A Real Options Model with Games Applied to the Rio de Janeiro Residential Real Estate Market.
| Autor | de Almeida, Glaudiane Lilian |
1 Introduction
Investment decisions are characterized by strategic competition between rival firms, as each firm assesses its comparative advantages over its competitors and market conditions, such as product value, volatility of revenue streams, and market share, where monopolies and duopolies directly affect results. In this sense, investments in competitive markets can be seen as a game between firms, since in making investment decisions firms implicitly take into account the reactions of their competitors to their actions. As noted by Porter (1992), investment is the most important factor of competitive advantage.
Investment decisions are traditionally analyzed based on the discounted cash flow method (DCF), which consists of projecting the expected future cash flows and discounting them at the project's risk adjusted rate. One disadvantage of this method, however, is its simplistic and static nature, which does not capture the value of managerial and strategic flexibility and ignores the reactions of competing firms.
As these flexibilities have options-like characteristics, they can only be assessed using pricing options methods, such as the Real Options (RO) approach, which models the exogenous dynamic uncertainties of the economy (such as product demand) and the company's flexibilities to adapt to changing scenarios.
However, RO does not endogenously consider the possible competitive interactions. Game theory, on the other hand, analyzes how firms make decisions when they are aware that their actions affect rival firms in the market and that they will respond rationally to the actions of their rivals. Therefore, a combination of Real Options with Game theory has the potential to generate promising results for an analysis of investment decisions, given the complementarity between these two theories.
Choosing the ideal time to exercise the option of investing is critical to creating value in the company and to gaining competitive advantage. In addition, decisions to invest or abandon a project involve different risks and uncertainties, especially in competitive environments where firms may have different optimal investment policies when compared to a monopolistic firm. This intersection of Game Theory with Real Options theory is known as Real Options Games, where competition is modeled endogenously, and the competitor enters rationally, not randomly, in addition to considering the uncertainties (stochastic processes) and flexibilities (RO).
In the classic case of real options, firms are only price takers and hold a monopoly over the option to invest, and ignore the fact that competition can affect the value of the real option as well as the optimal decision rule. In real options games, the firm's value maximization problem considers the presence of other firms as players, which react optimally to the relevant stochastic processes and the actions of other firms, enabling competition to be modeled in an endogenous way.
As noted by Grenadier (2002), a common issue in most papers that apply the Real Options approach is the lack of analysis regarding the strategic interactions of the holders of options where the optimal investment rule depends on the reaction of competitors to the project. Games with real options are seen as a way to overcome the shortcomings of the previously mentioned methods.
The objective of this paper is to determine the investment strategy in Nash equilibrium for the real estate market of the region of Rio de Janeiro, considering the uncertainty in the demand for real estate and the number of active competitors in the market.
To this end, a modified version of Grenadier's methodology was adopted with a more adequate and robust specification of the uncertainty for the demand function. Unlike previous studies, where traditional modeling of uncertainties was concentrated around multiplicative shocks in the demand function, it will be seen here that demand uncertainty is modeled from a multiplicative stochastic shock on its slope that includes a stochastic elasticity of demand factor.
This article is organized as follows. After this introduction, section 2 presents a review of the literature and section 3 develops the Real Options Game model. Following that, section 4 applies the proposed model to the residential market of the city of Rio de Janeiro and section 5 presents the results and the conclusions. The appendix presents some intermediate mathematical developments.
2 Review of the Literature
The first paper to address the contributions of combining Game theory and Real Options Theory is attributed to Smit & Ankum (1993), in which they demonstrated that competition among companies implies a decrease in the value of waiting, resulting in earlier investments. Dixit and Pindyck (1994) developed a basic model of Real Options Games for duopoly markets, where they evaluated investment timing.
Huisman (2000) proposed innovative models of real options games by adding to the literature the effect oftechnological uncertainty on the investment option, among other contributions. Chevalier-Roignant and Trigeorgis (2011) focused on other aspects of modeling real options, such as myopic investor behavior and capacity expansion.
Applications that use competitive structures from oligopolies were studied by Baldursson (1998) and Grenadier (2002) based on the result called "optimal myopia" for the competitive equilibrium discovered by Leahy (1993), as mentioned by Dixit and Pindyck (1994), where the optimal investment threshold (level of demand) of the monopolist case coincides with that of the perfect competition case, albeit for different reasons. In the case of the oligopoly in Grenadier (2002), with a modified demand function it is possible to use the concept of optimal myopia to obtain the solution in oligopolies, which will be used in this article. Murto et al. (2004) analyzed a game for oligopolies with stochastic demand, but in discrete time.
In Brazil, Costa et al (2015) studied the impact of preemption on optimal timing games for an asymmetric oligopoly applied in the Brazilian aluminum cans market and showed that firms need to anticipate their investments when there is a threat of preemption in the market, in relation to the case without competitors. Titman (1985) was the pioneer in applying the real options methodology to the real estate market, when he analyzed an option to postpone real estate investments in urban land. Williams (1991) considered an abandonment option as an alternative to land development, while Quigg (1993) and Holland et al (2000) provided empirical evidence that models based on the concept of real options may be useful in predicting values in real estate markets.
In the international literature, papers have been found that combine Real Options with Game Theory, such as that of Williams (1993), which derived symmetrical equilibrium exercise strategies for real estate developers by applying the model in the real estate market. Grenadier (1996) developed a game of real options in the real estate market suggesting a possible explanation for why some markets may experience booms in the face of declining demand and price depreciation. Grenadier (2005) made an equilibrium analysis for real estate leases using a Real Options Game model in a unified equilibrium approach to evaluate a wide variety of commercial real estate leases.
Wang and Zhou (2006) worked with demand and stochastic construction costs in a model with multiple real estate developers where the option to build a property could be exercised sequentially or simultaneously. The authors incorporated asymmetries in production capacity, allowing the impact of market power on the exercise strategies of the options to be examined.
In the national literature on RO, we find the works of Rocha et al (2007) and Fortunato et al. (2008), who applied the Real Options Theory in the real estate sector in Rio de Janeiro. The Rocha et al. (2007) approach was based on a discrete-time real options model to identify the optimal strategy for simultaneous or sequential investments. This model allowed the maximum value to be paid for exclusive use of the land. Fortunato et al. (2008) used the real options theory to determine the value of the abandonment option during the construction period of an investment in a residential property acquired based on blueprints, considering different levels of return for the amounts already paid by the buyer. These two papers did not consider the effect of competition in an endogenous way, as in this study. Costa and Samanez (2008), as in this paper, analyzed the real estate market of Rio de Janeiro from the perspective of real options games, where they sought to determine the equilibrium between supply and demand, comparing with the real business cycle of the real estate market. Besides working with a sample that was not representative for Rio de Janeiro, they used arbitrary and exogenous values as proxies for their estimates, as have most of the studies that have applied models of Real Options Games. The quantification of competitive pressures can be seen in the calculation of thresholds that vary according to the number of companies, demonstrating that companies are more engaged in the market.
This paper differs from existing ones by modifying the Grenadier (2002) model specification for the demand function to a particularly robust format that allows a more intuitive economic interpretation. To the best of our knowledge, this is the first study of Real Options Games that makes use of a stochastic demand function in which the stochastic variable changes the slope of the demand curve. Moreover, the parameters of the model were estimated using econometric tools for real estate data, unlike several models of RO Games that have used exogenous values for the parameters, which may be subjective and arbitrary choices. This can be found in studies such as Grenadier (1996), Grenadier (2000)...
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