MBA: Investment Management

   Investment Management Assignment Below is your assignment for this subject. Please read the brief and instructions thoroughly. o Write a report which addresses the questions (a to f) below. Where relevant, base your analysis on analysis of the data in the asset return table provided. a. Describe each of the asset classes, setting out their characteristics and risks. b. Calculate the AM (Arithmetic Mean) and GM (Geometric Mean) measures of the average annual yield on each of these asset classes during the period 1983-2003. Contrast the resulting measures of average yield for each asset class. c. What would be the main problems you would encounter if you tried using the efficient frontier you have identified for portfolio selection purposes? d. How does foreign exchange risk contribute to the risk of international investments? Is it worthwhile to hedge exchange rate risk? e. During a world financial crisis, all the major financial markets will usually move in the similar direction (i.e. become highly correlated). Do you think this will limit the benefits of international diversification? f. It is often said that Australian investors have an inefficient home bias in their asset portfolios. What does this mean? Why is it important? What are the principal causes of “home bias”? Asset returns on different asset classes over the period 1983 to 2003 Year Australian Shares % return Australian Bonds % return Cash % return International Shares % return Listed Property Trusts % return 1983 66.8 14.3 11.1 32.8 50.2 1984 -2.3 12.0 10.9 14.0 10.1 1985 44.1 8.1 15.2 70.2 5.3 1986 52.2 18.9 15.6 45.6 35.4 1987 -7.9 18.6 12.8 6.5 5.8 1988 17.9 9.4 12.9 4.3 16.1 1989 17.4 14.4 18.4 26.0 2.4 1990 -17.5 19.0 16.1 -15.1 8.7 1991 34.2 24.7 11.2 20.2 20.1 1992 -2.3 10.4 6.9 4.5 7.0 1993 45.4 16.3 5.4 24.4 30.1 1994 -8.7 -4.7 5.4 -8.1 -5.6 1995 20.2 18.6 8.0 25.9 12.7 1996 14.6 11.9 7.6 6.3 14.5 1997 12.2 12.2 5.6 41.1 20.3 1998 11.6 9.5 5.1 32.1 18.0 1999 16.1 -1.2 5.0 17.1 -5.0 2000 4.8 12.1 6.3 2.2 17.9 2001 10.5 5.5 5.2 -9.7 15.0 2002 -8.6 8.8 4.8 -27.2 11.9 2003 15.0 3.0 4.9 -0.5 8.8 Be sure to include in your responses to the questions above, these graphs and calculations: ? First, graph the efficient frontier. In order to do so you will need to determine the expected return [1], standard deviation and correlation of the 5 assets in your portfolio. ? Then, use Microsoft Excel to plot the efficient frontier on the XY scatter graph with risk on X axis and return on Y axis. ? Using your graph, discuss the concept of the Markowitz Portfolio Theory and the CAPM. Clearly show that, using a risk-free asset, you are able to obtain a higher return for a given risk. The data for this assignment is drawn from “Financial Markets and Institutions in Australia” by Tom Valentine, Guy Ford, Vic Edwards, Maike Sundmacher and Richard Copp , 2nd edn, Pearson Education Australia, 2006, pp. 92-93. – [1] Assume the expected return is equal to the average annual stock return (from 1983 to 2003). ? This assessment is an individual assessment (ie this is not a group assessment). Please ensure you avoid collusion and other practices which compromise individual assessment work. (Refer to the Academic Integrity Policy available on AIB website) o ________________________________________ Important Assignment Instructions ? The required word length for this assignment is 2500 words (plus or minus 10%). ? In terms of structure, presentation and style you are normally required to use: – AIB standard report format; and – AIB preferred Microsoft Word settings; and – Harvard style referencing (which includes in-text citations plus a reference list). These requirements are detailed in the AIB Style Guide. ? Reference lists for AIB assignments / projects normally contain the following number of relevant references from different sources: 6-12 (for MBA assignments). ? All references must be from credible sources such as books, industry related journals, magazines, company documents and recent academic articles. ? Your grade will be adversely affected if your assignment contains no/poor citations and/or reference list and also if your assignment word length is beyond the allowed tolerance level (see Assessment Policy available on AIB website). ? Useful resources when working on your assignments include: ¬ – AIB Online Library – AIB Assignment Guide ¬ – AIB Style Guide ? Select the link for the assignment assessment criteria – Please note that the new assessment criteria applies to all subjects starting on or after the 23 October 2015. Click to view info on Academic Integrity: Avoiding Plagiarism PLEASE SEE ATTACHED DOCUMENTS
Instruction:

1) Please make sure you follow the report format as requested by the AIB.
2) Please carefully read parts of the attached subject overview as this will help you identify the PRESCRIBED TEXT BOOK and other readings for referencing.
3) Pleas emake sure you reference the prescribed text.
4) And please, included the executive summary and table contents.

©Australian Institute of Business . V2Mar11 – CD:2011:10ed 0 Master of Business Administration LEARNING MATERIALS INVESTMENT MANAGEMENT ©Australian Institute of Business. V10Sep15 – BKM:2014:10ed 1 721INMT Investment Management Subject Overview SUBJECT OVERVIEW How to Use Your Study Pack ……………………………………………………………….. 2 Learning from the Workplace………………………………………………………………. 2 Synopsis…………………………………………………………………………………………… 5 Learning Outcomes……………………………………………………………………………. 5 Content……………………………………………………………………………………………. 6 Resources…………………………………………………………………………………………. 8 Assignment………………………………………………………………………………………10 Academic Integrity: Avoiding Plagiarism, Collusion and Other Issues…………12 Online Library User Guide …………………………………………………………………..12 Online Revision Quizzes ……………………………………………………………………..13 Information on Examination ……………………………………………………………….13 ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 2 721INMT Investment Management Subject Overview How to Use Your Study Pack Your study pack for this subject contains the following materials: – These learning materials, including the following: – Subject Overview (which includes the introduction, subject content, list of resources and assignment), and – Topics – Sample Exam Questions with Answer Guidelines – Articles – Supplementary Resources (if any) The information contained in your study pack has been designed to lead you through your learning process. Note that the learning materials are not a replacement for the textbook. Learning materials for each topic in the subject are based on specific chapters in the textbook. You should read the textbook along with these learning materials, and concentrate your study on the issues raised. Learning activities and/or discussion questions are included in the learning materials. Advanced students might wish to pursue more of the discussion questions at the end of the appropriate textbook chapters. Note that the examiner does not expect that you to memorise all of the issues that are discussed in the textbook or in these learning materials. It is more important in the exam to be able to demonstrate that you understand the various concepts and to show how they can apply to practical examples of organisations in your country or region. Some of the topics list one or more journal articles related to that topic’s content. For exam purposes, the textbook will be the primary source to answer exam questions, but if you are able to do additional reading, information from the journal articles or elsewhere may help you to achieve a higher grade. Finally, online quizzes and sample exam questions with answer guidelines are provided to help you test your understanding of the subject. Learning from the Workplace Studying at the Australian Institute of Business is a unique experience. There are no artificial boundaries between the workplace and the classroom. The world of work is never far away from everything we do. It is no coincidence that the Institute’s strap-line is ‘The Practical Business School’. Indeed, our very mission is ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 3 721INMT Investment Management Subject Overview to provide distinctive business and management education in national and international environments based on AIB’s orientation towards work-applied learning. So how do we do this and how will you experience the difference? The answer is that learning from the workplace is embedded in all aspects of your course. Let us see how this works in practice. Practitioner experience as entry requirement for students For a start, most students will already have experience of the workplace and in postgraduate programmes this is a prerequisite. This will enable you to see whether theories make sense in practice and, in turn, to bring real-life problems to the classroom. You will very quickly find, too, that you can also learn from each other, sharing experiences and looking for solutions. Academic facilitators with practical experience Of course, all of our facilitators are required to have appropriate academic qualifications, as well as relevant workplace experience. With this background, they can bring interesting examples into classroom discussions. In addition, with our international coverage we are very keen that facilitators can relate the various subjects to conditions in different parts of the world, making it all much more meaningful to you as the student. Design of courses and learning materials Work-applied research is integrated in all of our courses. This is why we include a work-based assignment in every subject in our undergraduate as well as postgraduate programmes. It is also why you will be asked to undertake at least one work-based research project in the course of your studies. With the guidance of an experienced project supervisor, you will be able to explore a topic of your own choosing, ideally based on a problem that you want to address in the workplace. Teaching and learning strategies Even the way you learn will often be more like a workplace situation than a traditional classroom. You will be encouraged to work in groups and to share your understanding of real-world situations. As well as your own selection of case studies, you might discuss one presented by the facilitator or perhaps taken from a textbook. Course objectives are achieved when you relate your readings, course materials and facilitator guidance to the workplace. It is a ‘to and fro’ process, backwards and forwards between the classroom and the workplace, reflecting on the links and developing your own ideas. ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 4 721INMT Investment Management Subject Overview Design of course assessment Finally, even the various forms of assessment are designed with the workplace in mind. You will be expected not merely to describe what you observe in the workplace, nor just to replicate what you have read in a textbook or journal article, but rather to achieve a combination of the two. We will be looking always for a balance between theory and practice. As you progress through your course this should become almost second nature to you – reading what others have written on the subject but also looking at what you see in the world around you. All of the above amounts to a distinctive approach to learning, known as work-applied learning. You will see in the following diagram that knowledge of various aspects of business and management is enriched through projects related to the workplace. This leads to questioning of what you already know and ultimately to well-informed, practical outcomes that can take you well beyond what you could find in libraries alone. To explain a little more, the natural starting point is where you see the Q. Start by asking questions about a problem that has to be solved through a project, which is shown as P1, then move on to read about the existing knowledge, K, on this subject. Armed with that material, back you go to P1 to see if the explanations make sense, and then you can achieve project and learning outcomes, P2. But that cycle is not the end of it because, on the basis of what you have learnt, you will now want to return to the questioning stage and repeat the whole process. In theory, you can repeat the cycle yet again as each time your understanding will be refined by more practical experience. Theory and practice, as you will discover, go hand in hand and this model helps to show how this is achieved. ©Australian Institute of Business. V10Sep15 –BKM:2014:10e
d 5 721INMT Investment Management Subject Overview Learning is an adventure, a journey of exploration. At AIB we encourage you to be bold, to cross the line between the classroom and the workplace. We will support you along the way and our hope is that the experience will be enjoyable as well as productive. There are no limits to what you can discover, no end to the learning process. Synopsis Subject Code: 721INMT Subject Credit Points: 10 AQF Level: 9 Associated higher education awards: – Graduate Diploma – Master of Business Administration Pre requisites and presumed knowledge: MBA core subjects (in particular AQF level 8 subjects) provide the foundation for specialisation and elective subjects (AQF Level 9 subjects). Hence, relevant core subjects should normally be attempted before progressing to specialisation and elective subjects. Particularly, Financial Management 712FMGT (previously known as Strategic Financial Issues AQF Level 9) must be completed before attempting this MBA subject. The objective of the subject is to provide comprehensive theoretical and practical knowledge on investment management. The subject covers major theoretical concepts, namely, modern portfolio theory, diversification, and equilibrium models of security prices. The subject also includes macroeconomic and industry analysis, pricing of main financial derivatives, and evaluation of portfolio performance. For information on the learning outcomes, course content, resources and assignment, please refer to the following pages of this subject overview. For any other information, please refer to the Student Handbook. Learning Outcomes This table lists the learning outcomes for the subject and shows how they are linked with the assessment. ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 6 721INMT Investment Management Subject Overview AQF’s Subject LO categories On completion of this subject participants should be able to: Assessed in written assignment Assessed in exam Knowledge LOs Demonstrate advanced knowledge about investment concepts, issues and theory (including investment steps, investment strategies, structure of interest rates, bond portfolios). x x Distinguish between active and passive investment strategies. x Skills LOs Price option and futures contracts. x x Predict the impact of changes in fiscal and monetary policies on key macroeconomic variables such as interest rate. x x Identify undervalued/overvalued securities. x Application LOs Construct an efficient portfolio. x x Evaluate portfolio performance. x x Content 1. Capital allocation to risky assets  Risk and risk aversion  Portfolio risk  Capital allocation across risky and risk-free portfolios  The risk-free asset  Portfolios of one risky asset and one risk-free asset  Risk tolerance and asset allocation  Passive strategies: the capital market line 2. Optimal risky portfolios  Diversification and portfolio risk  Portfolios of two risky assets  Asset allocation with stocks, bonds, and bills  The Markowitz portfolio selection model  A spreadsheet model  Risk pooling, risk sharing, and the risk of long-term investments  Optimal portfolios with restrictions on the risk-free asset 3. The capital asset pricing model and index models  The Capital Asset Pricing Model  Extensions of the CAPM  A single-factor security market  The single-index model  The index model and diversification  Practical aspects of portfolio management with the Index Model ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 7 721INMT Investment Management Subject Overview 4. Arbitrage Pricing Theory and Multifactor Models of Risk and Return  Multifactor Models: an overview  Arbitrage Pricing Theory  The APT, the CAPM, and the Index Model  A multifactor APT  The Fama-French (FF) Three-Factor Model 5. Macroeconomic and industry analysis  The global economy  The domestic macroeconomy  Demand and supply shocks  Federal government policy  Business cycle  Industry analysis 6. Options markets: introduction, and option valuation  The option contract  Values of options at expiration  Option strategies  The put-call parity relationship  Option-like securities  Financial Engineering  Exotic options  Option valuation: introduction  Restriction on option values  Binomial option pricing  Black-Scholes option valuation  Using the Black-Scholes formula  Empirical evidence on option pricing 7. Futures markets  The futures contract  Mechanics of trading in futures markets  Futures markets strategies  Futures prices  Future prices versus expected spot prices 8. Portfolio performance evaluation  The conventional theory of performance evaluation  Performance measurement of hedge funds  Performance measurement with changing portfolio composition  Market timing  Style analysis  Performance attribution procedures ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 8 721INMT Investment Management Subject Overview Resources Prescribed Text Book Bodie Z, Kane A & Marcus AJ 2014, Investments, 10th edn, McGraw-Hill Education. (ISBN: 9780077861674) However, the 10th edition is not too different from the 9 th edition. So students who cannot obtain the 10th edition might be able to the 9 th edition with only a slight disadvantage. Nevertheless, students should be cautioned that, generally speaking, using an old edition may make them dependent on out-of-date ideas and make them miss new concepts Required reading of journal articles Topic 1 Collins, P & Lam, HD 2011, ‘Asset allocation, human capital, and the demand to hold life insurance in retirement’, Financial Services Review, vol. 20, no. 4, pp. 303–325. Ostrov, DN & Wong, TG 2011, ‘Optimal asset allocation for passive investing with capital loss harvesting’, Applied Mathematical Finance, vol. 18, no. 4, pp. 291–329. Topic 2 Aroskar, R & Ogden, WA 2011, ‘Optimal Portfolios: Are they optimal for the long run?’, Applied Financial Economics, vol. 21, no. 11, pp. 763–770. Grote, J 2012, ‘Going to one: is diversification passé?’, Journal of Financial Planning, vol. 25, no. 6, pp. 20–25. Topic 3 Mandal, N 2013, ‘Optimal portfolio construction by using Sharpe’s Single Index Model’, Journal of Institute of Public Enterprise, vol. 36, no. 1/2, pp. 21–44. Unlu, U 2013, ‘Evidence to support multifactor asset pricing models: the case of the Istanbul Stock Exchange’, Asian Journal of Finance & Accounting, vol. 5, no. 1, pp. 197–2081 . Topic 4 Mohi-u-Din, S & Mubasher, HM 2013, ‘Macroeconomic variables on stock market interactions: the Indian experience’, Advances in Management, vol.6, no.8, pp. 39–51. Ramadan, IZ 2012, ‘The validity of the Arbitrage Pricing Theory in the Jordanian Stock Market’, International Journal of Economics & Finance, vol. 4, no. 5, pp. 177–1852 . 1 This article is licensed under Creative Commons Attribution 3.0 License. No changes have been made to the article. ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 9 721INMT Investment Management Subject Overview Topic 5 Rajput, N & Handa, H 2011, ‘Fundamental analysis and portfolio selection in practice’, BVIMR Management Edge, vol. 4, no. 2, pp. 35–38. Weyns, G, Perez, JL, Hurewitz, B & Jenkins, V 2011, ‘Morgan Stanley’s risk-reward views: unlocking the full potential of fundamental analysis’, Journal of Applied Corporate Finance, vol. 23, no. 2, pp.59–68. Topic 6 Chen, J & Chen, AW 2013, ‘Valuing employee stock options using the CRR Binomial Model’, Journal of International Business & Economics, vol. 13, no. 3, pp. 43–50. Choi, Y, Jordan, SJ & Ok, S 2012, ‘Dividend-Rollover Effect and the Ad Hoc Black-Scholes Model’, Journal of Futures Markets, vol. 32, no. 8, pp. 742–772. Topic 7 Prokopczuk, M 2011, ‘Pricing and hedging in the freight futures market’, Journal of Futures Markets, vol. 31, no. 5, pp. 440–464. Zakaria, Z & Shamsuddin, S 2012, ‘Relationship between Stock Futures Index and Cash Prices Index: em
