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Step 2. The shape of the curve shows the outcome of the risk-return combinations generated by the portfolio of the assets giving you the minimum variance for a given rate of return. Any set of combinations formed by the two assets with less than perfect correlation will lie within the minimum-variance portfolio and will be the convex. A perfect positive correlation +1 implies that as one security moves, either up or down, the other security will move in the same direction making a straight upward line. A perfectly negative correlation of -1 means that if one security moves in either direction the security that is perfectly negatively correlated will move in the opposite direction.

Step 3. The older investor would take the portfolio including Harris and Urban, because they have the lowest standard deviation, hence it is a less risky investment. The younger investor would take the portfolio with Maya and Urban, because it has the highest returns, and can they can take on the risk. At an expected return of .75, the S&P 500 has a lower standard deviation than the stock portfolio with a standard deviation of 6.03 with the same return.

Step 4. Bonds and stocks will not react in the same way to adverse events. By…...

...page 50 student accountant JUNe/JULY 2008 CAPM: THEORY, ADVANTAGES, AND DISADVANTAGES THE CAPITAL ASSET PRICING MODEL RELEVANT TO ACCA QUALIFICATION PAPER F9 Section F of the Study Guide for Paper F9 contains several references to the capital asset pricing model (CAPM). This article is the last in a series of three, and looks at the theory, advantages, and disadvantages of the CAPM. The first article, published in the January 2008 issue of student accountant introduced the CAPM and its components, showed how the model can be used to estimate the cost of equity, and introduced the asset beta formula. The second article, published in the April 2008 issue, looked at applying the CAPM to calculate a project-specific discount rate to use in investment appraisal. CAPM FORMULA The linear relationship between the return required on an investment (whether in stock market securities or in business operations) and its systematic risk is represented by the CAPM formula, which is given in the Paper F9 Formulae Sheet: E(ri) = Rf + βi(E(rm) - Rf) E(ri) = return required on financial asset i Rf = risk-free rate of return βi = beta value for financial asset i E(rm) = average return on the capital market The CAPM is an important area of financial management. In fact, it has even been suggested that finance only became ‘a fully-fledged, scientific discipline’ when William Sharpe published his derivation of the CAPM in 19861. CAPM ASSUMPTIONS The CAPM is often criticised as being......

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...Table of Contents 1. Introduction 3 2. CAPM 3 3. Global CAPM 4 4. International CAPM 4 5. Conclusion 5 6. Reference 5 According to the survey conducted among the most successful US enterprises, 73-85% of the respondent claims to use CAPM as their preferred methodology (Desai, 2005), thereby making CAPM most widely used model to estimate cost of equity. CAPM model is used to estimate the expected return on a risky asset by adding to the risk free rate of return a market risk premium. Sharpe and Lintner built CAPM theory on basis of Markowitz theory of mean- variance portfolio model. 1. Assumption of CAPM Markowitz mean- variance analysis refers to the theory of combining risky assets so as to minimize overall risk of the portfolio at desired level of return. The Markowitz theory is based on three assumption i.e. all investors minimize risk for desired level of expected return or demand additional return for additional risk (risk averse), all parameter of individual asset like expected returns, variance and covariance are known thereby all investors have same expectations of all asset parameter and there are no taxes or transaction cost. Sharpe and Lintner add two key assumptions to the Markowitz model to derive CAPM - individual buy and sell decision does not affect asset price (price takers) and investors can borrow and lend unlimitedly at risk free rate. 2. Limitation of CAPM Assumption The assumption that the investor consider only......

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...Copyright c 2005 by Karl Sigman 1 Capital Asset Pricing Model (CAPM) We now assume an idealized framework for an open market place, where all the risky assets refer to (say) all the tradeable stocks available to all. In addition we have a risk-free asset (for borrowing and/or lending in unlimited quantities) with interest rate rf . We assume that all information is available to all such as covariances, variances, mean rates of return of stocks and so on. We also assume that everyone is a risk-averse rational investor who uses the same ﬁnancial engineering mean-variance portfolio theory from Markowitz. A little thought leads us to conclude that since everyone has the same assets to choose from, the same information about them, and the same decision methods, everyone has a portfolio on the same eﬃcient frontier, and hence has a portfolio that is a mixture of the risk-free asset and a unique eﬃcient fund F (of risky assets). In other words, everyone sets up the same optimization problem, does the same calculation, gets the same answer and chooses a portfolio accordingly. This eﬃcient fund used by all is called the market portfolio and is denoted by M . The fact that it is the same for all leads us to conclude that it should be computable without using all the optimization methods from Markowitz: The market has already reached an equilibrium so that the weight for any asset in the market portfolio is given by its capital value (total worth of its shares) divided by the total......

