...accuracy of prices of selling or buying the stocks, what could be the risk, what are the factors should be considered that ignores uncertainty and the expected returns of the stock. The Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT) both are well known pricing model determines the risk factor for analyzing the appropriate returns for the investors in their own unique ways. CAPM model uses the whole market environment as one factor but on the other hand APT uses five different economics factor which is more detailed in describing risk which accelerates for these factors. The adoption of CAPM is in practice but other hand its various criticisms are documented on it as well and academics are working on the new approaches of it such as APT and others is discussed in later paragraphs. In this assignment I will discuss the assumptions of CAPM and APT model and their pros and cons and the limitations of CAPM over APT models. CAPM and its Shortcomings Hary Markowitz (1952) and Tobin (1958) first introduced the idea of asset pricing model. Markowitz (1952) observed that “when two risky assets are combined, their deviations from the mean are not additive, provided the returns from the two assets are not perfectly correlated and when portfolio of risky...
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...MODERN PORTFOLIO THEORY A N D INVESTMENT ANALYSIS EIGHTH EDITION INTERNATIONAL STUDENT VERSION EDWIN J. ELTON Leonard N. Stern School of Business New York University MARTIN J. GRUBER Leonard N. Stern School of Business New York University STEPHEN J. BROWN Leonard N. Stern School of Business New York University WILLIAM N. GOETZMANN Yale University WILEY John Wiley & Sons, Inc. Contents About the Authors Preface Part 1 Chapter 1 ix vii INTRODUCTION INTRODUCTION Outline of the Book 2 The Economic Theory of Choice: An Illustration Under Certainty Conclusion 8 Multiple Assets and Risk 8 Questions and Problems 9 Bibliography 10 4 1 2 Chapter 2 FINANCIAL MARKETS Trading Mechanics 11 Margin 14 Markets 18 Trade Types and Costs 25 Conclusion 27 Bibliography 27 1 1 Chapter 3 FINANCIAL SECURITIES Types of Marketable Financial Securities 2 8 The Return Characteristics of Alternative Security Types Stock Market Indexes 3 8 Bond Market Indexes 3 9 Conclusion 4 0 36 28 Part 2 Section I Chapter 4 P O R T F O L I O ANALYSIS MEAN VARIANCE PORTFOLIO THEORY THE CHARACTERISTICS OF THE OPPORTUNITY SET UNDER RISK Determining the Average Outcome 4 5 A Measure of Dispersion 4 6 Variance of Combinations of Assets 4 9 Characteristics of Portfolios in General 51 Two Concluding Examples 61 Conclusion 6 4 XIII 41 43 44 XIV CONTENTS Questions and Problems Bibliography 6 6 Chapter 5 64 DELINEATING EFFICIENT PORTFOLIOS Combinations...
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...2 Study of the theoretical fundamentals of the modern portfolio theory In the first paragraph we show the crucial differences between the modern portfolio theory and pre-Markowitz one, summarize the mathematical framework of the MPT and critically evaluate the core assumptions building the MPT. This paragraph is devoted to the second stage of the portfolio selection process assuming that all input parameters of the model are true. 2.1 Definition of the modern portfolio theory Harry Markowitz is highly regarded as a pioneer in theoretical justification of investor’s behavior and development of optimization model for portfolio selection process. In 1990, Markowitz shared a Nobel Prize for his contributions to financial economics and corporate...
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...Finance: The Capital Asset Pricing Model (CAPM) Prof. Alex Shapiro Lecture Notes 9 The Capital Asset Pricing Model (CAPM) I. II. III. IV. V. VI. Readings and Suggested Practice Problems Introduction: from Assumptions to Implications The Market Portfolio Assumptions Underlying the CAPM Portfolio Choice in the CAPM World The Risk-Return Tradeoff for Individual Stocks VII. The CML and SML VIII. “Overpricing”/“Underpricing” and the SML IX. X. Uses of CAPM in Corporate Finance Additional Readings Equilibrium Process, Supply Equals Demand, Market Price of Risk, Cross-Section of Expected Returns, Risk Adjusted Expected Returns, Net Present Value and Cost of Equity Capital. Buzz Words: 1 Foundations of Finance: The Capital Asset Pricing Model (CAPM) I. Readings and Suggested Practice Problems BKM, Chapter 9, Sections 2-4. Suggested Problems, Chapter 9: 2, 4, 5, 13, 14, 15 Web: Visit www.morningstar.com, select a fund (e.g., Vanguard 500 Index VFINX), click on Risk Measures, and in the Modern Portfolio Theory Statistics section, view the beta. II. Introduction: from Assumptions to Implications A. Economic Equilibrium 1. Equilibrium analysis (unlike index models) Assume economic behavior of individuals. Then, draw conclusions about overall market prices, quantities, returns. 2. The CAPM is based on equilibrium analysis Problems: – – There are many “dubious” assumptions. The main implication of the CAPM concerns expected returns, which can’t be...
