Strategy as a portfolio of real options

In financial terms, a business strategy is much more like a series of options than like a single projected cash flow. Executing a strategy almost always involves making a sequence of major decisions. Some actions are taken immediately while others are deliberately deferred so that managers can optimize their choices as circumstances evolve. While executives readily grasp the analogy between strategy and real options, until recently the mechanics of option pricing was so complex that few companies found it practical to use when formulating strategy. But advances in both computing power and our understanding of option pricing over the last 20 years now make it feasible to apply real-options thinking to strategic decision making. To analyze a strategy as a portfolio of related real options, this article exploits a framework presented by the author in "Investment Opportunities as Real Options: Getting Started on the Numbers" (HBR July-August 1998). That article explained how to get from discounted-cash-flow value to option value for a typical project; in other words, it was about reaching a number. This article extends that framework, exploring how, once you've worked out the numbers, you can use option pricing to improve decision making about the sequence and timing of a portfolio of strategic investments. Timothy Luehrman shows executives how to plot their strategies in two-dimensional "option space," giving them a way to "draw" a strategy in terms that are neither wholly strategic nor wholly financial, but some of both. Such pictures inject financial discipline and new insight into how a company's future opportunities can be actively cultivated and harvested.     

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 IFRS 2 and FASB 123 (R) Compatible Model for the Valuation of Employee Stock Options

In this paper, we show how employee stock options can be valued under the new reporting standards IFRS 2 and FASB 123 (revised) for share-based payments. Both standards require companies to expense employee stock options at fair value. We propose a new valuation model, referred to as Enhanced American model, that complies with the new standards and produces fair values often lower than those generated by traditional models such as the Black–Scholes model or the adjusted Black–Scholes model. We also provide a sensitivity analysis of model input parameters and analyze the impact of the parameters on the fair value of the option. The valuation of employee stock options requires an accurate estimation of the exercise behavior. We show how the exercise behavior can be modeled in a binomial tree and demonstrate the relevance of the input parameters in the calibration of the model to an estimated expected life of the option. JEL Classification G13, G30     

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.     

HOW TO USE EVA IN THE OIL AND GAS INDUSTRY

The use of EVA in the oil industry has lagged behind that in most other industries because the accounting information reported by oil and gas concerns does such a poor job of representing management's effectiveness in adding value for shareholders. The essence of the problem is that the exploration activities of oil companies create assets whose changes in value are recognized by the stock market long before they are reflected on income statements or balance sheets. As a result, all accountingbased performance measures, including generic measures of EVA (which are derived from accounting information), fail to provide meaningful goals, decision tools, or compensation benchmarks.
This article provides a new, EVAbased framework for performance measurement and incentive compensation for oil and gas firms—and for companies in extractive industries in general. The authors show that, when adjusted by a publicly available measure of hydrocarbon reserve value known as "SEC-10," EVA's ability to explain annual stock returns rises from under 10% to almost 50%. Moreover, because SEC-10 has several important limitations as a measure of reserve value, there is considerable additional room for improving EVA's explanatory power. And the actual implementation of an EVA financial management system for an individual oil company can and should be based on more precise estimates of reserve value than those provided by SEC-10.
To this end, the authors provide an approach to hydrocarbon reserve valuation that captures the "real option" value of undeveloped reserves. By incorporating real option values, this new EVA financial management system for oil companies aligns management's incentives with the goal of creating shareholder wealth by rewarding managers for creating real option value as well as current cash flow—and by forcing managers to consider the optimal "exercise" of such strategic options.     

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.     