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...Disadvantages of Markowitz approach: The Markowitz method is very sensitive to small changes in the initial conditions, that is in the choice of the data period. Sometimes even changing the analysed period by a few days will greatly alter the composition of the portfolio. Therefore, there is no certainty that the used parameters are stable enough over time. Markowitz’ optimizers maximize errors. It is not possible to estimate exactly the expected returns, variances and covariances. It is assumed that the returns of the optimised assets follow a normal distribution, which in practice does not hold in all cases. Therefore, estimation errors are inevitable. This is especially true when the number of stocks under consideration is large when compared to the return history in the sample - which is the typical situation in practice. As a result, the investor is suggested to invest in extremely under-diversified portfolios or in the portfolios which contain large short positions - which can be seen inVariance is a method of risk calculation through measuring variance around the expected return. However, only losses represent a real risk – therefore it is questionable, if variance is a proper risk-measuring tool. In Markowitz approach, only the expected return is taken into account when modelling the future expected uncertainties. It is a great simplification, as in fact many more factors are relevant – such as the employment rate, economic growth etc. In times of economic crisis......

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...Asset Pricing Model and Arbitrage Pricing Theory in the Italian Stock Market: an Empirical Study ARDUINO CAGNETTI∗ ABSTRACT The Italian stock market (ISM) has interesting characteristics. Over 40% of the shares, in a sample of 30 shares, together with the Mibtel market index, are normally distributed. This suggests that the returns distribution of the ISM as a whole may be normal, in contrast to the findings of Mandelbrot (1963) and Fama (1965). Empirical tests in this study suggest that the relationships between β and return in the ISM over the period January 1990 – June 2001 is weak, and the Capital Asset Pricing Model (CAPM) has poor overall explanatory power. The Arbitrage Pricing Theory (APT), which allows multiple sources of systematic risks to be taken into account, performs better than the CAPM, in all the tests considered. Shares and portfolios in the ISM seem to be significantly influenced by a number of systematic forces and their behaviour can be explained only through the combined explanatory power of several factors or macroeconomic variables. Factor analysis replaces the arbitrary and controversial search for factors of the APT by “trial and error” with a real systematic and scientific approach. The behaviour of share prices, and the relationship between risk and return in financial markets, have long been of interest to researchers. In 1905, a young scientist named Albert Einstein, seeking to demonstrate the existence of atoms, developed an elegant......

