic risk of a security. Beta describes the relationship between the stock return and market index return. Beta of a security may be positive, negative, zero. The beta of an asset is the measure of the variability of that asset
- 41. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 41 relative to the variability of the market as a whole. Beta is an index of the systematic risk of an asset Βi= 𝑵 𝒙𝒚− 𝒙 𝒚 𝑵 𝒙 𝟐 − 𝒙 𝟐 N = Number of Observation =750 Y = (Current Stock Price – Yesterday’s Stock Price)*100 Yesterday’s Stock Price X = Current Market Index- Yesterday’s Market Index ×100 Yesterday’s Market Index TABLE 3: Showing Beta Values Of Securities SECURITY βi ACC 0.685184039 AIRTEL 0.802056364 CIPLA 0.46972998 MRF 0.833538788 BRITANIA 0.279525438 APOLLOTYRES 1.173529896 IOC 0.447230221 INFOSYS 0.876494436 JETAIR 1.257658321 BOSCH 0.283724534 DABUR 0.350578089 BAJAJ AUTO 0.690437997 Source: Computed by the researcher Using Primary Data collected from BSE Ltd
- 42. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 42 CHART 5: Showing Beta Value of Securitie INFERENCE: From the above table and graph it can be seen that JETAIR has the maximum beta value, which means maximum sensitivity to market (1.26). The minimum sensitivity to market is for BRITANIA (0.27). ALPHA The alpha value indicates the extra return earned by the stock over and above the market return. Alpha measures the unsystematic risk of a security. Return of stock = alpha + (Beta ×Market Return per Year) Ri = αi+ (βi×Rm) So Alpha (αi) = Ri-( βi×Rm) Where, αi - Alpha of the security Ri - return of the security βi - Beta of the security Rm - Return of the market 0 0.2 0.4 0.6 0.8 1 1.2 1.4 βi βi
- 43. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 43 TABLE 4: Showing Alpha Value of Securities SECURITY αi ACC 0.029405585 AIRTEL 0.003670965 CIPLA 0.018992773 MRF 0.080427947 BRITANIA 0.041792417 APOLLOTYRES 0.034807687 IOC 0.001330647 INFOSYS 0.012538027 JETAIR 0.048641814 BOSCH 0.087645832 DABUR 0.078078122 BAJAJ AUTO 0.081716885 Source: Computed by the researcher Using Primary Data collected from BSE Ltd CHART 6: Showing Alpha Values of Securities INFERENCE: BOSCH has the maximum Alpha (0.08) indicating that it has maximum extra return and INDIAN OIL CORPORATION has the minimum Alpha (0.001). DECOMPOSITION OF TOTAL RISK OF SECURITIES The total risk of security can be resolved in to two components; the systematic or market risk, which cannot be diversified, and the unsystematic or specific risk, which can be 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 αi αi
- 44. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 44 diversified by construction of the portfolio. An investor would be interested in knowing these two risks of the security in order to plan his portfolio. For the purpose of the analysis the systematic and unsystematic risk of the securities are measured by using Sharpe’s single index model. According to Sharpe’s single index model: Systematic risk = β 1 2 2 m Unsystematic risk = 2 - β 1 2 2 m TABLE 5: Showing Systematic Risks of Securities Security β¡ β¡² σᵐ σᵐ² β¡²·σᵐ² ACC 0.685184039 0.469477167 17.06847467 291.3328274 136.7741106 AIRTEL 0.802056364 0.643294412 17.06847467 291.3328274 187.4127798 CIPLA 0.46972998 0.220646254 17.06847467 291.3328274 64.28149698 MRF 0.833538788 0.694786912 17.06847467 291.3328274 202.4142354 BRITANIA 0.279525438 0.07813447 17.06847467 291.3328274 22.76313613 APOLLOTYRES 1.173529896 1.377172418 17.06847467 291.3328274 401.2155342 IOC 0.447230221 0.20001487 17.06847467 291.3328274 58.27089766 INFOSYS 0.876494436 0.768242496 17.06847467 291.3328274 223.8142585 JETAIR 1.257658321 1.581704453 17.06847467 291.3328274 460.8024304 BOSCH 0.283724534 0.080499611 17.06847467 291.3328274 23.45217934 DABUR 0.350578089 0.122904997 17.06847467 291.3328274 35.8062602 BAJAJ AUTO 0.690437997 0.476704628 17.06847467 291.3328274 138.8797072 Source: Computed by the researcher Using Primary Data collected from BSE Ltd CHART 7: Showing Systematic Risks of Securities 0 50 100 150 200 250 300 350 400 450 500 β¡²·σᵐ² β¡²·σᵐ²
