Lecture Notes in Economics and Mathematical Systems Founding Editors: M Beckmann H.P Künzi Managing Editors: Prof Dr G Fandel Fachbereich Wirtschaftswissenschaften Fernuniversität Hagen Feithstr 140/AVZ II, 58084 Hagen, Germany Prof Dr W Trockel Institut für Mathematische Wirtschaftsforschung (IMW) Universität Bielefeld Universitätsstr 25, 33615 Bielefeld, Germany Editorial Board: A Basile, A Drexl, H Dawid, K Inderfurth, W Kürsten 611 Rainer Brosch Portfolios of Real Options Dr Rainer Brosch Berlin, Germany rainer.brosch@whu.edu ISBN 978-3-540-78298-8 e-ISBN 978-3-540-78299-5 DOI 10.1007/978-3-540-78299-5 Lecture Notes in Economics and Mathematical Systems ISSN 0075-8442 Library of Congress Control Number: 2008923931 © 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permissions for use must always be obtained from Springer-Verlag Violations are liable for prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Production: le-tex Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: WMX Design GmbH, Heidelberg Printed on acid-free paper 987654321 springer.com To my sister Christina Foreword Valuing portfolios of options embedded in investment decisions is arguably one of the most important and challenging problems in real options and corporate finance in general Although the problem is common and vitally important in the value creation process of almost any corporation, it has not yet been satisfactorily addressed It is key for any corporation facing strategic resource allocation decisions, be it a pharmaceutical firm valuing and managing its pipeline of drugs, a telecom company having to select a set of technological alternatives, a venture capital or private equity firm investing in a portfolio of ventures, or any company allocating resources Portfolios of real options typically interact such that the value of the whole differs from the sum of the separate parts Thus one must address and value the particular configuration of options embedded in a specific situation, taking into account the configuration of other options already present in the portfolio, which in turn depends on the correlation structure among the various underlying assets and the strategic dependencies among the options themselves (e.g., mutual exclusivity, strategic additivity, compoundness, complementarity etc.) In that sense, optimal decisions also depend on past option exercise decisions by management and organizational capabilities put in place in the past The optimal decision today as to whether to continue operating in the current mode or following the current strategy versus switching to the best among a set of alternative modes or strategies depends in part on the asymmetric costs of switching strategies and potentially the costs and probability of switching back in the future Such asymmetric costs of switching and re-switching contribute to the breakdown of the standard value additivity That is, the overall problem is path dependent and history matters! In a practical setting, organizations oftentimes face internal budgetary, human capital and other organizational constraints From a portfolio perspective, any investment or financial resource commitment explicitly com- VIII Foreword petes with everything else As a result, current commitments of financial, managerial or engineering resources or projects may need to be reduced or abandoned altogether to free up resources that can be devoted to more attractive future investment opportunities The implications of this sort of options portfolio analysis can be non-conventional and far reaching These aspects represent modeling challenges that the thesis of Mr Brosch addresses by a tractable model solving important managerial decision problems In particular, it tackles the portfolio problem head on within an overall budget constraint context in which interdependencies among optional decisions at each point in time and dynamically over time are explicitly considered His thesis sets up a general portfolio valuation framework as a multi-dimensional real options problem involving path-dependent investment and dis-investment decisions and changes in the characteristics of the underlying assets A key aspect of his model is that he explicitly links dynamic (dis-) investment decisions with a global dynamic budget constraint that is both pivotal for deriving the optimal operating policy while it remains relevant in practical applications Mr Brosch formulates his model as a constrained stochastic dynamic program that he subsequently solves He then employs extensive numerical analysis and provides sensitivity results to investigate various portfolio effects He confirms hypothesized deviations from value additivity and that the management of portfolios of real options is a complex task that requires careful, detailed, situation-specific analysis in order to properly capture the value that can be distilled from managing portfolios of real options His model helps provide a general structure capable of handling these real-life complexities, both for the design of an optimal portfolio as well as for the execution or optimal exercise of the embedded options The model properly reflects