OPTION EXERCISE GAMES: THE INTERSECTION OF REAL OPTIONS AND GAME THEORY

While the real options approach has proven useful in providing an analytical framework for analyzing the timing of investment decisions, a notable failure of the approach has been an almost complete lack of strategic considerations. In standard real options models, invest-ment (and exercise) strategies are for-mulated in isolation, without considering the potential impact of other firms' exercise strategies. This paper illustrates how the intersection of real options and game theory provides powerful new insights into the behavior of economic agents under uncertainty.
Introducing strategic considerations into the real options framework can lead to a rethinking of standard real option analysis. For example, one of-ten cited conclusion of the real options literature is the overturning of the standard capital budgeting rule of in-vesting immediately in any project with a positive NPV. Because the fu-ture value of the asset is uncertain, there may be significant benefits to deferring the investment until condi-tions prove even more favorable. But this result clearly depends on the lack of competitive access to the project. If firms fear preemption, then the option to wait becomes less valuable. For example, while the standard real op-tions models suggest that a real estate developer should wait until the devel-opment option is considerably "in the money," competition and the fear of preemption will likely force develop-ers to build much earlier.     

The non-neutrality of debt in investment timing: a new NPV rule

Summary Limited liability debt financing of irreversible investments can affect investment timing through an entrepreneur’s option value, even after compensating a lender for expected default losses. This non-neutrality of debt arises from an entrepreneur’s unique investment opportunity, and it is shown in a standard model of irreversible investment that includes the equilibrium effect of a competitive lending sector. The analysis is partial, in that it takes as exogenously given an entrepreneur’s use of debt. Intuitively, limited liability lowers downside risk for the entrepreneur by truncating the lower tail of risks, and lowers the investment threshold. Compensating the lender for expected default losses reduces project profitability to the entrepreneur, and increases the investment threshold. The net effect is negative, because lower downside risk has an additional impact on the option value of delaying investment. The standard NPV rule in real options theory implicitly assumes debt to be neutral. With non-neutrality of debt, an investment threshold is higher than investment cost, but lower than the standard NPV rule. Comparisons with other standard investment thresholds show similar relationships.     

Brealey,Myers, and Allen on Real Options

Real options are valuable sources of flexibility that are either inherent in, or can be built into, corporate assets. The value of such options are generally not captured by the standard discounted cash flow (DCF) approach, but can be estimated using a variant of financial option pricing techniques. This article provides an overview of the basics of real option valuation by examining four important kinds of real options:

• 1 The option to make follow‐on investments. Companies often cite “strategic” value when taking on negative‐NPV projects. A close look at the payoffs from such projects reveals call options on follow‐on projects in addition to the immediate cash flows from the projects. Today's investments can generate tomorrow's opportunities.
• 2 The option to wait (and learn) before investing. This is equivalent to owning a call option on the investment project. The call is exercised when the firm commits to the project. But often it's better to defer a positive‐NPV project in order to keep the call alive. Deferral is most attractive when uncertainty is great and immediate project cash flows—which are lost or postponed by waiting—are small.
• 3 The option to abandon. The option to abandon a project provides partial insurance against failure. This is a put option; the put's exercise price is the value of the project's assets if sold or shifted to a more valuable use.
• 4 The option to vary the firm's output or its production methods. Companies often build flexibility into their production facilities so that they can use the cheapest raw materials or produce the most valuable set of outputs. In this case they effectively acquire the option to exchange one asset for another.

The authors also make the point that, in most applications, real‐option valuation methods are a complement to, not a substitute for, the DCF method. Indeed DCF, which is best suited to and usually sufficient for safe investments and “cash cow” assets, is typically the starting point for real‐option analyses. In such cases, DCF is used to generate the values of the “underlying assets”—that is, the projects when viewed without their options or sources of flexibility.     

A Bayesian Approach to Real Options: The Case of Distinguishing between Temporary and Permanent Shocks

Traditional real options models demonstrate the importance of the “option to wait” due to uncertainty over future shocks to project cash flows. However, there is often another important source of uncertainty: uncertainty over the permanence of past shocks. Adding Bayesian uncertainty over the permanence of past shocks augments the traditional option to wait with an additional “option to learn.” The implied investment behavior differs significantly from that in standard models. For example, investment may occur at a time of stable or decreasing cash flows, respond sluggishly to cash flow shocks, and depend on the timing of project cash flows.     