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...for over 25 years, and which the Royal Swedish Academy of Sciences has cited in honoring me with the award of the Prize in Economic Sciences in Memory of Alfred Nobel. I first present the Capital Asset Pricing Model (hence, CAPM), incorpo1 rating not only my own contributions but also the outstanding work of Lintner (1965, 1969) and the contributions of Mossin (1966) and others. My goal is to do so succinctly yet in a manner designed to emphasize the economic content of the theory. Following this, I modify the model to reflect an extreme case of an institutional arrangement that can preclude investors from choosing fully optimal portfolios. In particular, I assume that investors are unable to take negative positions in assets. For this version of the model I draw heavily from papers by Glenn (1976), Levy (1978), Merton (1987) and Markowitz (1987, 1990). Finally, I discuss the stock index futures contract - a major financial innovation of worldwide importance that postdates the development of the CAPM. Such contracts can increase the efficiency of capital markets in many ways. In particular, they can bring actual markets closer to the idealized world assumed by the Capital Asset Pricing Model. THE CAPITAL ASSET PRICING MODEL The initial version of the CAPM, developed over 25 years ago, was extremely parsimonious. It dealt with the central aspects of equilibrium in capital markets and assumed away many important aspects of such markets as they * I am particularly grateful for the...
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...Rate method and the Certainty Equivalent Method. TRACKING PORTFOLIOS AND REAL ASSET VALUATION Portfolio tracking is monitoring a collection of stocks, for the purpose of learning how the prices move and/or profiting from those movements. The market price of a combination of financial investments that track the future cash flows of the project should be the same as the value of the projects future cash flows. Analyst’s need to generate tracking portfolio’s with tracking error (a measure of how closely a portfolio follows the index to which it is benchmarked), PV=0 in order to value projects in these cases, i.e. Tracking Error = Cash Flows of Tracking Portfolio – Cash Flows of Project. When tracking error exists, analysts use Asset Pricing Models, Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT), to derive projects PV. If the CAPM holds, the tracking portfolio is a combination of the market portfolio and a risk free asset. How to use tracking portfolio valuation The idea is that we are trying to find the future cash flows of the project using a tracking portfolio Assume there is perfect correlation between the Market Portfolio and the Project. 1. Value project using probabilities 2. Assume Tracking Portfolio with mix of Market Portfolio and Risk Free Asset 3. Calculate how much investment is required to track portfolio 4. Conclusion: Since portfolio of financial assets...
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...requirements as well as thinness and discontinuity of trading. It is generally assumed that the emerging markets are less efficient than the developed markets. Raihan, et al (2007) found that in Chittagong Stock Exchange (CSE) in Bangladesh, stock return series do not follow random walk model and the significant autocorrelation co-efficient at different lags do not accept the hypothesis of weak form efficiency. Mobarek and Keasay (2000) also found the same result after conducting research in Dhaka Stock Exchange (DSE) of Bangladesh. Conducting research in Dhaka Stock Exchange (DSE) Rahman, et al (2006) found the negative correlation between the beta and stock return, which is reason for inefficiency of market where the assumptions behind the CAPM model is not supported....
