Real Options Tutorial (page 1)

Investment:

"Economics defines investment as the act of incurring an immediate cost in the expectation of future rewards" (Dixit & Pindyck, 1994, p.3)

Three important investment decision characteristics are relevant in Real Options Approach:

Most investments are like a call option on a common stock, that gives the holder the right to make an investment and receive a project (see the call option analogy). The project value fluctuates stochastically and most investments options (or investment opportunities) are not a "now or never" opportunity. There is a value of waiting to invest. You will exercise the option (not the obligation) of investment only if the project is sufficiently "deep in the money". In others words, if the project's output price and/or the dividend yield of the project are sufficiently high.
Some financial options solutions may be useful in the real investments context (with some relevant adaptations and parameters interpretations) using analogies like the dividend yield analogy.

Investment's Return:

The return of an investment, like the return of a stock, comprises the addition of two parcels: the capital gain and the dividends. Over the time, the expected rate of return from a real investment is equal the sum of the expected growth rate (capital gain rate) plus the dividend yield (net cash flow distribution rate or the convenience yield of the underlying commodity, depending of context), see the next equation:

The expected rate of return corresponds to the "risk-adjusted" discounting rate, from a financial market models like the CAPM (Capital Asset Pricing Model). In presence of managerial flexibility the discounting rate changes over time, and the DCF approach becomes quite complex and inadequate.

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Irreversibility:

Investments in productive capacity are, in general, irreversible: you cannot recover all the money, if the business doesn't become prosperous. The cost of investment is partially or completely sunk.

Petroleum examples:

• Completely Sunk:
• the drilling of one well is completely sunk (the cost of recover material like casings is more or equal the material value itself). If the well productivity is worse than you expected or if the oil's price falls, nobody get back the money spent; and
• offshore pipeline (rigid material): the material recovering cost is more or equal the material value itself.
• Partially Sunk:
• the subsea well's completion (production equipment installation into the subsea well) is partially irreversible because the equipment named Wet Christmas Tree (WCT) owns a high value and the net money recovered may reach 20 to 30% from the total well's completion investment; and
• offshore flexible pipeline is partially irreversible. In opposition to the rigid pipeline, the flexible material is more expensive but the service cost is cheaper, so there is a valuable switching option in the flexible pipelines case.

But even in the partially sunk examples, there is a alternative value for the second-hand material only if the problem is technical (a well with low productivity or an exhausted short-lived reserve, for example). If the problem is economic (a depressing oil's price affecting the industry as a whole), the recovered material value is reduced to a little more than the scrap value (the "little" is because the option value of the material to be valuable again in next future).

There are others equipment that are valuable (much more than scrap value) even in large industry specific crisis. Examples are electric generators, computers, trucks, and so on, but the "market for lemons" effect lowers the real value of the equipments. If the industry crisis is not specific ( is a consequence from a world's recession), even these less specific equipments values are affected (depressed) by the lower demand.

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Uncertainty:

Some few concepts:

Certainty : "refers to situations when the investor knows with probability 1 what the return on his investment is going to be in the future" (Levy & Sarnat, 1984, p.77). So uncertainty is when a collection of values (associated with respective uncertain "states of nature") can happen, with strictly positive probabilities for, at least, two different possible values.
Investors are assumed to have rational expectations in that they agree on the mappings of the assets values (for all states-of-nature along the time). See for example Huang & Litzemberger (1988, p.188). In others words, they have rational expectations about the underlying stochastic processes of the assets. This is an equilibrium model under uncertainty. See also the source Lucas & Prescott (1971) and Muth (1961) This concept is more powerful than the adaptive expectations from past prices or the static expectations concept that underlies the traditional Marshallian's microeconomic theory. For this last point and for an example of the rational expectations at work, see (Dixit & Pindyck, 1994, pp.219-221). The problem is to maximize the firm's wealth, supposing as given the assets' stochastic processes, that all the investors with rational expectations agree when reaching the prices equilibrium.
Although some authors make a theoretic distinction between risk and uncertainty, in finance practice these terms are used with the same meaning. From a practical point of view, I prefer the term uncertainty because its neutral connotation is more appropriated for a scientific economic study (risk has frequently a negative connotation, or emphasizes the "bad side" of the uncertainty). The term "risk" is usual (and useful) in financial markets and financial operations (hedging, dividend and debt policy) in corporations, not in economic decisions.

