Marek Jarzęcki, MSc. The use of prospect theory in the option approach to the financial evaluation of corporate investments

Transcription

1 FACULTY OF MANAGEMENET DEPARTMENT OF CORPORATE FINANCE Marek Jarzęcki, MSc The use of prospect theory in the option approach to the financial evaluation of corporate investments Abstract of the Doctoral Thesis Supervisor: Jacek Mizerka, Prof. PUEB Auxiliary supervisor: Joanna Lizińska, PhD Poznań 2017

2 1. Justification of the thesis subject Within the neoclassical finance literature numerous corporate investment evaluation methods have been developed, including those based on discounted cash flows, whose aggregated net present value (NPV) is used as a criterium of investment profitability. The above-mentioned approach of investment project valuation is widely accepted both in theory and in practice. Despite obvious advantages of the NPV method, some shortcomings of this measure have been noticed over time. These include its static nature, understood as the failure to take into account the decision-making flexibility associated with corporate investments. An investment project usually involves a certain degree of flexibility related to the possibility to delay its launch as well as to influence its later execution (change its scale, suspend, terminate, etc.). The NPV overlooks the possibility (but not the obligation) to take actions that affect the value of an investment project at its implementation phase, as new information about the environment arise. As an analogy between this flexibility and financial options had been identified, it was proposed to estimate its value by using financial option valuation methods, and the approach itself was called the real option approach. Real option valuation based on the simple analogy to financial options, however, encounters numerous limitations, like ignoring the existence of competition. Meanwhile, most real options are shared, what translates to the possibility of their earlier exercise by competitors. In such a situation, within the neoclassical approach, it is proposed to use elements of game theory, useful in the analysis of strategic situations. Under the real option approach, developed within the neoclassical finance theory, both full rationality of individuals and their decision-making based on the expected utility theory are assumed. Moreover, game theory requires the fulfilment of rigorous assumptions about players full rationality and common knowledge. At the same time, rich achievements of behavioural economics point to numerous limitations of individuals rationality, including psychological and social inclinations related to economic decision making. While the expected utility theory is fully validated as a normative concept of economic decision making by individuals, its descriptive qualities are the subject of lively academic discussions. The game-theoretical models of strategic situations are, likewise, consistent with the homo oeconomicus concept, while their descriptive and predictive qualities may be limited in some situations. Particularly in the case of interdependent decisions of competitors, in order to derive normative prescriptions which would allow to make optimal economic decisions, it is crucial to accurately forecast the real actions of the opponents. In this context, a model based on the assumption of 2

3 full rationality of all players can lead to suboptimal solutions. A fully rational player should strive to take into account the limited rationality of other players. It requires appropriate modelling of their actual perception and decision-making processes, bearing in mind the achievements of behavioural economics. In the case of shared options, this means valuing options including behavioural inclinations of the competitors. A descriptive model of decision-making under risk, developed by behavioural economics, is prospect theory [Kahneman and Tversky 1979]. It points to people s perception of values in relative terms, as gains or losses relative to a certain reference point. Prospect theory reflects the phenomena related to the perception of values and probabilities such as limited sensitivity to subsequent increases in gains and losses, loss aversion or limited sensitivity to changes of probabilities. In its later, cumulative form, prospect theory [Tversky and Kahneman 1992] assumes that the process of assigning weights to decision scenarios is based on the increments of probabilities rather than their absolute values. Prospect theory is a descriptive model of decision-making under risk, where risk is embedded in the essence of real options. The value of decision-making flexibility associated with an investment project is based on the chance to exploit emerging opportunities, which are related to the uncertainty concerning the future state of the environment. Attempting to model the actual valuation of real options made by competitors requires consideration of the accompanying behavioural inclinations. It is necessary to use an adequate descriptive model of perception of values under risk, which is prospect theory. Numerous examples of studies demonstrating the influence of behavioural factors on the option value, including especially the phenomena described by prospect theory, can been found in the literature. This relates both to financial options [Shefrin and Statman 1993; Poteshman and Serbin 2003; Abbink and Rockenbach 2005; Blackburn and Ukhov 2006; Versluis, Lehnert and Wolff 2010; Nardon and Pianca 2012, 2014, 2015] and real options [Miller and Shapira 2004; Yavas and Sirmans 2005; Tiwana et al. 2007; Oprea et al. 2009; Hackbarth 2009; Wang, Bernstein, and Chesney 2012a, 2012b; Murphy, Andraszkiewicz, and Knaus 2016]. There are also some propositions of introducing behavioural factors into the valuation models [Gentry 2006; Grenadier and Wang 2007; Wang, Beng and Zhang 2007; Hoang 2008; Jost and Wolff 2010; Wu-Xiang 2006, 2007], which includes prospect theory [Versluis, Lehnert, and Wolff 2010; Nardon and Pianca 2012, 2014, 2015]. However, none of the contributions mentioned above deals with real options, which would allow to take into account their specificity, especially its impact of individualized perception of values and probabilities on their values [Abbink and Rockenbach 2005]. Real option valuation is to 3