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...Introduction Managing portfolio and investing in stocks is very risky and could be tricky, as a result, financial experts and investors view it as necessary or smart to know what to expect when they invest. Due to this, different statistical models have emerged to attempt to scientifically measure the potential returns on an investment. The Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) are two of such models. The purpose of this essay is to critically compare the Arbitrage Pricing Theory with the Capital Asset Pricing Model as used by fund managers in the United Kingdom. Captial Asset Pricing Model (CAPM) When Sharpe (1964) and Lintner (1965) proposed the Capital Asset Pricing Model (CAPM), it was seen as a leading tool in measuring if an investment will yield in positive or negative returns. It attempts to explain the relationship between investment risk and expected reward of risky securities (Ushad, 2011; Reilly and Brown, 2011; Heshmat, 2012). The CAPM helps to determine the required rate of return for any risky asset (Reilly and Brown, 2011). “The CAPM states that the expected return on a security or a portfolio equals the rate on a risk-free security plus a risk premium” (Heshmat, 2012: 504). It indicates that the expected return on an asset has a positive linear relationship with the non-diversifiable risk of the security (beta) (Heshmat, 2012). Ushad (2011) explains that the CAPM is based on the premise that higher returns should be...
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...research in the a titled “Common Factors in the Expected Returns of Stocks and Bonds” that is known as the “Fama-French Three-Factor Model” Studying the company’s size or the book-to-market ratio may shed light on exposure to sources of systemic risk not captured by the CAPM beta, Fama and French developed the Three Factor Model believing that small stocks may be more sensitive to changes in business conditions and that these variables may capture sensitivity to macroeconomic risk factors. Also, using international data collected by Morgan Stanley Capital International, Fama and French found that high book-to-market stocks outperformed low in almost every country studied. Fama and French also found that in certain years value portfolios were outperformed by growth portfolios across a wide array of countries. Investor cannot expect to lower their risk by diversifying their investments in different countries, which also confirms the belief that value stock is risky. Based on the high level of correlation between value-growth portfolios, DFA introduced international value funds. 2. What do these findings imply for CAPM and EMH? The finds of Fama and French imply that CAPM measure of risk, “beta”, was inaccurate. CAPM was based on the idea that investors...
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...DFA. The company was founded on a sound investment style based on its core belief in sound academic research, passive fund management. Until almost the end of the 20th century DFA had found a way to make money actively with a passive investment strategy. But looking forward, according to me it needs to evolve with the times and look for questions regarding its own strategy and its evolution with the times and the questions facing the financial future. As highlighted by the boom in the I.T sector towards the end of the last century that DFA missed out on completely, DFA on principle is always poised to miss out on new technology companies, as they intrinsically have low book to market value. Also my another objection to DFA’s selection of small cap stocks only is that these category of companies are among the worst hit companies during a financial crisis because of their limited access to credit and most of these companies don’t survive a major recession. Even some proponents of the efficient market hypothesis have argued that due to DFA and similar companies investing in this particular style, this style’s edge had been eroded. Lastly many prominent academicians and financial institutions have called into question the efficacy of the efficient market theory due the financial bubble created in the financial markets. That fact that market price of a stock represents the fair price has been called into question. Most of the big banks now act as quassi-exchanges and...
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...The Development of Modern Finance "A Short History of Value" David Roubaud & Jean-Charles Bagneris 10/2011 The Main Steps of the Theory Building • Portfolio Selection (Markowitz, 1952) • CAPM (Sharpe, 1963) • Financing and Dividend Decisions Neutrality (Modigliani et Miller, 1958, 1961,1963) • Efficient Markets (Fama, 1965, 1970) • Options Pricing Theory (Black & Scholes, 1973, Myers, 1977) • Agency Theory (Jensen, Meckling, 1976) • Efficient Markets II (Fama, 1991) • Behavioural Finance (Kahneman & Tversky, 1979, Shiller, 1981, 2000) Portfolio Selection • Investors are rationals and risk averse • Diversification lowers specific risk • Any portfolio is a combination of the market portfolio and the riskless asset The CAPM Capital Asset Pricing Model • Systematic risk of an asset is measured by its beta coefficient • The model calibrates the risk-return relationship • Simple, elegant and linear model => big success • Low explaining power (strong assumptions) • Alternative models are difficult to use 1 The Development of Modern Finance 2 Financial Markets Efficiency "At any given point in time, assets prices on financial markets account for all available information." • Strong assumptions on: – markets organization – investors behaviour • One consequence of EMH is Random Walk Hypothesis • Assumptions are not always true: 3 forms of efficiency (strong, semi-strong, weak) The irrelevance of financing and dividends decisions In a world without taxes and with perfect financial markets...
