Real options valuation

Real options valuation, also often termed Real options analysis,^[1] (ROV or ROA) applies option valuation techniques to capital budgeting decisions.^[2] A real option itself, is the right — but not the obligation — to undertake some business decision; typically the option to make, abandon, expand, or contract a capital investment. For example, the opportunity to invest in the expansion of a firm's factory, or alternatively to sell the factory, is a real call or put option, respectively.

Real Options, as a discipline, extends from its application in Corporate Finance, to decision making under uncertainty in general, adapting the techniques developed for financial options to "real-life" decisions. For example, R&D managers can use Real Options Valuation to help them determine where to best invest their money in research; a non business example might be the decision to join the work force, or rather, to forgo several years of income to attend graduate school. It thus forces decision makers to be explicit about the assumptions underlying their projections, and for this reason ROV is increasingly employed as a tool in business strategy formulation.^[3][4]

Comparison with standard techniques

ROV is often contrasted with more standard techniques of capital budgeting, such as discounted cash flow (DCF) analysis / net present value (NPV).^[2]

• Using a DCF model, only the most likely or representative outcomes are modelled, and the "flexibility" available to management is "ignored"; see Valuing flexibility under Corporate finance. The NPV framework (implicitly) assumes that management is "passive" with regard to their Capital Investment once committed. Analysts usually account for this uncertainty by adjusting the discount rate (e.g. by increasing the cost of capital) or the cash flows (using certainty equivalents, or applying (subjective) "haircuts" to the forecast numbers).^[5] These methods normally do not properly account for changes in risk over a project's lifecycle and fail to appropriately adapt the risk adjustment.^[6]

• By contrast, ROV assumes that management is "active" and can modify the project as necessary. ROV models consider "all" future outcomes and management's response to these contingent scenarios.^[7] Because management responds to each outcome - i.e. the options are exercised - the possibility of a (large) negative outcome is reduced (or even eliminated), and /or greater profit is achieved. Risk is therefore reduced or "eliminated" under ROV, and uncertainty is accounted for using the techniques applied to financial options. Here the approach is to risk-adjust the probabilities - as opposed to the discount rate, as for NPV - and the cash flows can then be discounted at the risk-free rate. This technique is known as the certainty-equivalent or martingale approach, and uses a Risk-neutral measure. For technical considerations here, see below.

Given these different treatments, the real options value of a project is typically higher than the NPV - and the difference will be most marked in projects with major flexibility, contingency, and volatility.^[8] (As for financial options higher volatility of the underlying leads to higher value).

Valuation

From the above it is clear that there is an analog between the modelling of real options and financial options:^[9][10]

“

First, you must figure out the full range of possible values for the underlying asset.... This involves estimating what the asset's value would be if it existed today and forecasting to see the full set of possible future values... [These] calculations provide you with numbers for all the possible future values of the option at the various points where a decision is needed on whether to continue with the project...[9]

”

However, ROV is distinguished from these approaches in that it takes into account uncertainty about the future evolution of the parameters that determine the value of the project, and management's ability to respond to the evolution of these parameters.^[11][12] It is the combined effect of these that makes ROV technically more challenging than its alternatives. When valuing the real option, the analyst must consider the inputs to the valuation, the valuation method employed, and whether any technical limitations may apply.

Valuation inputs

Given the similarity in valuation approach, the inputs required for modelling the real option correspond, generically, to those required for a financial option valuation.^[9][10] The specific application, though, is as follows:

• The option's underlying is the project in question - it is modelled in terms of:
  • spot price: the starting or current value of the project is required: this is usually based on management's "best guess" as to the gross value of the project's cash flows and resultant NPV;
  • volatility: uncertainty as to the change in value over time is required:
    • the volatility in project value is generally used, usually derived via monte carlo simulation; sometimes the volatility of the first period's cash flows are preferred;^[12]
    • project NPV is often difficult to estimate, and some analysts therefore substitute a listed security as a proxy, using either the volatility of the price of the security (historical volatility), or, if options exist on this security, their implied volatility.^[1]

See further under Corporate finance for a discussion relating to the estimation of NPV and project volatility.

• Option characteristics:
  • Strike price: this corresponds to the investment outlays, typically the prospective costs of the project. In general, management would proceed (i.e. the option would be in the money) given that the present value of expected cash flows exceeds this amount;
  • Option term: the time during which management may decide to act, or not act, corresponds to the life of the option. Examples include the time to expiry of a patent, or of the mineral rights for a new mine. See Option time value.