The Two Sides of the Uncertainty and the Asymmetry Effects:
Uncertainty means for example, that the future price of oil's barrel will be up or down, in relation to the forecasted price. So uncertainty has two sides: the "good" side and the "bad" one. (See also in "Real Options by Slides" page, the
picture "The Two Sides of the Uncertainty").
Rational managers are not passive: management can revise investment and operating decisions in response to market conditions, in order to maximize the firm's wealth. They act to take advantage in "good times" (market's upside) and mitigate losses in "bad times" (market's downside). So, in presence of economic uncertainty, active management adds value to investment opportunity, which is not captured by the traditional use of discounted cash flows (DCF) method. See for example Trigeorgis & Mason (1987, p.15)
For example, the ability to wait permits that the manager "see" the evolution of the oil prices, before takes an irreversible decision to invest in a new oilfield or abandon an old oilfield: if the oil's price increases to a sufficiently high level (the good side of uncertainty), the manager makes the investment in the new oilfield (in better conditions or with less probability of losses) or reopen the old oilfield. However, if the oil's price decreases (the bad side of uncertainty), the manager doesn't invest in the new oilfield and can abandon the old oilfield (at a sufficiently low price).
If the uncertainty is technical, for example a R&D investment, again the uncertainty adds value to this opportunity: a step by step investment reveals informations. So, a rational manager will stop the project (or reduce the investment) if the information is unfavorable (bad side), and continue the investment (or even speed it up) if is a favorable one (good side).
So, an increase of uncertainty, increases the investment opportunity value ( the opposite that tells the traditional DCF) in view of the asymmetric manager's action in response to uncertainty. This is the asymmetry on the value of the opportunity to invest in a project (or option to invest), the first asymmetric effect of the uncertainty.
However, increasing the value of the option to invest doesn't mean increasing the willingness to invest: an increase of economic uncertainty reduces the willingness to invest (or delays the investment decision), because the increment in the investment opportunity value is due to the waiting value.
What side of uncertainty is more important for decisions? The answer is: depends on the kind of decision to be taken (see, in the "Real Options by Slides" page, the picture "The Managerial Decisions"). If the decision is to invest or wait, the bad side is the relevant one, and the decision is governed by the "bad news principle" (or fear/caution principle).
If the decision is to abandon or wait, the good side is the relevant one, and the decision is governed by the "good news principle" (or the hope principle). See for example Dixit & Pindyck, 1994 , pp.18 and 40-41.
These different roles played by the two sides of the uncertainty is the asymmetry on the decision rule, the second asymmetric effect of the uncertainty.

Economic Uncertainty and Technical Uncertainty
There are two types of uncertainty which has different (opposite) effects on investment decision rule:
The economic uncertainty is correlated with the general movements of the economy (industry's prices/costs movements). So the oil price (or the reserve price, or the rig rental rates, etc.) is an example of variable with economic uncertainty. This uncertainty is exogenous to the decision process: the oil price (or its variance) doesn't change because you go ahead with the oilfield development or not (supposing a decision from a price taker firm, not an OPEC decision). The economic uncertainty incentives the waiting (for better conditions) to invest, leading to postpone investments. A project with a considerable positive Net Present Value (NPV) can be insufficient to immediate investment: it is necessary that the project to be "deep in the money".
The technical uncertainty is NOT correlated with the general movements of the economy/industry. This uncertainty is endogenous to the decision process. An example is a non-delimited new oilfield: the oil-in-place volume (or the gas, or the water-in-place, or the average permeability, etc.) is a variable with technical uncertainty. In this case, waiting doesn't change the variable value. Only with a step-by-step investment strategy (3D-seismic, drilling some wells, pilot production, etc.) is possible to reduce this kind of uncertainty. So investing (step-by-step) provides valuable information (reduce the variance of the uncertainty and revise the expected value). This additional value is called a shadow value, because it is not a directly measurable cash flow (traditional DCF doesn't "see" this). The technical uncertainty, on the contrary of the economic uncertainty, incentives the starting of the investments (but its necessary to be staged investments). In presence of relevant technical uncertainty, a project with negative NPV, can be economically optimal to begin investing. For each new relevant information is necessary to revise the investment decision: go ahead (or even speed it up) if the true value is on the "good side" of uncertainty, or stop if the "bad side" is the true one.
For a modern technical uncertainty explanation, including a model with the two types of uncertainty combined into the same variable (cost), see Dixit & Pindyck, 1994 , pp.11, 47-48, Chapter 10/section 4, and p.397 footnote 2) and also Pindyck, R.S. (1993)
One last question: What the difference between a investor holding a common stocks' portfolio, and a manager with a projects' portfolio? In the first case the investors can't take advantage of the technical uncertainty (investors can only change the portfolio composition, and eliminate this kind of uncertainty by diversification, cannot maximize the value of each stock), but in the second case the managers can take advantage of this, with optimal management of these projects. Managers don't want eliminates technical uncertainty by diversification, they want maximize the firm value by taking advantage of this one.
So technical uncertainty is important only for managers.