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...Premium และคำนวณ Standard Deviationเพื่อนำไปคำนวณหา Sharpe Ratio ที่มีอัตราส่วนที่สูงที่สุด ซึ่งอธิบายถึงผลตอบแทนที่ถูกปรับด้วยความเสี่ยง ที่ดีที่สุด เมื่อได้ทำการวิเคราะห์และคำนวณ Sharpe Ratio แล้ว พบว่า หุ้นที่เหมาะสมที่จะทำการลงทุนเพิ่ม ได้แก่ Pioneer Gypsum โดยลงทุนในสัดส่วน 4% จึงทำให้การลงทุนในตลาดเป็น 96% เนื่องจากเป็นสัดส่วนที่ทำให้ Sharpe Ratio มีค่าสูงที่สุด คือ 0.4702 ซึ่งถือได้ว่าเป็นการกระจายการลงทุนที่ทำให้ความเสี่ยงลดลง 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 ...
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...The History of Finance An eyewitness account. Merton H. Miller MERTON H. MILLER is Robert R. McCormick distinguished ser- vice professor emeritus at the University of Chicago (IL 60637). SUMMER 1999 * * * IT IS ILLEGAL TO REPRODUCE THIS ARTICLE IN ANY FORMAT * * *| t five years, the German Finance Association A is not very old as professional societies go, but then neither is the field of finance itself. Finance in its modern form really dates only from the 1950s. In the forty years since then, the field has come to surpass many, perhaps even most, of the more traditional fields of economics in terms of the numbers of students enrolled in finance courses, the numbers of faculty teaching finance courses, and above all in the quantity and quality of their combined schol-arly output. The huge body of scholarly research in finance over the last forty years falls naturally into two main streams. And no, I don’t mean “asset pricing” and “cor-porate finance,” but instead a deeper division that cuts across both. The division I have in mind is the more fundamental one between what I will call the business school approach to finance and the economics department approach. Let me say immediately, however, that my distinction is purely “notional,” not physical — a dis-tinction over...
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...model is based on two parameter portfolio analysis model developed by Markowitz (1952). This model was simultaneously and independently developed by John Lintner (1965), Jan Mossin (1966) and William Sharpe (1964). In equation form the model can be expressed as follows: E (Ri) = Rf + (i [E(rm) – Rf] = Rf +(im / (m (E(Rm) – Rf / (m) Where E(Ri) is expected return on asset i, Rf is the risk-free rate of return, E(Rm) is expected return on market proxy and (i; is a measure of risk specific to asset i. This relationship between expected return on asset i and expected return on market portfolio is also called the security market line. If CAPM is valid, all securities will lie in a straight line called the security market line in the E(R), (i frontier. The security market line implies that return is a linearly increasing function of risk. Moreover, only the market risk affects the return and the investor receive no extra return for bearing diversifiable (residual) risk. The set of assumptions employed in the development of the CAPM can be summarized as follows [Sears and Trennepohl (1993)]: 1. Investors are risk-averse and they have a preference for expected return and a dislike for risk. 2. Investors make investment decisions based on expected return and the variances of security returns, i.e. two-parameter utility function. 3. Investors behave in a normative sense and desire to hold a portfolio that lies along the efficient...
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...------------------------------------------------- MAF707 Portfolio investments and Financial Planning ------------------------------------------------- Group Assignment Group 77: Weizhe Shi_900443906 Ran Li_210037023 Yichao FU_900387184 Contents Question 1 3 Analysis of securities and the market index 3 Summary 3 Question 2 7 Question 3 8 Question 4. 9 Standard Consumption of CAPM 9 Expectation errors relied on ex-post data 12 Reference List 14 Question 1 Analysis of securities and the market index Summary Firstly we calculated the monthly return of each securities which depend on the data of adjust close price every month. The formula is the latter month’s adjust close price minus the previous monthly adjust close price then divide the latter month’s adjust close price. On the basis of the results, we moved forward the steps that calculate the mean, median, skewnes, kurtosis, variance and correlation coefficients. Those data have been calculated and presented in excels. Definition and Formula 1. Mean The mean value is the average value of monthly return from Jun 2003 to Dec 2010. The formula is: μ=i=1NXiN where N is the number of the month we count of the return and Xi is the total value of the monthly return. 2. Median The median is the value of the middle item of a set of items that has been sorted into ascending or descending order. In an odd-numbered sample...
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