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Portfolio Theory & Financial Analyses: Exercises Robert Alan Hill Portfolio Theory & Financial Analyses: Exercises Download free ebooks at bookboon.com 2 Portfolio Theory & Financial Analyses: Exercises © 2010 Robert Alan Hill & Ventus Publishing ApS ISBN 978-87-7681-616-2 Download free ebooks at bookboon.com 3 Portfolio Theory & Financial Analyses: Exercises Contents Contents Part I: An Introduction 7 1. An Overview 7 Introduction 7 Exercise 1.1: The Mean-Variance Paradox 8 Exercise 1.2: The Concept of Investor Utility 10 Summary and Conclusions 10 Selected References (From PTFA) 11 Part II: The Portfolio Decision 13 2. Risk and Portfolio Analysis 13 Introduction 13 Exercise 2.1: A Guide to Further Study 13 Exercise 2.2: The Correlation Coefficient and Risk 14 Exercise 2.3: Correlation and Risk Reduction 16 Summary and Conclusions 18 Selected References 19 3. The Optimum Portfolio 20 Introduction 20 Exercise 3.1: Two-Asset Portfolio Risk Minimisation 21 Exercise 3.2: Two-Asset Portfolio Minimum Variance (I) 24 e Graduate Programme I joined MITAS because for Engineers and Geoscientists I wanted real responsibili Maersk.com/Mitas Month 16 I wwasas a construction supervisor in Please click the advert the North Sea advising and Real work hhelpinge foremen InternationalInternationaal opportunities reeree workworo placements ssolve problems Download free ebooks at bookboon.com 4 Portfolio Theory & Financial Analyses: Exercises Contents Exercise 3.3: Two-Asset Portfolio Minimum Variance (II) 27 Exercise 3.4: The Multi-Asset Portfolio 29 Summary and Conclusions 30 Selected References 30 4. The Market Portfolio 31 Introduction 31 Exercise 4.1: Tobin and Perfect Capital Markets 32 Exercise 4.2: The Market Portfolio and Tobin’s Theorem 34 Summary and Conclusions 39 Selected References 40 Part III: Models of Capital Asset Pricing 41 5. The Beta Factor 41 Introduction 41 Exercise 5.1: The Derivation of Beta Factors 42 Exercise 5.2: The Security Beta Factor 43 Exercise 5.3: The Portfolio Beta Factor 45 Summary and Conclusions 46 Selected References 46 6. The Capital Asset Pricing Model (CAPM) 48 Introduction 48 Exercise 6.1: Market Volatility and Portfolio Management 48 Please click the advert www.job.oticon.dk Download free ebooks at bookboon.com 5 Portfolio Theory & Financial Analyses: Exercises Contents Exercise 6.2: The CAPM and Company Valuation 54 Summary and Conclusions 56 Selected References 58 7. Capital Budgeting, Capital Structure and the CAPM 59 Introduction 59 Exercise 7.1: The CAPM Discount Rate 59 Exercise 7.2: MM, Geared Betas and the CAPM 60 Exercise 7.3: The CAPM: A Review 62 Conclusions 66 Summary and Conclusions 67 Selected References 68 Appendix 69 Please click the advert Download free ebooks at bookboon.com 6 Portfolio Theory & Financial Analyses: Exercises An Overview Part I: An Introduction 1. An Overview Introduction In a world where ownership is divorced from control, characterised by economic and geo-political uncertainty, our companion text Portfolio Theory and Financial Analyses (PTFA henceforth) began with the following question. How do companies determine an optimum portfolio of investment strategies that satisfy a multiplicity of shareholders with different wealth aspirations, who may also hold their own diverse portfolio of investments? We then observed that if investors are rational and capital markets are efficient with a large number of constituents, economic variables (such as share prices and returns) should be random, which simplifies matters. Using standard statistical notation, rational investors (including management) can now assess the present value (PV) of anticipated investment returns (ri) by reference to their probability of occurrence, (pi) using linear models based on classical statistical theory. Once returns are assumed to be random, it follows that their expected return (R) is the expected monetary value (EMV) of a symmetrical, normal distribution (the familiar “bell shaped curve” sketched overleaf). Risk is defined as the variance (or dispersion) of individual returns: the greater the variability, the greater the risk. Unlike the mean, the statistical measure of dispersion used by the market or management to assess risk is partly a matter of convenience. The variance (VAR) or its square root, the standard deviation ( = VAR) is used. When considering the proportion of risk due to some factor, the variance (VAR = 2) is sufficient. However, because the standard deviation () of a normal distribution is measured in the same units as the expected value (R) (whereas the variance (2) only summates the squared deviations around the mean) it is more convenient as an absolute measure of risk. Moreover, the standard deviation () possesses another attractive statistical property. Using confidence limits