Uncertainty and Hedge: It's very known the Modigliani & Miller (MM) proposition II (see MM's propositions). There is another example of application for the MM's theorem, as indicated by Dixit & Pindyck (1994, p.11), for the investment opportunity (or investment option): "the option value is not affected if the firm is able to hedge the risk by trading in forward or futures market. In efficient markets such risk is fairly priced, so any decrease in risk is offset by the decrease in return" and the financial operation "has no effect on firm's real decisions".
For non-perfect markets, in general is possible to say that financial operations (like hedge) has a secondary (second-order) effect in real investment of corporations. So first the firm takes an economic decision about the production project investment (most cases a preference-free decision). After this, the firm takes the financial and/or hedging decision (most cases a preference-dependent decision).
Here has NOT been saying the financial decision is unimportant. Only argues this is a separated/independent decision that takes place after the investment (economic) decision. Hedging and Capital Structure aren't scope of this site.

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Call Option Analogy:

An irreversible investment opportunity (F) is like a financial call option: the manager can (but is not obligated) spend the investment cost (D) to obtain a production asset (V), and frequently this investment opportunity remains only by a time interval (T-t).
The financial call option is like F, their exercise price is like D, the stock (received with the exercise of the option) is like V, and the call's expiration time is like (T-t). The financial analogy is more adequate with financial assets paying a continuous dividends (or interest) because the analogy with cash flows (see below the dividend yield analogy).
The expiration time in real investment can be the time from a patent's right, the time from a lease in a offshore tract, or an estimate time considering the threat of preemption or intense industry rivalry (for this last point, see Kester, 1984).
However, there are some differences and considerations when performing this analogy: Sick, 1995 (abstract) gives some lessons: "the early exercise decision is more important in real options analysis, greater flexibility in modelling project is needed" and his instructive practical lesson: "The ability to be able to build a useful and understandable model, is more important to the analyst than precise estimates of option value."

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Dividend Yield Analogy:

The net cash flows from a production project is analogous to a dividend from a stock, or a periodic revenue from assets in general.
There is an analogy between the dividend yield from a project and the dividend yield characterized by the currency interest rate, in the currency option market, for example, because the dividends are close to continually distributed over the time. This analogy is more general: the option in a project paying a continuous net cash flow is analogous with the options written on commodities and commodity futures contracts. The underlying commodity varies from a natural resource like petroleum or silver to a financial issue such as foreign currency or a Treasury bond. Each case has its particulars adaptations, but the general understanding is the same
In most cases, is reasonable to consider the dividend yield from the project as a constant even when the cash flows falls over the time (like a depletive oil field), because the project value (the oilfield value) also decreases, so that the percentage variations can be considered more or less the same (or when using an average value is reasonable). With a constant dividend yield, a simplified solution could be used, like an analytic approximation. Some analytic approximation models are available in the literature on financial options that could be used in the real options context (see in the bibliographical page). Others approaches probably just find numerical solutions, such as interesting models that consider the dividend yield as a function of the underlying project value or even models considering the dividend yield as stochastic process itself, correlated with the project's value stochastic process.