A Fuzzy Set Approach for Generalized CRR Model: An Empirical Analysis of S&;P 500 Index Options

This paper applies fuzzy set theory to the Cox, Ross and Rubinstein (CRR) model to set up the fuzzy binomial option pricing model (OPM). The model can provide reasonable ranges of option prices, which many investors can use it for arbitrage or hedge. Because of the CRR model can provide only theoretical reference values for a generalized CRR model in this article we use fuzzy volatility and fuzzy riskless interest rate to replace the corresponding crisp values. In the fuzzy binomial OPM, investors can correct their portfolio strategy according to the right and left value of triangular fuzzy number and they can interpret the optimal difference, according to their individual risk preferences. Finally, in this study an empirical analysis of S&P 500 index options is used to find that the fuzzy binomial OPM is much closer to the reality than the generalized CRR model.This project has been supported by NSC 93-2416-H-009-024.JEL Classification:     

A note on the efficiency of the binomial option pricing model

We discuss the efficiency of the binomial option pricing model for single and multivariate American style options. We demonstrate how the efficiency of lattice techniques such as the binomial model can be analysed in terms of their computational cost. For the case of a single underlying asset the most efficient implementation is the extrapolated jump-back method: that is, to value a series of options with nested discrete sets of early exercise opportunities by jumping across the lattice between the early exercise times and then extrapolating from these values to the limit of a continuous exercise opportunity set. For the multivariate case, the most efficient method depends on the computational cost of the early exercise test. However, for typical problems, the most efficient method is the standard step-back method: that is, performing the early exercise test at each time step.     

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.     

Option Exercise Games: An Application to the Equilibrium Investment Strategies of Firms

Under the standard real options approach to investment underuncertainty, agents formulate optimal exercise strategies inisolation and ignore competitive interactions. However, in manyreal-world asset markets, exercise strategies cannot be determinedseparately, but must be formed as part of a strategic equilibrium.This article provides a tractable approach for deriving equilibriuminvestment strategies in a continuous-time Cournot–Nashframework. The impact of competition on exercise strategiesis dramatic. For example, while standard real options modelsemphasize that a valuable "option to wait" leads firms to investonly at large positive net present values, the impact of competitiondrastically erodes the value of the option to wait and leadsto investment at very near the zero net present value threshold.     

VALUE CREATION AT ANHEUSER-BUSCH: A REAL OPTIONS EXAMPLE

The management of Anheuser-Busch created $11.5 billion of shareholder value between 1996 and 1998, a period in which U.S. demand for beer was flat and the company's profits grew only modestly. Of that $11.5 billion, the authors estimate that nearly $10 billion can be attributed to the growth options created or expanded by the company during that period. While divesting itself of unrelated businesses, such as snack foods, Busch stadium, and the St. Louis Cardinals baseball franchise, the company began purchasing minority equity interests in brewing concerns in markets with growing demand for beer, including Mexico, Brazil, Chile, Argentina, and the Philippines.
The main undertaking of the paper is to use the real options valuation method to estimate the growth option value that Anheuser-Busch has created through its investments in joint ventures in foreign markets. The authors focus specifically on a joint venture in the Argentina/Chile market, and argue that this arrangement gives the company the flexibility to invest in a complete brewing and distribution system in that market after learning about the market's potential. In other words, the joint venture creates a call option on the Argentina/Chile market. Traditional DCF analysis, which ignores the flexibility in the strategy, assigns a negative NPV to the joint venture. But explicit recognition of the "option-ality" built into the investment results in a very different valuation—as well as a plausible explanation of the growth option value in the company's stock price.
As the Anheuser-Busch example also illustrates, valuation of the real option depends critically on the assumption about the volatility of the future value of the investment projects. The authors provide an intuitively useful way for managers to examine their own volatility assumptions—one that draws on the probability assessments that are part of the well-known Black-Scholes model.     

An adjusted binomial model for pricing Asian options

We propose a model for pricing both European and American Asian options based on the arithmetic average of the underlying asset prices. Our approach relies on a binomial tree describing the underlying asset evolution. At each node of the tree we associate a set of representative averages chosen among all the effective averages realized at that node. Then, we use backward recursion and linear interpolation to compute the option price.     