4 a greater extent influenced by specific characteristics of individuals than financial options, as real options are not traded on a public market. Besides, the models indicated above do not include the reference point, which is of particular relevance within prospect theory and may significantly affect the value and exercise time of an option. Moreover, no numerical option valuation model (such as a binomial model) including elements of prospect theory has been identified in the literature so far. Such a model would be of much broader applicability than an analytical one, by reason of simplicity. Also no model of American option valuation has been found, while most of real options can be exercised before their expiration date. As a consequence, none of the previous option valuation models incorporating elements of prospect theory allows for the analysis of when options are exercised, depending on individual perception of values and probabilities of the option holder. 2. Research objectives Following the motivation for the research presented above, the main goal of the dissertation was formulated to contribute to the literature. The main purpose of the dissertation is to create a model of real option valuation including elements of prospect theory. The analysis covers the evaluation phase, based on specific and known characteristics of real options. The constructed model assumes the perception of values and probabilities according to prospect theory, that is in the form of gains or losses relative to a certain reference point, and the calculation of the prospect value by using the weighting function and the value function. The implementation of the presented main objective requires the achievement of the following detailed objectives: 1. discussion of the neoclassical approach to the evaluation of investment efficiency, taking into account the value of decision-making flexibility associated with the project, 2. systematization of the elements of behavioural finance, including prospect theory, relevant for the valuation of real options, 3. construction of a one-period binomial real option valuation model including elements of prospect theory, 4. construction of a one-period analytical 1 real option valuation model including elements of prospect theory, 1 Within this dissertation, two versions of the model are proposed: a numerical model, based on a discretetime analysis of binomial trees, as well as a continuous-time model in analytical form. The author of the dissertation is aware of the varied nature of the two categories "binomial model" and "analytical model", but chose to use them nonetheless, for the sake of clarity of both terms, reflecting the essential features of both approaches. 4

5 5. construction of a multi-period binomial real option valuation model including elements of prospect theory, 6. examination of the impact of an individual s specific characteristics of value and probabilities perception of the perceived real option value, 7. examination of the impact of an individual s specific characteristics of value and probabilities perception of the time of real option exercise, 8. examination of the impact of competitors characteristics concerning their values and probabilities perception of the payoffs distribution in shared options. 3. Methodology The real option valuation model including elements of prospect theory is designed in two versions as a numerical model, based on binomial trees, and as an analytical model. The Cox, Ross and Rubinstein approach is used as a starting point for the development of the binomial model, while the analytical model is an extension of the Verstuis, Lehnert, and Wolff [2010] proposition. Within the binomial model, elements of prospect theory in its original form are introduced [Kahneman and Tversky 1979], while the analytical model is based on its cumulative version [Tversky and Kahneman 1992], as proposed by Davies and Satchell [2007]. Based on the developed model, a number of numerical simulations are performed using the MS Excel spreadsheet and the built-in Visual Basic for Application programming tool. An example of competitors decision about investing in the local market, accompanied by the timing flexibility of the investment, is considered. The numerical simulations are carried out by changing the values of parameters of value and weighting function, together with the value of the reference point. The impact of these variables on the perceived option value and the moment of its exercise is analysed. This allows for the validation of the impact of the perception of values and probabilities on the option value and the time of its exercise. 4. Structure of the thesis The dissertation is structured in accordance with the detailed objectives listed in Section 2. The thesis begins with a chapter summarizing the neoclassical approach to investment efficiency evaluation, taking into account the value of decision flexibility referred to as real options. It identifies the key assumptions underlying the neoclassical approach to investment valuation, presents the concept of real options, outlines the main approaches to their valuation, and summarizes the theory concerning shared option analysis. 5