- 45. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 45 INFERENCE: Systematic risk or non-diversifiable risk is the component of the total risk, which cannot be diversified. From the above table it is clear that JETAIR has the maximum systematic risk (460.80) and BRITANIA has minimum systematic risk (22.76) TABLE 6: Showing Unsystematic Risk or Residual Variance of Securities Security σ¡ σ¡² β¡²·σᵐ² σei2 = σi² - βi².σm² ACC 24.74421321 612.2760872 136.7741106 475.5019766 AIRTEL 31.42032496 987.2368205 187.4127798 799.8240407 CIPLA 22.92643112 525.6212437 64.28149698 461.3397467 MRF 30.75069892 945.6054838 202.4142354 743.1912484 BRITANIA 22.79374556 519.5548368 22.76313613 496.7917007 APOLLOTYRES 40.25893133 1620.781551 401.2155342 1219.566017 IOC 27.9595705 781.7375825 58.27089766 723.4666848 INFOSYS 26.92425907 724.9157265 223.8142585 501.101468 JETAIR 52.68658093 2775.87581 460.8024304 2315.07338 BOSCH 18.8487195 355.2742267 23.45217934 331.8220474 DABUR 22.2483177 494.9876407 35.8062602 459.1813805 BAJAJ AUTO 26.04673059 678.4321746 138.8797072 539.5524674 Source: Computed by the researcher Using Primary Data collected from BSE Ltd CHART 8: Showing Unsystematic Risk or Residual Variance of Securities 0 500 1000 1500 2000 2500 σei2 = σi² - βi².σm²
- 46. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 46 INFERENCE: From the above table and chart it is clear that JETAIR has maximum residual variance or unsystematic risk 2315.07 (%) ² and BOSCH has minimum unsystematic risk 331.82(%)² TABLE 7: Showing Risks of Securities Security σei² βi².σm² σi² = σei² + βi².σm² ACC 475.5019766 136.7741106 612.2760872 AIRTEL 799.8240407 187.4127798 987.2368205 CIPLA 461.3397467 64.28149698 525.6212437 MRF 743.1912484 202.4142354 945.6054838 BRITANIA 496.7917007 22.76313613 519.5548368 APOLLOTYRES 1219.566017 401.2155342 1620.781551 IOC 723.4666848 58.27089766 781.7375825 INFOSYS 501.101468 223.8142585 724.9157265 JETAIR 2315.07338 460.8024304 2775.87581 BOSCH 331.8220474 23.45217934 355.2742267 DABUR 459.1813805 35.8062602 494.9876407 BAJAJ AUTO 539.5524674 138.8797072 678.4321746 Source: Computed by the researcher Using Primary Data collected from BSE Ltd CHART 9: Showing Risks of Securities 0 500 1000 1500 2000 2500 3000 σi² = σei² + βi².σm² σi² = σei² + βi².σm²
- 47. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 47 INFERENCE: TYPE OF RISK MAXIMAM MINIMUM SYSTEMATIC RISK JETAIR BRITANIA UNSYSTEMATIC RISK JETAIR BOSCH TOTAL RISK JETAIR BOSCH ANALYSIS PART -2 PORTFOLIO OPTIMIZATION Portfolio optimization is one of the most important stages in the portfolio management. Portfolio selection process involves identification of optimal portfolio. Optimal portfolio is that portfolio for which return is maximum and risk is minimum. In order to identify the optimal portfolio, Portfolio managers use different numerical algorithms known as portfolio optimization models. This stage of the analysis focuses on the application of different portfolio optimization models in deriving the optimal portfolio. Here researches uses sharpe’s optimization model for building optimal portfolio. The Sharpe’s optimization model uses excess return- to- beta ratio as the performance measure of individual securities so as to include in optimal portfolio.
- 48. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 48 CONSRUCTION OF OPTIMAL PORTFOLIO USING SHARPE’S OPTIMIZATION MODEL TABLE 8(a): SHOWING CALCULATION OF CUT OFF POINT Security name Mean return Ri Excess return beta Ri-Rf Beta β Unsystematic risk σ²ei Excess return to beta Ri-Rf/βi ACC 9.77543415 1.675434154 0.68518404 475.5019766 2.445232315 8 AIRTEL 3.7552491 -4.344750898 0.80205636 799.8240407 -5.417014427 11 CIPLA 6.40999974 -1.690000256 0.46972998 461.3397467 -3.597812209 10 MRF 23.0558728 14.95587277 0.83353879 743.1912484 17.94262364 4 BRITANIA 11.4370068 3.337006785 0.27952544 496.7917007 11.93811488 5 APOLLOTYRES 12.8536253 4.753625271 1.1735299 1219.566017 4.050706578 7 IOC 1.91486877 -6.185131226 0.44723022 723.4666848 -13.82985975 12 INFOSYS 6.23536078 -1.864639219 0.87649444 501.101468 -2.127382836 9 JETAIR 16.6097858 8.509785788 1.25765832 2315.07338 6.766373381 6 BOSCH 22.915216 14.815216 0.28372453 331.8220474 52.21690133 1 DABUR 20.7598026 12.65980261 0.35057809 459.1813805 36.11122027 2 BAJAJ AUTO 22.8718465 14.77184654 0.690438 539.5524674 21.39489223 3 Source: Computed by the researcher Using Primary Data collected from BSE Ltd TABLE 8(b): SHOWING CALCULATION OF CUT OFF POINT (CONTINUED) RANK SECURITY (Ri-Rf) βi σ²ei (Ri-Rf)*βi (Ri-Rf)*βi/σ²ei 1 BOSCH 14.815216 0.28372453 331.82205 4.20344026 0.012667755 2 DABUR 12.65980261 0.35057809 459.18138 4.43824941 0.009665569 3 BAJAJ AUTO 14.77184654 0.690438 539.55247 10.1990441 0.018902785 4 MRF 14.95587277 0.83353879 743.19125 12.4663001 0.016774014 5 BRITANIA 3.337006785 0.27952544 496.7917 0.93277828 0.001877604 6 JETAIR 8.509785788 1.25765832 2315.0734 10.7024029 0.004622922 7 APOLLOTYRES 4.753625271 1.1735299 1219.566 5.57852137 0.004574186 8 ACC 1.675434154 0.68518404 475.50198 1.14798074 0.00241425 9 INFOSYS -1.86463922 0.87649444 501.10147 -1.6343459 -0.003261507 10 CIPLA -1.69000026 0.46972998 461.33975 -0.7938438 -0.001720736 11 AIRTEL -4.3447509 0.80205636 799.82404 -3.4847351 -0.004356877 12 IOC -6.18513123 0.44723022 723.46668 -2.7661776 -0.003823504