• Option style. Management's ability to respond to changes in value is modeled at each decision point as a series of options:
  • the option to contract the project (an American styled put option);
  • the option to abandon the project (also an American put);
  • the option to expand or extend the project (both American styled call options);
  • switching options, composite options or rainbow options which may also apply to the project.

Valuation methods

The valuation methods usually employed, likewise, are adapted from techniques developed for valuing financial options. Note though that, in general, while most "real" problems allow for American style exercise at any point (many points) in the project's life and are impacted by multiple underlying variables, the standard methods are limited either with regard to dimensionality, to early exercise, or to both. In selecting a model, therefore, analysts must make a trade off between these considerations; see Option (finance): Model implementation. The model must also be flexible enough to allow for the relevant decision rule to be coded appropriately at each decision point.

• The most commonly employed are Closed form solutions—often modifications to Black Scholes^[12]—and binomial lattices.^[8] The latter are probably more widely used due to their flexibility, particularly given that most real options are American styled, although cannot readily handle high dimensional problems.
• Specialised Monte Carlo Methods have also been developed and are increasingly applied particularly to high dimensional problems,^[13] although for American styled real options, this application is somewhat more complex.
• When the Real Option can be modelled using a partial differential equation, then Finite difference methods for option pricing are sometimes applied. Although many of the early ROV articles discussed this method,^[14] its use is relatively uncommon today—particularly amongst practitioners—due to the required mathematical sophistication; these too cannot readily be used for high dimensional problems.

Various other methods, aimed mainly at practitioners, have been developed for real option valuation. These typically use cash-flow scenarios for the projection of the future pay-off distribution, and are not based on restricting assumptions similar to those that underlie the closed form (or even numeric) solutions discussed. The most recent additions include the Datar–Mathews method^[15][16] and the Fuzzy Pay-Off Method.^[17]

Limitations

The relevance of Real options, even as a thought framework, may be limited due to organizational and / or technical considerations.^[18] When the framework is employed, therefore, the analyst must first ensure that ROV is relevant to the project in question. These considerations are as below.

Organizational considerations

Real options are “particularly important for businesses with a few key characteristics”,^[8] and may be less relevant otherwise.^[12] At the same time the market in question must be one where "change is most evident", and the "source, trends and evolution" ^[8] in product demand and supply, create the volatility and contingencies discussed above.

In overview:

1. The business must be positioned such that it has appropriate information flow, and opportunities to act. This will often be a market leader and / or a firm enjoying economies of scale and scope.
2. Management must understand options, be able to identify and create them, and appropriately exercise them. (This contrasts with business leaders focused on maintaining the status quo and / or near-term accounting earnings.)
3. The financial position of the business must be such that it has the ability to fund the project as required (i.e. issue shares, absorb further debt and / or use internally generated cash flow); see Financial statement analysis. Management must also have appropriate access to this capital.

Technical considerations

Limitations as to the use of these models arise due to the contrast between Real Options and financial options, for which these were originally developed. The main difference is that the underlying is often not tradeable - e.g. the factory owner cannot easily sell the factory upon which he has the option. Additionally, the real option itself may also not be tradeable - e.g. the factory owner cannot sell the right to extend his factory to another party, only he can make this decision (some real options, however, can be sold, e.g., ownership of a vacant lot of land is a real option to develop that land in the future). Even where a market exists - for the underlying or for the option - in most cases there is limited (or no) market liquidity.

The difficulties:

1. As above, data issues arise as far as estimating key model inputs. Here, since the value or price of the underlying cannot be (directly) observed, there will always be some (much) uncertainty as to its value (i.e. spot price) and volatility (further complicated by uncertainty as to management's actions in the future).
2. It is often difficult to capture the rules relating to exercise, and consequent actions by management: Some real options are proprietary (owned or exercisable by a single individual or a company) while others are shared (can be exercised by many parties). Further, a project may have a portfolio of embedded real options, some of which may be mutually exclusive.
3. Theoretical difficulties, which are more serious, may also arise.^[19]

• Option pricing models are built on rational pricing logic. Here, essentially: (a) it is presupposed that one can create a "hedged portfolio" comprising one option and "delta" shares of the underlying. (b) Arbitrage arguments then allow for the option's price to be estimated today; see Rational pricing: Delta hedging. (c) When hedging of this sort is possible, since delta hedging and risk neutral pricing are mathematically identical, then risk neutral valuation may be applied, as is the case with most option pricing models. (d) Under ROV however, the option and (usually) its underlying are clearly not traded, and forming a hedging portfolio would be difficult, if not impossible.
• Standard option models: (a) Assume that the risk characteristics of the underlying do not change over the life of the option, usually expressed via a constant volatility assumption. (b) Hence a standard, risk free rate may be applied as the discount rate at each decision point, allowing for risk neutral valuation. Under ROV, however: (a) managements' actions actually change the risk characteristics of the project in question, and hence (b) the Required rate of return could differ depending on what state was realised, and a premium over risk free would be required, invalidating (technically) the risk neutrality assumption.