drawn from a Table of z statistics, it is possible to establish the percentage probabilities that a random variable lies within one, two or three standard deviations above, below or around its expected value, also illustrated below. Download free ebooks at bookboon.com 7 Portfolio Theory & Financial Analyses: Exercises An Overview Figure 1.1: The Symmetrical Normal Distribution, Area under the Curve and Confidence Limits Armed with this statistical information, investors and management can then accept or reject investments (or projects) according to a risk-return trade-off, measured by the degree of confidence they wish to attach to the likelihood (risk) of their desired returns occurring. Using decision rules based upon their own optimum criteria for mean-variance efficiency, this implies management and investors should determine their desired: - Maximum expected return (R) for a given level of risk, (). - Minimum risk () for a given expected return (R). Thus, it follows that in markets characterised by multi-investment opportunities: The normative wealth maximisation objective of strategic financial management requires the optimum selection of a portfolio of investment projects, which maximises their expected return (R) commensurate with a degree of risk () acceptable to existing shareholders and potential investors. Exercise 1.1: The Mean-Variance Paradox From our preceding discussion, rational-risk averse investors in reasonably efficient markets can assess the likely profitability of their corporate investments by a statistical weighting of expected returns. Based on a normal distribution of random variables (the familiar bell-shaped curve): - Investors expect either a maximum return for a given level of risk, or a given return for minimum risk. - Risk is measured by the standard deviation of returns and the overall expected return measured by a weighted probabilistic average. Download free ebooks at bookboon.com 8 Portfolio Theory & Financial Analyses: Exercises An Overview To illustrate the whole procedure, let us begin simply, by graphing a summary of the risk-return profiles for three prospective projects (A, B and C) presented to a corporate board meeting by their financial Director These projects are mutually exclusive (i.e. the selection of one precludes any other). Expected Return (R) R (B) B A R (A,C) C Risk () (A) (B), (C) Figure 1.2: Illustrative Risk-Return Profiles Required: Given an efficient capital market characterised by rational, risk aversion, which project should the company select, assuming that management wish to maximise shareholder wealth? AN INDICATIVE OUTLINE SOLUTION Mean-variance efficiency criteria, allied to shareholder wealth maximisation, reveal that project A is preferable to project C. It delivers the same return for less risk. Similarly, project B is preferable to project C, because it offers a higher return for the same risk. - But what about the choice between A and B? Here, we encounter what is termed a “risk-return paradox” where investor rationality (maximum return) and risk aversion (minimum variability) are insufficient managerial wealth maximisation criteria for selecting either project. Project A offers a lower return for less risk, whilst B offers a higher return for greater risk. Think about these trade-offs; which risk-return profile do you prefer? Download free ebooks at bookboon.com 9 Portfolio Theory & Financial Analyses: Exercises An Overview Exercise 1.2: The Concept of Investor Utility The risk-return paradox cannot be resolved by statistical analyses alone. Accept-reject investment criteria also depend on the behavioural attitudes of decision-makers towards different normal curves. In our previous example, corporate management’s perception of project risk (preference, indifference and aversion) relative to returns for projects A and B. Speculative investors among you may have focussed on the greater upside of returns (albeit with an equal probability of occurrence on their downside) and opted for project B. Others, who are more conservative, may have been swayed by downside limitation and opted for A. For the moment, suffice it to say that, there is no universally correct answer. Ultimately, investment decisions depend on the current risk attitudes of individuals towards possible future returns, measured by their utility curve. Theoretically, these curves are simple to calibrate, but less so in practice. Individually, utility can vary markedly over time and be unique. There is also the vexed question of group decision making. In our previous Exercise, whose managerial perception of shareholder risk do we calibrate; that of the CEO, the Finance Director, all Board members, or everybody who contributed to the decision process? And if so, how do we weight them? Required: Like much
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