- 49. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 49 TABLE 8(c): SHOWING CALCULATION OF CUT OFF POINT (CONTINUED) SECURITY σ²ei (Ri-Rf)*βi/σ²ei ∑(Ri- Rf)*βi/σ²ei β¡ βi²/σ²ei ∑βi²/σ²ei BOSCH 331.8220474 0.012667755 0.012667755 0.2837245 0.000243 0.000243 DABUR 459.1813805 0.009665569 0.022333324 0.3505781 0.000268 0.00051 BAJAJ AUTO 539.5524674 0.018902785 0.041236108 0.690438 0.000884 0.001394 MRF 743.1912484 0.016774014 0.058010122 0.8335388 0.000935 0.002329 BRITANIA 496.7917007 0.001877604 0.059887726 0.2795254 0.000157 0.002486 JETAIR 2315.07338 0.004622922 0.064510648 1.2576583 0.000683 0.003169 APOLLOTYRES 1219.566017 0.004574186 0.069084834 1.1735299 0.001129 0.004298 ACC 475.5019766 0.00241425 0.071499084 0.685184 0.000987 0.005286 INFOSYS 501.101468 -0.003261507 0.068237577 0.8764944 0.001533 0.006819 CIPLA 461.3397467 -0.001720736 0.066516841 0.46973 0.000478 0.007297 AIRTEL 799.8240407 -0.004356877 0.062159964 0.8020564 0.000804 0.008101 IOC 723.4666848 -0.003823504 0.05833646 0.4472302 0.000276 0.008378 TABLE 8(d) SHOWING CONTINUTATION OF CUT OFF POINT C*={[σ²m∑(Ri-Rf)βi/σ²ei]/[1+σ²m∑β²i/σ²ei]} SECURITY σ²m ∑(Ri-Rf)*βi/σ²ei ∑βi²/σ²ei cut off point Ci BOSCH 291.332827 0.012667755 0.000242599 3.446915206 DABUR 291.332827 0.022333324 0.00051026 5.664388211 BAJAJ AUTO 291.332827 0.041236108 0.001393778 8.544079477 MRF 291.332827 0.058010122 0.002328648 10.06919442 BRITANIA 291.332827 0.059887726 0.002485926 10.1188597 JETAIR 291.332827 0.064510648 0.003169146 9.771902957 APOLLOTYRES 291.332827 0.069084834 0.004298378 8.936220974 ACC 291.332827 0.071499084 0.005285707 8.201122034 INFOSYS 291.332827 0.068237577 0.006818815 6.656470487 CIPLA 291.332827 0.066516841 0.007297088 6.199384481 AIRTEL 291.332827 0.062159964 0.008101383 5.389335455 IOC 291.332827 0.05833646 0.00837785 4.939435272 TABLE 9: SHOWING CALCULATION OF OPTIMAL PORTFOLIO SECURITY βi σ²ei βi/σ²ei (Ri-Rf)/βi CUT OFF POINT Ci Xi BOSCH 0.283725 331.822 0.000855 52.21690133 3.44691521 0.457019 DABUR 0.350578 459.1814 0.000763 36.11122027 5.66438821 0.254761 BAJAJ AUTO 0.690438 539.5525 0.00128 21.39489223 8.54407948 0.180224 MRF 0.833539 743.1912 0.001122 17.94262364 10.0691944 0.096779 BRITANIA 0.279525 496.7917 0.000563 11.93811488 10.1188597 0.011218 1
- 50. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 50 TABLE 10: SHOWING OPTIMAL PORT FOLIO SECURITY WEIGHT(%) BOSCH 45.70188656 DABUR 25.47607128 BAJAJ AUTO 18.02235084 MRF 9.677852489 BRITANIA 1.121838829 100 Source: Computed by the researcher Using Primary Data collected from BSE Ltd OPTIMAL PORTFOLIO TABLE 11(a): SHOWS PORTFOLIO ALPHA FOR OPTIMAL PORTFOLIO SECURITY αi Xi Xi*αi BOSCH 21.9114579 0.457018866 10.01394963 DABUR 19.51953061 0.254760713 4.972809531 BAJAJ AUTO 20.42922123 0.180223508 3.681825925 MRF 20.10698676 0.096778525 1.945924519 BRITANIA 10.44810422 0.011218388 0.11721089 Total 92.41530072 1 20.7317205 Source: Computed by the researcher Using Primary Data collected from BSE Ltd Portfolio alpha = 20.73 % TABLE 11(b): SHOWS PORTFOLIO BETA FOR OPTIMAL PORTFOLIO SECURITY βi Xi Xi*βi BOSCH 0.283724534 0.45701887 0.129667465 DABUR 0.350578089 0.25476071 0.089313524 BAJAJ AUTO 0.690437997 0.18022351 0.124433158 MRF 0.833538788 0.09677852 0.080668654 BRITANIA 0.279525438 0.01121839 0.003135825 Total 2.437804847 1 0.427218626 Source: Computed by the researcher Using Primary Data collected from BSE Ltd Portfolio beta = 0.43
- 51. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 51 TABLE 11(c): SHOWS PORTFOLIO RESIDUAL VARIANCE FOR OPTIMAL PORTFOLIO SECURITY σ²ei wi wi² wi²*σ²ei BOSCH 331.8220474 0.4570189 0.20886624 69.3064245 DABUR 459.1813805 0.2547607 0.06490302 29.8022587 BAJAJ AUTO 539.5524674 0.1802235 0.03248051 17.5249409 MRF 743.1912484 0.0967785 0.00936608 6.96079083 BRITANIA 496.7917007 0.0112184 0.00012585 0.06252235 Total 2570.538844 1 0.31574171 123.656937 Source: Computed by the researcher Using Primary Data collected from BSE Ltd Portfolio Residual variance = 123.66(%) ² TABLE 11(d): SHOWS PORTFOLIO RISK, RETURN, ALPHA, BETA, AND RESIDUAL VARIANCE FOR OPTIMAL PORTFOLIO PORTFOLIO RETURN (Rp) σ²p αp Βp σei² Σp OPTIMAL PF 22.24 176.83 20.73 0.43 123.66 13.3 Source: Computed by the researcher Using Primary Data collected from BSE Ltd MEASURING PORTFOLIO RETURN AND RISK PORTFOLIO RETURN (RP) PORTFOLIO RETURN = PORTFOLIO ALPHA + (PORTFOLIO BETA×MARKET RETURN) RP = αP+ (βp×Rm) αP = 20.73 βp = 0.43 Rm = 3.54 RP = 20.73+ (0.43* 3.54) = 22.24%
