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Article Excerpt
We test the implications of real option pricing models with competitive interactions for commercial real estate development. The competitive nature of a local commercial real estate market relies on a Herfindahl ratio derived from individual developers' shares of total office construction in their market. All else being equal, greater competition among local developers is associated with more building starts. Other variables suggested by the real options pricing model, including the volatility of local lease rates, are also found to be statistically important. In addition, we provide evidence consistent with greater competition attenuating the extent to which increases in volatility delay commercial real estate development.
Introduction
There are numerous applications of real option pricing models to investment decision making in commercial real estate. Examples include, among others, Titman (1985), Williams (1991, 1997), Quigg (1993), Childs, Riddiough and Triantis (1996) and Holland, Ott and Riddiough (2000). (1) However, by treating the exercise price as exogenously given, traditional real option pricing models do not take into account the fact that the exercise of the option ("investment") by one developer may affect the building price faced by other developers and so influence their exercise strategy. Recently researchers have begun to systematically investigate the effects of one developer's exercise of this option on the investment decisions of others. (2) In particular, Grenadier (2002, 2005) has developed a model to value real estate leases, which explicitly takes these competitive interactions into account.
This article takes advantage of an extensive commercial real estate database to empirically investigate the implications of real option pricing models with competitive interactions for commercial real estate development. Competition in a particular market is measured by relying on a Herfindahl concentration ratio based on individual developers' shares of total office construction in their market. We focus on a developer's option to develop additional office space and investigate the effects of various explanatory variables, including the degree of competition, on the trigger point at which such development occurs. Movements in the trigger point are proxied by the number of buildings starts, with a greater number of starts corresponding to a lower trigger point. We then statistically test whether these variables do indeed influence the observed number of building starts in the direction posited by these real option pricing models.
Our empirical results are consistent with the observed number of building starts being systematically affected by these variables and in the directions predicted by the real options theory. For example, an increase in the volatility of lease rates, all else being equal, results in a statistically reliable decrease in the number of building starts. The number of building starts is also influenced by the competitive nature of the local commercial real estate market. All else being equal, more competition amongst local developers, as measured by a correspondingly lower Herfindahl ratio, results in a greater number of building starts or, equivalently, a lower trigger point at which the option to develop is exercised. Furthermore, consistent with Grenadier's model, we find evidence that the effect of volatility on a developer's option to delay is attenuated by greater competition in a particular market.
Bulan, Mayer and Sommerville (2002) also investigate the effects of competition on option values in commercial real estate. In particular, they examine condominium development in Vancouver, Canada, between 1979 and 1998 and find that increases in risk, both systematic as well as unsystematic, delay condominium investment. They also find that an increase in competition, measured by the actual number of future developments that will be built nearby, attenuates this relation. Our articles differ in more than how the degree of competition prevailing in a particular market is measured. For example, Bulan, Mayer and Sommerville (2002) look at only one market but over a longer period of time. We, by contrast, consider a number of different markets over time which allows us to exploit these cross-sectional data in testing the implications of the real option pricing model.
The plan of this article is as follows. The next section relies on Grenadier's model to provide a framework in which to summarize the comparative statics of the trigger level at which commercial real estate investment will occur with respect to variables suggested by real option pricing models with competitive interactions. The section "Data" discusses the data and details the dependent and independent variables used to test the implications of these models. The section "Empirical Method and Results" puts forward our empirical methodology and discusses our empirical results. We conclude in the final section.
The Comparative Statics of a Real Option Pricing Model with Competitive Interactions
In this section we briefly overview the implications of real option pricing models with competitive interactions for commercial real estate development. We couch our discussion in the context of Grenadier's (2002, 2005) model. This model allows us to succinctly capture within a real options framework the effects of competition on a developer's decision to build. Many of these effects, however, are not unique to Grenadier's model but characterize real option pricing models with competitive interactions in general.
A local real estate market is assumed to be oligopolistic and made up of n identical developers who develop and lease identical office buildings. To fix matters, at time t, developer i owns [q.sub.i](t) units of completed and rentable space. The space is infinitely divisible, and a continuous time framework is assumed. At any point in time, developers can develop new rentable units at a constant cost of K per unit of space. This investment decision is irreversible. The model also abstracts from the issue of land use choice and concentrates only on determining the optimal size of the development.
The value of owning an office building arises from its underlying service flow. The instantaneous lease rate, P(t), is the price of the flow of these services. It is assumed that the lease rate evolves in such a way as to clear this market at each point in time. Following Dixit and Pindyck (1994), the market inverse demand function is assumed given by
P(t) = X(t)Q(t)[.sup.-1/[gamma]], (1)
where the price elasticity of demand, [gamma], satisfies (3) [gamma] > 1/n and Q(t) = [[summation].sub.j=1.sup.n] [q.sub.j](t) and is the industry supply process. Here X(t) represents a multiplicative demand shock. Examples of demand shocks include, among others, changes in job growth, changes in industrial production and changes in disposable income. The demand shock itself evolves as a geometric Brownian motion:
dX(t) = [alpha]X(t)dt + [sigma]X(t)dZ, (2)
where [alpha] is the instantaneous conditional expected percentage change in X(t) and [sigma] is the instantaneous conditional standard deviation. The risk-free interest rate r is assumed to be constant with r > [alpha] to ensure convergence. The cash flows are valued in a risk-neutral framework. That is, the process for X(t) is assumed to be risk adjusted.
Under the above assumptions, Grenadier (2005) derives the corresponding symmetric Nash equilibrium development strategy. In particular, he obtains the equilibrium value of each identical office building in closed form:
G(X, Q) = [[X[Q.sup.[[gamma]-1]/[gamma]]]/[n(r - [alpha])]] + B(Q)[X.sup.[beta]] (3)
where
[beta] = [-([alpha] - [1/2][[sigma].sup.2]) + [square root of (([alpha] - [1/2][[sigma].sup.2])[.sup.2] + 2r[[sigma].sup.2])]]/[[sigma].sup.2] > 1
B(Q) = ([U.sub.n.sup.-[beta]]/n) ([gamma]/[[gamma] - [beta]]) [K - ([v.sub.n]/[r - [alpha]]) ([[gamma] - 1]/[gamma])][Q.sup.[[gamma] - [beta]]/[gamma]]
[v.sub.n] = ([beta]/[[beta] - 1])...
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