pirical evidence based on Malaysia data’, Journal of Business Studies Quarterly, vol. 4, no. 2, pp. 103–112. Topic 8 Menardi, G & Lisi, F 2012,’Are performance measures equally stable?’, Annals of Finance, vol. 8, no. 4, pp. 553–570. Wee, S & Clive, MO 2011, ‘Are Philippine fixed income fund managers generating alpha for their clients?’, Journal of International Business Research, Supplement 2, vol. 10, pp. 129– 152. Recommended reading Reilly, FK & Brown KC 2011, Investment analysis and portfolio management, 10th edn, Thomson South-Western. 2 This article is licensed under Creative Commons Attribution 3.0 License. No changes have been made to the article. ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 10 721INMT Investment Management Subject Overview Assignment Write a report which addresses the questions (a to f) below. Where relevant, base your analysis on analysis of the data in the asset return table provided. (a) Describe each of the asset classes, setting out their characteristics and risks. (b) Calculate the AM and GM measures of the average annual yield on each of these asset classes during the period 1983-2003. Contrast the resulting measures of average yield for each asset class. (c) What would be the main problems you would encounter if you tried using the efficient frontier you have identified for portfolio selection purposes? (d) How does foreign exchange risk contribute to the risk of international investments? Is it worthwhile to hedge exchange rate risk? (e) During a world financial crisis, all the major financial markets will usually move in the similar direction (i.e. become highly correlated). Do you think this will limit the benefits of international diversification? (f) It is often said that Australian investors have an inefficient home bias in their asset portfolios. What does this mean? Why is it important? What are the principal causes of “home bias”? Asset returns on different asset classes over the period 1983 to 2003 Year Australian Shares % return Australian Bonds % return Cash % return International Shares % return Listed Property Trusts % return 1983 66.8 14.3 11.1 32.8 50.2 1984 -2.3 12.0 10.9 14.0 10.1 1985 44.1 8.1 15.2 70.2 5.3 1986 52.2 18.9 15.6 45.6 35.4 1987 -7.9 18.6 12.8 6.5 5.8 1988 17.9 9.4 12.9 4.3 16.1 1989 17.4 14.4 18.4 26.0 2.4 1990 -17.5 19.0 16.1 -15.1 8.7 1991 34.2 24.7 11.2 20.2 20.1 1992 -2.3 10.4 6.9 4.5 7.0 1993 45.4 16.3 5.4 24.4 30.1 1994 -8.7 -4.7 5.4 -8.1 -5.6 1995 20.2 18.6 8.0 25.9 12.7 1996 14.6 11.9 7.6 6.3 14.5 1997 12.2 12.2 5.6 41.1 20.3 1998 11.6 9.5 5.1 32.1 18.0 1999 16.1 -1.2 5.0 17.1 -5.0 2000 4.8 12.1 6.3 2.2 17.9 2001 10.5 5.5 5.2 -9.7 15.0 2002 -8.6 8.8 4.8 -27.2 11.9 2003 15.0 3.0 4.9 -0.5 8.8 ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 11 721INMT Investment Management Subject Overview Be sure to include in your responses to the questions above, these graphs and calculations:  First, graph the efficient frontier. In order to do so you will need to determine the expected return3 , standard deviation and correlation of the 5 assets in your portfolio.  Then, use Microsoft Excel to plot the efficient frontier on the XY scatter graph with risk on X axis and return on Y axis.  Using your graph, discuss the concept of the Markowitz Portfolio Theory and the CAPM. Clearly show that, using a risk-free asset, you are able to obtain a higher return for a given risk. The data for this assignment is drawn from “Financial Markets and Institutions in Australia” by Tom Valentine, Guy Ford, Vic Edwards, Maike Sundmacher and Richard Copp , 2nd edn, Pearson Education Australia, 2006, pp. 92-93. Important assignment instructions  The required word length for this assignment is 2500 words (plus or minus 10%).  In terms of structure, presentation and style you are normally required to use: – AIB standard report format; and – AIB preferred Microsoft Word settings; and – Harvard style referencing (which includes in-text citations plus a reference list). These requirements are detailed in the AIB Style Guide.  Reference lists for AIB assignments / projects normally contain the following number of relevant references from different sources: 6-12 (for MBA assignments).  All references must be from credible sources such as books, industry related journals, magazines, company documents and recent academic articles.  Your grade will be adversely affected if your assignment contains no/poor citations and/or reference list and also if your assignment word length is beyond the allowed tolerance level (see Assessment Policy available on AIB website).  Useful resources when working on your assignments include: – AIB Online Library – AIB Assignment Guide – AIB Style Guide 3 Assume the expected return is equal to the average annual stock return (from 1983 to 2003). ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 12 721INMT Investment Management Subject Overview Academic Integrity: Avoiding Plagiarism, Collusion and Other Issues It is important to adhere to high standards of academic integrity. Academic integrity refers to ethical, honest and responsible conduct in writing and reporting. Breaches of academic integrity include:  Plagiarism – submitting another person’s words or ideas as your own without appropriate acknowledgement and referencing.  Collusion – submitting work as if it is one’s own when in reality it has been completed with others.  Fabrication – submitting work with results or data that do not exist and that have been made up.  Double submission – submitting the same piece of work for more than one subject or by more than one person. Please note that AIB checks assignments for plagiarism (using Turnitin text-matching software) and for other academic misconduct. AIB penalises work and/or people found to have been in breach of academic integrity. For more details please see Academic Integrity policy on AIB website. Online Library User Guide AIB uses the EBSCO Host online library. Below are the instructions on how to use the online library. 1. Go to the AIB website www.aib.edu.au. 2. Click ‘Student Resources’. 3. Click ‘Online Library’. 4. Click on the link Access EBSCO Host which will take you to the login screen. 5. Once you can see the login screen, type in your user name and password that have been provided to you. 6. Once logged in, you should be able to see the search bar. 7. Start your research by keying in different key words. Click search to get the search results. 8. Review the article abstract or the full text (depending on its availability). Some articles may be restricted and may need to be purchased. ©Australian Institute of Business. V10Sep15 –BKM:2014:10ed 13 721INMT Investment Management Subject Overview 9. Refine your research by checking any of option boxes e.g. scholarly (Peer reviewed) Journals. This is the most credible and respected resource for your research. 10. To learn more about EBSCO Host and how to fully benefit from its features you may visit EBSCO Host Support and Tutorials site at http://support.ebsco.com/. Online Revision Quizzes AIB has created various online quizzes which it makes available on its website, to assist students in undertaking their MBA course. There is one quiz for each MBA subject. The purpose of the quiz is to provide students with a self-assessment tool prior to sitting their exam. The quizzes are not assessable and are merely provided to assist students with their study of each subject. While it is not compulsory to use the quiz, we would highly recommend it. To access the quizzes for your MBA subjects please visit this site: http://www.aib.edu.au/www/pages/misc/quiz/mba We trust that you will find these quizzes useful in your studies. Information on Examination Scientific calculator Casio FX 115ES (or FX100AU or FX100AU-BP or FC-200V or FC-100V or FX-115MS or FX-82TL or FX-82AU/ FX-82 AU Plus II or FX100S or FX82MS) or Sharp EL-738 (or EL-738 S or EL-735 or EL-735S or EL-531XH), HP 10bll+ (or 10bll, 12c, 17bll+) or TI BA11 Plus may be used during the exam for this subject. No other scientifi
c calculator brand or model is permitted. Standard calculators (non-scientific) are also permitted; however, students might be slightly disadvantaged if they are not using one of the allowed models above.

Optimal Portfolio Construction by Using Sharpe’s Single Index Model 21 Dr.Niranjan Mandal* In this research article an attempt has been made to explore the idea embedded in SIM and to construct an optimal portfolio empirically using this model. Considering daily indices of BSE sensex as MPI along with the daily stock prices of the ten selected public sector enterprises for the period of April 2001 to March 2011, the proposed mechanism formulates a unique cut off rate and selects securities having ‘excess-return to beta’ ratio greater than or equals to the cut off rate. To arrive at the optimal portfolio, proportion of investment in each of the selected securities is computed on the basis of its beta value, unsystematic risk, risk free rate of return excess-return to beta ratio and cut off rate. It is found that SIM gives an easy mechanism of constructing optimal portfolio and requires lesser input than the input requirement of Markowitz’s model to achieve the risk and return of the optimal portfolio. It is also observed that there is a significant difference between the total risk of the optimal portfolio under SIM and that of under Markowitz’s model. * Dr.Niranjan Mandal, M.Com, MLIS, M.Phil (Commerce), PhD (Economics), Associate Professor, Department of Commerce, Dr.Bhupendranath Dutta Smriti Mahavidyalaya, Affiliated to the University of Burdwan,Wesr Bengal – 713407, India. Keywords : Portfolio Construction, Sharpe’s Single Index Model, Return and Risk, Risk Characteristic Line, Optimal Portfolio, Diversification, Cut off Rate. Introduction Harry Markowitz, in early 1950’s, developed a comprehensive model in which he made a simple premise that almost all investors invest in multiple securities rather than a single security for obtaining benefits from the investment in a portfolio consisting of different stocks. In this theory, he tried to show that the variance of the rates of return is a meaningful measure of portfolio risk under a reasonable set of assumptions and also derived a formula for computing the variance of a portfolio. His work gives emphasis on the importance of the diversification of investments to reduce the risk of a portfolio and also shows how to diversify such risk effectively. Though Markowitz’s model is viewed as a classic attempt to develop a comprehensive technique to incorporate first the concept of diversification of investments in a portfolio The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise Optimal Portfolio Construction by Using Sharpe’s Single Index Model (An Empirical Study on Stocks of Some Selected Public Sector Enterprises in India) The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise 22 as a risk-reduction mechanism, it has many limitations that need to be resolved. One of the most significant limitations of Markowitz’s model is the increased complexity of computation that the model faces as the number of securities in the portfolio grows. To determine the variance of the portfolio, the covariance between each possible pair of securities must be computed, which is represented in a co-variance matrix. Thus, increase in the number of securities, results in a large co-variance matrix, which in turn, results in a more complex computation. Due to this practical difficulties security analysts do not like to perform their tasks taking the huge burden of data-inputs of this model. They quest for a more simplified model for performing their task comfortably. To this direction, in 1963 William F. Sharpe has developed a simplified Single Index Model (SIM) for portfolio analysis by taking the cue from Markowitz’s concept of index for generating covariance terms. This model gives us an estimate of a security’s return as well as of the value of index. Not only that Markowitz’s model was further extended by Sharpe and introduced the capital Assets Pricing Model (Sharpe, 1964) to solve the problem behind the determination of correct, arbitrage-free, fair or equilibrium price of an asset (say security). John Lintner in 1965 and Mossin in 1966 also derived similar theories independently. William F. Sharpe got the Nobel Prize in 1990, shared with Markowitz and Miller, for such a seminal contribution in the field of investment finance in economics. SIM is very much useful to construct optimal portfolio by analyzing how and why the inclusion or exclusion of securities in an optimal portfolio with their respective weights calculated on the basis of some important variables under consideration. Review of Literature i) Gregory and Shapiro (1986) in their research study examined a cross-section of 464 stocks and identified that average return is more closely related to the beta measured with respect to a stock market index than to the beta measured with respect to consumption growth. ii) Steven C. Blank (1991) conducted a research study in which he applied SIM as a tool for evaluating the riskreturn trade off faced in agricultural enterprise selection. The study shows that the country level data does not support SIM hypothesis indicating that more robust results might come from Multiple Index Model. iii)Rachel Campbell, Ronald Huisoman and Kees Koedijk (2001) in their study highlighted the influence of both non-normal characteristics of the expected return distribution Optimal Portfolio Construction by Using Sharpe’s Single Index Model 23 and the length of investment time horizon on the optimal portfolio selection. iv) Asmita Chitnis’s (2010) study optimized two portfolios tend to spread risk over many securities and thus help to reduce overall risk associated with them. The greater the Sharpe’s ratio of portfolio, the better will be the performance of it. v) Saravanan and Natarajan (2012) conducted an analytical study in which they found returns on either individual securities or on portfolio comprises of securities of different companies listed in Nifty 50 stocks under various sectors are asymmetrical and heterogeneous. They found that in Indian stock market SIM performs in a better way. vi) Javed Bin Kamal (2012) conducted research study on the construction of an optimal portfolio by applying Sharpe’s SIM considering daily prices of sample securities under Dhaka Stock Exchange (DSE) for the period of 2005-2009 in which he found that all stocks failed to make the pass SIM criteria. Objective of the Study The main objectives of the study are : i) To explore an idea embedded in SIM, ii) To construct an optimal portfolio empirically by using SIM, iii)To determine return and risk of the optimal portfolio constructed by using SIM, and iv) To compare the total risk of the optimal portfolio by using two different mechanisms found in SIM and Markowitz’s model. Methodology The study is based on secondary data procured by surfing www.bseindia.com/ www.riskcontrol.com. For the purpose of the study,BSE sensex is taken as the Market Performance Index (MPI). Daily indices of BSE Sensex along with daily share prices of ten (sampled) leading Public Sector Enterprises for the period between April 2001 and March 2011 are taken into account for the purpose of computing daily return of each security as well as calculating the daily market return. Taking the computed mean daily return of each security and that of the market, the proposed method formulates a unique cut off rate and selects those securities whose “excess-return to beta” ratio is greater than or equals to the cut off rate. To arrive at the optimal portfolio, the proportion of investment in each of the selected securities in the optimal portfolio is computed on the basis of its The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise 24 beta value, unsystematic risk, risk free rate of return, excess-return to beta ratio and the cut off rate. Different journals, periodicals, conference proceedings, books and other relevant documents have been consulted to supplement the theory as well as the data. The available data have been analyzed and interpreted by using diff