Cross-sectional tests of deterministic volatility functions

We study the cross-sectional performance of option pricing models in which the volatility of the underlying stock is a deterministic function of the stock price and time. For each date in our sample of FTSE 100 index option prices, we fit an implied binomial tree to the panel of all European style options with different strike prices and maturities and then examine how well this model prices a corresponding panel of American style options. We find that the implied binomial tree model performs no better than an ad-hoc procedure of smoothing Black–Scholes implied volatilities across strike prices and maturities. Our cross-sectional results complement the time-series findings of Dumas et al. [J. Finance 53 (1998) 2059].     

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.     

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.     

Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models

In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black–Scholes dynamics. The proposed techniques, called GPR Tree (GRP-Tree) and GPR Exact Integration (GPR-EI), are both based on Machine Learning, exploited together with binomial trees or with a closed form formula for integration. Moreover, these two methods solve the backward dynamic programing problem considering a Bermudan approximation of the American option. On the exercise dates, the value of the option is first computed as the maximum between the exercise value and the continuation value and then approximated by means of Gaussian Process Regression. The two methods mainly differ in the approach used to compute the continuation value: a single step of the binomial tree or integration according to the probability density of the process. Numerical results show that these two methods are accurate and reliable in handling American options on very large baskets of assets. Moreover we also consider the rough Bergomi model, which provides stochastic volatility with memory. Despite that this model is only bidimensional, the whole history of the process impacts on the price, and how to handle all this information is not obvious at all. To this aim, we present how to adapt the GPR-Tree and GPR-EI methods and we focus on pricing American options in this non-Markovian framework.     

Implied Binomial Trees

This article develops a new method for inferring risk-neutral probabilities (or state-contingent prices) from the simultaneously observed prices of European options. These probabilities are then used to infer a unique fully specified recombining binomial tree that is consistent with these probabilities (and, hence, consistent with all the observed option prices). A simple backwards recursive procedure solves for the entire tree. From the standpoint of the standard binomial option pricing model, which implies a limiting risk-neutral lognormal distribution for the underlying asset, the approach here provides the natural (and probably the simplest) way to generalize to arbitrary ending risk-neutral probability distributions.     

Binomial basis for linear information dynamics: real options, dividends and the valuation of equity

Analytical research has confirmed that real options give rise to the kind of nonlinearities observed in practice between equity prices and the figures appearing on corporate financial statements. We develop these real option values in terms of a quasi 'supply-side' model of linear information dynamics based on simple discrete time binomial filtration processes. Our analysis shows that the linear models that pervade the empirical (and analytical) work of the area, will almost certainly suffer from an omitted variables problem. Parameter estimation will then be inconsistent and inefficient.     

An FFT-network for Lévy option pricing

This paper develops a simple network approach to American exotic option valuation under Lévy processes using the fast Fourier transform (FFT). The forward shooting grid (FSG) technique of the lattice approach is then generalized to expand the FFT-network to accommodate path-dependent variables. This network pricing approach is applicable to all Lévy processes for which the characteristic function is readily available. In other words, the log-value of the underlying asset can follow finite-activity or infinite-activity Lévy processes. With the powerful computation of FFT, the proposed network has a negligible additional computational burden compared to the binomial tree approach. The early exercise policy and option values in the continuation region are determined in a way very similar to that of the lattice approach. Numerical examples using American-style barrier, lookback, and Asian options demonstrate that the FFT-network is accurate and efficient.     

Laboratory Evidence on How Managers Intuitively Value Real Growth Options

We asked 82 experienced managers to value, in effect, a set of real options, by taking decisions on invented case studies. The classic Black Scholes model should set an upper bound for rational valuations of these options (since it assumes a risk neutral discount rate, which may be optimistic). The managers valued their options erratically, and generally optimistically, though their responses to changes in moneyness, volatility and maturity tended to be in the 'correct' directions. Oil industry managers over-valued least, relative to Black-Scholes, and Brewery managers most. Questionnaires explored managers' perceptions of the real option parameters encountered in their workplaces.