These issues are addressed via several interrelated assumptions:

1. As discussed above, the data issues are usually addressed using a simulation of the project, or a listed proxy. Various new methods - see for example those described above - also address these issues.
2. Specific exercise rules can often be accommodated by coding these in a bespoke binomial tree; see: ^[9].
3. The theoretical issues:

• To use standard option pricing models here, despite the difficulties relating to rational pricing, practitioners adopt the "fiction" that the real option and the underlying project are both traded (the so called, Marketed Asset Disclaimer (MAD) approach). Although this is a strong assumption, it is pointed out that, interestingly, a similar fiction in fact underpins standard NPV / DCF valuation (and using simulation as above). See: ^[1] and ^[9].
• To address the fact that changing characteristics invalidate the use of a constant discount rate, some practitioners use the "replicating portfolio approach", as opposed to Risk neutral valuation, and modify their models correspondingly.^[9] Under this approach, we "replicate" the cash flows on the option by holding a risk free bond and the underlying in the correct proportions. Then, since the value of the option and the portfolio will be identical in the future, they may be equated today, and no discounting is required.

History

Whereas business managers have been making capital investment decisions for centuries, the term "real option" is relatively new, and was coined by Professor Stewart Myers of the MIT Sloan School of Management in 1977. It is interesting to note though, that in 1930, Irving Fisher wrote explicitly of the "options" available to a business owner (The Theory of Interest, II.VIII). The description of such opportunities as "real options", however, followed on the development of analytical techniques for financial options, such as Black–Scholes in 1973. As such, the term "real option" is closely tied to these option methods.

Real options are today an active field of academic research. Professor Lenos Trigeorgis (University of Cyprus) has been a leading name for many years, publishing several influential books and academic articles. Other pioneering academics in the field include Professors Eduardo Schwartz and Michael Brennan (UCLA Anderson). An academic conference on real options is organized yearly (Annual International Conference on Real Options).

Amongst others, the concept was "popularized" by Michael J. Mauboussin, then chief U.S. investment strategist for Credit Suisse First Boston.^[8] He uses real options to explain the gap between how the stock market prices some businesses and the "intrinsic value" for those businesses. Trigeorgis also has broadened exposure to real options through layman articles in publications such as The Wall Street Journal.^[7] This popularization is such that ROV is now a standard offering in postgraduate finance degrees, and often, even in MBA curricula at many Business Schools.

Recently, real options have been employed in business strategy, both for valuation purposes and as a conceptual framework.^[3][4] The idea of treating strategic investments as options was popularized by Timothy Luehrman ^[20] in two HBR articles:^[10] "In financial terms, a business strategy is much more like a series of options, than a series of static cash flows". Investment opportunities are plotted in an "option space" with dimensions "volatility" & value-to-cost ("NPVq").