erent statistical and financial tools and techniques, charts, diagrams etc. Sharpe’s Single Index Model : The Conceptual Framework This simplified model proposes that the relationship between each pair of securities can indirectly be measured by comparing each security to a common factor ‘Market Performance Index (MPI)’ that is shared amongst all the securities. As a result, the model can reduce the burden of large input requirements and difficult calculations in Markowitz’s mean-variance settings (Sharpe, 1963). This model requires only (3n+2) data inputs i.e. estimates of Alpha (a) and Beta (b) for each security, estimates of unsystematic risk ( 2 sei) for each security, estimates for expected return on market index and estimates of variance of return on the market index ( 2 sm ). Due to this simplicity SIM has gained its popularity to a great extent in the arena of investment finance as compared to Markowitz’s model. Assumptions Made SIM is based on the following assumptions : i) All investors have homogeneous expectations. ii) A uniform holding period is used in estimating risk and return for each security. iii)The price movements of a security in relation to other do not depend primarily upon the nature of those two securities alone. These two securities are more suitable to reflect a greater influence that might be cropped up as general business and economic conditions. iv) The relation between securities occurs only through their individual influences along with some indices of business and economic activities. v) The indices, to which the return of each security is correlated, are likely to be some securities’ market proxy. vi) The random disturbance term (ei) has an expected value zero (0) and a finite variance. It is not correlated with the return on market portfolio (Rm) as well as with the error term (ei) for any other securities. Symbols and Notations Used Following symbols and notations are used to build up this model : Optimal Portfolio Construction by Using Sharpe’s Single Index Model 25 Ri = Return on security i (the dependent variable) Rm = Return on market index (the independent variable) ai = Intercept of the best fitting straight line of Ri on Rm drawn on the Ordinary Least Square (OLS) method or ‘Alpha Value’. It is that part of security i’s return which is independent of market performance. bi = Slope of the straight line (Ri on Rm) or ‘Beta Coefficient’. It measures the expected change in the dependent variable (Ri) given a certain change in the independent variable (Rm) i.e. i m dR dR . ei = random disturbance term relating to security i Wi = Porportions (or weights) of investment in securities of a portfolio. 2 sei = unsystematic risk (in terms of variance) of security i Rp = Portfoli Return 2 sp = Portfolio Variance (risk) bp = Portfolio Beta ep = Expected value of all the random disturbance terms relating to portfolio. 2 sep = Unsystematic risk of the portfolio i = 1, 2, 3, ………….., n Mathematical Mechanism Developed a) SIM : Return in the context of security According to the assumptions and notations above it is found that the return on security Ri depends on the market index Rm and a random disturbance term ei. Symbolically, Ri m i = f(R ,e ) ……………….(1) Let the econometric model of the above function with Ri as the explained variable and Rm as the explanatory variable be : Ri = ai + b + iR e m i ……………(2) where ai and bi are two parameters and ei be the random disturbance term which follows all the classical assumptions i.e. E(ei) = 0, E(ei Rm) = 0, E (ei ej) = 0 ” i j ¹ (non-auto correlation) and E (ei, ej) = 2 se ” = ij (homosedasticity). To determine the value of ai and bi we use the OLS method and get the following two normal equations : å å Ri = n R ai + bi m ……………(3) 2 åRiRm = aiå å R R m + bi m …….(4) Solving these two normal equations above by ‘Cramer’s Rule’, we get The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise 26 i m 2 i m m i m 2 m m R R R R R n R R R a = å å å å å å å or ( ) 2 i m m i m i 2 2 m m R R R R R n R R – a = – å å å å å å ……(5) and i m i m i m 2 m m n R R RR n R R R b = å å å å å å or ( ) i m i m i 2 2 m m n R R R R n R R – b = – å å å å å or i m i m i 2 2 m m 1 R R R R n n n 1 R R n n æ öæ ö – ç ÷ç ÷ ç ÷ è øè ø b = æ ö – ç ÷ è ø å å å å å …(6) (Dividing both sides by 2 1 n ) or i m i m Cov(R R ) Var(R ) b = ……….(7) or i m i 2 m rs s b = s ……………(8) Putting Cov(RiRm) = rim or i i m r s b = s …………..(9) Putting the respective table values of åRi , åR m , 2 åR m , åR Ri m and n in equation (6) we get the value of ai and bi and then using the value of ai and bi we get required estimated (or regression) line of Ri on Rm as under : R R i = ai + bi m ……….(10), which establishes the linear relationship between security return and market return and is known as the Sharpe’s Single Index Model. This model can graphically be represented in Exhibit-1. Thus, SIM divides the return into two parts : (i) Unique part ai and (ii) Market related part bi m R . The unique part a , the intercept term, is called by its Greek name ‘Alpha’ and is a micro event affecting an individual security but not all security in general. It is obviously the value of Ri when Ri =0. The market Optimal Portfolio Construction by Using Sharpe’s Single Index Model 27 related part bi m R , on the other hand, is a macro event that is broad based and affects all or most of the firms. Beta (b ), the slope of the line, is referred to as ‘Beta Coefficient’. It is a measure of sensitivity of the security return to the movements in the market returns. It shows how risky a security is, if the security is held in a well diversified portfolio. b) SIM : The Risk Characteristic Line The line representing SIM is also known as the Risk Characteristic Line (RCL). The concept of risk characteristic line conveys the message about the nature of security simply by observing its b value as follows : i) Securities having b >1 are classified as aggressive securities, since they go up faster than the market in a ‘bull’ (i.e. rising market), go down in a ‘bear’ (i.e. falling market). ii) Securities having b <1 are categorized as defensive securities, since their returns fluctuate less than the market variability as a whole. iii)Finally, limiting case of securities having b =1, are neutral securities, since their returns fluctuate at the same rate with the rate of market variability of return. The RCLs of the above three cases are represented in Exhibit-2. Exhibit-1 : Sharpe’s Single Index Model (Graphical Exposition) ® ® O(0,0) ai Security Return (Ri) Ri=ai+biRm Slope of the line (bi) = i m dR ® dR Market Return (Rm) { The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise 28 c) SIM : Return in the Context of Portfolio For establishing the relation between portfolio return and market return it is required to take the weighted average of the estimated returns of all the securities in the portfolio consisting of n-securities, as under : ( ) n n i i i i i m i i 1 i 1 WR W R e = = å å= a +b + ……(11) or n n n n i i i i m i i i i i 1 i 1 i 1 i 1 W R W R W W e = = = = å = å a + å å b + or Rp = ap +b + pR e m p ………..(12), where n n n p i i p i i p i i i 1 i 1 i 1 R W R , W , W = = = = ååå a = a b = b and n p i i i 1 e W e = = å According to the classical assumption, n p i i i 1 e W e 0 = = = å and hence, R R p = ap + bp m ……….(13). This is the required estimated (or regression) equation of Rp on Rm , which establishes the relationship between portfolio return (Rp) and market return (Rm). d) SIM : Risk in Context of Security In Sharpe’s index model total risk of a security, as measured by variance, can be deduced by using the relationship Exhibit-2: Risk-characteristic Lines of Security having b < 1, b > 1 and b = 1 ® ® O(0,0) Security Return (Ri) 45 0 line Market Return (Rm) b=1 b<1 (Neutral Security) (Defensive Sec
urity) ® ® O(0,0) Security Return (Ri) Market Return (Rm) b>1 (Neutral Security) (Aggres sive Security) 450 line (b=1) Optimal Portfolio Construction by Using Sharpe’s Single Index Model 29 between security return and market return (equation 2) as under : Var (Ri i i m i ) = Var (a + b + R e ) or Var (Ri i i m i ) = Var (a ) +b+ Var( R ) Var(e ) or Var (Ri i m i ) = Var( Rb +) Var(e ) [ i Q Var ()0 a = , ai being a parameter] or 2 2 2 2 si = bi sm + sei …………..(14) Thus, total variance ( ) 2 si = Explained variance ( ) 2 2 b si m + Unexplained variance ( ) 2 sei . According to Sharpe, the variance explained by the market index is referred to as systematic risk. The unexplained variance is called residual variance or unsystematic risk. It follows : Total risk of a security ( ) 2 si = Systematic risk ( ) 2 2 b si m + unsystematic risk ( ) 2 sei . e) SIM : Risk in the context of portfolio In SIM, the total portfolio risk (measured by variance) can similarly be deduced by using the relationship between portfolio return and market return [using equation-11] as under : ( ) n n i i i i i m i i 1 i 1 Var W R Var W R e = = ì ü ì ü í ý = í ý a + b + î þ î þ å å or n n i i i i i 1 i 1 Var W R Var W = = ì ü ì ü í ý = í ý a + î þ î þ å å + n n m i i i i i 1 i 1 Var R W Var W e = = ì ü ì ü í b +ý í ý î þ î þ å å or 2 n 2 2 2 p i i m ep i 1 W = æ ö s = ç ÷ b s + s è ø å [ 1 0, = Q å = n i i i Var Wa weights being constants and ai’s being parameters] or 2 2 2 2 sp = bpsm + sep ……….(15) Sharpe’s analysis suggests that total risk of the portfolio also consists of two components : (i) systematic risk and (ii) unsystematic risk of the portfolio. Therefore, we have Total Portfolio Risk ( ) 2 sp = Systematic risk of the portfolio ( ) 2 2 b sp m + Unsystematic risk of the portfolio ( ) 2 sep . Advantages of SIM The following are the main advantages of SIM : The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise 30 a) The apparent advantage to SIM is that it considerably simplifies the portfolio problem in comparison to Markowitz’s Full-Covariance Model. If we have n securities at our disposal, it requires (3n+2) estimates [i.e. ai , bi , 2 sei for each security] but Markowitz’s model requires n(n 3) 2 + estimates [i.e. Ri and 2 si for each security and n(n 1) 2 – covariance terms]. b) It simplifies the computational techniques required to solving the problem. c) It gives us an estimate of security’s return as well as of the value of index. d) It greatly helps in obtaining the following inputs required for applying the Markowitz’s model : i) the expected return on each security i.e. E(Ri i i m ) = a + b E(R ) , ii) the variance of return on each security i.e. 2 Var(Ri i m i ) = b + Var(R ) Var(e ) , and iii)the covariance of return between each pair of securities i.e Cov(R Ri j i j m ) =bb Var(R ) All of the above inputs may be estimated on the basis of historical analysis and/or judgemental evaluation (i.e. expost and/or ex-ante analysis). e) It is very much useful to construct optimal portfolio for an investor by analyzing the logic behind the inclusion or exclusion of securities in the portfolio with their respective weights. Sharpe found that there is a considerable similarity between the efficient portfolios generated by SIM and the Markowitz’s model. From other studies (such as Elton et al 1978; and Benari 1988), it is found that SIM performs fairly well. Since SIM simplifies considerably the input requirements and performs well, it represents a greater practical advance in portfolio analysis. Limitations Found One of the most important limitations with SIM is that it does not consider uncertainty in the market as time progresses instead of that the model optimizes for a single point in time. Moreover, this model assume that security prices move together only because of common co-movement with the market. Many researchers (such as Gregory and Shapiro, 2001; and Campbell et all 2001) have identified that there are influences beyond the Optimal Portfolio Construction by Using Sharpe’s Single Index Model 31 general business and market conditions, like industry oriented factors that cause securities to move together. However, empirical evidence shows that the more complicated models have not been in a posi-tion to outperform the single index model in terms of their ability to predict ex-ante covariance’s between security returns (Chandra, 2009). Construction of Optimal Portfolio by using SIM The construction of optimal portfolio is an easy task if a ‘single value’ explains the desirability of the inclusion of any security in a portfolio (Fischer and Jordan, 1995). This single value exists in SIM where it is found that the desirability of any security is directly related to its ‘excess return to beta ratio’ (i.e. i f i R r – b ). This means that the desirability of any security is solely a function of its excess return-to-beta ratio. If securities are ranked on the basis of excess return-to-beta ratio (from highest to lowest), the ranking represents the desirability of including a security in the portfolio. The selection of securities to construct an optimal portfolio depends on a unique cut off rate, C* such that all the securities having * – ³ i f i R r C b will be included and at the same time all the securities having * – < i f i R r C b will be excluded. Thus, to determine how and in what way judicious inclusion of securities is made in the construction of the optimal portfolio by using Sharpe’s Single Index Model, the following steps are necessary : i) Calculation of ‘Excess Return-toBeta ratio for each and every securities under consideration. ii) Ranking of securities from highest ‘Excess Return to Beta’ i f i R r i.e. æ ö – ç ÷ è ø b to lowest. iii)Calculation of values of a variable Ci for each and every security by using following formula : 2 2 1 2 2 2 1 ( ) 1 = = – = + å å b s s b s s n i f i m ei i i n i m i ei R r C iv) Finding out the optimum * Ci (i.e.C ) upto which all the securities under review have excess return to beta above * * . . æ ö – ç ÷ ³ è ø b i f i R r C i e C and after that point all the securities have excess return to beta below * * . . æ ö – ç ÷ < è ø b i f i R r C i e C . The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise 32 v) Inclusion of securities having * – ³ i f i R r C b in the optimal portfolio. vi) Arriving at the optimal portfolio by computing the proportion of investment in each security included in the portfolio. The proportion of investment in each of such security is given by : i i K i i 1 Z W Z = = å , where 2 i i f * i 2 ei i R r Z C b – æ ö = – ç ÷ s b è ø i = 1, 2, ……, K out of n securities under review. It is to be noted that to determine how much to invest in each security the residual variance on each security, 2 sei has a great role of play here. Analysis of Data To construct optimal portfolio using SIM various statistical measures have been made on the basis of collected data relating to daily stock prices along with daily market indices for the period April 2001 to March 2011. Various statistics such as mean daily return (Ri), variance ( ) 2 si and standard deviation (si ) of daily return, standard deviation of market return (s m ) covariance (sim ) and correlation (rim ) between the series of daily security return and the daily market return, beta (bi ), systematic risk ( ) 2 2 b si m and unsystematic risk ( ) 2 sei of all the ten sampled securities have been calculated on the basis of the collected data. All these statistics as data input have been arranged in Table-1. From Table-1 it is found that the security of MTNL has contributed negative return and SAIL has contributed positive return with negative beta. The situation of negative return and negative beta may arise due to some macro economic events in the secondary market. From the table it is also observed that out of ten sampled PSEs securities only one security viz BHEL has beta greater than