the inherent complexity of the underlying real-life constrained problem and the non-additivity and path-dependent challenges embedded therein The framework developed by Mr Brosch makes an important theoretical contribution in addressing this important and intellectually challenging portfolio problem, while at the same time it can be of significant value to practicing managers in facing this admittedly complex and difficult practical task of evaluating, managing and optimally exercising the set of interdependent corporate real options Arnd Huchzermeier Vallendar, Germany Lenos Trigeorgis Nicosia, Cyprus Preface Ever since I was a little boy, I was fascinated by investment decisions – not with financial assets in mind, but trucks The bigger, the better However, once it occurred to me that beyond sheer size, equipment with a broader application range may turn out to be more desirable Many years later, taking a Master’s degree in Finance at Frankfurt University, I got hold of a copy of Lenos Trigeorgis’s book “Real Options” It was all there: investment and flexibility, which is at the core of real options However, I didn’t understand how this would work for portfolios So when I met Lenos at the Real Options Conference and asked, he just smiled: “An interesting field – let’s work on it!” Now the work is ready and I hope it can be instrumental to managers and academics alike when dealing with portfolios of real options It was submitted as doctoral thesis at WHU, Otto Beisheim School of Management, chaired by Professor Dr Arnd Huchzermeier and Professor Lenos Trigeorgis, Ph.D I would like to thank Arnd Huchzermeier for his guidance and the inspiring environment he creates at the Department of Production Management, including my opportunity to teach and to visit Stanford University I am grateful to Lenos Trigeorgis who was always close despite the distance, by email or unforgettable meetings, and added both his great esprit and expertise I am thankful to Stefan Spinler, for always being happy to discuss and help Furthermore my thank goes to a friend at a Hightech Company, preferring to remain anonymous, who greatly contributed by discussing the applications I thank my colleagues at the department for making my time at WHU an enjoyable one Also I am grateful to Christian Artmann and Rolf Hellermann for tremendous intellectual and personal support, and for being a pleasure to be with far beyond research Finally, I thank The Boston Consulting Group for financial support X Preface The most thankful I am to my parents, Arnold and Barbara, and my godmother Margret, who created many growth options for my education and my future To my sister Christina and Peter, who are always with me And to Jens and Thomas, for being the great friends they are From my first thoughts about flexibility to my dissertation it has been a challenging but inspiring and rewarding journey The journey goes on and I am looking forward to it Berlin, January 2008 Rainer Brosch Contents Introduction 1.1 Research Questions 1.2 Contribution and Main Results 1.3 Structure 3 Portfolio Approach to Real Options 2.1 Motivation of the Portfolio Approach to Real Options 2.1.1 Real Options and Financial Options 2.1.2 Definition of Portfolios of Real Options 2.1.3 Difference Between Financial Portfolios and Portfolios of Real Options 2.2 Implications for Modeling Approach 2.2.1 Portfolio Aspects 2.2.2 Management of Portfolios of Real Options 2.2.3 Translation into Model Features 7 11 Literature Review 3.1 Financial Portfolio Theory 3.1.1 Mean–Variance Portfolio Analysis 3.1.1.1 Traditional Markowitz Portfolio Selection 3.1.1.2 Capital Asset Pricing Model 3.1.1.3 Intertemporal Capital Asset Pricing Model and Consumption 3.1.1.4 Arbitrage Pricing Theory 3.1.1.5 Conclusion on Mean–Variance Portfolio Analysis 3.1.2 Advanced Financial Portfolio Analysis 3.1.2.1 Portfolio Analysis Considering Higher Moments of Distributions 12 13 14 15 16 21 21 22 22 25 26 27 27 28 28 References 143 Fama, E F (1970): Multiperiod Consumption-Investement Decisions American Economic Review 60(1), pp 163–174 Fama, E F (1976): Foundations of finance: portfolio decisions and securities prices Basic Books, New York (NY) Fama, E F and K F French (1995): Size and Book-to-Market Factors in Earnings and Returns Journal of Finance 50(1), pp 131–155 Fama, E F and K R French (1992): The Cross-Section of Expected Stock Returns Journal of Finance 47(2), pp 427–465 Fama, E F and K R French (1993): Common Risk Factors in the Returns on Stocks and Bonds Journal of Financial Economics 33(1), pp 3–56 Fama, E F and K R French (1996): Multifactor Explanations of Asset Pricing Anomalies Journal of Finance 51(1), pp 55–84 Fang, H and T.-Y Lai (1997): Co-Kurtosis and Capital Asset Pricing Financial 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Management 2(1), pp 25–33 Williams, H P (1993): Model building in mathematical programming 3rd ed., John Wiley & Sons, Chichester Wilmott, P (1998): Derivatives: The theory and practice of financial engineering John Wiley & Sons, Chichester Wong, H Y and Y.