Real Options: Experimental Evidence

Empirical testing of the real options theory has been very limited. This is primarily due to various inherent problems with obtaining field data for many components of real options theory. This paper utilizes experimental methodology to generate the data. The advantage of the experimental approach is that it enables the investigator to generate reliable and replicable data in a controlled environment. The results of the experiment indicate that fundamental insights of real options theory are not evident to individual investors. The majority invested too early and thus failed to recognize the benefit of the option to wait. However, when the investors had to compete with others for the right to invest, their bids generally reflected the value of the embedded option. Furthermore, as predicted by the theory, their bids increased with greater uncertainty about future cash flows from the investment.     

Investment timing,agency, and information

This paper provides a model of investment timing by managers in a decentralized firm in the presence of agency conflicts and information asymmetries. When investment decisions are delegated to managers, contracts must be designed to provide incentives for managers to both extend effort and truthfully reveal private information. Using a real options approach, we show that an underlying option to invest can be decomposed into two components: a manager's option and an owner's option. The implied investment behavior differs significantly from that of the first-best no-agency solution. In particular, greater inertia occurs in investment, as the model predicts that the manager will have a more valuable option to wait than the owner.     

Real Options: Meeting the Georgetown Challange

In response to the demand for a single, generally accepted real options methodology, this article proposes a four‐step process leading to a practical solution to most applications of real option analysis. The first step is familiar: calculate the standard net present value of the project assuming no managerial flexibility, which results in a value estimate (and a “branch” of a decision tree) for each year of the project's life. The second step estimates the volatility of the value of the project and produces a value tree designed to capture the main sources of uncertainty. Note that the authors focus on the uncertainty about overall project value, which is driven by uncertainty in revenue growth, operating margins, operating leverage, input costs, and technology. The key point here is that, in contrast to many real options approaches, none of these variables taken alone is assumed to be a reliable surrogate for the uncertainty of the project itself. For example, in assessing the option value of a proven oil reserve, the relevant measure of volatility is the volatility not of oil prices, but of the value of the operating entity—that is, the project value without leverage. The third step attempts to capture managerial flexibility using a decision “tree” that illustrates the decisions to be made, their possible outcomes, and their corresponding probabilities. The article illustrate various kinds of applications, including a phased investment in a chemical plant (which is treated as a compound option) and an investment in a peak‐load power plant (a switching option with changing variance, which precludes the use of constant risk‐neutral probabilities as in standard decision tree analysis). The fourth and final step uses a “no‐arbitrage” approach to form a replicating portfolio with the same payouts as the real option. For most corporate investment projects, it is impossible to locate a “twin security” that trades in the market. In the absence of such a security, the conventional NPV of a project (again, without flexibility) is the best candidate for a perfectly correlated underlying asset because it represents management's best estimate of value based on the expected cash flows of the project.     

Analyzing firms' strategic investment decisions in a real options' framework

Within the context of investment under uncertainty, the real options literature has led to models that capture primarily the time to wait flexibility of monopolistic corporations' investment decision. In this paper, we propose an approach which relies on barrier options to model production and/or sales delocalization flexibility for multinational enterprises making decisions under exchange rate uncertainty. We then extend the model by introducing game theoretic considerations to show how the information set and the competitive structure of the market may lead firms to act strategically and exercise their delocalization options preemptively at an endogenously fixed exchange rate barrier.     

Investment,consumption, and hedging under incomplete markets

Entrepreneurs often face undiversifiable idiosyncratic risks from their business investments. We extend the standard real options approach to an incomplete markets environment and analyze the joint decisions of business investments, consumption/savings, and portfolio selection. For a lump-sum investment payoff and an agent with a sufficiently strong precautionary savings motive, an increase in volatility can accelerate investment, contrary to the standard real options analysis. When the agent can trade the market portfolio to partially hedge against investment risk, the systematic volatility is compensated via the standard CAPM argument, and the idiosyncratic volatility generates a private equity premium. Finally, when the investment payoff is a series of flows, the agent's idiosyncratic risk exposure alters both the implied option value and the implied project value, causing a reversal of the results in the lump-sum payoff case.     

Investment options with debt-financing constraints

A contingent claims model is used to study the impact of debt-financing constraints on firm value, optimal capital structure, the timing of investment and other variables, such as credit spreads. The optimal investment trigger follows a U shape as a function of exogenously imposed constraint. Risky, equity-financed R&D growth options increase firm value by increasing the option value on unlevered assets, while their impact on the net benefits of debt is small.     