- 52. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 52 PORTFOLIO RISK (σP2) Portfolio risk (σp2) = 𝛽𝑝²𝜎𝑚² + 𝑤𝑖²𝜎𝑖𝑒²𝑛 𝑖=1 βp2 = 0.183 σm2 = 291.31 ∑wi2σie2 = 123.66 σp2 = 176.83(%)² σp = 13.30 TABLE 11(e): SHOWS BENEFIT OF DIVERSIFICATION RISK CLASS TOTAL RISK OF SECURITIES (%)² PORTFOLIO RISK (%)² BENEFIT OF DIVERSIFICATION (%)² RISK REDUCTION (%) UN SYS RISK 9066.41 123.65 8942.76 98.63 SYS RISK 1955.88 53.17 1902.71 97.25 TOTAL RISK 11022.30 176.83 10845.47 98.40 Source: Computed by the researcher Using Primary Data collected from BSE Ltd Effectiveness of Optimization To examine the effectiveness of optimization, three different portfolios are constructed with the securities included in the optimal portfolio. The criteria used for construction of these portfolios are: 1. Equal investment in each security (We name it as Portfolio Gamma, Г). 2. Investment in each security in random proportion (We name it as Portfolio Pi, Π)
- 53. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 53 3. Investment in each security in proportion to the P/E multiple of each security (We name it as Portfolio Omega, Ω) The return and risk of these portfolios are determined for the purpose of evaluation of the performance of these portfolios. Thereafter the performance of these portfolios was measured by using Sharpe Ratio, Treynor Ratio and Jensen Measure. The performance of these portfolios was then compared with that of the optimal portfolio. In all the performance measures, the optimal portfolio came out to be the best, thereby confirming its optimality. The analysis is shown below: PORTFOLIO BASED ON EQUAL WEIGHT (PORTFOLIO GAMMA, Г) The first portfolio is constructed by giving equal weights to the five securities and then the portfolio alpha, portfolio beta and weighted residual variance are calculated to arrive at portfolio return and risk TABLE 12(a): SHOWS PORTFOLIO ALPHA IN EQUAL WEIGHT Security ALPHA (αi) WEIGHT(Wi) ALPHA x WEIGHT (αiWi) BOSCH 21.9114579 0.2 4.38229158 DABUR 19.51953061 0.2 3.903906121 BAJAJ AUTO 20.42922123 0.2 4.085844246 MRF 20.10698676 0.2 4.021397353 BRITANIA 10.44810422 0.2 2.089620843 1 18.48306014 Portfolio alpha =18.48 % TABLE 12(b): SHOWS PORTFOLIO BETA IN EQUAL WEIGHT Security BETA (βi) WEIGHT(Wi) BETA x WEIGHT (βiWi) BOSCH 0.283724534 0.2 0.056744907 DABUR 0.350578089 0.2 0.070115618 BAJAJ AUTO 0.690437997 0.2 0.138087599 MRF 0.833538788 0.2 0.166707758 BRITANIA 0.279525438 0.2 0.055905088 1 0.487560969 Portfolio beta =0.49
- 54. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 54 TABLE 12(c): SHOWS PORTFOLIO RESIDUAL VARIANCE IN EQUAL WEIGHT Security RESIDUAL VARIANCE (σαi) WEIGHT(Wi) Wi² Wi²*σei² BOSCH 331.8220474 0.2 0.04 13.2728819 DABUR 459.1813805 0.2 0.04 18.36725522 BAJAJ AUTO 539.5524674 0.2 0.04 21.5820987 MRF 743.1912484 0.2 0.04 29.72764994 BRITANIA 496.7917007 0.2 0.04 19.87166803 2570.538844 1 0.2 102.8215538 Source Table 12: Computed by the researcher Portfolio residual variance =102.82 (%)² MEASURING 1ST PORTFOLIO RETURN AND RISK PORTFOLIO RETURN (RP) PORTFOLIO RETURN = PORTFOLIO ALPHA + (PORTFOLIO BETA×MARKET RETURN) RP = αP+ (βp×Rm) αP = 18.48 βp = 0.49 Rm = 3.54 RP = 18.48+ (0.49*3.54) = 20.21 % PORTFOLIO RISK (σP2) Portfolio risk (σp2) = 𝛽𝑝²𝜎𝑚² + 𝑤𝑖²𝜎𝑖𝑒²𝑛 𝑖=1 βp2 = 0.24 σm2 = 291.33 ∑wi2σie2 = 102.82 σp2 = 172.08 (%)² σp = 13.12%
