...Derivation of the Capital Asset Pricing Model - CAPM [pic] E(xi) expected return on the asset i r risk free rate E(xm) expected return on the market portfolio (S&P index) (i i-th asset’s systematic risk (a proportion of market risk) Optimal investment proportions - each individual investor on the market attempts to reach the highest feasible market line. The Market line can be found by minimising the standard deviation (o for any given portfolio‘s expected return E(xo). [pic] [1] [pic] [2] where pi is the proportion of the portfolio invested in i-th asset. Define the function C as follows [pic] [3] where ( is a Lagrange multiplier, and the expression in brackets equals zero. We are trying to find the optimal proportion of each asset, which minimises the risk of optimal portfolio. The Market line can be found analytically by differentiating equation [3] with respect to each pi and with respect to Lagrange multiplier and setting the first derivatives equal to zero. This yields n+1 equations. [pic] [4.1] [pic] [4.2] [pic] [4.3] [pic] [4.4] Let’s now take the set of equations [4.x] and multiply them by p1, p2 etc. We obtain: [pic] [5.1] [pic] [5.2] … [pic] [5.3] [pic] [5.4] If we sum up the equations [5.1] to [5.3], we obtain [pic] [6] The term in the bracket on the left-hand side is a variance of the optimal portfolio (o2. Substituting it for the bracketed expression on the LHS and...
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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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...MSc Corporate Finance Dr. Kirak Kim Before we start Main branches of finance Corporate Finance How do we value projects and (optimally) finance them? Asset Pricing How do we price securities more precisely? What’s the difference? Is it a Corporate Finance question or an Asset Pricing question? □ You are the manager of Intel Corp. You are reviewing the proposal for the new plant to be built in China. The new plant requires a large onetime investment but will provide significant capacity addition as well as cost savings over the next 10 years. Should you approve the proposal for the new plant? □ “HSBC FTSE 100” is a index fund that replicates FTSE 100 index. The fund offers investors a convenient diversification at a low price. Would you be interested in investing in the fund (or somewhere else)? » What if it was TESCO that was considering HSBC FTSE 100 as an investment vehicle? □ In 2004, Sergey Brin and Larry Page, the founders of Google Inc., were talking to investment bankers from Morgan Stanley. They hope to finance a number of potential opportunities through IPO (initial public offering). One of the most important concerns is of course what the offering price should be. Part 1 Project Valuation Dr. Kirak Kim MSc Corporate Finance EFiMM0017 Project Valuation Investment decision Revisit: Valuing unlevered cash flows Revisit: Uncertainty and the notion of risk Weighted average cost of capital Adjusted present value Two Main...
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...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 unrealistic because...
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...1) The four components of Marriott’s financial strategy are to manage rather than own hotel assets, to invest in projects that increase shareholder value, to optimize the use of debt in the capital structure, and to repurchase undervalued shares when necessary. Marriott’s growth objective is to become the preferred employer and provider in lodging, contract services (such as catering), and restaurants, and to be the most profitable company in their industry. By choosing to manage hotel properties instead of owning them Marriott lowers their accounting assets on the books, therefore increasing their return on assets as compared to owning the properties outright. This strategy also effectively shares the risk that comes from the properties, and lets Marriott operate with more liquidity, offering them the opportunity to relocate their hotel or restaurant operations without the need to sell properties, for instance. Marriott can analyze potential projects and discount the future cash flows to determine which projects will have a higher net present value, and ultimately which will be most profitable to Marriott at the present time, therefore increasing shareholder wealth. Balance sheets reflect all company debt, so by reducing debt Marriott can decrease their Debt to Equity ratio, becoming more attractive to new and existing shareholders. Marriott’s plan to repurchase shares when they are undervalued can positively affect share price and therefore shareholder value, but it is not...