A real-world way to manage real options

Each corporate growth project is an option, in the sense that managers face choices--push ahead or pull back--along the way. Yet many companies hesitate to apply options theory to initiatives such as R&D and geographic expansion, partly because these "real" options are highly complex. In this article, the authors make the case that the complexity of real options can be eased through the use of a binomial valuation model. Many of the problems with real-options analysis stem from the use of the Black-Scholes-Merton model, which isn't suited to real options. Binomial models, by contrast, are simpler mathematically, and you can tinker with a binomial model until it closely reflects the project you wish to value. Suppose your company is considering investing in a new plant. To use the binomial model, you must create an "event tree" to figure out the full range of possible values for the plant during the project's lifetime--next year, at the end of the design phase, upon completion. Then you work backward from the value at completion, factoring in the various investments, to determine the value of the project today. These calculations provide you with numbers for all the possible future values of the option at the various points where a decision needs to be made on whether to continue with the project. The authors also address another criticism of real options: that gaps often arise between theoretical and realized values of options of all types. Such gaps may be largely the result of managers exercising options at the wrong time. To improve the way it manages its real options, a company can look out for the decision trigger points that correspond to the nodes on a binomial decision tree. The trigger points should not only tell managers when they need to decide on exercise but also specify rules governing the exercise decisions.     

Superannuation: Switching and Roulette Wheels

The introduction of choice has resulted in Australia's superannuation system providing unprecedented flexibility (through increased investment options and the timing choices) for members to optimise their expected benefits. This paper examines the impact of switching between investment options using a normalised ranked return or "roulette wheel" approach developed by Bauer and Dahlquist (2001) for the Australian setting. The paper tests various switching strategies for both single-sector and blended options, for the period 1985–2005, finding that members require forecast accuracy of around 70% to be successful at market timing. Finally, the paper considers the impact of switching strategies on accumulated balances.     

Assessing the Risk Potential of Premium Payment Options in Participating Life Insurance Contracts

Most life insurance contracts embed the right to stop premium payments during the term of the contract (paid-up option). Thereby, the contract is not terminated but continues with reduced benefits and often provides the right to resume premium payments later, thus increasing the previously reduced benefits (resumption option). In our analysis, we start with a basic contract with two standard options, namely, an interest rate guarantee and annual surplus participation. Next, in addition to the features of the basic contract, a paid-up and resumption option is included in the framework. The valuation process is not based on assumptions about a particular policyholders' exercise strategy but instead assesses the risk potential from the insurer's viewpoint by providing an upper bound for any possible exercise behavior. This approach provides important information to the insurer about the potential hazard of offering the paid-up and resumption option. Further, the approach allows an analysis of the impact of guaranteed interest rate, annual surplus participation, and investment volatility on the values of the premium payment options.     

The agency problem,investment decision,and optimal financial structure

This article constructs a real options model in which a firm has a privileged right to exercise an irreversible investment project with a stochastic payoff. Supposing that the investment costs are fully sunk, a firm that exercises the investment option after debt is in place will then choose a better state to exercise this option as it issues more bonds. This debt-overhang phenomenon, however, benefits the firm since waiting is itself valuable. Accordingly, the firm will both exercise the investment option later and issue more bonds as compared with a firm that issues bonds upon exercising the investment option.     

The Expected Return and Exercise Time of Merton-style Real Options

We analyse the rate of return and expected exercise time of Merton-style options (1973) employed in many real option situations where the possibility of exercise is both perpetual and American in nature. Using risk-neutral and risk-adjusted pricing techniques, Merton-style options are shown to have an expected return that is a constant percentage of the option value and independent of the proximity to the critical exercise boundary. Merton options thus remain at the same point on the Security Market Line, unlike European options whose position and rate of return change dynamically. We also present formulae for the expected time and discounted times to exercise and analyse the dependency of these variables on volatility.     