6 The second chapter contains a discussion about the behavioural context of real option analysis and valuation, with particular emphasis on prospect theory. It requires a summary of the achievements in behavioural economics which are relevant to the valuation of real options, an analysis of the main assumptions and the construction of prospect theory in its basic and cumulative form, as well as a systematization of behavioural determinants of economic decision-making in the context of their significance for the analysis and valuation of real options. The third chapter covers a presentation of the main assumptions and discusses the construction of the option valuation model including elements of prospect theory. This model is presented in binomial and analytical form, where the binomial model is developed into a multi-period version. The thesis concludes with the fourth chapter, which presents the assumptions and results of numerical simulations carried out using the proposed model. The influence of variables describing the individual values and probabilities perception on the real option value is validated, using both binomial and analytical models. Finally, the effects of values and probabilities perception, as described by prospect theory, for the valuation of real options are analysed using the multi-period valuation model of a real option. This includes the impact of prospect theory perception on the moment of option exercise as well as on payoff distributions in the case of shared options. 5. Main research results The real option valuation model including elements of prospect theory was constructed. Then, a series of numerical simulations were carried out, allowing to examine the relationship between individual perception of values and probabilities and the perceived value and moment of exercise of a real option. The research was multistage. First, the real options valuation approach was analysed. The real option method is an investment efficiency evaluation approach formulated within the neoclassical theory of corporate finance, taking into account the decision-making flexibility associated with the possibility to delay an investment and to subsequently influence its future realisation. This approach is based on the assumption that individuals behave rationally and make decisions in line with the expected utility theory. In the case of shared options, where the condition of exclusive possession of the option is not fulfilled, the elements of game theory are employed, which additionally requires the fulfilment of the common knowledge assumption. 6

7 This approach is a perfect solution in the world of homo oeconomicus, but its descriptive power and applicability are questionable. Working out normative recommendations in strategic situations requires proper forecasting of the opponents behaviour, which in the case of shared options involves accurate modelling of the actual valuation made by the competitors. This valuation process depends on a number of psychological and social factors described by behavioural economics. Hence, within the dissertation the main achievements of behavioural finance relevant for the valuation of real options have been summarised, with particular emphasis on prospect theory. Behavioural economics points out limited rationality of individuals and numerous psychological and social determinants of economic decision-making, also in respect to financial management. These include, inter alia, inclinations related to economic decision-making under risk, where the risk is inherently connected to the essence of real options. A descriptive theory describing the reality of making this type of choice is prospect theory. It points to the perception of values as gains or losses relative to a certain reference point, in a way defined by an S-shaped value function. Based on the probabilities of future states of nature, decision weights are assigned to scenarios in a way illustrated by a convex weighting function. Inclusion of these assumptions about values and probabilities perception into the model of real option valuation allows for a better mapping of the perceived option value and a more accurate understanding of when real options are exercised. This is of particular importance in strategic situations in which a rational player should strive for proper prediction of the opponents behaviour in order to maximize her/his own economic benefits, taking into account the limited rationality of the competitors. Based on the systematized knowledge of the option approach, a new model of real option valuation has been constructed. It includes elements of prospect theory, such as the reference point, the value function, and the weighting function. It was considered important to formulate this model in two variants: a binomial and an analytical form, with the first being developed by introducing a multi-period horizon, allowing for an analysis of the exercise moment of an American option. The proposition of the model makes it possible to fill in the identified research gap by introducing the reference point, which is of particular importance from the point of view of prospect theory, though omitted within the previous research. The contribution to the literature is also related to the focus on real options, where individual aspects, including the specific determinants of decision-making under risk, play a special role. The models available in the literature do not take into account such a context of analysis. As a binomial version of the model was constructed, applicability was broadly extended, regarding its simplicity, allowing for 7