- 55. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 55 TABLE 12(d): SHOWS BENEFIT OF DIVERSIFICATION RISK CLASS TOTAL RISK OF SECURITIES (%)² PORTFOLIO RISK (%)² BENEFIT OF DIVERSIFICATION (%)² RISK REDUCTION (%) UN SYS RISK 9066.41 102.82 8963.59 98.87 SYS RISK 1955.88 69.25 1886.63 96.45 TOTAL RISK 11022.30 172.08 10850.22 98.44 Source Table 12(d): Computed by the researcher PORTFOLIO 2 BASED ON RANDOM WEIGHT (PORTFOLIO PI, Π) Third portfolio is constructed on the basis on Random weight of the seven securities and then the portfolio alpha, portfolio beta and weighted residual variance are calculated to arrive at portfolio return and risk. For this purpose the risk free rate return is taken as 8.1%. TABLE 13(a): SHOWS PORTFOLIO ALPHA IN RANDOM WEIGHT Security ALPHA (αi) random nor WEIGHT(Wi) ALPHA x WEIGHT BOSCH 21.9114579 0.224100148 0.075943184 1.664025875 DABUR 19.5195306 0.881503146 0.29872428 5.830957726 BAJAJ AUTO 20.4292212 0.183002511 0.062015993 1.266938449 MRF 20.1069868 0.809161033 0.274208944 5.513515613 BRITANIA 10.4481042 0.853125356 0.289107599 3.020626319 1 17.29606398 Portfolio alpha = 17.30% TABLE 13(b): SHOWS PORTFOLIO BETA IN RANDOM WEIGHT Security BETA (βi) WEIGHT(Wi) BETA x WEIGHT (βiWi) BOSCH 0.28372453 0.075943184 0.021546944 DABUR 0.35057809 0.29872428 0.104726187 BAJAJ AUTO 0.690438 0.062015993 0.042818198 MRF 0.83353879 0.274208944 0.228563791 BRITANIA 0.27952544 0.289107599 0.080812928 2.43780485 1 0.478468049
- 56. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 56 Portfolio beta = 0.48 TABLE 13(c): SHOWS PORTFOLIO RESIDUAL VARAINCE IN RANDOM WEIGHT Security RESIDUAL VARIANCE (σαi)WEIGHT(Wi) Wi² Wi²*σei² BOSCH 331.8220474 0.075943184 0.005767367 1.913739582 DABUR 459.1813805 0.29872428 0.089236195 40.97559941 BAJAJ AUTO 539.5524674 0.062015993 0.003845983 2.075109854 MRF 743.1912484 0.274208944 0.075190545 55.8809551 BRITANIA 496.7917007 0.289107599 0.083583204 41.52344183 1 0.257623295 142.3688458 Source For Table 14: Computed by the researcher Portfolio Residual variance = 142.37 (%) ² MEASURING 2nD PORTFOLIO RETURN AND RISK PORTFOLIO RETURN (RP) PORTFOLIO RETURN = PORTFOLIO ALPHA + (PORTFOLIO BETA×MARKET RETURN) RP = αP+ (βp×Rm) αP = 17.30 βp = 0.48 Rm = 3.54 RP = 17.30+ (0.48* 3.54) = 18.99% PORTFOLIO RISK (σP2) Portfolio risk (σp2) = 𝛽𝑝²𝜎𝑚² + 𝑤𝑖²𝜎𝑖𝑒²𝑛 𝑖=1 βp2 = 0.23 σm2 = 291.33 ∑wi2σie2 = 142.37 σp2 = 209.06(%) ²
- 57. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 57 σp = 14.46% TABLE 13(d): SHOWS BENEFIT OF DIVERSIFICATION RISK CLASS TOTAL RISK OF SECURITIES (%)² PORTFOLIO RISK (%)² BENEFIT OF DIVERSIFICATION (%)² RISK REDUCTION (%) UN SYS RISK 9066.41 142.37 8924.04 98.43 SYS RISK 1955.88 66.69 1889.19 96.60 TOTAL RISK 11022.30 209.06 10813.24 98.10 Source : Computed by the researcher Using Primary Data collected from BSE Ltd PORTFOLIO 3 BASED ON PRICE EARNINGS RATIO (PORTFOLIO OMEGA, Ω) Fourth portfolio is constructed on the basis on price earnings ratio of the five securities and then the portfolio alpha, portfolio beta and weighted residual variance are calculated to arrive at portfolio return and risk. For this purpose the risk free rate return is taken as 8.1%. TABLE 14(a): SHOWS PORTFOLIO ALPHA IN PRICE EARNINGS RATIO Security ALPHA (αi) P/E ratio weight Wi alpha*weight (Wi*ἀ¡) BOSCH 21.9114579 32.19 0.230224574 5.044556071 DABUR 19.5195306 46.08 0.329566586 6.432985055 BAJAJ AUTO 20.4292212 17.5 0.125160921 2.556940148 MRF 20.1069868 9.32 0.066657131 1.340274043 BRITANIA 10.4481042 34.73 0.248390788 2.595212841 139.82 1 17.96996816 Portfolio alpha = 17.97%
- 58. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 58 TABLE 14(b): SHOWS PORTFOLIO BETA IN PRICE EARNINGS RATIO Security P/E ratio BETA (βi) WEIGHT(Wi) BETA x WEIGHT (βiWi) BOSCH 32.19 0.2837245 0.23022457 0.06532036 DABUR 46.08 0.3505781 0.32956659 0.115538824 BAJAJ AUTO 17.5 0.690438 0.12516092 0.086415856 MRF 9.32 0.8335388 0.06665713 0.055561304 BRITANIA 34.73 0.2795254 0.24839079 0.069431544 139.82 1 0.392267887 Porfolio Beta =0.39 TABLE 14(c): SHOWS PORTFOLIO RESIDUAL VARIANCE IN PRICE EARNINGS RATIO Security RESIDUAL VARIANCE WEIGHT(Wi) Wi² Wi²*σei² BOSCH 331.8220474 0.230224574 0.053003 17.58768 DABUR 459.1813805 0.329566586 0.108614 49.87359 BAJAJ AUTO 539.5524674 0.125160921 0.015665 8.452228 MRF 743.1912484 0.066657131 0.004443 3.302127 BRITANIA 496.7917007 0.248390788 0.061698 30.65105 1 0.243424 109.8667 Source: Computed by the researcher Using Secondary Data collected Portfolio Residual variance = 109.87 (%) ² MEASURING 3RD PORTFOLIO RETURN AND RISK PORTFOLIO RETURN (RP) PORTFOLIO RETURN = PORTFOLIO ALPHA + (PORTFOLIO BETA×MARKET RETURN RP = αP+ (βp×Rm) αP = 17.97 βp = 0.39 Rm = 3.54
- 59. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 59 RP = 17.97+ (0.39*3.54 ) = 19.35% PORTFOLIO RISK (σP2) Portfolio risk (σp2) = 𝛽𝑝²𝜎𝑚² + 𝑤𝑖²𝜎𝑖𝑒²𝑛 𝑖=1 βp2 = 0.15 σm2 = 291.33 ∑wi2σie2 = 109.87 σp2 = 154.70(%)² σp = 12.44% TABLE 14(d): SHOWS BENEFIT OF DIVERSIFICATION RISK CLASS TOTAL RISK OF SECURITIES (%)² PORTFOLIO RISK(%)² BENEFIT OF DIVERSIFICATION (%)² RISK REDUCTION (%) UN SYS RISK 9066.41 109.87 8956.54 98.79 SYS RISK 1955.88 44.83 1911.05 97.71 TOTAL RISK 11022.30 154.69 10867.61 98.60 Source: Computed by the researcher Using Primary Data collected from BSE Ltd