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... ซึ่งสอดคล้องกับทฤษฎี Modern Portfolio Theory ของ Harry M. Markowitz (1952) ที่กล่าวไว้ว่า “Don’t put all your eggs in one basket” สรุปรายละเอียดของ Mini-Case : John & Marsha on Portfolio Selection John ทำหน้าที่บริหาร Portfolio ซึ่งมีมูลค่า 125 ล้านดอลลาร์ของนักลงทุนอยู่ เขาปรึกษากับ Marsha เกี่ยวกับปัญหาของการบริหารจัดการหุ้นใน Portfolio ของเขา โดย John คิดว่าที่ผ่านมาผลตอบแทนจาก portfolio ที่เขาดูแลอยู่นั้นมักจะใกล้เคียงกับอัตราผลตอบแทนของตลาดและอิงจากกราฟ S&P 500 market index ที่จัดทำขึ้น เขาจึงรู้สึกว่าการบริหารของเขาอ้างอิงแต่กับตัวเลขของตลาดมากเกินไป เขาอยากจะบริหารจัดการ portfolio เสียใหม่ให้มีความเป็นตัวของตัวเองมากขึ้น และได้รับผลตอบแทนที่สูงขึ้นกว่าอัตราผลตอบแทนของตลาด เพื่อทำให้การทำงานของเขามีประโยชน์ต่อลูกค้ามากขึ้น โดยเขาเลือกบริษัทที่ราคาตลาดของหุ้นต่ำกว่ามูลค่าที่ประเมินได้ (Undervalued) และที่ราคาตลาดของหุ้นสูงกว่ามูลค่าหุ้นที่ประเมินได้ (Overvalued) ามาส่วนหนึ่ง โดยบริษัทที่เขาคาดว่าน่าจะมีมูลค่า Undervalued และสมควรซื้อมากคือบริษัท Pioneer Gypsum และหุ้นของ Global mining นั้น Overvalued จึงไม่สมควรซื้อโดยข้อมูลต่างๆของทั้ง2บริษัทที่เขาหามาได้มีค่าตามตารางนี้ | Pioneer Gypsum | Global Mining | Expected return | 11% | 12.90% | Standard Deviation | 32% | 24% | Beta | 0.65 | 1.22 | Stock Price | $87.50 | $105 | | | | ตารางที่ 1 : รายละเอียดของผลตอบแทน,ค่าเบี่ยงเบนมาตรฐาน,ค่าเบต้า และราคาหุ้นของหุ้นแต่ละตัว เขาพยายามจะตัดสินใจว่าสมควรจะซื้อหุ้นของ Pioneer มากน้อยเพียงใดอย่างไร แต่เพียง Modern Portfolio Theory......

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...Bill Shackelford From: Zahir Cassam Date: February 3, 2014 ------------------------------------------------- Re: Proposing a Project Portfolio Evaluation and Selection Process Executive Summary Taking into account the poor performance of our current projects due to a weak portfolio management process in place, the Operations SBU has come to the determination that if we are to move forward in accommodating new projects along with our existing ones, the current system must be reviewed and redesigned for better decision-making. This proposal defines a framework for project portfolio evaluation and a project selection for adoption and it elaborates on the two phases that involve project screening, selection, prioritizing and balancing. More emphasis is given to the project selection criteria and score model as this is the main area where the gap of knowledge has been identified. Rationale Our recent organizational determination to sustain by controlling costs and expanding our frontiers shall require much effort from all our SBUs and most importantly, it is crucial that we are able to incubate a proper process that shall boost good decision-making and mitigate conflicts when we come to screening multimillion dollar projects and implementing them as part of our operations. The said process shall be about evaluating our project portfolio and devising a methodology of selecting specific projects with the highest probability of helping our company achieve its strategic......

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...wealthy) private investors may often refer to their services as money management or portfolio management often within the context of so-called "private banking". The provision of investment management services includes elements of financial statement analysis, asset selection, stock selection, plan implementation and ongoing monitoring of investments. Coming under the remit of financial services many of the world's largest companies are at least in part investment managers and employ millions of staff. Security Analysis Security analysis is the analysis of tradable financial instruments called securities. These can be classified into debt securities, equities, or some hybrid of the two. More broadly, futures contracts and tradable credit derivatives are sometimes included. Security analysis is typically divided into fundamental analysis, which relies upon the examination of fundamental business factors such as financial statements, and technical analysis, which focuses upon price trends and momentum. Quantitative analysis may use indicators from both areas. Portfolio A grouping of financial assets such as stocks, bonds and cash equivalents, as well as their mutual, exchange-traded and closed-fund counterparts. Portfolios are held directly by investors and/or managed by financial professionals. .A portfolio is planned to stabilize the risk of non-performance of various pools of investment. Portfolio management is all about strengths, weaknesses, opportunities and......