8 implementation in many areas without the need for conducting sophisticated analysis. The model has been expanded to a multi-period version, allowing for an analysis of the value and exercise time of American options. Although most of the real options are American options, a valuation model of such options including elements of prospect theory could not be found within the current literature. As a consequence the previous models did not allow to analyse the moment of option exercise. This earlier research gap has also been filled in with this dissertation, where observations in this regard are relevant for a more intuitive understanding of the effects of prospect theory perception of real options as well as for the formulation of practical conclusions. Using the constructed model, a series of simulations have been carried out. Within the simulations the influence of values and probabilities perception, described by the reference point and the parameters of the weighting and value functions, on the value and the exercise moment of a real option was analysed. A numerical example of an investment project in a telecommunications industry, with an embedded option to delay, has been used. Simulations have been performed using a set of functions and macros programmed by the author using the Visual Basic for Application tool and MS Excel spreadsheets. The number of simulations performed concerning the value and exercise time of an option exceeded fifteen thousand in the case of the binomial model and more than two thousand as for the analytical model. On the basis of the simulations, the particular importance of the reference point for the perceived option value and the moment of its exercise has been shown, as it determines the interpretation of values as profits or losses. The impact of the evaluation function on the option value and the time of its exercise is greatest in the case of moderate reference point values, while at its extreme values the significance of the weighting function parameters grows. This observation demonstrates the validity of introducing the reference point into the real option valuation model including elements of prospect theory, which has been omitted in the current research. This is the fundamental variable from the point of view of value perception in terms of profits and losses, so its introduction to the model is necessary to capture the essence of prospect theory. Furthermore, the relationship between value and weighting parameters on the real option value and the time of its exercise has been analysed. A positive relation was observed in the case of the function parameter describing the sensitivity to subsequent increases in gains, as well as the parameters of the weighting function corresponding to the level of optimism of the decision maker and the sensitivity of its probabilities perception in the area of profits. At the same time, the positive influence of the above parameters on the option value translates into its later exercise. On the other hand, the option value is negatively related to the sensitivity to 8

9 subsequent increases in losses, the loss aversion, and the sensitivity of probabilities perceptions in the area of losses, translating into an earlier exercise of the real option. The typical values of the parameters of the value function and the weighting function imply moderate sensitivity to increases in gains and losses, loss aversion, and reduced sensitivity of probabilities perception. According to the observations made based on the simulations outcome, moderate sensitivity to increases in gains and loss aversion negatively affect the option value, accelerating its exercise. The opposite effect has the low sensitivity to successive incremental losses, though under typical conditions it is not strong enough to compensate for the effect of the other value function parameters. Moreover, according to the simulation results, an optimistic individual overestimates the value of the option, deferring its exercise to a larger extent than a pessimist. Also, the low sensitivity of probabilities perception translates into a higher value of the option and its later exercise. The impact of the subjective values and probabilities perception on the perceived value of the option has been illustrated in the context of shared options. The perception of the benefits of holding a real option, as described by prospect theory, influences the distribution of payoffs in strategic situations. The specific psychological characteristics of a competitor may affect the moment of option exercise by her/him. In consequence, This influences, in turn, both the value of such a shared option from a fully rational player s point of view, and the optimal moment of its exercise. Only proper modelling of the actual competitors behaviour allows for the optimal option exercise, thus a fully rational player should strive to take into account the limited rationality of her/his competitors. A step in this direction is including elements of prospect theory into the shared real option valuation process, as is done in the dissertation. The discussion presented in the thesis lead to a reflection on the value drivers of business ventures. Those pointed out in the current literature on real options are: the value of cash flows generated by investment projects, the benefits of the decision flexibility associated with the ability to actively influence the projects, and the impact of competition, understood as possible rational actions of other market players sharing the real options. This catalogue should therefore be extended by behavioural inclinations of market players. The psycho-social background of perceiving reality, shaping beliefs, or updating preferences may affect the perceived value of investment projects and, consequently, the moment real options are exercised. This moment, in turn, determines the shared option value for other market players, including hypothetical fully rational individuals. As a result, indirectly, behavioural factors influence not only the value of the option subjectively perceived by the entities affected by these factors, but also the objective value from the point of view of a fully rational player. The individual sphere of psychological and social determinants of the competitors perception and their decision-making processes 9

10 influences the objective value of the shared option. Among the value drivers of business ventures, it is therefore necessary to name the subjective behavioural aspects of other individuals activities on the market, which has not been emphasised in the current literature. 10