- 60. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 60 TABLE 15: SHOWS EFFECT OF DIVERSIFICATION PORTFOLIO RISK REDUCTION (%) UNSYSTEMATIC RISK(%)² SYSTEMATIC RISK(%)² TOTAL RISK(%)² OPTIMAL PORTFOLIO 123.66 53.17 176.83 PORTFOLIO GAMMA, Г 102.82 69.25 172.08 PORTFOLIO PI, Π 142.37 66.69 209.06 PORTFOLIO OMEGA, Ω 109.86 44.82 154.69 INFERENCE: From above table, it is also clear that diversification has resulted in considerable reduction of not only unsystematic risk but also systematic risk. OPTIMALITY TEST The optimality of the optimal portfolio constructed with Sharpe’s Optimization Model is tested by comparing its performance against the performance of other four portfolios. The traditional performance evaluation measures like Sharpe ratio, Treynor ratio and Jensen measure are used for this purpose. In all these measures, the optimal portfolio came out with maximum value thereby validating its optimality. PORTFOLIO EVALUATION Portfolio evaluation is the process to determine the performance of the portfolio. The best measure for evaluation of portfolio is the risk adjusted rate of return as determined by SHARPE RATIO and TREYNOR RATIO and JENSEN MEASURE. The evaluation process using these retios is discussed below:
- 61. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 61 TABLE 16: SHOWS SHARPE RATIO OF THE PORTFOLIOS PORTFOLIO Rp(%) Rf(%) σpi(%) (Rp-Rf)/σp OPTIMAL PORTFOIO 68.26655599 8.1 29.6679969 2.03 PORTFOLIO GAMMA, 1 20.20902598 8.1 13.11777193 0.92 PORTFOLIO Pi, 2 18.98984088 8.1 14.45905106 0.75 PORTFOLIO OMEGA , 3 19.35859648 8.1 12.43765437 0.91 Source: Computed by the researcher CHARTNO 10 SHARPE RATIO OF PORTFOLIOS INFERENCE: Sharpe ratio is maximum for the optimal portfolio whereas minimum for Portfolio PI,Π with random weights. TREYNOR RATIO Treynor ratio is also the ratio of excess return to risk. But here risk is defined as the systematic risk or market risk on the assumption that the portfolio is well diversified. 0.00 0.50 1.00 1.50 2.00 2.50 OPTIMAL GAMMA Pi OMEGA SHARPE RATIO (Rp-Rf)/σp
- 62. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 62 TABLE 17: SHOWS TREYNOR RATIO OF THE PORTFOLIO PORTFOLIO Rp(%) Rf(%) βp (Rp-Rf)/βp OPTIMAL 68.27 8.10 0.98 61.65 GAMMA 20.21 8.10 0.49 24.84 Pi 18.99 8.10 0.48 22.76 OMEGA 19.36 8.10 0.39 28.70 Source: Computed by the researcher CHART NO 11: TREYNOR RATIOS OF THE PORTFOLIOS INFERENCE: Treynor ratio is maximum for the optimal portfolio whereas minimum for Portfolio Pi, with Random weights. JENSEN ALPHA Jensen Measure Gives Differential Return earned by a portfolio over and above the expected return as mandated by capital asset pricing model. A positive alpha indicates superior performance of the portfolio. 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 OPTIMAL GAMMA Pi OMEGA TERYNOR RATIO (Rp-Rf)/βp
- 63. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 63 TABLE 18: SHOWS JENSEN ALPHA OF THE PORTFOLIOS PORTFOLIO Rp(%) Rf(%) βp Rm(%) E(Rp)= Rf+βp(Rm- Rf) Rp- E(Rp) OPTIMAL 68.27 8.10 0.98 3.54 3.65 64.62 GAMMA 20.21 8.10 0.49 3.54 5.88 14.33 Pi 18.99 8.10 0.48 3.54 5.92 13.07 OMEGA 19.36 8.10 0.39 3.54 6.31 13.05 Source: Computed by the researcher CHART NO 12: JENSEN ALPHA INFERENCE: Jensen alpha is maximum for the optimal portfolio whereas minimum for Portfolio OMEGA, Ω with PE ratio weights. Optimality Test for the Optimal Portfolio The above analysis shows that all performance measures, namely, Sharpe Ratio, Treynor Ratio and Jensen Measure, are maximum for Optimal Portfolio thereby proving the optimality of the Optimal Portfolio. 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 OPTIMAL GAMMA Pi OMEGA JENSON MEASURE Rp-E(Rp)
- 64. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 64 VALUE AT RISK MONTE CARLO SIMULATION: Under this method VaR for a portfolio is calculated using a one day time horizon at 95% and 99% confidence level for 500 days of data. The following tables show the estimation of VaR using this method .the first table gives the value of the opening value of the portfolio for 31st march 2013. Only part of the table containing the critical values of VaR is shown in the following table. The detailed calculation for the change in the value of the portfolio for 500 scenarios are shown in a separate table in Appendix no.1 TABLE 19: SHOWING PORTFOLIO VALUE ON 31ST MARCH 2013 FOR THE MONTE CARLO SIMULATION SECURITY WEIGHT(Xi) CLOSING PRICE TOTAL VALUE NUMBER OF SHARES ACTUAL NUMBER OF SHARES ACTUAL VALUE BOSCH 0.45701887 9054.35 914037.7 100.950121 101 914489.4 DABUR 0.25476071 137.05 509521.4 3717.77764 3718 509551.9 BAJAJ AUTO 0.18022351 1794.9 360447 200.817325 201 360774.9 MRF 0.09677852 11992.6 193557 16.139707 16 191881.6 BRITANIA 0.01121839 524.3 22436.78 42.7937757 43 22544.9 1 2000000 4079 1999243 Source: calculated by researcher taking 20,00,000 as the size of lot
