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# There's No Shortcut to Real Options

Mathematical Insight Allows Valuation of Options

The mathematical insight that allows valuation of options involves the creation of a portfolio of risk-free debt (i.e. government bonds), the asset (whether it be a share of stock or an oil and gas project) and an option on the asset.

By constructing the portfolio correctly, it can be both risk-free and self-financing.

Once this is done, the value of an option to acquire the asset (or invest to develop it) is a function of the uncertainty of the economic return the asset will generate (which can be estimated) and four factors that are known:

• The exercise price.
• The risk free rate of interest.
• The current value of the asset.
• The time remaining during which the option can be exercised.

By pricing the risk (chance) in the project explicitly the method does away with the need to estimate risk-adjusted discount rates.

The connection to standard net present value is very simple: If one looks at the Black-Scholes formula for pricing call options and sets the uncertainty factor to zero plus the time remaining prior to expiry of the option to zero, the formula says the option's value is equal to the asset's value less the exercise price.

The mathematical insight that allows valuation of options involves the creation of a portfolio of risk-free debt (i.e. government bonds), the asset (whether it be a share of stock or an oil and gas project) and an option on the asset.

By constructing the portfolio correctly, it can be both risk-free and self-financing.

Once this is done, the value of an option to acquire the asset (or invest to develop it) is a function of the uncertainty of the economic return the asset will generate (which can be estimated) and four factors that are known:

• The exercise price.
• The risk free rate of interest.
• The current value of the asset.
• The time remaining during which the option can be exercised.

By pricing the risk (chance) in the project explicitly the method does away with the need to estimate risk-adjusted discount rates.

The connection to standard net present value is very simple: If one looks at the Black-Scholes formula for pricing call options and sets the uncertainty factor to zero plus the time remaining prior to expiry of the option to zero, the formula says the option's value is equal to the asset's value less the exercise price.

In a real options context this would equate to the net present value being equal to the present value of future cash flows less the investment required to realize them.

In simple terms, when you calculate a net present value you are calculating an option price assuming no uncertainty in outcome and no time available to defer investment. Calculating the uncertainty factor is a much more precise exercise than estimating a risk-adjusted discount rate, which makes option-pricing the preferred method for analyzing investments under conditions of uncertainty.

Several criticisms of the real option approach are mentioned repeatedly:

➤ First, the reasonable comment that, used incorrectly, it is merely a black box where one can specify some relatively unchallengeable assumptions of uncertainty and produce a precise (but not accurate) value for a risky investment.

To be frank, real option analysis is frequently dismissed as a flaky approach used to justify higher lease bonuses and inflated acquisition prices by undisciplined — or worse, unethical — analysts and prospectors.

➤ Second (and related), specifying option value requires that a company have the discipline to act when the method requires it.

This means that if value is predicated in part on the option to abandon a project at a specific decision point if results fall below a certain expectation, then abandon you must if all conditions of the analysis prevail.

➤ Third, most other criticisms flow from a single shortcoming of the method.

The mathematics underlying the theory is intractable and the insight of the replicating portfolio approach is not as intuitively satisfying in a real option context as it is in evaluating financial options where the underlying asset, usually a share of stock, is freely traded in a public market.

If one wishes to understand the method there is no real shortcut — although the math involved in the binomial lattice approach is not that difficult, and the calculations can be done with a spreadsheet.

Real option valuation of complex oil and gas investment decisions is not easy, but it does provide a much better approach to such decisions — and, when done properly (rather than by some shortcut, cookbook approach), it actually prevents the kind of over-valuation of risky investments that it is often accused of enabling.

The true value of the approach is not that it provides an estimate of the value of undertaking a specific investment, but rather the discipline of approaching a complex set of decisions as a series of embedded options — and developing a strategy to manage the project as uncertainty resolves.

For those interested in pursuing the subject further there are several excellent books that are intended for practitioners rather than financial theorists. These include:

• Martha Amram and Nalin Kulatilaka's Real Options: Managing Strategic Investment In An Uncertain World (Harvard Business School Press, 1999).
• Thomas Copeland and Vladimir Antikarov's Real Options: A Practitioners Guide (TEXERE, 2001).
• Gordon Sick's Capital Budgeting with Real Options, Monograph Series in Finance and Economics, Monograph 1989-3 (Salomon Brothers Center for the Study of Financial Institutions, Leonard N. Stern School of Business, New York University, 1989)
• Lenos Trigeorgis' Real Options: Managerial Flexibility and Strategy in Resource Allocation (MIT Press, 1999)
• "Journal of Applied Corporate Finance," Volume 13, Number 2 (Summer 2000) & Volume 14, Number 2 (Summer 2001), published by Stern Stewart & Co. These were special issues devoted to Real Options and both contain excellent papers on the subject.
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