one. This security is called aggressive security and contributes 0.1406 per cent mean daily return with standard deviation 2.8148 per cent. The rest of the securities (viz. ONGC, BPCL, NALCO etc.) having beta less than one are called defensive securities. All of such defensive securities have contributed positive return ranging from 0.0696 per cent to 0.1406 per cent with their respective beta value lies between 0 and 1 (i.e. 0 < b < 1), except MTNL (having return –0.0197 per cent) and SAIL (having negative beta, –1.3134 per cent with positive return, 0.1906 per cent). The systematic risk ( ) 2 2 b si m Table-1 : Data Need to Construct Optimal Portfolio Using Sharpe’s Single Index Model sm = 1.67 Sl. Companyi Mean Daily Variance Standard Covariance Correlation with Beta (Systematic Unsystematic No. Security Return (Ri) ( 2 si ) Deviation ( sijm ) with the Market ( bi ) bi m ´ s risk)2 Risk ( si) Market rim 2 2 b si m ( 2 sei ) 1 ONGC 0.09354146 8.62416090 2.93669217 0.00023736 0.48387015 0.85067810 1.42063242 2.01819649 6.60596441 2 BPCL 0.10146048 7.86666643 2.80475782 0.00017244 0.36806358 0.61801100 1.03207837 1.0651857 6.80148073 3 SAIL 0.19059022 12.72599158 3.56735078 -0.00036954 0.61757295 -1.31344593 -2.1934547 4.81124353 7.91474805 4. BHEL 0.14064942 7.92329822 2.81483538 0.00028252 0.60086421 1.01252867 1.69092288 2.85922018 5.06407804 5. NALCO 0.10046810 11.83528449 3.44024483 0.00024778 0.43116904 0.88800397 1.48296663 2.19919002 9.63609447 6. NTPC 0.07937121 4.59124749 2.14271965 0.00024799 0.6448048 0.76976635 1.28550980 1.65253545 2.93871204 7. MTNL -0.01972479 4.27890853 2.06855228 0.00017841 0.60836555 0.88766810 1.48240573 2.19752674 2.08138179 8. GAIL 0.12277797 7.08111014 2.66103554 0.00024316 0.54702753 0.87142443 1.45527879 2.11783638 4.96327376 9. COAL 0.06965161 4.01883828 2.00470404 0.00006830 0.27742122 0.45286009 0.75627635 0.57195392 3.44688436 INDIA 10. ENGINEERS 0.11720708 13.63777682 3.69293607 0.00022860 0.37010238 0.81716231 1.36466105 1.86229980 11.77547702 INDIA LTD. Source : www.bseindia.com / www.riskcontrol.com (from 01-04-2001 to 31-03-2011) 33 Optimal Portfolio Construction by Using Sharpe’s Single Index Model The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise 34 of all the securities ranges from 0.5719 per cent to 4.8112 per cent and the domain of unsystematic risk component ( ) 2 sei of all those securities is 2.0813 per cent to 11.7754 per cent. The total risk ( ) 2 si of all those securities ranges from 4.0188 per cent to 13.6377 per cent. The correlation coefficient between of each of the securities return and the market return ranges from 0.2774 to 0.6448. From the analysis of data contained in Table-1, it is seen that most of the securities of PSEs are defensive in nature. The risk averse type of investors may prefer these securities to include in their portfolio investment. As a criterion for the selection of securities, the Sharpe’s Single Index Model proposes that the stocks having negative return are to be ignored. Actually, for determining which of these securities should be selected in the portfolio depends on the ranking of securities (from highest to lowest) based on excess return to beta ratio i f i æ ö R r – ç ÷ è ø b . The rule of ranking, applied here, states that the securities having highest ‘excess return to beta ratio’ would be placed first, then comes the securities having second highest ‘excess return to beta ratio’ and so on and so forth. From Table-2 it is seen that BPCL having the highest “excess-return to beta” ratio (0.12870753) occupies the first place. The security of BHEL, having the second highest “excess-return to beta” ratio (0.11726247), occupies the second place. In this way Engineers Ltd, GAIL, Coal India, ONGC and NTPC occupy their respective 3 rd , 4 th , 5 th , 6 th and 7 th positions within the ambit of the data set. Now it is necessary to determine the securities for which excess return to beta ratio is greater than a particular cut off value * C of the variable Ci. In Table-3 securities are arranged according to their rank and finally value of Ci for each of such securities are computed using the formula of Ci given as : n 2 i f i m 2 ei i 1 i n 2 2 i m 2 ei i 1 (R r ) C 1 = = – b s s = b + s s å å , where 2 sm indicates the market index and 2 sei refers to the variance of a security’s movement that is not associated with the fluctuation of the market index. From Table-3 it is found that i f i R r – b values of the first seven securities exceed the Ci values of the corresponding securities. The Ci value of the 7th 35 Table-2 : Ranking of Securities on the Basis of Excess Return to Beta Value where rf = 8% p.a. = 0.02192% per day is taken Company Security Excess of Excess Return Rank according i having Positive Mean Daily Mean Daily Beta to Beta to Highest to Sl. Mean Return Return Return over Value Lowest No. and Positive (Ri) Risk-free Rate ( bi ) Beta Value (daily) (Ri-rf) 1 ONGC 0.09354146 0.07162365 0.85067810 0.08419595 6 2 BPCL 0.10146048 0.07954267 0.61801100 0.12870753 1 3. BHEL 0.14064942 0.11873161 1.01252867 0.11726247 2 4. NALCO 0.10046810 0.02191781 0.88800397 0.02468211 8 5. NTPC 0.07937121 0.0574534 0.76976635 0.07463745 7 6. GAIL 0.12277797 0.10086016 0.87142443 0.11574172 4 7. COAL INDIA 0.06965161 0.0477338 0.45286009 0.10540518 5 8. ENGINEERS. 0.11720708 0.09528927 0.81716231 0.11660997 3 INDIA LTD Source : www.bseindia.com / www.riskcontrol.com (from 01-04-2001 to 31-03-2011) i f i æ ö R r – ç ÷ è ø b i f i æ ö R r – ç ÷ è ø b Optimal Portfolio Construction by Using Sharpe’s Single Index Model Table-3 : Calculations for Determining the Cut off Rate, C where , rf = 8% p.a. = 0.02192% per day. Rank on the Company Basis of Security i Excess according Return to Rank to Beta 1. BPCL 0.12870753 0.00722758 0.05615506 0.00722758 0.05615506 0.01744196 2. BHEL 0.117262467 0.02373959 0.20244836 0.03096717 0.25860342 0.05017626 3. ENGINEERS 0.116609967 0.00661262 0.05670719 0.03757979 0.31531061 0.05576671 INDIA LTD. 4. GAIL 0.11574172 0.01770847 0.15299993 0.05528826 0.46831054 0.06686412 5. COAL INDIA 0.10540518 0.00627138 0.05949786 0.06155964 0.5278084 0.06945119 6. ONGC 0.08419595 0.00922328 0.10954543 0.07078292 0.63735383 0.07107303 7. NTPC 0.07463745 0.01504934 0.20163263 0.08583226 0.83898646 0.07167317 8. NALCO 0.02468211 0.00201981 0.08183305 0.08785207 0.92081951 0.06866748 Source : www.bseindia.com / www.riskcontrol.com (from 01-04-2001 to 31-03-2011) i f i æ ö R r – ç ÷ b è ø i f i 2 ei (R – b r ) s 2 i 2 ei b s n i f i 2 i 1 ei (R r ) = – b å s n 2 i 2 i 1= ei b ås n 2 i f i m 2 i 1 ei i n 2 2 i m 2 i 1 ei (R r ) C 1 = = – b s s = b + s s å å 36 The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise Optimal Portfolio Construction by Using Sharpe’s Single Index Model 37 security (NTPC) would be the cut off value * C C7 = =( 0.07167317) below which ‘excess return to beta ratio’ is less than the respective Ci value of the security i f i i R r C æ ö – ç ÷ á è ø b and the collection of these top seven securities, having i f * i R r C – ³ b , make it to the optimal portfolio. After identifying the composition of the optimal portfolio, the next step is to determine the proportion of investment (i.e. weights) in each of the securities in the optimal portfolio as shown in Table-4, using the formula of Wi cited earlier. From Table-4 it is seen that Wi for the selected securities in the optimal portfolio of stocks viz BPCL, BHEL, Engineer’s Ltd., GAIL Coal India, ONGC and NTPC are 13 per cent, 37 per cent, 10 per cent, 23 per cent, 8 per cent, 6 per cent and 3 per cent respectively. This proportion of stocks in the composition of optimal portfolio can be shown in the following Pie diagram : Now the portfolio return, portfolio beta and risk components of the optimal portfolio constructed above can be computed on the basis of the compiled data shown in Table-5. On the basis of information arranged in Table-5 the following results can be extracted : i) P
ortfolio Return (R p ) = = åW Ri i 0.1188% per day = 3.564 per cent per month = 43.362 per cent per annum. ii) Portfolio beta, p i i b =åW b = 0.8475 which is less than one indicating the defensive nature of the portfolio. iii)Systematic risk of the portfolio ( ) 2 2 bp m ´ s = (0.8475)2 x (1.67)2 = 2.0031 per cent (approx), which comes from economy wide factors. iv) Unsystematic risk of the portfolio, ( ) ( ) 2 2 sep = s å Wi ei = 6.1509 per cent which comes from firm specific factors i.e. the internal environmental factors. v) Total risk of the portfolio ( ) 2 sp = 2.0031 + 6.1509 = 8.154 per cent (in terms of variance) Or Total risk of the portfolio (sp ) = = 8.154% 2.86 per cent (in terms of S.D.) From the above result it is observed that the portfolio return (0.1188 per cent) is higher than the average returns of all 38 Table-4 : Calculation of Zi and Wi for the Selected Securities in the Optimal Portfolio Percentage of Selected Investment of each Approximate Securities in Selected Securities Value of the Optimal Wi (%) Portfolio BPCL 0.12870753 0.05615506 0.00320276 0.1297 13 BHEL 0.117262467 0.20244836 0.00922945 0.3739 37 ENGINEER’S LTD. 0.116609967 0.05670719 0.00254824 0.1032 10 GAIL 0.11574172 0.15299993 0.00572888 0.2321 23 COAL INDIA 0.10540518 0.05949786 0.00200698 0.0813 8 ONGC 0.08419595 0.10954543 0.00137181 0.0555 6 NTPC 0.07463745 0.20163263 0.00059769 0.0243 3 TOTAL — — åZi = 0.02468581 å Wi = 100 100 Source : www.bseindia.com/www.riskcontrol.com (from 01-04-2001 to 31-03-2011) The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise i f i R r – b 2 2 b s i ei 2 i i f * i 2 ei i R r Z C b – æ ö = – ç ÷ s b è ø = ´100 å i i i Z W Z Optimal Portfolio Construction by Using Sharpe’s Single Index Model 39 the stocks in the portfolio with the exception of GAIL (0.1228 per cent) and BHEL (0.1406 per cent). The beta value (0.8475 per cent) of the optimal portfolio is less than one which indicates that the returns from the portfolio fluctuates at a slower rate than the fluctuation of market rate of return. The unsystematic risk of the optimal portfolio is 6.1509 per cent in terms of variance which is much higher than the systematic risk (2.0031 per cent) of that portfolio. This indicates that there is an enough scope to reduce the total risk of the portfolio through diversification (i.e. inclusion or exclusion of favorable securities in the portfolio). The total risk of the portfolio (2.86 per cent, in terms of SD) is more than that of the securities in the portfolio with the exception of Engineer Ltd. and ONGC. According to Markowitz’s Mean-Variance Model, portfolio risk (in terms of variance) is given by : n n n 2 2 2 p i i i j ij i 1 i 1 j 1 W W W = = = s =å s + s åå …..(16) i = j i j ¹ In terms of S.D. it as under : n n n 2 2 p i i i j ij i 1 i 1 j 1 W W W = = = s = å s + s åå ….(16A) i = j i j ¹ [Symbols have their usual meanings.] Pie Diagram : Stock Composition in the Optimal Portfolio (Constructed) Weights (%) ®BPCL 13% ®BHEL 37% Engineer’s Ltd. 10% GAIL 23% Coal India 8% ONGC 6% NTPC 3% ® Table-5 : Calculation for Computing Portfolio Return (R ) p and Portfolio Risk p ( ) b Selected Mean Standard Proportion securities in Daily Deviation Beta Value of sei WRi i Wi i b Wisei the optimal Return of Returns bi Investment portfolio Ri si Wi BPCL 0.10146048 2.80475782 0.6180100 0.13 2.60796486 0.01318986 0.08034143 0.33810354 BHEL 0.14064942 2.81483538 1.01252867 0.37 2.25035064 0.05204023 0.37463561 0.83262973 Engineer’s 0.11720708 3.69293607 0.81716231 0.10 3.43154149 0.01172071 0.08171623 0.34315415 Ltd. GAIL 0.12277797 2.66103554 0.87142443 0.23 0.22784061 0.02823893 0.20042762 0.61203817 Coal India 0.06965161 2.00470404 0.45286009 0.08 1.85657867 0.00557213 0.03622881 0.14852629 ONGC 0.09354146 2.93669217 0.85067810 0.06 2.57020707 0.00561248 0.05104068 0.15421242 NTPC 0.07937121 2.14271965 0.76976635 0.03 1.71426720 0.00238113 0.02309299 0.05142802 TOTAL — — — Wi å = 1.00 — å Wi i R = 0.1188 åW . i i b = 0 8475 å Wis = ei 2.4801 Source : www.bseindia.com / www.riskcontrol.com (from 01-04-2001 to 31-03-2011) 40 The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise Optimal Portfolio Construction by Using Sharpe’s Single Index Model 41 Using the inputs from SIM, the covariance variance matrix is shown in Table-6. On the basis of information compiled in Table-6 the risk of the 7-security portfolio is calculated to be : 7 7 7 2 2 2 p i i i j ij i 1 i 1 j 1 W W W = = = s =å s + s åå = 1.79% + 1.654% + 3.444% or sp = = 3.444% 1.86% Therefore, it is found that there is a significant difference between the total risk of the optimal portfolio calculated under two different mechanisms found in SIM and Markowitz’s model. The total risk of the optimal portfolio is 2.86 per cent (in terms of SD) under SIM and the total risk of the portfolio is found to be 1.86 per cent (in terms of SD) in Markowitz’s model taking the necessary input from SIM. Findings i) It is found that comparatively SIM gives an easy mechanism of constructing optimal portfolio of stocks for a rational investor by analyzing the reason behind the inclusion of securities in the portfolio with their respective weights. Actually, it simplifies the portfolio problems found in the Markowitz’s model to a great extent. ii) As regards the construction of optimal portfolio is concerned, there is a considerable similarity between SIM and the Markowitz’s model though, in reality, SIM requires lesser input than the input requirement of Markowitz’s model to arrive at the risk and return of the optimal portfolio. iii)From the study, it is observed that only seven securities out of ten sampled securities are allowed to include in the optimal portfolio using the steps behind its construction under SIM. To arrive at the risk and return of this portfolio, the number of inputs required in SIM is 23 (applying 3n+2) whereas the same is 35 (applying n(n 3) 2 + ) in Markowitz’s model. Therefore, SIM, obviously, reduces the burden of calculation under Markowitz’s model and claims an extra credit in the field of investment finance. iv) Since unsystematic risk is much higher than the systematic risk, of the optimal portfolio (constructed through SIM) there is an enough scope to reduce the total risk of the portfolio though proper diversification. v) There is a significant different between the total risk of the optimal portfolio calculated under two different mechanisms found in SIM The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise 42 and Markowitz’s model respectively. It is observed that the total risk of the optimal portfolio is 2.86 per cent (in terms of SD) under SIM whereas the same is found to be 1.86 per cent in Markowitz’s model taking the nece-ssary input from SIM. vi) It is found that most of the PSEs securities have beta less than one and hence they have been considered as defensive securities. The risk averse type of decision makers may prefer these securities in their portfolio. Table-6 : Variance – Co-variance Matrix (77 order) 1 2 3 4 5 6 7 1 2 2 W1 1 s 0.133 2 W1W2 2 2 W2 2 s Cov (1,2) 1.085 0.084 3 W1W3 W2W3 2 2 W3 3 s Cov (1,3) Cov (2,3) 0.136 0.018 0.085 4 W1W3 W2W3 W1W3 2 2 W4 4 s Cov (1,4) Cov (2,4) Cov (3,4) 0.375 0.045 0.209 0.046 5 W1W3 W2W3 W1W3 W2W3 2 2 W5 5 s Cov (1,5) Cov (2,5) Cov (3,5) Cov (4,5) 0.026 0.008 0.038 0.111 0.020 6 W1W3 W2W3 W1W3 W2W3 W2W3 2 2 W6 6 s Cov (1,6) Cov (2,6) Cov (3,6) Cov (4,6) Cov (5,6) 0.031 0.012 0.053 0.012 0.029 0.005 7 W1W3 W2W3 W1W3 W2W3 W1W3 W2W3 2 2 W7 7 s Cov (1,7) Cov (2,7) Cov (3,7) Cov (4,7) Cov (5,7) Cov (6,7) 0.004 0.005 0.024 0.005 0.013 0.002 0.003 Total 0.172 0.409 0.174 0.062 0.007 0.003 0.827 Source : Computed values N.B. – 1. BPCL, 2. BHEL, 3. Engineer’s Ltd., 4. GAIL, 5. Coal India, 6. ONGC, 7. NTPC Optimal Portfolio Construction by Using Sharpe’s Single Index Model 43 Concluding Remarks From the discussion and analysis so far it is clear that the construction of optima
l portfolio investment by using SIM is more easy and comfortable than that of by using Markowitz’s Mean-Variance Model. From this analysis, investors to some extent, can able to forecast individual security’s return through the market movement. In his seminal contribution, Sharpe argued that there is a considerable similarity between efficient portfolios generated by SIM and Markowitz’s Model. This model can show how risky a security is, if the security is held in a well-diversified portfolio. It is worthwhile to mention that India’s stock market, in the context of information, SIM will hold good. It helps to elicit that the return on securities in portfolio is independent of the systematic risk prevailing in the market. This study is made on the basis of small sample (n<30) i.e. 10 sampled securities. It can be extended for a large sample to get more accurate result. Hope, this study will contribute a little about a lot in the field of investment finance. References Benari Y (1988); “An Asset Allocation Paradigm” Journal of Portfolio Management, Winter pp. 22-26. Blank S.C. (1991); “The Robustness of Single Index Model in Crop Markets : A Multiple Index Model Test”, Western Journal of Agricultural Economics, Vol. 16, No. 2, pp. 259-267. Campbell R, Huisiman R & Kodedijk K (2001); “Optimal Portfolio Selection in Value at Risk Framework” Journal of Banking & Finance; Vol. 25, pp. 1789-1804. Chandra P (2009); Investment Analysis and Portfolio Management (3rd ed), Tata McGraw-Hill Publishing Company Ltd., New Delhi. Chitnis A. (2010); “Performance Evaluation of Two Optimal Portfolios by Sharpe’s Ratio” Global Journal of Finance and Management, Vol. 2, No. 1, pp. 35-46. Elton, E.J. et al (1978); Optimum Portfolio from Simple Ranking Devices”, Journal of Portfolio Management, Spring, pp. 15-19. Fischer D.E. & Jordan R.J (1995); “Security Analysis and Portfolio Management (6th ed), Pearson Education, Inc., New Delhi. Gregory M.N. & Shapiro M.D. (1986); “Risk and Return: Consumption Beta versus Market Beta” The Review of Economics and Statistics, Vol. 68(3), pp. 452-459. Kamal J.B. (2012); “Optimal Portfolio Selection in Ex-ante Stock Price Bubble and Further more Bubble Burst Scenario from Dhaka Stock Exchange with Relevance to Sharpe’s Single Index Model” Financial Assets and Investing, Vol. No. 3, pp. 29-42. Lintner J. (1965); “Volatility of Risky Assets and the Selection of Risky Investments in Stock Portfolio and Capital Budget”,Review of Economics and Statistics, Vol. 47, pp. 13-37. The Journal of Institute of Public Enterprise, Vol. 36, No. 1&2 © 2013, Institute of Public Enterprise 44 Mossin J (1966); “Equilibrium in Capital Asset Market”, Econometrica, Vol. 35, pp. 768- 783. Saravanan A and Natarajan P (2012); Optimal Portfolio Construction with Nifty Stocks (An Analytical Prescription for Investor) Advances in Management Vol. 5(8), pp. 47-53. — x — x — Sharpe W.F. (1963); “A Simplified Model for Portfolio Analysis”. Management Science, 9, Jan, pp. 277-93. Sharpe W.F. (1964); “Capital Asset Prices : A Theory of Market Equilibrium under Condition of Risk”, Journal of Finance, Vol. 19, pp. 425-442. Copyright of Journal of Institute of Public Enterprise is the property of Institute of Public Enterprise and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder’s express written permission. However, users may print, download, or email articles for individual use.