- 65. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 65 TABLE 20: SHOWING CHANGES IN TOTAL VALUE OF PORTFOLIO (SORTED IN ASCENDING ORDER). SLNO PORTFOLIOCHANGE IN VALUEVALUE AT RISK 1 2003801 4557.89 -42005.7 2 1988733 -10509.3 -41776.3 3 2008240 8997.4 -40911.6 4 1990446 -8797.1 -40431.4 5 1990285 -8957.16 -39647.1 At 99% confidence level 6 2021773 22530.35 -37115.8 7 2006973 7730.65 -36975.6 8 2017059 17816.63 -34972.2 9 1969070 -30173.1 -34054.1 10 2019442 20198.85 -33824.3 11 2007171 7928.32 -31134.8 12 2006385 7142.38 -30173.1 13 2034476 35233.34 -28577.7 14 2036307 37064.82 -28540.2 15 2009301 10057.99 -28523.9 16 2013397 14154.6 -27299.2 17 2008386 9143.01 -26941.6 18 1958811 -40431.4 -26790.4 19 1989160 -10083.1 -26511.4 20 1982344 -16898.3 -25885.2 21 2014891 15648.79 -25504.7 22 2007886 8643.49 -25378.2 23 2001835 2592.02 -25280.6 24 2000334 1091.67 -25125.5 At 95% confidence level 25 1965189 -34054.1 -24816.1 26 2038552 39308.89 -23960.2 27 2005652 6409.64 -22900.2 28 2031756 32513.34 -22714.1 29 1986444 -12798.3 -22506 30 1990699 -8544.14 -22427.6 31 2013936 14693.71 -21706.4 32 2019240 19997.57 -21231.2 33 1984821 -14422.1 -20996.4 34 2040799 41556.03 -20857.6 35 2009212 9969.69 -20838.4 36 1992501 -6741.57 -20547 37 1993785 -5457.82 -20315.4
- 66. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 66 INFERENCE: From the above table it is clear that:- Value at Risk At 99% of confidence level = -39647.14 At 99% confidence level the maximum daily loss or gain of the portfolio will be RS - 39647.14; that is portfolio value will lie between 1959595.51 and 2038889.79 Value at Risk at 95% of confidence level= -24816.15 At 95% confidence level the maximum daily loss or gain of the portfolio will be RS. - 24816.15; that is portfolio value will be lie between Rs.1974426.5 and 2024058.8
- 67. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 67 CHAPTER 5 FINDINGS, SUGGETIONS AND CONCLUSION
- 68. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 68 FINDINGS SECURITY ANALYSIS Return MRF is giving the maximum return 23.06% and INDIAN OIL CORPORATION is giving the minimum return 1.91%. Total Risk JET AIR has the maximum risk of 52.68% and BOSCH has the minimum risk of 18%. Security Beta The beta value is maximum for JETAIR (1.25) indicating the highest systematic risk and the minimum beta is for BRITANIA (0.27) indicating the minimum systematic risk. Security Alpha The alpha value is maximum for BOSCH (0.087) i.e. it earns the maximum extra return over market return. INDIAN OIL CORPORATION (0.0013) have the least alpha value. Systematic Risk Systematic risk is maximum for JETAIR with variance (460.80) and minimum for BRITANIA with variance(22.76) Unsystematic Risk Unsystematic risk is maximum for JETAIR with a variance of (2315.07)% and minimum for BOSCH with a variance of (331.82%). PORTFOLIO ANALYSIS Portfolio Return and Risk The return of optimal portfolio with Sharpe’s model is highest (68.27) and the return of Portfolio Pi (with RANDOME weight proportion) is the minimum (18.99). Portfolio with
- 69. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 69 Random weight has the highest risk with a standard deviation of 14.46 % and Portfolio Omega (Portfolio based on P/E ratio) has the lowest risk with a standard deviation of 12.44%. Portfolio Alpha and Beta Portfolio alpha is maximum for optimal portfolio with Sharpe’s Model (20.73) and minimum for Portfolio Pi (with Random weight proportion) (17.29) Portfolio beta is maximum for portfolio Pi (0.48) and is minimum for portfolio Omega (PE ratio portfolio) (0.39) Portfolio Optimization An optimal portfolio is constructed by using Sharpe’s Optimization Models. The findings are summarized below: The return of optimal portfolio is 22.24% The risk of optimal portfolio is 176.82% The beta value of optimal portfolio is 0.43 The alpha value of optimal portfolio is 20.73% The residual variance of optimal portfolio is 123.66(%)2 Sharpe Ratio = 2.03% Treynor Ratio = 61.65% Jensen Measure = 64.62% The portfolio is tested for optimality by comparing its performance against the three other portfolios using Sharpe’s ratio, Treynor ratio, and Jensen ratio. All performance measures were highest for the optimal portfolio thereby proving its optimality. Value at Risk VaR is calculated using Monte Carlo Simulation method and the findings are below Value at Risk At 99% of confidence level = -39647.14