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...Outline 1 Portfolios 2 Portfolio Expected Return 3 Portfolio Variance 4 Systematic Risk, Speciﬁc Risk, and Diversiﬁcation 5 Market Portfolio and Measure of Systematic Risk 6 CAPM: From Risk to Return COMM 298 Return, Risk, and the Security Market Line 1 / 54 Outline 1 Portfolios 2 Portfolio Expected Return 3 Portfolio Variance 4 Systematic Risk, Speciﬁc Risk, and Diversiﬁcation 5 Market Portfolio and Measure of Systematic Risk 6 CAPM: From Risk to Return COMM 298 Return, Risk, and the Security Market Line 1 / 54 Portfolios Investors are risk averse. COMM 298 Return, Risk, and the Security Market Line 2 / 54 Portfolios Investors are risk averse. To reduce risk, it is good idea “not to put all your eggs in one basket”. COMM 298 Return, Risk, and the Security Market Line 2 / 54 Portfolios Investors are risk averse. To reduce risk, it is good idea “not to put all your eggs in one basket”. This is achieved by building a portfolio, which is a collection of assets. COMM 298 Return, Risk, and the Security Market Line 2 / 54 Portfolios Investors are risk averse. To reduce risk, it is good idea “not to put all your eggs in one basket”. This is achieved by building a portfolio, which is a collection of assets. The process is called diversiﬁcation. COMM 298 Return, Risk, and the Security Market Line 2 /......

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...Copyright c 2005 by Karl Sigman 1 Capital Asset Pricing Model (CAPM) We now assume an idealized framework for an open market place, where all the risky assets refer to (say) all the tradeable stocks available to all. In addition we have a risk-free asset (for borrowing and/or lending in unlimited quantities) with interest rate rf . We assume that all information is available to all such as covariances, variances, mean rates of return of stocks and so on. We also assume that everyone is a risk-averse rational investor who uses the same ﬁnancial engineering mean-variance portfolio theory from Markowitz. A little thought leads us to conclude that since everyone has the same assets to choose from, the same information about them, and the same decision methods, everyone has a portfolio on the same eﬃcient frontier, and hence has a portfolio that is a mixture of the risk-free asset and a unique eﬃcient fund F (of risky assets). In other words, everyone sets up the same optimization problem, does the same calculation, gets the same answer and chooses a portfolio accordingly. This eﬃcient fund used by all is called the market portfolio and is denoted by M . The fact that it is the same for all leads us to conclude that it should be computable without using all the optimization methods from Markowitz: The market has already reached an equilibrium so that the weight for any asset in the market portfolio is given by its capital value (total worth of its shares)......

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...pricing model (CAPM) is a very useful model and it is used widely in the industry even though it is based on very strong assumptions. Discuss in the light of recent developments in the area.’ MN 3365 Strategic Finance Table of Contents Introduction Concept of CAPM Assumptions of CAPM . Other Suggested Models Disadvantages of CAPM Advantages of CAPM Problems in applying CAPM Conclusion Bibliography / References INTRODUCTION This essay will highlight the use of Capital asset pricing model ( CAPM ) to be considered as a pricing theory model for assets . CAPM model helps investors to analyse the risk and what expectation to keep from an investment (Banz , 1981) . There are two types of risk associated with CAPM known as systematic and unsystematic risk . The systematic risks are market risk which cannot be diversified such as fluctuations in interest rates and recession in the economy .Unsystematic risk are risks associated with an individual stock , it occurs when an investor increases the number of stocks on his portfolio. The unsystematic risk cannot be diversified as it is related an individual stock irrespective to the general market . (Amihud and Lev, 1981). The CAPM was introduced independently by Jack Trenor (1961 , 1962) , Jan Mossin (1996) and William F . Sharpe (1964) , it is basically an uplifment of the existing work of Harry Markowitz on modern portfolio therory as well as diversification which was given a name as CAPM ......

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...The Chinese University of Hong Kong Department of Computer Science and Engineering Final Year Project Trading Strategy and Portfolio Management (LWC 1301) Implementing Portfolio Selection By Using Data mining Tseng Ling Chun (1155005610) Supervisor: Professor Chan Lai Wan Marker: Professor Xu Lei 1 Table of Contents Table of Contents………………………………………….…………………………………………………2 1. Introduction………………………………………….…………………………………………................4 1.1 Financial Portfolios.......................................................................................................4 1.2 Data Mining and Decision Trees………………………………………..................….4 1.3 Flow of Report……………………………………….....................................................….5 2. Classification and Regression Trees (CART) …………………………………..........……….6 2.1 Detailed description of CART……………………………………................................6 2.2 Tree Construction………………………………………..............................................….8 2.2.1 Application of Impurity Function in CART……………………...…...9 2.3 Splitting Rules…………........……………...………….………………………….......……11 3. Optimizing Size of Tree……………………………....………..................................................….12 3.1 Parameterization of Trees…………………………………...........................……….13 3.2 Cost – Complexity Function……………………………………....….........................14 3.3 V – Fold Cross – Validation……………………………………..........................…….15 4. Iterative Dichotomiser 3 (ID3)......