Advances In Management Vol. 6 (8) Aug. (2013) (39) Case Study: Macroeconomic Variables on Stock Market Interactions: The Indian Experience Sangmi Mohi-u-Din and Hassan Mohd. Mubasher* Department of Business and Financial Studies, University of Kashmir, Kashmir (J and K), INDIA *MMMHASSAN@gmail.com Abstract To examine the effect of macroeconomic variables on the stock price movement in Indian Stock Market, six variables of macro-economy (inflation, exchange rate, Industrial production, Money Supply, Gold price, interest rate) are used as independent variables. Sensex, Nifty and BSE 100 are indicated as dependent variable. The monthly time series data are gathered from RBI handbook over the period of April 2008 to June 2012. Multiple regression analysis is applied in this paper to construct a quantitative model showing the relationship between macroeconomics and stock price. The result of this paper indicates that significant relationship occurred between macroeconomics variables and stock price in India. Keywords: Bombay Stock Exchange, National Stock Exchange, Arbitrage pricing theory. Introduction The capital market promotes economic growth and prosperity by providing an investment channel that contributes to attract domestic and foreign capital. The aggregate performance of capital market can be easily seen by its indices that represent the movement of stock prices being traded in capital market. As we know that the economic stability in a country could be measured by macroeconomics variables. Inflation, interest rate and exchange rate are some macroeconomics variables that reflect economic condition in India and the economic condition will affect the industry condition which ultimately will affect the company activity that is why it is said macroeconomic variables are factors that could not be controlled by the companies which might be affecting the volatility of the stock price. In modern portfolio theory, the Arbitrage Pricing Theory (APT) assumes that the return on asset is a linear function of various macroeconomic factors or theoretical market indices where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The APT states that the realized return on asset is composed of the expected return on that asset at the beginning of a time period and the unexpected realization of krisk factors during that time period plus firm specific risk. The aim of this paper is to analyze the effects of macroeconomic variables on the Indian Stock market in the APT framework. To have a deeper insight of this financial-economic phenomenon the three broad based and much observed indices of Indian stock market viz: Sensex, Nifty and BSE- 100 are being analyzed based on monthly data from April 2008 to June 2012 by six macroeconomic fundamental indicators. The macroeconomic variables used in this study are whole sale price index, foreign exchange rate, industrial production index, money supply, gold price, money market interest rate etc. In the analyses of time series descriptive statistics, Jarque-Bera test, Unit root test, Correlation matrix, Multi linear regression method, Durbin-Watson test and Whites Heterocadasticity test were used. Review of Literature Many authors have tried to show reliable associations between macroeconomic variables and stock returns. They identified several key macroeconomic variables which influenced stock market returns based on the Arbitrage Pricing Theory (APT). A brief overview of the studies is presented in this section. Maysami and Koh9 tested the relationships between the Singapore stock index and selected macroeconomic variables over a seven-year period from 1988 to 1995 and they found that there existed a positive relationship between stock returns and changes in money supply but negative relationships between stock returns with changes in price levels, short- and long-term interest rates and exchange rates. To examine the interdependence between stock markets and fundamental macroeconomic factors in the five South East Asian countries (Indonesia, Malaysia, Philippines, Singapore and Thailand) was the main purpose of Wongbangpo and Sharma13 . Monthly data from 1985 to 1996 is used in this study to represent GNP, the consumer price index, the money supply, the interest rate and the exchange rate for the five countries. Their results showed that high inflation in Indonesia and Philippines influences the long-run negative relation between stock prices and the money supply while the money growth in Malaysia, Singapore and Thailand induces the positive effect for their stock markets. The exchange rate variable is positively related to stock prices in Indonesia, Malaysia and Philippines, yet negatively related in Singapore and Thailand. Similar research also has been done in New Zealand. The Advances In Management Vol. 6 (8) Aug. (2013) (40) effect of seven macroeconomics variables (inflation rate, long term interest rate, short term interest rate, the real trade weighted exchange rate index, real gross domestic product, money supply and domestic retail oil prices) to the New Zealand Stock Index (NZSE40) return for the period of January 1990 until January 2003 was analyzed using co integration test, with specifically employ Johansen Multivariate, Granger-causality Test and innovation accounting in processing the data. In general, the result shows that the NZSE40 is consistently determined by the interest rate, money supply and real GDP. Ahmad Rehman et al2 observed the impact of interest rate and exchange rate to the Stock Return in Pakistan. The dependent variable used in their research is the stock return of KSE-100 where the independent variables used are interest rate and exchange rate (Rs/USD). The data is collected from the State Bank of Pakistan and Karachi Stock Exchange over period of 1998 – 2009 on yearly basis. As a result of multiple regression model analysis, it shows that the change in interest rate and exchange rate has a significant impact on stock returns. The change in interest rate is giving negative impact, while change in exchange rate is giving positive to the stock returns. Ahmet Büyükşalvarcı1 analyzes the effect of seven variables of macroeconomics in the Turkish Stock Exchange Market using the Arbitrage Pricing Theory framework. The method used in processing the data is Multiple Regression with seven variables macroeconomic (variables consumer price index, money market interest rate, gold price, industrial production index, oil price, foreign exchange rate and money supply) as independent variables and Turkish stock market Index (Istanbul Stock Exchange Index-100) as dependent variable. The data used are on monthly basis over the period of January 2003 to March 2010. As a result, interest rate, industrial production index, oil price, foreign exchange rate have a negative effect while money supply has positive impact on ISE-100 Index returns. Moreover, inflation rate and gold price do not have any significant effect on ISE-100 Index returns. Xiufang Wang14 tries to find some evidence on the relationship between stock price and macroeconomic variables (Real GDP, CPI, short term interest rate) in China Stock Market. The research aims to estimate the volatility of each variable using Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) and to determine the causal relationship between the stock price volatility and macroeconomic variables by using Lag-Augmented VAR (LA-VAR) models. The first finding of this research is that there is no causal relationship between stock price and real GDP volatility. Bilateral causal relationship is found between inflation and stock price volatility. Xiufang Wang14 also found that there is a unidirectional causal relationship between stock market volatility and interest rate volatility, with the direction from stock prices to the interest rate. Research Methodology On the basis of literature review this study hypothesize the model between three leading Indian stock market indices namely Sensex, Nifty and BSE 100 and set of six macroeconomic variables. This study has used the follow
ing model. SMI =β0+ β1WPI + β2ExR+ β3IIP + β4 M3 + β5 GP + β6 IR + υi; where SMI= Monthly percentage change in the stock market index; WPI= Monthly percentage change in the Wholesale price index; ExR= Monthly change in the exchange rate; IIP= Monthly percentage change in the index of production; M3= Monthly change in the money supply; GP= Monthly change in the gold price; IR= Monthly change in the interest rate and υi= Error term. In the above equation, β0 is constant and β is coefficient of variables while εt is the residual error of the regression. The ordinary least squares (OLS) method is used to compute the estimates of the regression model stated above and all estimations have been performed in the econometrical software program SPSS whereas the ordinary calculations in Excel. On the basis of the literature review, the following hypotheses have been generated. H1: There is a positive effect of inflation on stock market return in India. H2: There is a negative effect of exchange rate on stock market return in India. H3: There is a positive effect of index of industrial production on stock market return in India. H4: There is a positive effect of money supply on stock market return in India. H5: There is a negative effect of gold price on stock market return in India. H6: There is a negative effect of the interest on stock market return in India. Sampling and Data Collection Procedure: The sampling period for the paper begins from April 2008 and ends in June 2012. Macro variables and stock indices data are collected from the Annual report of Reserve Bank of India. Measures of Variables Stock Market Return: The stock indices employed are Sensex, Nifty, BSE-100. Firstly from the daily closing price index, the monthly average price index is calculated. Then, the stock market return is calculated by the following Advances In Management Vol. 6 (8) Aug. (2013) (41) formula12: MR= {(Mt-Mt-1)/Mt-1}*100 where Mt = Average Monthly Closing price index of t time and Mt-1= Average Monthly Closing price index of t-1 time. Thus the dependent variable is the Monthly percentage change of closing values of the respective indices. Inflation Rate: Inflation rate has been calculated from Wholesale Price Index as per the following formula.12 IF = {(WPIt-WPIt-1)/WPIt-1}*100 where WPIt is monthly WPI in time t and WPIt-1 is monthly WPI in time t-1. Exchange Rate: Monthly change in weighted average exchange rate (the buying rate of the US dollar) is used and calculated by the below-mentioned formula5 : ER = (ERt-ERt-1) where ERt is monthly weighted average exchange rate in time t and ERt-1is monthly weighted average exchange rate in time t-1. Index of Production: Percentage change in Monthly index of production has been used and calculated by the following formula12: IP= {(IPt-IPt-1)/IPt-1}*100 where IPt is monthly index of production in time t and IPt-1 is monthly index of production in time t-1. Money Supply: Changes in Monthly money supply have been used and calculated by the following formula12: MS = (M2t– M2t-1) where M2t is monthly money supply (M2) in time t and M2t- 1 is monthly money supply (M2) in time t-1. Gold Price: Monthly change in weighted average of gold price is used and calculated by the below-mentioned formula10 : GP = (GPt-GPt-1) where GPt is monthly weighted average of gold price in time t and GPt-1is monthly weighted average of gold price in time t-1. Interest Rate: Monthly change in interest rate is used. It is the weighted average rate of the month end. The formula is as follows5 : IR = (IRt-IRt-1) where IRt is monthly interest rate in time t and IRt-1 is monthly interest rate in time t-1. Results and Discussion Various descriptive statistics are calculated of the variables under study in order to describe the basic characteristics of these variables. Table 1 presents the descriptive statistics of the data, containing sample means, medians, maximums, minimums, standard deviations, skewness, kurtosis as well as the Jarque-Bera statistics and probabilities (p-values). Table 1 Descriptive Statics of Study Variables Sensex Nifty BSE 100 WPI Ex.