- 70. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 70 Value at Risk at 95% of confidence level= -24816.15 that is portfolio value will lie between 1959595.51 and 2038889.79 at 99% of confidence level and will be lie between Rs.1974426.5 and 2024058.8 at 95% of confidence level Benefit Of Diversification From the calculations, we can find that diversification has resulted in considerable reduction of not only unsystematic risk but also systematic risk to some extent. SUGGESTIONS An investor should neither make investment decisions on the basis of tips and rumors nor adopt a naïve investment strategy, especially in a volatile market as we have now. A naïve investment strategy based on tips and rumors might result in poor investment decisions which might seriously undermine their long-term welfare and wealth accumulation. Investors should make investment decisions on the basis of scientific and analytical asset allocation techniques. Financial modeling using portfolio is very helpful for risk reduction and optimal portfolio construction also very efficient in risk diversification for securities. Investors should make use of these portfolio optimization algorithms in order ensure efficient asset allocation and superior portfolio performance. Investors should clearly define their investment objectives and select appropriate asset allocation techniques in order to achieve their investment objectives. CONCLUSION Scientific investment involves, investors clearly specifying their investment objectives and developing an efficient asset allocation strategy to achieve those objectives. One of the important investment objectives of a rational investor would be to maximize the return on his investment while minimizing the risk associated with his investment. This involves striking an optimal trade-off between risk and return. But achieving an optimal trade-off between risk and return in a volatile and complex investment environment is a difficult task and involves application of financial modeling and portfolio optimization
- 71. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 71 techniques. In such volatile and uncertain investment environment, applying native investment strategies and making poor investment decisions will result in significant investment losses to the investors. In a dynamic, uncertain and volatile investment environment, investors should use superior asset allocation techniques by employing efficient portfolio optimization models, in order to ensure superior performance of their investment portfolio. The objective of using a portfolio optimization technique is to ensure efficient asset allocation. An efficient asset allocation would in turn ensure superior portfolio performance by ensuring maximum return with minimum risk. Portfolio optimization is a complex process. .It involves identification of optimal portfolio from a domain of feasible and efficient set of portfolios. Different portfolio optimization models are developed for identification of optimal portfolio. This study examines the use of Sharpe’s optimization Model in ensuring efficient asset allocation. The study has revealed the effectiveness of Sharpe’s portfolio optimization models in ensuring superior portfolio performance. The optimization process has also resulted in considerable reduction of risk by diversification.
- 72. Financial Modeling For Risk Management Using Portfolio School of management studies, Chintech Page 72 BIBLIOGRAPHY BOOKS Kevin S – Portfolio Management, Prentice Hall, New Delhi 2003 Punithavathy Pandyan – Security Analysis and Portfolio Management, Vikas Publishing House, New Delhi 2001 Simon Benninga, Financial Modelling ,Sloan Institute Of management, MIT publications,2008 WEBSITES http://www.bseindia.com www.money.rediff.com www.moneycontrol.com www.indiainfoline.com www.google.com www.wikipedia.com www.equitymaster.com www.emeraldinsight.com 2

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