|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 , 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. –  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|
1) Please make sure you follow the report format as requested by the AIB.
©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
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
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
© 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
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