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...AC 3047 CORPORATE FINANCE Lecture #1: Introduction Portfolio theory Intro to CAPM ©Professor Hans K. Hvide Do not quote without permission. Although considerable effort will be exerted to avoid errors in these notes, I do not guarantee that they are error-free. 1 Central concepts for this week • Risk-return trade-off • Covariance (between individual assets) • Efficient Frontier • Market portfolio (choice of the rational investor) ↓ • Capital Market Line • Security Market Line • Cost of capital - Firm: the returns that are necessary to attract capital - Investor: returns that the capital markets offers for comparable investments Readings this week: Brealey, Myers & Allen (BMA), Corporate Finance 8th edition, chapters 7, 8, 9. 10 1. Portfolio theory • Criteria for choice of optimal portfolio by risk-averse rational agents • Mean/variance analysis • Market portfolio Note: static world with only one point in time. Definitions: - Financial asset = stream of income, typically uncertain, with a given risk/return profile - Portfolio = mix of financial assets 11 1.1 Expected returns for portfolio (2 assets) Let E(Z) be the expectation (expected value) of a random variable Z = probability-weighted midpoint of the distribution of Z. E(RP) = x1E(r1) + (1-x1)E(r2) (1) E(RP) = Expected portfolio return xi = Share of investment in asset i, (i = 1, 2) E(ri) = Expected return asset i, (i=1, 2) Expected portfolio...
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...McDonald / J Zhejiang Univ SCI 2004 5(5):499-508 499 Journal of Zhejiang University SCIENCE ISSN 1009-3095 http://www.zju.edu.cn/jzus E-mail: jzus@zju.edu.cn The Q theory of investment, the capital asset pricing model, and asset valuation: a synthesis MCDONALD John F. (College of Business Administration, University of Illinois at Chicago, Chicago, USA) E-mail: mcdonald@uic.edu Received Feb. 23, 2004; revision accepted Mar. 6, 2004 Abstract: The paper combines Tobin’s Q theory of real investment with the capital asset pricing model to produce a new and relatively simple procedure for the valuation of real assets using the income approach. Applications of the new method are provided. Key words: Investment theory, Asset pricing, Appraisal Document code: A CLC number: F832.48 INTRODUCTION This paper combines the economic theory of real investment and the standard financial model of asset pricing to produce a method for the valuation of real assets; and intentionally uses relatively simple versions of these two theories to link economics, finance, and appraisal. Numerical examples using data on real estate assets illustrate the valuation method. The Q theory of investment, introduced by James Tobin (1969), is popularly accepted theory of real investment hypothesized to be a positive function of Q, defined as the ratio of the market value to the replacement cost of capital. Standard presentation of the theory, such as that of Romer (1996), shows that Q is the...
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...Notes 9: Expansion Decisions Objectives: To review analytical techniques used to justify expansion decisions To compare and contrast the NPV and APV methods of analysis Nature of expansion decisions Expansion cash flows Valuation alternatives: NPV; APV Derivation of NPV model Derivation of APV model Capital structure issues Topics: Initial Capital investment Additional Capital investment For replacement and expansion - $ FCF FCFs are a function of value chain and industry economics Expansion FCFs are incremental to the base case and are attributable to the project. Because they include incremental revenues the full NPV equation is used to accept (accept if NPV>0) If we are using the EBIT formulation for estimating FCF we have: FCF= (EBIT)(1-T) + T(CCA) + NWC + Capex The cash flow elements to be estimated are: • net operating cash flows after tax (a.k.a. NOPAT, net operating profit after tax)(EBIT)(1-T) • the tax shield on Capital Cost TCCA • Incremental net working capital requirements NWC • incremental long-term assets Capex. At the end of the study period we also have estimates of cash inflow from sale of residual assets (RV), or the present value of FCFs which extend beyond the study period called continuing value (CV) RSM 2301 Financial Management - Fall 2011 © Asher Drory All rights reserved 9- 3 Valuation Alternatives: NPV vs. APV Models Net Present Value (NPV) NPV Expansion Decisions...