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...C H A P T E R 3 Project Selection and Portfolio Management Chapter Outline 70 Project Management: Achieving Competitive Advantage, Second Edition, by Jeffrey K. Pinto. Published by Prentice Hall. Copyright © 2010 by Pearson Education, Inc. 000200010270649984 PROJECT PROFILE Project Selection Procedures: A Cross-Industry Sampler INTRODUCTION 3.1 PROJECT SELECTION 3.2 APPROACHES TO PROJECT SCREENING AND SELECTION Method One: Checklist Model Method Two: Simplified Scoring Models Limitations of Scoring Models Method Three: The Analytical Hierarchy Process Method Four: Profile Models 3.3 FINANCIAL MODELS Payback Period Net Present Value Discounted Payback Internal Rate of Return Options Models Choosing a Project Selection Approach PROJECT PROFILE Project Selection and Screening at GE: The Tollgate Process 3.4 PROJECT PORTFOLIO MANAGEMENT Objectives and Initiatives Developing a Proactive Portfolio Keys to Successful Project Portfolio Management Problems in Implementing Portfolio Management Summary Key Terms Solved Problems Discussion Questions Problems Case Study 3.1 Keflavik Paper Company Project Profile Case Study 3.2 Project Selection at Nova Western, Inc. Internet Exercises Notes Chapter Objectives After completing this chapter you should be able to: 1. Explain six criteria for a useful project-selection/screening model. 2. Understand how to employ checklists and simple scoring models to select projects. 3. Use more......

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...Capital Assets Pricing Model (CAPM) , is a method of pricing assets of capital nature. This model applies Beta (non-diversifiable risk) to link risks and returns of investments. According to Stahl (2016), Beta is a standard for measuring the systematic risk or the non-diversifiable risk. The uncertainty in the economy of a particular country causes the systematic risk. Systematic risk is that risk sharing or risk diversification cannot reduce. Economic downturns, war, natural calamities and a change of government policy are some of the activities that cause systematic risk. Both CAPM and Beta are measures of risk (Anon 2014). The capital assets pricing model defines the required rate of return of security. CAPM can be a mathematical equation, or a graphical representation is known as the security market line (SML) (Stahl 2015). An analysis of CAPM indicates that there are several critiques of this model. Nevertheless, there are multivariate models used to overcome these critiques. A).Formulas to Calculate CAPM and Beta 1). Capital Assets Pricing Model CAPM= [pic]= [pic]+ [pic] (RM-RF) Where; [pic] is the cutoff rate or even minimum required rate of return RM- RF is the risk premium and is above free rate RM is the market returns [pic] is the risk-free rate of returns [pic] is the beta of asset j Illustration Assuming that [pic]= 1.2, RM= 12% and [pic]= 4%. Use the CAPM to calculate the required rate of return. Solution CAPM= [pic]= [pic]+ [pic] (RM-RF) ...

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...Description of CAPM. The Capital Asset Pricing Model CAPM was introduced by Treynor ('61), Sharpe ('64) and Lintner ('65). By introducing the notions of systematic and specific risk, it extended the portfolio theory. In 1990, William Sharpe was Nobel price winner for Economics. "For his contributions to the theory of price formation for financial assets, the so-called Capital Asset Pricing Model (CAPM)." The CAPM model says that the expected return that the investors will demand, is equal to: the rate on a risk-free security plus a risk premium. If the expected return is not equal to or higher than the required return, the investors will refuse to invest and the investment should not be undertaken. CAPM decomposes a portfolio's risk into systematic risk and specific risk. Systematic risk is the risk of holding the market portfolio. When the market moves, each individual asset is more or less affected. To the extent that any asset participates in such general market moves, that asset entails systematic risk. Specific risk is the risk which is unique for an individual asset. It represents the component of an asset's return which is not correlated with general market moves. According to CAPM, the marketplace compensates investors for taking systematic risk but not for taking specific risk. This is because specific risk can be diversified away. When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk. But through......

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