($) IIP M3 Gold MIR Mean 0.3232 0.32 -0.46767 0.5741 0.320156 0.504 737.5958 360.2 0.0406 Median 0.052 0.26 -0.04056 0.5387 0.1689 0.117 577.255 346.1 0.045 Standard Deviation 7.3677 7.15 10.0416 0.7573 1.2118353 5.85 529.01683 738.7 0.678 Kurtosis 3.0659 2.72 8.17815 2.4924 -0.268993 0.664 -0.694775 3.958 3.4176 Skewness -0.0115 -0.18 -1.73882 -0.61 0.2771453 0.057 0.359929 1.168 -1.1709 Jarque-Bera 0.0101 0.43 81.0567 3.6376 22.903236 11.39 29.519916 13.27 11.789 p-value 0.9949 0.81 2.5E-18 0.1622 1.063E-05 0.003 3.889E-07 0.001 0.0028 Range 45.633 43.6 67.3286 4.4698 5.2641 28.87 2243.09 4418 3.75 Minimum -24.336 -23.7 -45.3255 -1.891 -2.1721 -13.9 -365.08 -1167 -2.33 Maximum 21.297 19.9 22.0031 2.5786 3.092 14.94 1878.01 3251 1.42 Sum 16.158 16.2 -23.3836 28.706 16.0078 25.18 36879.79 18008 2.03 Count 50 50 50 50 50 50 50 50 50 Advances In Management Vol. 6 (8) Aug. (2013) (42) As can be seen from the table 1, all the variables are asymmetrical. More precisely, Sensex, Nifty, BSE- 100,Wholesale price index and Interest rate have a negative skewness which indicates the fat tails on the left-hand side of the distribution. Kurtosis value of all variables also shows data is not normally distributed because values of kurtosis are deviated from 3. The calculated Jarque-Bera statistics and corresponding p-values are used to test for the normality assumption. Based on the Jarque-Bera statistics and p-values the joint null hypothesis, (H0) is rejected for all variables, except for Sensex and Nifty where null hypothesis was accepted. So the descriptive statistics shows that the values are not normally distributed about its mean and variance or in other words, we can say no randomness in data and therefore, is sensitive to periodic change and speculation. This indicated that individual investor can earn considerably higher normal rate of profit from the Indian Stock Market. So the results of above descriptive statistics raise the issue of the inefficiency of Indian stock market. Time series data are assumed to be non-stationary and thus it is necessary to perform a pre-test to ensure there is a stationary co-integration relationship among variables before proceeding with the OLS estimations, it is necessary to investigate the time series properties of the variables by utilizing unit root test. The Augmented Dickey Fuller test has been performed in this study. The ADF test results are resented in table 2. Table 2 Unit root test Results of Augmented Dickey-Fuller Test (Constant and Trend) Variables Level p-value First difference p-value BSE Sensex Index -2.41701 0.3705 -4.10265 0.006174* BSE 100 Index 0.28712 0.9986 -3.48946 0.04044* Nifty -1.61261 0.7884 -3.90972 0.01168* WPI -4.56803 0.001116* -3.37547 0.05467* ExR($) -1.01721 0.9402 -4.10671 0.006089* IIP -3.6286 0.02741* -4.24013 0.003826* M3 -0.462238 0.9853 -4.84631 0.0003549* Gold Price -1.27 0.8947 -3.98929 0.009029* Interest rate -2.10047 0.545 -3.70887 0.02169* Asterisk (*) indicatesrejection of null hypothesis of non-stationarity at the 5% level. Results clearly indicate that the index series are not stationary at level except inflation rate and industrial production but the first differences of the series are stationary, so the data is further analyzed at first difference. Another test to be conducted on the sample data is Ordinary Lest Square whose one of the basic assumptions is that regressors are not mutually correlated. If more than one of them is correlated with other, multicollinearity is said to exist. Logic behind assumption of no multicollinearity is simple that if two or more independent variables are linearly dependent on each other, one of them should be included instead of both, otherwise it will increase standard error thereby making our results biased. In order to check multicollinearity among independent variables, a Pearson’s correlation analysis has been performed. A suggested rule of thumb is that if the pairwise correlation between two regressors is very high in excess of 0.8, multicollinearity may pose ser
ious problem. 2 The correlation analysis results are reported in table 3. Since the highest correlation numbers are lower than 0.8, the results clearly show that none of the independent variables are highly correlated and no multicollinearity amongst independent variables exist. Table 3 Correlation Matrix Sensex Nifty BSE 100 WPI Ex.($) IIP M3 Gold MIR Sensex 1.0 Nifty 1.0 1.0 BSE 100 0.8 0.8 1.0 WPI 0.2 0.2 0.2 1.0 Ex.($) -0.6 -0.6 -0.6 -0.2 1.0 IIP 0.0 0.0 0.0 -0.1 0.1 1.0 M3 0.1 0.1 0.1 0.0 0.0 0.1 1.0 Advances In Management Vol. 6 (8) Aug. (2013) (43) Gold -0.2 -0.2 -0.2 -0.1 0.2 0.0 -0.1 1.0 MIR 0.0 0.0 0.0 0.4 0.1 0.3 -0.1 0.1 1.0 Estimation Results from Multiple Regression Models. Analysis of Sensex Table 4 Regression Statistic Multiple R 0.6 R Square 0.4 Adjusted R Square 0.3 Standard Error 6.1 Observations 50.0 The R value of 0.6 indicates the moderate correlation between Sensex with six macroeconomic variables. R square value of 0.4 shows that 40% of Sensex fluctuations could be explained by macroeconomics variables while the 60% can be explained by other factors. Table 5 Anova df SS MS F Significance F Regression 6 1051.3 175.2 4.7 0.0 Residual 43 1608.5 37.4 Total 49 2659.9 From the Anova or F test, the value of F is 4.7 with significance of 0.000. Because of the probability, level of significant of 0.000 is less than 0.05. It proves that inflation, exchange rate, Industrial production, Money supply, Gold price and interest rate are simultaneously affecting the Sensex price. Table 6 Coefficient of Regression Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.8 1.8 0.4 0.7 -2.8 4.3 WPI 0.5 1.4 0.4 0.7 -2.3 3.2 Ex.($) -3.6 0.8 -4.7 0.0 -5.1 -2.0 IIP 0.1 0.2 0.5 0.6 -0.2 0.4 M3 0.0 0.0 0.6 0.5 0.0 0.0 Gold 0.0 0.0 -0.8 0.4 0.0 0.0 IR 0.5 1.6 0.3 0.8 -2.7 3.6 As for the individual coefficients of macroeconomic variables are concerned, none of the variables was found significant except Exchange rate with the theoretically expected sign while Gold price and interest rate showed spurious results. Table 7 Durbin-Watson Test Observation Predicted Sensex Residuals 1 -5.8 9.8 2 0.0 -11.5 3 1.1 -9.6 4 2.5 4.8 5 -7.5 2.2 6 -10.4 -13.9 7 -1.7 -8.7 8 0.7 -0.1 9 -0.3 -1.5 10 -2.0 0.3 11 -4.4 2.3 12 6.2 15.1 13 7.2 12.4 14 4.0 9.3 15 -0.3 -0.6 16 1.9 3.4 17 0.5 5.5 18 7.5 -4.5 19 1.2 -2.0 20 1.6 0.8 21 5.6 -4.6 22 0.2 -6.4 23 6.7 0.2 24 4.6 -2.4 25 -4.5 -0.2 26 -1.8 4.5 27 2.5 0.7 28 1.2 0.6 Advances In Management Vol. 6 (8) Aug. (2013) (44) 29 3.1 3.4 30 9.1 -4.5 31 -2.0 1.4 32 2.9 -3.9 33 1.1 -4.4 34 1.3 -7.8 35 5.2 -2.9 36 3.1 2.2 37 -1.3 -4.5 38 1.7 -2.2 39 3.3 -1.2 40 -5.2 -4.0 41 -8.5 7.3 42 -3.1 3.9 43 -5.7 4.7 44 -2.5 -1.8 45 5.9 -3.4 46 8.7 0.3 47 -0.7 -1.6 48 -4.2 3.4 49 -8.4 3.3 50 -4.3 6.4 Numerator 2079.081149 D 1.292542 Denominator 1608.521399 At 5% level of significance. dl=1.291 du=1.822 4-dl=2.709 4-du=2.178 The d lies between dl and du so the D-W test is Inconclusive about autocorrelation. Table 8 Whites General Heterocadasticity Test Observation Residuals Residuals Square Predicted Sensex Predicted Sensex Sq. 1 9.8 96.18 -5.8 33.51 2 -11.5 132.29 0.0 0.00 3 -9.6 93.11 1.1 1.23 4 4.8 23.07 2.5 6.41 5 2.2 4.97 -7.5 56.60 6 -13.9 194.42 -10.4 108.01 7 -8.7 75.47 -1.7 2.89 8 -0.1 0.01 0.7 0.50 9 -1.5 2.14 -0.3 0.06 10 0.3 0.09 -2.0 4.17 11 2.3 5.13 -4.4 19.01 12 15.1 228.07 6.2 38.38 13 12.4 153.46 7.2 51.53 14 9.3 87.12 4.0 15.80 15 -0.6 0.42 -0.3 0.12 16 3.4 11.84 1.9 3.56 17 5.5 29.85 0.5 0.28 18 -4.5 20.27 7.5 56.01 19 -2.0 4.15 1.2 1.43 20 0.8 0.68 1.6 2.59 21 -4.6 21.18 5.6 31.33 22 -6.4 41.10 0.2 0.03 23 0.2 0.03 6.7 45.48 24 -2.4 5.75 4.6 20.89 25 -0.2 0.03 -4.5 20.60 26 4.5 20.13 -1.8 3.18 27 0.7 0.47 2.5 6.18 28 0.6 0.38 1.2 1.50 29 3.4 11.43 3.1 9.54 30 -4.5 20.27 9.1 83.48 31 1.4 1.90 -2.0 3.95 Advances In Management Vol. 6 (8) Aug. (2013) (45) 32 -3.9 15.21 2.9 8.49 33 -4.4 18.98 1.1 1.32 34 -7.8 60.93 1.3 1.73 35 -2.9 8.25 5.2 27.07 36 2.2 5.04 3.1 9.83 37 -4.5 20.32 -1.3 1.63 38 -2.2 5.02 1.7 2.94 39 -1.2 1.33 3.3 10.75 40 -4.0 16.33 -5.2 27.52 41 7.3 53.59 -8.5 71.60 42 3.9 15.21 -3.1 9.82 43 4.7 22.39 -5.7 32.18 44 -1.8 3.15 -2.5 6.02 45 -3.4 11.56 5.9 34.71 46 0.3 0.12 8.7 75.56 47 -1.6 2.68 -0.7 0.52 48 3.4 11.68 -4.2 17.48 49 3.3 10.75 -8.4 70.73 50 6.4 40.59 -4.3 18.42 Table 9 Associated analysis of Whites Hetoerocadasticity test Regression Statistics Multiple R 0.322693851 R Square 0.104131321 5.206566064 Adjusted R Square 0.06600925 Standard Error 49.05562751 Observations 50 ANOVA df SS MS F Significance F Regression 2 13146.57292 6573.286462 2.731523166 0.07546443 Residual 47 113103.3657 2406.45459 Total 49 126249.9387 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 19.06881168 9.008683788 2.116714508 0.039606726 0.94567752 37.19195 Predicted Sensex -0.242779338 1.516503675 -0.160091493 0.873495071 -3.29359122 2.808033 Predicted Sensex Sq. 0.623729393 0.269389044 2.315348037 0.02500843 0.08178854 1.16567 nR2 ~Chi-Square distribution with degrees of freedom 2, WGH=5.20, Critical value at 5% level of significance and 2 degrees of freedom =5.99 We conclude on the basis of test that there is no Heterocadasticity in the above model. Analysis of Nifty Table 10 Regression Statistic Multiple R 0.6 R Square 0.4 Adjusted R Square 0.3 Standard Error 5.9 Observations 50.0 The R value of .6 indicates moderate correlation between Nifty with macroeconomic variables. R square value of .4 shows that 40% of volatility in Nifty could be explained by macroeconomics variable while the 60% is explained by other factors. Advances In Management Vol. 6 (8) Aug. (2013) (46) Table 12 Coefficient of Regression Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.7 1.7 0.4 0.7 -2.7 4.1 WPI 0.3 1.3 0.2 0.8 -2.3 2.9 Ex.($) -3.6 0.7 -4.9 0.0 -5.1 -2.1 IIP 0.1 0.2 0.6 0.5 -0.2 0.4 M3 0.0 0.0 0.7 0.5 0.0 0.0 Gold 0.0 0.0 -0.7 0.5 0.0 0.0 IR 0.6 1.5 0.4 0.7 -2.4 3.6 As for the individual coefficients of macroeconomic variables are concerned, none of the variables was found significant except Exchange rate with the theoretically expected sign while Gold price and interest rate showed spurious results. Table 13 Durbin-Watson Test Observation Predicted Nifty Residuals 1.0 -5.7 8.3 2.0 -0.3 -10.9 3.0 1.2 -8.8 4.0 2.4 4.7 5.0 -7.2 2.4 6.0 -10.5 -13.2 7.0 -2.0 -9.7 8.0 1.0 1.1 9.0 -0.3 -1.1 10.0 -1.6 0.4 11.0 -4.1 3.5 12.0 5.7 14.2 13.0 7.1 10.7 14.0 3.8 8.3 15.0 -0.5 -1.6 16.0 1.7 3.5 17.0 0.6 5.7 18.0 7.4 -4.7 19.0 1.1 -2.0 20.0 1.6 1.3 21.0 5.4 -4.3 22.0 0.1 -6.3 23.0 7.0 0.0 24.0 4.2 -1.9 25.0 -4.3 -0.2 26.0 -1.6 4.3 27.0 2.5 0.9 28.0 1.1 0.7 29.0 3.2 3.3 30.0 9.5 -4.6 31.0 -2.0 1.4 32.0 2.9 -4.3 33.0 0.8 -4.0 34.0 1.4 -8.0 35.0 5.5 -2.9 36.0 2.9 2.6 37.0 -1.2 -4.8 38.0 1.7 -2.0 39.0 3.3 -1.1 40.0 -4.7 -4.5 41.0 -8.4 7.2 42.0 -3.3 4.2 43.0 -5.3 4.2 44.0 -2.2 -2.2 45.0 5.5 -2.6 46.0 8.8 1.2 47.0 -0.8 -1.3 48.0 -4.4 3.6 49.0 -8.5 3.0 50.0 -4.0 6.2 Numerator 1981.9 d 1.3 Denominator 1475.9 At 5% level of significance. dl=1.291 du=1.822 4-dl=2.709 4-du=2.178 The d lies between dl and du so the D-W test is Inconclusive about autocorrelation. Advances In Management Vol. 6 (8) Aug. (2013) (47) Table 14 Whites General Heterocadasticity Test Observation Residuals Residuals Square Predicted Nifty Predicted Nifty Square 1.0 8.3 69.3 -5.7 32.9 2.0 -10.9 119.3 -0.3 0.1 3.0 -8.8 76.7 1.2 1.3 4.0 4.7 22.4 2.4 5.5 5.0 2.4 5.8 -7.2 51.5 6.0 -13.2 174.5 -10.5 109.8 7.0 -9.7 94.1 -2.0 4.0 8.0 1.1 1.3 1.0 1.0 9.0 -1.1 1.2 -0.3 0.1 10.0 0.4 0.2 -1.6 2.7 11.0 3.5 12.4 -4.1 17.0 12.0 14.2 201.0 5.7 32.7 13.0 10.7 114.1 7.1 50.7 14.0 8.3 68.5 3.8 14.5 15.0 -1.6 2.6 -0.5 0.2 16.0 3.5 12.6 1.7 2.9 17.0 5.7 32.6 0.6 0.4 18.0 -4.7 21.7 7.4 55.3 19.0 -2.0 3.8 1.1 1.3 20.0 1.3 1.8 1.6 2.6 21.0 -4.3 18.5 5.4 29.2 22.0 -6.3 39.5 0.1 0.0 23.0 0.0 0.0 7.0 48.3 24.0 -1.9 3.7 4.2 17.5 25.0 -0.2 0.1 -4.3 18.9 26.0 4.3 18.4 -1.6 2.6 27.0 0.9 0.7 2.5 6.0 28.0 0.7 0.5 1.1 1.2 29.0 3.3 11.1 3.2 10.0 30.0 -4.6 21.3 9.5 90.5 31.0 1.4 1.9 -2.0 4.2 32.0 -4.3 18.5 2.9 8.5 33.0 -4.0 15.6 0.8 0.6 34.0 -8.0 63.9 1.4 1.9 35.0 -2.9 8.7 5.5 30.1 36.0 2.6 6.6 2.9 8.2 37.0 -4.8 22.9 -1.2 1.3 38.0 -2.0 4.1 1.7 2.8 39.0 -1.