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...Interpreting Beta Introduction: In 1990, William Sharpe won a Nobel Prize in Economics for his work in developing the Capital Asset Pricing Model (CAPM). Traditionally the CAPM has been the basis for calculating the required return to the shareholder. This figure in turn has been used to calculate the economic value of the stock and the Weighted Average Cost of Capital (WACC) for capital budgeting. In recent years, the CAPM has been attacked as an incomplete model for explaining market pricing behavior, but academics and practitioners cannot agree on a good replacement. And so the CAPM remains an important model in practical investment and financial management decision making. Calculating Beta: The most important component in calculating the required return to shareholder (from the CAPM) is the company’s beta. The CAPM can be succinctly stated as: k s k RF k M k RF s k RF Market Risk Premium s [1] The original model was conceived of theoretically, and was expected to be forward looking. Careful reading of Sharpe’s original work show that the market assesses systematic risk looking at expected future covariance of the company’s returns with that of the overall market. It is assumed that these covariances are unbiased and efficient estimates of the observed relationships ex post facto. Traditionally the CAPM relationship is estimated using simple regression on historical outcomes, where ks is the y variable, and kM-kRF (or the market risk premium)...
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...relationship of assets and their valuation. For the single asset held in isolation, risk is measured with the probability distribution and its associated statistics: the mean, the standard deviation, and the coefficient of variation. The concept of diversification is examined by measuring the risk of a portfolio of assets that are perfectly positively correlated, perfectly negatively correlated, and those that are uncorrelated. Next, the chapter looks at international diversification and its effect on risk. The Capital Asset Pricing Model (CAPM) is then presented as a valuation tool for securities and as a general explanation of the risk-return trade-off involved in all types of financial transactions. PMF DISK This chapter's topics are not covered on the PMF Tutor or PMF Problem-Solver. PMF Templates Spreadsheet templates are provided for the following problems: Problem Topic Self-Test 1 Portfolio analysis Self-Test 2 Beta and CAPM Problem 5-7 Coefficient of variation Problem 5-26 Security market line, SML Study Guide The following Study Guide examples are suggested for classroom presentation: Example Topic 4 Risk attitudes 6 Graphic determination of beta 12 Impact of market changes on return ANSWERS TO REVIEW QUESTIONS 5-1 Risk is defined as the chance of financial loss, as measured by the variability of expected returns associated with a given asset. A decision maker should evaluate an investment by measuring the chance of...
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...FIN 7013 - Assignment 5 Dennis Agnew Northcentral University FIN 7013 - Assignment 5 According to theory stock returns have shown a noticeable volatility; thus if an investor desires to increase expected returns she must face a higher level of risk. Similarly, it has been proven that owing a group of financial securities can assist the investor to improve the return/risk tradeoff; that is owing eight stocks will produce an improved return/risk product over time versus owing one stock. Therefore, in evaluating a portfolio it is critically important to compare returns and risks involved; but in order to compare and evaluate returns and risks the investor has to know how to calculate these two important criteria (Markowitz, 1970). The return of a stock is based on its current price, its expected price plus distributed dividends. Therefore, if the current price of a stock is $40.00, its expected market price, let us say after a year, is increased to $50.00 and the distributed dividends amount to $5.00, its return is calculated as: [(Pt-Po) + DIV]/Po; Po is the current price of the stock, Pt is the price of the stock after one year and DIV are the distributed dividends per share. Substituting the above assumed numbers into the equation we have [($50-$40) +$5]/$40 = 0.25 or 25%. The risk of a stock is mainly measured by the standard deviation (Markowitz, 1987). In the case of a portfolio the expected return is the weighted average return of the returns of all the stocks...
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...THE BOEING 7E7 Teaching Note Synopsis and Objectives In 2003, the Boeing Company announced plans to build a new “super-efficient” commercial jet called the “7E7” or “Dreamliner.” This was a “bet the farm” gamble by Boeing, similar in magnitude to its earlier introductions of the 747 and 777 airliners. The technological superiority of the new airframe, as well as the fact that it would penetrate a rapidly growing market segment, were arguments for approval of the project. On the other hand, the current market for commercial airplanes was depressed because of terrorism risks, war, and SARS, a contagious illness that resulted in global travel warnings. Boeing’s board of directors would need to weigh those considerations before granting final approval to proceed with the project. The task for students is to evaluate the 7E7 project against a financial standard, the investors’ required returns. The case gives internal rates of return (IRR) for the 7E7 project under base-case and alternative forecasts. The students must estimate a weighted-average cost of capital (WACC) for Boeing’s commercial-aircraft business segment in order to evaluate the IRRs. As a result of that analysis, the students identify the key value drivers and distinguish, on a qualitative basis, the key gambles that Boeing is making. The general objective of this case is to exercise students’ skills in estimating a weighted-average cost of capital and cost of equity. The need for students...