REAL OPTIONS PRIMER: A PRACTICAL SYNTHESIS OF CONCEPTS AND VALUATION APPROACHES

Strategic capital investment decisions are being made every day in an increasingly uncertain world. While the traditional NPV approach does a reasonable job of valuing simple, passively managed projects, it does not capture the many ways in which a highly uncertain project might evolve, and the ways in which active managers will influence this evolution. In cases where managerial flexibility is a major source of strategic value, companies will want to use real options valuation methods.
This article serves as a managerial tutorial on this newer, less understood approach. It uses simple examples to illustrate the essence of four basic categories of real options—timing, growth, production, and abandonment. The examples begin by taking a "binomial" approach to option valuation, in which the value of an investment initiative is allowed to take on two possible future values. Besides being used to illustrate the distinctive features of a real option, the binomial approach also serves to help the reader understand the alternative Black-Scholes valuation approach (though without requiring the reader to master the complex mathematics underlying Black-Scholes). Basic instructions for implementing both approaches are provided, along with a discussion of how to set appropriate discount rates and the important role of volatility assessment in the valuation process.     

An option pricing approach to the valuation of real estate contaminated with hazardous materials

This paper uses option pricing to examine how the presence of hazardous materials affects real estate value. The property owner has two options. The first option is to remove the hazardous materials at the best time. The second option, embedded in the first one, is to redevelop the property at the best opportunity. The owner has three possible timing strategies with respect to the exercise of these two options: remove the hazardous materials first and retain the option to redevelop the property later, remove and redevelop at the same time, or do nothing. Conditions under which the presence of the hazardous materials may either expedite or postpone the decision to redevelop are also derived. If the regulatory environment does not allow the property owner to make optimal timing decisions with respect to the exercise of these options, then our results provide an indication of the cost of regulation as measured by the additional loss in property value.     

Investment in internet banking as a real option: theory and tests

This paper examines the optimal exercise of strategic real options to invest in Internet banking (IB) technology within a two-stage game, parameterized by the distribution of bank size and uncertainty over the profitability of investment, and empirically tests the results. The value of the strategic investment option to a strategically significant entrant into IB depends on both expected future profits as well as the variance of those profits. Expected profits to an entrant depend, in equilibrium, on its size, as measured by existing market share (concentration) or total assets, relative to its rivals. Conditional on the degree of uncertainty, larger banks should, as a consequence, exercise their options earlier than smaller banks, for purely strategic advantages, and act as market leaders in the provision of IB services. Like ordinary options, however, the value of the strategic investment option to both large and small banks increases in uncertainty, implying that early exercise will be more likely the more information is available about potential demand. We test these hypotheses on investment in IB services with data from a sample of 1618 commercial banks in the tenth Federal Reserve District during 1999. Consistent with our hypotheses, relative bank size, as measured by measures of concentration, and demographic information predictive of future demand both positively influence the probability of entry into IB in our sample.     

Accelerated investment effect of risky debt

In this paper we examine a new effect of risky debt on a firm’s investment strategy. We call this effect “accelerated investment”. It stems from a potential loss of investment option in the event of default. The possibility of default reduces the value of the option to wait and provides equity holders with an incentive to speed up investment. As a result, in the absence of wealth expropriation by a levered firm’s debt holders, its shareholders exercise their investment option earlier than the shareholders of an otherwise identical all-equity firm. This result is at odds with the generally accepted intuition that in the absence of potential wealth transfers and taxes the shareholders of a levered firm would follow the same investment policy as that of an unlevered firm. In addition to providing various illustrations of the accelerated investment effect, we relate its magnitude to the presence of competition for investment opportunities.     

Making real options really work

As a way to value growth opportunities, real options have had a difficult time catching on with managers. Many CFOs believe the method ensures the overvaluation of risky projects. This concern is legitimate, but abandoning real options as a valuation model isn't the solution. Companies that rely solely on discounted cash flow (DCF) analysis underestimate the value of their projects and may fail to invest enough in uncertain but highly promising opportunities. CFOs need not--and should not--choose one approach over the other. Far from being a replacement for DCF analysis, real options are an essential complement, and a project's total value should encompass both. DCF captures a base estimate of value; real options take into account the potential for big gains. This is not to say that there aren't problems with real options. As currently applied, they focus almost exclusively on the risks associated with revenues, ignoring the risks associated with a project's costs. It's also true that option valuations almost always ignore assets that an initial investment in a subsequently abandoned project will often leave the company. In this article, the authors present a simple formula for combining DCF and option valuations that addresses these two problems. Using an integrated approach, managers will, in the long run, select better projects than their more timid competitors while keeping risk under control. Thus, they will outperform their rivals in both the product and the capital markets.