1 1.1 3.3 11.1 40.0 -4.5 20.6 -4.7 22.5 41.0 7.2 51.4 -8.4 70.1 Advances In Management Vol. 6 (8) Aug. (2013) (48) 42.0 4.2 17.8 -3.3 11.1 43.0 4.2 17.7 -5.3 28.2 44.0 -2.2 5.0 -2.2 4.9 45.0 -2.6 6.9 5.5 30.3 46.0 1.2 1.4 8.8 76.7 47.0 -1.3 1.6 -0.8 0.6 48.0 3.6 12.7 -4.4 19.3 49.0 3.0 9.1 -8.5 72.2 50.0 6.2 38.6 -4.0 16.3 Table 15 Associated analysis of Whites Hetoerocadasticity test Regression Statistics Multiple R 0.302631216 R Square 0.091585653 4.579282653 Adjusted R Square 0.052929723 Standard Error 42.81922068 Observations 50 ANOVA df SS MS F Significance F Regression 2 8687.9805 4343.99025 2.369252373 0.1046342 Residual 47 86173.82602 1833.48566 Total 49 94861.80652 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 19.75334816 7.742538349 2.551275469 0.014047135 4.17737008 35.32933 Predicted Nifty -0.699663669 1.337798143 -0.522996442 0.603433736 -3.39096639 1.991639 Predicted Nifty Square 0.484166276 0.231927107 2.087579507 0.042282624 0.01758912 0.950743 nR2 ~Chi-Square distribution with degrees of freedom 2, WGH=4.57, Critical value at 5% levelof significance and 2 degrees of freedom =5.99 We conclude on the basis of test, that there is no Heterocadasticity in the above model. Analysis of BSE 100 Table 16 Regression Statistic Regression Statistics Multiple R 0.991596771 R Square 0.983264156 Adjusted R Square 0.980928922 Standard Error 1.382035489 Observations 50 The R value of 0.99 indicates high correlation between BSE- 100 with macroeconomic variables, R- square value of 0.98 implies that 98% of BSE-100 price movement could be explained by six macroeconomics variable while the 2% by unexplained factors. Table 17 Anova ANOVA df SS MS F Significance F Regression 6 4825.35697 804.22616 421.055947 0.0000 Residual 43 82.13094999 1.9100221 Total 49 4907.48792 From the Anova or F test, the value of F is 421.05 and is significant at 5% at because of the probability (level of significant) of 0.000 is less than 0.05, it proves that all six macroeconomic variables are simultaneously affecting the BSE-100 movement. Advances In Management Vol. 6 (8) Aug. (2013) (49) Table 18 Coefficient of Regression Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -0.44341 0.23327 -1.90086 0.06404 -0.91383 0.02702 WPI 2.00552 0.86533 2.31763 0.02530 0.26041 3.75062 ExR -6.29548 0.37727 -16.6869 0.00000 -7.05632 -5.5346 IIP 0.16238 0.05751 2.82349 0.00717 0.04640 0.27835 M3 0.00723 0.00069 10.41752 0.00000 0.00583 0.00863 GP -0.00073 0.00040 -1.83089 0.07405 -0.00152 0.00007 IR 5.55692 0.56701 9.80037 0.00000 4.41343 6.70041 As for the individual coefficients of macroeconomic variables are concerned, quite interestingly six of the variables have theoretically expected signs with WPI, ExR, IIP, M3 influencing significantly, while gold price having expected sign but affecting insignificantly, on the contrary Interest rate have theoretically unexpected sign but influence significantly. Table 19 Durbin-Watson Test Observation Predicted BSE 100 Residuals 1 -1.0620283 1.5741254 2 0.0694221 -0.8411776 3 0.1128322 -0.6715090 4 68.6398747 0.1194486 5 -7.0184752 -0.9099287 6 -1.6852103 -0.0802571 7 -1.8753364 0.8716480 8 -2.0007640 2.2138287 9 -0.9516093 0.6851657 10 -0.4031400 0.0204199 11 -2.8013159 -1.5816224 12 0.7886717 1.5384385 13 1.8252450 1.3703331 14 0.8176871 1.8430564 15 0.6012426 -0.7916568 16 4.5647642 1.1707806 17 8.3280928 3.5866571 18 0.8335980 -0.5546868 19 0.4878664 -0.5682828 20 1.1975959 0.4165699 21 1.1520056 -1.0027791 22 -0.1573863 -0.3749167 23 2.5732972 -1.6666396 24 0.7673438 -0.5208531 25 -1.2172699 0.0610953 26 3.2383215 -0.7136371 27 2.4529662 -1.6665768 28 -0.4444621 0.9343369 29 2.7250573 -0.6885939 30 1.5416596 -1.2414586 31 -0.6643703 0.3844289 32 0.9409985 -1.2003132 33 -0.0565269 -0.3834480 34 0.0960759 -0.5574829 35 1.7690050 -1.4945558 36 2.0214938 -0.8656634 37 -0.3008683 -0.3085306 38 0.2929880 -0.3276821 39 1.1127054 -0.8570338 40 -0.6676573 -0.2587213 41 -2.2800671 2.0764668 42 -2.2404880 2.6081319 43 -4.2205646 3.0807617 44 0.5886470 -1.4211680 45 0.3943319 -0.0388432 46 2.0185985 -0.6005657 47 1.0044107 -1.4763514 48 0.1795743 -1.6377339 49 -0.8568249 -0.3917840 50 -0.1719672 1.1387600 Numerator 119.1829 Denominator 82.13094999 d= 1.451132612 At 5% level of significance. dl=1.291 du=1.822 4-dl=2.709 The d lies between dl and du so the test is inconclusive about the presence of autocorrelation. Advances In Management Vol. 6 (8) Aug. (2013) (50) Table 20 Whites Heterocadasticity Test Observation Residuals Residuals square Predicted BSE 100 Predicted BSE 100 Square 1 1.574125 2.477871 -1.062028 1.127904 2 -0.841178 0.707580 0.069422 0.004819 3 -0.671509 0.450924 0.112832 0.012731 4 0.119449 0.014268 68.639875 4711.432395 5 -0.909929 0.827970 -7.018475 49.258994 6 -0.080257 0.006441 -1.685210 2.839934 7 0.871648 0.759770 -1.875336 3.516887 8 2.213829 4.901038 -2.000764 4.003057 9 0.685166 0.469452 -0.951609 0.905560 10 0.020420 0.000417 -0.403140 0.162522 11 -1.581622 2.501529 -2.801316 7.847371 12 1.538438 2.366793 0.788672 0.622003 13 1.370333 1.877813 1.825245 3.331519 14 1.843056 3.396857 0.817687 0.668612 15 -0.791657 0.626721 0.601243 0.361493 16 1.170781 1.370727 4.564764 20.837072 17 3.586657 12.864109 8.328093 69.357130 18 -0.554687 0.307677 0.833598 0.694886 19 -0.568283 0.322945 0.487866 0.238014 20 0.416570 0.173531 1.197596 1.434236 21 -1.002779 1.005566 1.152006 1.327117 22 -0.374917 0.140563 -0.157386 0.024770 23 -1.666640 2.777687 2.573297 6.621859 24 -0.520853 0.271288 0.767344 0.588817 25 0.061095 0.003733 -1.217270 1.481746 26 -0.713637 0.509278 3.238322 10.486726 27 -1.666577 2.777478 2.452966 6.017043 28 0.934337 0.872985 -0.444462 0.197547 29 -0.688594 0.474162 2.725057 7.425937 30 -1.241459 1.541219 1.541660 2.376714 31 0.384429 0.147786 -0.664370 0.441388 32 -1.200313 1.440752 0.940998 0.885478 33 -0.383448 0.147032 -0.056527 0.003195 34 -0.557483 0.310787 0.096076 0.009231 35 -1.494556 2.233697 1.769005 3.129379 36 -0.865663 0.749373 2.021494 4.086437 37 -0.308531 0.095191 -0.300868 0.090522 38 -0.327682 0.107376 0.292988 0.085842 39 -0.857034 0.734507 1.112705 1.238113 40 -0.258721 0.066937 -0.667657 0.445766 41 2.076467 4.311714 -2.280067 5.198706 42 2.608132 6.802352 -2.240488 5.019787 43 3.080762 9.491093 -4.220565 17.813166 44 -1.421168 2.019719 0.588647 0.346505 45 -0.038843 0.001509 0.394332 0.155498 46 -0.600566 0.360679 2.018598 4.074740 47 -1.476351 2.179613 1.004411 1.008841 48 -1.637734 2.682172 0.179574 0.032247 49 -0.391784 0.153495 -0.856825 0.734149 50 1.138760 1.296774 -0.171967 0.029573 Advances In Management Vol. 6 (8) Aug. (2013) (51) Table 21 Associated analysis of Whites Hetoerocadasticity test Regression Statistics Multiple R 0.132106778 R Square 0.017452201 0.87261004 Adjusted R Square -0.024358344 Standard Error 2.477617461 Observations 50 ANOVA df SS MS F Significance F Regression 2 5.1246343 2.56231714 0.417411466 0.661168 Residual 47 288.51365 6.13858828 Total 49 293.63828 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1.651164694 0.3557734 4.64105703 2.79912E-05 0.935441 2.366888 Predicted BSE 100 0.112182092 0.160115 0.7006346 0.486985288 -0.20993 0.434292 Predicted BSE 100 Square -0.001942114 0.0023869 -0.81366965 0.419937418 -0.00674 0.00286 nR2 ~Chi-Square distribution with degrees of freedom 2, WGH=.8726, Critical value at 5% level of significance and 2 degrees of freedom =5.99 We conclude on the basis of test that there is no Homocadasticity in the above model. Conclusion Macroeconomics is considered as important factor for investing in India. It is proved that macroeconomics brings significant impact to the stock price. From the Sensex and Nifty, it is indicated that increase in inflation leads to higher stock price which is higher rate of return. In contrast, increase in exchange rate causes lower price of stock which results in lower return. Referring to the statistical results that there is a probability of other factor influencing stock price volatility, further research using other independent variables is necessary. References 1. Ahmet Buyukşalvarcı, “The Effects Of Macroeconomics
Variables On Stock Returns:Evidence From Turkey”, European Journal Of Social Sciences, 14 (3), 404-415 (2010) 2. Ahmad Muhammad Ishfaq, Rehman Ramizur and Raoof Awais, Do Interest Rate, Exchange Rate effect Stock Returns? A Pakistani Perspective, International Research Journal of Finance and Economics (2010) 3. Burmeister Edwin and Wall K., “The Arbitrage Pricing Theory and Macroeconomic Factor Measures”, Financial Review, 21, 1–20 (1986) 4. Chen N.F., Roll R. and Ross S. A., “Economic Forces and the Stock Market”, Journal of Business, 59, 383-403 (1986) 5. Joseph N. L. and Vezos P., ”The sensitivity of US banks to stock returns to interest rates and exchange rates changes”, Managerial Finance, 32, 182-199 (2006) 6. Christopher Gan et al, “Macroeconomic Variables And Stock Market Interactions: New Zealand Evidence”, Investment Management and Financial Innovations, 3 (4), 89-101 (2006) 7. Dhira D., Anggoro B. and Novika Candra, “The Efffect of Macroeconomic Variables on Stock Price Volatility: Evidence from Jakarta Composite Index, Agriculture and Basic Industry Sector”, IPEDR, 46, 18 (2012) 8. Fama E. F., “The Behavior of Stock-Market Prices”, Journal of Business, 38, 34-105 (1965) 9. Maysami R.C. et al, “Vector Error Correction Model of the Singapore Stock Market”, International Review of Economics and Finance, 9, 79-96 (2000) 10. Md. Mohiuddin et al, “An Empirical Study of the Relationship Between Macroeconomic Variables And Stock Price: A Study On Dhaka Stock Exchange (DSE)”, Working Paper No. AIUB-BusEcon-2008-21 (2008) 11. Muhammed Monjurul Quadir, “The Effect Of Macroeconomic Variables On Stock Returns On Dhaka Stock Exchange”, International Journal of Economics and Financial Issues, 2 (4), 480- 487 (2012) 12. Pearce D. K. and Roley V. V., Stock prices and economic news, Journal of Business, 58 (1), 49-67 (1985) 13. Wongbangpo P. and Sharma S.C., Stock market and macroeconomic fundamental dynamic interactions: ASEAN-5 countries”, Journal of Asian Economics, 13 (1), 27-51 (2002) 14. Xiufang Wang, The Relationship Between Stock Market Volatility And Macroeconomic Volatility: Evidence From China”, International Research Journal Of Finance And Economics, 49, 149-160 (2010). (Received 4th June 2013, accepted 25th June 2013)  Copyright of Advances in Management is the property of Advances in Management and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder’s express written permission. However, users may print, download, or email articles for individual use.