See also

• Option
• Financial modeling
• Fuzzy Pay-Off Method for Real Option Valuation

References

1. ^ ^{a b c} Adam Borison (Stanford University). Real Options Analysis: Where are the Emperor’s Clothes?.
2. ^ ^{a b} Campbell, R. Harvey. Identifying real options, Duke University, 2002.
3. ^ ^{a b} Justin Pettit: Applications in Real Options and Value-based Strategy; Ch.4. in Trigeorgis (1996)
4. ^ ^{a b} Joanne Sammer: Thinking in Real (Options) Time, businessfinancemag.com
5. ^ Aswath Damodaran: Risk Adjusted Value; Ch 5 in Strategic Risk Taking: A Framework for Risk Management. Wharton School Publishing, 2007. ISBN 0-13-199048-9
6. ^ Dan Latimore: Calculating value during uncertainty. IBM Institute for Business Value
7. ^ ^{a b} Lenos Trigeorgis, Rainer Brosch and Han Smit. Stay Loose, copyright 2010 Dow Jones & Company.
8. ^ ^{a b c d e} Michael J. Mauboussin, Credit Suisse First Boston, 1999. Get Real: Using Real Options in Security Analysis
9. ^ ^{a b c d e f} Copeland, T. and Tufano. P. (2004). A Real-World Way to Manage Real Options. Harvard Business Review. 82, no. 3.
10. ^ ^{a b c} Timothy Luehrman: "Investment Opportunities as Real Options: Getting Started on the Numbers". Harvard Business Review 76, no. 4 (July - August 1998): 51-67.; "Strategy as a Portfolio of Real Options". Harvard Business Review 76, no. 5 (September–October 1998): 87-99.
11. ^ Jenifer Piesse and Alexander Van de Putte: Volatility estimation in Real Options
12. ^ ^{a b c d} Aswath Damodaran: The Promise and Peril of Real Options
13. ^ Marco Dias. Real Options with Monte Carlo Simulation
14. ^ Brennan, J.; Schwartz, E. (1985). "Evaluating Natural Resource Investments". The Journal of Business 58 (2): 135–157. JSTOR 2352967. 
15. ^ Datar, V.; Mathews, S. (2004). "European Real Options: An Intuitive Algorithm for the Black Scholes Formula". Journal of Applied Finance 14 (1). SSRN 560982. 
16. ^ Mathews, S.; Datar, V. (2007). "A Practical Method for Valuing Real Options: The Boeing Approach". Journal of Applied Corporate Finance 19 (2): 95–104. 
17. ^ Collan, M.; Fullér, R.; Mezei, J. (2009). "Fuzzy Pay-Off Method for Real Option Valuation". Journal of Applied Mathematics and Decision Sciences 2009 (13601): 1–15. doi:10.1155/2009/238196. 
18. ^ Ronald Fink: Reality Check for Real Options, CFO Magazine, September, 2001
19. ^ See Marco Dias Does Risk-Neutral Valuation Mean that Investors Are Risk-Neutral?, Is It Possible to Use Real Options for Incomplete Markets?
20. ^ valuebasedmanagement.net

Further reading

• Amram, Martha; Kulatilaka,Nalin (1999). Real Options: Managing Strategic Investment in an Uncertain World. Boston: Harvard Business School Press. ISBN 0-87584-845-1. 
• Copeland, Thomas E.; Vladimir Antikarov (2001). Real Options: A Practitioner's Guide. New York: Texere. ISBN 1-587-99028-8. 
• Dixit, A.; R. Pindyck (1994). Investment Under Uncertainty. Princeton: Princeton University Press. ISBN 0-691-03410-9. 
• Moore, William T. (2001). Real Options and Option-embedded Securities. New York: John Wiley & Sons. ISBN 0-471-21659-3. 
• Müller, Jürgen (2000). Real Option Valuation in Service Industries. Wiesbaden: Deutscher Universitäts-Verlag. ISBN 3-824-47138-8. 
• Smit, T.J.; Trigeorgis, Lenos (2004). Strategic Investment: Real Options and Games. Princeton: Princeton University Press. ISBN 0-691-01039-0. 
• Trigeorgis, Lenos (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation. Cambridge: The MIT Press. ISBN 0-262-20102-X. 

External links

Theory

• Identifying real options, Prof. Campbell R. Harvey. Duke University, Fuqua School of Business
• How Do You Assess The Value of A Company's "Real Options"?, Prof. Alfred Rappaport Columbia University and Michael Mauboussin
• Real Options Tutorial, Prof. Marco Dias, PUC-Rio
• The Promise and Peril of Real Options, Prof. Aswath Damodaran, Stern School of Business
• Case Studies And White Papers, Dr. Jonathan Mun

Journals

• Journal of Real Options
• Journal of Real Options and Strategy

Applications

• Evaluating Natural Resource Investments, Michael Brennan and Eduardo Schwartz, UCLA Anderson.
• Applications of option pricing theory to equity valuation, Prof. Aswath Damodaran, Stern School of Business
• Valuing Alternative Market Entry Strategies as “Real-Options”, Prof. Daryl G. Waldron, Trinity University, San Antonio, Texas
• Real options in public infrastructures, course materials, Prof. Richard de Neufville, MIT
• Strategic Technology Investment Decisions in Research & Development David Lackner MIT Lean Advancement Initiative
• Patent Damages and Real Options: How Judicial Characterization of Non-Infringing Alternatives Reduces Incentives to Innovate Hausman, Jerry A., Leonard, Gregory K. and Sidak, J. Gregory
• Establishing Licensing Rates Through Options Fernando Torres MSc
• Real Options and Energy Management, Ehud Ronn, Valery Kholodnyi, Shannon Burchett and others