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...THE BOEING 7E7 Teaching Note Synopsis and Objectives In 2003, the Boeing Company announced plans to build a new “super-efficient” commercial jet called the “7E7” or “Dreamliner.” This was a “bet the farm” gamble by Boeing, similar in magnitude to its earlier introductions of the 747 and 777 airliners. The technological superiority of the new airframe, as well as the fact that it would penetrate a rapidly growing market segment, were arguments for approval of the project. On the other hand, the current market for commercial airplanes was depressed because of terrorism risks, war, and SARS, a contagious illness that resulted in global travel warnings. Boeing’s board of directors would need to weigh those considerations before granting final approval to proceed with the project. The task for students is to evaluate the 7E7 project against a financial standard, the investors’ required returns. The case gives internal rates of return (IRR) for the 7E7 project under base-case and alternative forecasts. The students must estimate a weighted-average cost of capital (WACC) for Boeing’s commercial-aircraft business segment in order to evaluate the IRRs. As a result of that analysis, the students identify the key value drivers and distinguish, on a qualitative basis, the key gambles that Boeing is making. The general objective of this case is to exercise students’ skills in estimating a weighted-average cost of capital and cost of equity. The need...
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...CONCORDIA UNIVERSITY John Molson School of Business - Department of Finance Portfolio Management - FINA 411/2/A, C Course Outline – Fall 2014 Instructor: Dr. Abraham I. Brodt Office: MB 12.215 Tel: 848-2424-2997 Fax: 848-4500 E-mail: ABrodt@jmsb.concordia.ca [SUBJECT: FINA 411 …….] Classes: FINA 411/2A Mondays 11:45 - 14:30 [MB1.437] FINA 411/2C Wednesdays 11:45 - 14:30 [MB5.255] Office Hours: Mondays and Wednesdays 15:30 -- 16:30 [Please e-mail me first to confirm] and by appointment COURSE DESCRIPTION: This course focuses on modern investment theory and its application to the management of entire portfolios. It will consist of lectures, discussions of cases and articles, and video presentations. Topics include: a) construction of optimal asset portfolios using techniques such as the single index model, b) extensions of the capital asset pricing model: theory and tests; example, the zero-beta model, c) criteria for evaluation of investment performance, d) active vs. passive portfolio management, e) investment strategies. The Formula Growth Investment Centre Lab will be used to demonstrate the use of specialized investment software. Computer exercises are assigned to illustrate the application of the theory. Prerequisites: FINA 380 or 385; FINA 390 or 395. LEARNING OBJECTIVES To understand the theory and practice of Portfolio Management for Individuals and Institutions, e.g. Endowments, Mutual Funds, Pension Plans, etc. ...
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...Corporate Evaluation of Philip Morris International Study Programme Master of Business Administration (MBA) Module: Assignment: Course Instructor: Financial Management No 1/1 Authors: Student ID Number: 1st Academic Semester 2013 Place, Date Dortmund, 28th February 2014 Corporate Evaluation of Philip Morris International I Executive Summary The task of this assignment was to evaluate a company (if possible, listed) by two different evaluation methods: DCF method and multiplier method. The DCF analysis is divided into two separate evaluations: DCF entity method (WACC) and DCF equity method. In addition to calculating a corresponding theoretical foundation as well as a critical analysis of assessment methods / results was expected. Philip Morris International, as one of the biggest cigarette sellers of the world, is evaluated in this assignment to date of 31st December 2012. During evaluation by multiplier method the multipliers “price-earnings-ratio” and “market capitalization / EBITDA” were chosen and as peer companies British American Tobacco p.l.c., Imperial Tobacco Group p.l.c. and Japan Tobacco Inc. were used. The result of Philip Morris International evaluation by multiplier method is a value between $111 billion and $160 billion. The theoretical analysis of the different evaluation methodologies indicated that an evaluation by multiplier method can only give a rough guidance of the real corporate value. The evaluation by DCF method result...
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