© BVIMR Management Egde, Vol. 4, No. 2 (2011) PP 35-39 35 Introduction Selection of stocks that are suitable for a portfolio is a challenging task. Technical Analysis provides a framework for studying investor behaviour, and generally focuses only on price and volume data. Technical Analysis using this approach has short-term investment horizons, and access to only price and exchange data. Fundamental analysis involves analysis of a company’s performance and profitability to determine its share price. By studying the overall economic conditions, the company’s competition, and other factors, it is possible to determine expected returns and the intrinsic value of shares. This type of analysis assumes that a share’s current (and future) price depends on its intrinsic value and anticipated return on investment. As new information is released pertaining to the company’s status, the expected return on the company’s shares will change, which affects the stock price. So the advantages of fundamental analysis are its ability to predict changes before they show up on the charts. Growth prospects are related to the current economic environment. Stocks have been selected by us on the bases of fundamental analysis criteria. These criteria are evaluated for each stock and compared in order to obtain a list of stocks that are suitable for our portfolio. Stocks are selected by applying one common criteria on the stocks listed on Indian National Stock Exchange (NSE). proven that it is a straight line and that it has the following equation. In this formula P is the risky portfolio, F is the riskless portfolio, and C is a combination of portfolios P and F. The efficient frontier Every possible asset combination can be plotted in risk-return space, and the collection of all such possible portfolios defines a region in this space. The line along the upper edge of this region is known as the efficient frontier (sometimes “the Markowitz frontier”). Combinations along this line represent portfolios (explicitly excluding the risk-free alternative) for which there is lowest risk for a given level of return. Conversely, for a given amount of risk, the portfolio lying on the efficient frontier represents the combination offering the best possible return. Mathematically the Efficient Frontier is the intersection of the Set of Portfolios with Minimum Variance (MVS) and the Set of Portfolios with Maximum Return. Formally, the efficient frontier is the set of maximal elements with respect to the partial order of product order on risk and return, the set of portfolios for which one cannot improve both risk and return. The efficient frontier is illustrated above, with return µ on the y-axis, and risk Ó on the x-axis; an alternative illustration from the diagram in the CAPM article is at right. The efficient frontier will be convex – this is because the risk-return characteristics of a portfolio change in a non-linear fashion as its component weightings are changed. (As described above, portfolio risk is a function of the correlation of the component assets, and thus changes in a non-linear fashion as the weighting of component assets changes.) The efficient frontier is a parabola (hyperbola) when expected return is plotted against variance (standard deviation). p p Literature Review Capital allocation line The capital allocation line (CAL) is the line of expected return plotted against risk (standard deviation) that connects all portfolios that can be formed using a risky asset and a riskless asset. It can be E(rp) – rF Q p CAL : E ( rc ) = r F + Q c Fundamental Analysis and Portfolio Selection in Practice Dr. Namita Rajput Dr. Harish Handa 36 © BVIMR Management Egde, Vol. 4, No. 2 (2011) PP 35-39 S R – Rf = Q = E [R-R]f var [R-R ]f var [R-R ]f = var[R]. The market portfolio The efficient frontier is a collection of portfolios, each can be concluded that introduction of SSF in the NSE has resulted in improvement of liquidity in the cash market. Research Methodology List of NSE Stocks For Portfolio Analysis 1. ACC 2. WIPRO 3. Maruti Suzuki 4. NTPC 5. SBI Price data was collected over the last 3 years (starting 25th September, 2006 till 24th September, 2009) for each of the above stocks from the site of NSE. The daily ARITHMETIC returns were calculated for the period. Using these return figures, the average historical daily return and risk standard deviation of daily returns was calculated. Next, using the data in the “Daily Returns” column from all the five stocks, taking two at a time, we calculate the correlation between two stock returns. Using the Solver function from Excel, we got the portfolio statistics and weights for the minimum variance portfolio. Efficient frontier and Capital Allocation Line was plotted to get Optimal Risky Portfolio. Analysis And Interpretation Of Data I collected the price data over the last 3 years (starting 25th September, 2006 till 24th September, 2009) for each of the above stocks. The daily ARITHMETIC returns were calculated for the period (as shown in the “Daily Returns” column in the data sheets. Using these return figures, the average historical daily return and risk (standard deviation of daily returns was calculated for each of the stocks, which came out to be : Next, using the data in the “Daily Returns” column from all the five stocks, taking two at a time, we calculate the correlation between two stock returns. For e.g., if we have to calculate the correlation between returns of ACC and that of Wipro, we take the 1st array (as required by the correlation formula in Excel) as the returns of ACC and the 2nd array as that of Wipro. Following this procedure, we get the correlation matrix as : Using the Solver function from Excel, we get the portfolio statistics and weights for the minimum variance portfolio as : © BVIMR Management Egde, Vol. 4, No. 2 (2011) PP 35-39 37 Minimum Variance Portfolio Statistics : Minimum Variance Portfolio Weights : Now, in order to plot the Efficient Frontier, I incremented the average return in steps of 0.00005 and used the Solver to determine the Standard deviation at the average return values. Using this method, we get a set of portfolio weights at different values of Risk and Returns. Now, in order to plot the CAL, we need to maximise the Sharpe Ratio which is again done using the Solver. We find out that the Sharpe Ratio is maximum at 0.04255 (for Mean = 0.00140 and SD = 0.02615. This gives us the optimal portfolio. The statistics and weights for the Optimal Risky Portfolio are as follows : Optimal Risky Portfolio Statistics: Optimal Risky Portfolio Weights : Using the figures every time from the Solver, we get various points, which help us plot the Efficient Frontier (in which the horizontal axis shows the SD and the vertical axis shows the daily returns). Also, we plot the Capital Allocation Line (CAL) (in which the horizontal axis is again SD and the vertical axis is the Risk Premium on CAL (which is calculated by multiplying the maximum slope with the SD of each portfolio). The point where these two lines meet is the Optimal Risky Portfolio. Conclusion And Findings • Average return of all the five stocks varies from 0.02% to 0.16% with standard deviation of This done, next we prepare the Bordered Covariance Matrix as under: BORDERED COVARIANCE MATRIX 0.23 0.26 0.22 0.29 0.00 PORTFOLIO WEIGHTS ACC WIPRO MARUTI NTPC SBI 0.23 ACC 0.000043 0.000019 0.000016 0.000023 0.000000 0.26 WIPRO 0.000019 0.000061 0.000016 0.000025 0.000000 0.22 MARUTI 0.000016 0.000020 0.000033 0.000018 0.000000 0.29 NTPC 0.000023 0.000025 0.000018 0.000059 0.000000 0.00 SBI 0.000000 0.000000 0.000000 0.000000 0.000000 1 0.000101 0.000125 0.000084 0.000125 0.000000 SECURITY STANDARD AVERAGE DEVIATION (%) RETURN (%) ACC WIPRO MARUTI NTPC SBI 2.83% 0.02% 2.95% 0.06% 2.67% 0.11% 2.67% 0.11% 3.14% 0.16% 1.0000 0.3709 0.4309 0.4479 0.5188 0.3709 1.0000 0.4465 0.4236 0.4677 0.4309 0.4465 1.0000 0.4119 0.5283 0.4479 0.4236 0.4119 1.0000 0.5246 0.5188 0.4677 0.5283 0.5246 1.0000 ACC WIPRO MARUTI NTPC SBI ACC WIPRO MARUTI NTPC SBI 2.83% to 3.14% .Maximum return is on SBI which has max
imum standard deviation i.e. risk which shows that return is directly proportional to risk. • Correlation of stocks of SBI with stocks of Maruti is highest followed by correlation PORTFOLIO VARIANCE 0.00044 PORTFOLIO STANDARD 0.02086 DEVIATION PORTFOLIO MEAN 0.00075 SHARPE RATIO 0.02217 38 © BVIMR Management Egde, Vol. 4, No. 2 (2011) PP 35-39 ACC WIPRO MARUTI NTPC SBI 0.23 0.26 0.22 0.29 0.00 PORTFOLIO VARIANCE 0.00068 PORTFOLIO STANDARD DEVIATION 0.02615 PORTFOLIO MEAN 0.00140 SHARPE RATIO 0.04255 between SBI and NTPC. EFFICIENT FRONTIER AND CAL FOR 5 NSE STOCKS 0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.004 0.0002 0 STANDARD DEVIATION EFFICIENT FRONTIER CAL AVERAGE PORTFOLIO RETURN 0 0.01 0.02 0.03 0.04 • Minimum variance portfolio statistics shows that the overall portfolio variance at 0.00044 which is very less with portfolio mean at 0.00075. • Sharpe Ratio was maximum at 0.04255 which helped in plotting CAL and this gives us the optimal portfolio Bibliography 1. Som based stock index performs better than nse- 50 index.Full Text Available By: Khan, Asif Ullah; Bandopadhyaya, T. K.; Sharma, Sudhir. Estudios de Economía Aplicada, Aug2008, Vol. 26 Issue 2, p802-806, 5p, 1 chart, 2 diagrams, 1 graph; (AN 35128470) ACC WIPRO MARUTI NTPC SBI 0 0 0.16 0.20 0.64 2. Liquidity Effect of Single Stock Futures on the Underlying Stocks: A Case of NSE.Full Text Available By : Sadath, Anver; Kamaiah, B.. IUP Journal of Applied Economics, Sep2009, Vol. 8 Issue 5/6, p142-160, 19p 3. Investment analysis and portfolio management by Prasanna Chandra. 4. Modeling of Share Price Movements in NSE: An Empirical Study of Selected Cases.Citation Only Available By: Prakash, Shri; Ramasubramanian, A.. Finance India, Dec2006, Vol. 20 Issue 4, p1339-1364, 26p 5. An Empirical Analysis of Price Discovery in the NSE Spot and Futures Markets of India.Full Text Available By: Srinivasan, P.. IUP Journal of Applied Finance, Nov2009, Vol. 15 Issue 11, p24-36, 13p Copyright of BVIMR Management Edge is the property of Bharati Vidyapeeth Deemed University, Institute of Management & Research and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder’s express written permission. However, users may print, download, or email articles for individual use.© BVIMR Management Egde, Vol. 4, No. 2 (2011) PP 35-39 35 Introduction Selection of stocks that are suitable for a portfolio is a challenging task. Technical Analysis provides a framework for studying investor behaviour, and generally focuses only on price and volume data. Technical Analysis using this approach has short-term investment horizons, and access to only price and exchange data. Fundamental analysis involves analysis of a company’s performance and profitability to determine its share price. By studying the overall economic conditions, the company’s competition, and other factors, it is possible to determine expected returns and the intrinsic value of shares. This type of analysis assumes that a share’s current (and future) price depends on its intrinsic value and anticipated return on investment. As new information is released pertaining to the company’s status, the expected return on the company’s shares will change, which affects the stock price. So the advantages of fundamental analysis are its ability to predict changes before they show up on the charts. Growth prospects are related to the current economic environment. Stocks have been selected by us on the bases of fundamental analysis criteria. These criteria are evaluated for each stock and compared in order to obtain a list of stocks that are suitable for our portfolio. Stocks are selected by applying one common criteria on the stocks listed on Indian National Stock Exchange (NSE). proven that it is a straight line and that it has the following equation. In this formula P is the risky portfolio, F is the riskless portfolio, and C is a combination of portfolios P and F. The efficient frontier Every possible asset combination can be plotted in risk-return space, and the collection of all such possible portfolios defines a region in this space. The line along the upper edge of this region is known as the efficient frontier (sometimes “the Markowitz frontier”). Combinations along this line represent portfolios (explicitly excluding the risk-free alternative) for which there is lowest risk for a given level of return. Conversely, for a given amount of risk, the portfolio lying on the efficient frontier represents the combination offering the best possible return. Mathematically the Efficient Frontier is the intersection of the Set of Portfolios with Minimum Variance (MVS) and the Set of Portfolios with Maximum Return. Formally, the efficient frontier is the set of maximal elements with respect to the partial order of product order on risk and return, the set of portfolios for which one cannot improve both risk and return. The efficient frontier is illustrated above, with return µ on the y-axis, and risk Ó on the x-axis; an alternative illustration from the diagram in the CAPM article is at right. The efficient frontier will be convex – this is because the risk-return characteristics of a portfolio change in a non-linear fashion as its component weightings are changed. (As described above, portfolio risk is a function of the correlation of the component assets, and thus changes in a non-linear fashion as the weighting of component assets changes.) The efficient frontier is a parabola (hyperbola) when expected return is plotted against variance (standard deviation). p p Literature Review Capital allocation line The capital allocation line (CAL) is the line of expected return plotted against risk (standard deviation) that connects all portfolios that can be formed using a risky asset and a riskless asset. It can be E(rp) – rF Q p CAL : E ( rc ) = r F + Q c Fundamental Analysis and Portfolio Selection in Practice Dr. Namita Rajput Dr. Harish Handa 36 © BVIMR Management Egde, Vol. 4, No. 2 (2011) PP 35-39 S R – Rf = Q = E [R-R]f var [R-R ]f var [R-R ]f = var[R]. The market portfolio The efficient frontier is a collection of portfolios, each can be concluded that introduction of SSF in the NSE has resulted in improvement of liquidity in the cash market. Research Methodology List of NSE Stocks For Portfolio Analysis 1. ACC 2. WIPRO 3. Maruti Suzuki 4. NTPC 5. SBI Price data was collected over the last 3 years (starting 25th September, 2006 till 24th September, 2009) for each of the above stocks from the site of NSE. The daily ARITHMETIC returns were calculated for the period. Using these return figures, the average historical daily return and risk standard deviation of daily returns was calculated. Next, using the data in the “Daily Returns” column from all the five stocks, taking two at a time, we calculate the correlation between two stock returns. Using the Solver function from Excel, we got the portfolio statistics and weights for the minimum variance portfolio. Efficient frontier and Capital Allocation Line was plotted to get Optimal Risky Portfolio. Analysis And Interpretation Of Data I collected the price data over the last 3 years (starting 25th September, 2006 till 24th September, 2009) for each of the above stocks. The daily ARITHMETIC returns were calculated for the period (as shown in the “Daily Returns” column in the data sheets. Using these return figures, the average historical daily return and risk (standard deviation of daily returns was calculated for each of the stocks, which came out to be : Next, using the data in the “Daily Returns” column from all the five stocks, taking two at a time, we calculate the correlation between two stock returns. For e.g., if we have to calculate the correlation between returns of ACC and that of Wipro, we take the 1st array (as required by the correlation formula in Excel) as the returns of ACC and the 2nd array as that of Wipro. Following this procedure, we get the correlation matrix as : Using the Solver function from Excel, we get the portfolio statistics and weights for the minimum variance portfolio as : © BVIM
R Management Egde, Vol. 4, No. 2 (2011) PP 35-39 37 Minimum Variance Portfolio Statistics : Minimum Variance Portfolio Weights : Now, in order to plot the Efficient Frontier, I incremented the average return in steps of 0.00005 and used the Solver to determine the Standard deviation at the average return values. Using this method, we get a set of portfolio weights at different values of Risk and Returns. Now, in order to plot the CAL, we need to maximise the Sharpe Ratio which is again done using the Solver. We find out that the Sharpe Ratio is maximum at 0.04255 (for Mean = 0.00140 and SD = 0.02615. This gives us the optimal portfolio. The statistics and weights for the Optimal Risky Portfolio are as follows : Optimal Risky Portfolio Statistics: Optimal Risky Portfolio Weights : Using the figures every time from the Solver, we get various points, which help us plot the Efficient Frontier (in which the horizontal axis shows the SD and the vertical axis shows the daily returns). Also, we plot the Capital Allocation Line (CAL) (in which the horizontal axis is again SD and the vertical axis is the Risk Premium on CAL (which is calculated by multiplying the maximum slope with the SD of each portfolio). The point where these two lines meet is the Optimal Risky Portfolio. Conclusion And Findings • Average return of all the five stocks varies from 0.02% to 0.16% with standard deviation of This done, next we prepare the Bordered Covariance Matrix as under: BORDERED COVARIANCE MATRIX 0.23 0.26 0.22 0.29 0.00 PORTFOLIO WEIGHTS ACC WIPRO MARUTI NTPC SBI 0.23 ACC 0.000043 0.000019 0.000016 0.000023 0.000000 0.26 WIPRO 0.000019 0.000061 0.000016 0.000025 0.000000 0.22 MARUTI 0.000016 0.000020 0.000033 0.000018 0.000000 0.29 NTPC 0.000023 0.000025 0.000018 0.000059 0.000000 0.00 SBI 0.000000 0.000000 0.000000 0.000000 0.000000 1 0.000101 0.000125 0.000084 0.000125 0.000000 SECURITY STANDARD AVERAGE DEVIATION (%) RETURN (%) ACC WIPRO MARUTI NTPC SBI 2.83% 0.02% 2.95% 0.06% 2.67% 0.11% 2.67% 0.11% 3.14% 0.16% 1.0000 0.3709 0.4309 0.4479 0.5188 0.3709 1.0000 0.4465 0.4236 0.4677 0.4309 0.4465 1.0000 0.4119 0.5283 0.4479 0.4236 0.4119 1.0000 0.5246 0.5188 0.4677 0.5283 0.5246 1.0000 ACC WIPRO MARUTI NTPC SBI ACC WIPRO MARUTI NTPC SBI 2.83% to 3.14% .Maximum return is on SBI which has maximum standard deviation i.e. risk which shows that return is directly proportional to risk. • Correlation of stocks of SBI with stocks of Maruti is highest followed by correlation PORTFOLIO VARIANCE 0.00044 PORTFOLIO STANDARD 0.02086 DEVIATION PORTFOLIO MEAN 0.00075 SHARPE RATIO 0.02217 38 © BVIMR Management Egde, Vol. 4, No. 2 (2011) PP 35-39 ACC WIPRO MARUTI NTPC SBI 0.23 0.26 0.22 0.29 0.00 PORTFOLIO VARIANCE 0.00068 PORTFOLIO STANDARD DEVIATION 0.02615 PORTFOLIO MEAN 0.00140 SHARPE RATIO 0.04255 between SBI and NTPC. EFFICIENT FRONTIER AND CAL FOR 5 NSE STOCKS 0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.004 0.0002 0 STANDARD DEVIATION EFFICIENT FRONTIER CAL AVERAGE PORTFOLIO RETURN 0 0.01 0.02 0.03 0.04 • Minimum variance portfolio statistics shows that the overall portfolio variance at 0.00044 which is very less with portfolio mean at 0.00075. • Sharpe Ratio was maximum at 0.04255 which helped in plotting CAL and this gives us the optimal portfolio Bibliography 1. Som based stock index performs better than nse- 50 index.Full Text Available By: Khan, Asif Ullah; Bandopadhyaya, T. K.; Sharma, Sudhir. Estudios de Economía Aplicada, Aug2008, Vol. 26 Issue 2, p802-806, 5p, 1 chart, 2 diagrams, 1 graph; (AN 35128470) ACC WIPRO MARUTI NTPC SBI 0 0 0.16 0.20 0.64 2. Liquidity Effect of Single Stock Futures on the Underlying Stocks: A Case of NSE.Full Text Available By : Sadath, Anver; Kamaiah, B.. IUP Journal of Applied Economics, Sep2009, Vol. 8 Issue 5/6, p142-160, 19p 3. Investment analysis and portfolio management by Prasanna Chandra. 4. Modeling of Share Price Movements in NSE: An Empirical Study of Selected Cases.Citation Only Available By: Prakash, Shri; Ramasubramanian, A.. Finance India, Dec2006, Vol. 20 Issue 4, p1339-1364, 26p 5. An Empirical Analysis of Price Discovery in the NSE Spot and Futures Markets of India.Full Text Available By: Srinivasan, P.. IUP Journal of Applied Finance, Nov2009, Vol. 15 Issue 11, p24-36, 13p Copyright of BVIMR Management Edge is the property of Bharati Vidyapeeth Deemed University, Institute of Management & Research and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder’s express written permission. However, users may print, download, or email articles for individual use.