-K Kwok (2003): Multi-asset barrier options and occupation time derivatives Applied Mathematical Finance 10(3), pp 245–266 Zenios, S A and M S Shtilman (1993): Constructing Optimal Samples from a Binomial Lattice Journal of Information and Optimization Sciences 14(2), pp 125–147 Index applications manufacturing, 2, 39, 40, 53, 94 R&D, 38, 52 supply chain management, 2, 32, 39 budget constraint balance equation, 18, 51, 55, 106, 109, 133 hard rationing, 35 modeling, 52, 54 soft rationing, 35 capital budgeting decision tree analysis, 33 definition, 32 interactions, 34 knapsack, 33 mathematical programming, 32 portfolio perspective, 33, 34 synergies, 35 financial options American Option, barrier option, 107, 128 call option, compound option, 11, 14, 31, 37, 43, 49, 50, 62, 114, 132, 133 definition, 2, European option, option on the maximum, 31, 36, 61, 64, 98, 109, 110, 127, 133 financial portfolio theory APT, 27 CAPM, 25 diversification, 23 efficient frontier, 23 frictions, 29 higher moments, 28 ICAPM, 26 Markowitz, 22 minimum variance portfolio, 23 portfolio selection, 22 interactions inter–project, 12, 14, 17, 38, 39, 50, 131, 133 intra–project, 12, 14, 17, 38, 50, 131, 133 model formulation change of underlying, 4, 10, 17, 80, 131 correlation, 14, 16, 24, 30, 32, 33, 38, 48, 59, 109, 114, 117, 118, 122, 125, 128 forward–backward looking, 17, 42, 55, 68, 75, 133 lattice tree, 42, 48, 51, 56, 59, 64, 66, 71, 79, 88 overview, 16 path dependency, 14, 15, 17, 39, 52, 53, 66, 86, 90, 91, 93, 107, 112, 127, 133 risk–neutral valuation, 33, 47, 54, 56, 64, 71, 75, 78, 83, 110, 118, 122 152 Index stochastic process, 9, 40, 48, 54, 56, 66, 75, 80, 83, 84, 95, 133 stochastic program, 4, 17, 39, 41, 48, 54, 60, 63, 66, 71, 75, 84, 133 model implementation efficiency, 85, 87, 136 GAMS, 17, 55, 85, 133 linearization, 85, 134 optimality, 55, 63, 86, 87, 133 option pricing redundant, 29 replication, 21, 22, 29, 52, 84 self–financing, 29, 52 portfolios of real options definition, 12 design, 15 execution, 15 portfolio aspects, 14 portfolio management, 6, 15, 51, 53, 106, 109, 128, 134–137 real options definition, 1, interdependencies, parameters, types, recursion, 39, 55, 58, 59, 63, 65 strategic management, 2, 15, 30, 129, 132, 137 utility, 23, 26, 28 List of Tables 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 Capacity factors for two underlying assets Switching costs for asset (two underlying assets) Switching costs for asset (two underlying assets) Portfolio highlighting budget effects Portfolio with value decreasing in volatility Portfolio highlighting path–dependency for T=3 Capacity factors for three underlying assets Switching costs for asset (three underlying assets) Switching costs for asset (three underlying assets) Switching costs for asset (three underlying assets) Portfolio examples with underlying assets Correlation structure Scenarios and risk–neutral probabilities for three underlying assets Specification of risk–neutral probabilities for n = assets (i = 1, 2, 3) in scenarios Three underlying assets – base case Three underlying assets – changed correlation Three underlying assets – increased budget allowance Three underlying assets – increased budget allowance and increased volatility Stand–alone vs portfolio perspective on real options 95 97 97 100 107 113 116 116 116 116 117 118 119 121 121 122 123 125 129 List of Figures 2.1 2.2 2.3 Payoff structure of a call option Portfolio design process Modeling approach 16 18 3.1 Mean–variance efficient portfolios 24 4.1 4.2 4.3 Dynamic budgets depending on time, scenarios, and actions Recombining binomial lattice tree for one underlying asset Recombining binomial lattice tree for two underlying assets, with ρ12 = Three–dimensional risk–neutral probabilities Non–recombining binomial lattice tree for one underlying asset Indexing in a three–dimensional lattice tree Change of the underlying asset Change of the underlying asset in the multinomial grid Dimensionality for two underlying assets 51 58 Portfolio landscape Portfolio value as a step–function of budget allowance Small change in portfolio value Substantial change in portfolio value Comparison of optimal investment strategies Portfolio value decreasing in σ1 Portfolio value decreasing in ρ Portfolio value increasing in α1 and α2 Path–dependency of underlying asset Optimal strategy for three underlying assets - base case Optimal strategy for three underlying assets - changed correlation 99 100 101 102 103 108 110 112 113 120 4.4 4.5 4.6 4.7 4.8 4.9 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 59 60 66 72 80 81 88 122 156 List of Figures 5.12 Optimal strategy for three underlying assets - increased budget 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portfolios of real options as a sum of the parts • Adding to the non–additivity of real options, budget constraints... volatility of an underlying asset can increase the value of a portfolio of real options related to this asset, but in fact can also reduce the value of a portfolio of real options • Portfolio values of. .. focused introduction of the general concept of real options, and the definition of the resulting portfolio problem 2.1.1 Real Options and Financial Options The term real options was coined by