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• Call Option: gives the holder the right (not the obligation) to buy the underlying asset by a certain expiration date for a certain exercise price.
In finance the underlying asset could be stocks, commodities contracts, futures contracts, foreign currencies, stock indices, and so on. In real investments context, the value of the implanted project (after the investment) is the underlying asset, and the net cash flows represents the dividends (see also the dividend yield analogy and the call option analogy ).
There are two kinds of calls: "American Call Options" and "European Call Options".

• Theoretic Distinction Between Risk and Uncertainty: as Simonsen (1994, p.399) and Levy & Sarnat, 1984, p.104) point out, the distinction between risk and uncertainty is creditable to F. Knight (in Risk, Uncertainty and Profit, 1921, Chapter VII). Risk is when the random variable has a known probability distribution. Uncertainty is when the random variable has an unknown probability distribution. It is always possible to convert uncertainties into risks by introducing subjective probabilities. Levy & Sarnat (p.106) argues that "In the case of financial investment, probability beliefs are almost invariably subjective" and in the book they "use the terms risk and uncertainty interchangeably".

• The "Bad News Principle": In a world with uncertainty , a "good" project (with positive net present value) can be postponed if a firm can wait to invest, because of the "bad news principle": there is a positive probability of a downward price movement, so that the waiting avoids the possibly losses from the project investment. The threshold price (that warrants immediate investment) depends of the size of the downward movement (not of the upward movement size) and the probability (besides the investment cost, of course), as shown in the equation 16, p.41, in the Dixit & Pindyck book.
This "bad news principle" was first pointed out by Bernanke, 1983, and some ideas can also be found in Cukierman, 1980.
A nice and instructive argument is presented by Dixit, 1992 (see p.123), illustrating the "bad news principle": Why the Japanese firms (despite their larger fixed costs) are more aggressive investors than the American ones? Because they are protected from the downside risk through the government supports. So the value of waiting to invest is quite small, because the downside movement potential is small.
For disinvestment (abandon) the argument turns around and becomes the "good news principle": the option value of keeping the operation alive is governed mainly by the upside potential.

BIBLIOGRAPHICAL REFERENCES

• Bernanke, B.S. (1983): Irreversibility, Uncertainty, and Cyclical Investment
Quarterly Journal of Economics, 98, February 1983, pp.85-106

• Brealey, R.A. & S.C. Myers (1991): Principles of Corporate Finance
McGraw-Hill, Inc., fourth ed., 1991

• Cukierman, A. (1980): The Effects of Uncertainty on Investment under Risk Neutrality with Endogenous Information
Journal of Political Economy, vol.88, June 1980, pp.462-475

• Dixit, A.K. (1992): Investment and Hysteresis
Journal of Economic Perspectives, vol.6, no 1, Winter 1992, pp.107-132

• Dixit, A.K. & R.S. Pindyck (1994): Investment under Uncertainty
Princeton University Press, Princeton, N.J., 1994

• Huang & Litzemberger (1988): Foundations for Financial Economics
Elsevier Science Publishers Co., Inc., 1988

• Kester, W.C. (1984): Today’s Options for Tomorrow’s Growth
Harvard Business Review, no 62, March-April 1984, pp.153-160

• Levy, H. & M. Sarnat (1984): Portfolio and Investment Selection: Theory and Practice
Prentice-Hall International, Englewood Cliffs, NJ, 1984

• Lucas, R.E. Jr. & E.C. Prescott (1971): Investment under Uncertainty
Econometrica, vol.39, no 5, September 1971, pgs.659-681

• Modigliani, F & M.H. Miller (1958): The Cost of Capital, Corporation Finance, and the Theory of Investment
American Economic Review, vol.48, June 1958, pp.261-297

• Muth (1961): Rational Expectations and the Theory of Price Movements
Econometrica, vol. 29, 1961, pp. 315-335

• Pindyck, R.S. (1993): Investments of Uncertain Cost
Journal of Financial Economics, vol. 34, August 1993, pp.53-76

• Sick, G. (1995): Real Options
Paper presented at INFORMS International Singapore, June 25-28, 1995, 70 pp.

• Simonsen, M.H. (1994): Analytical Essays
FGV-RJ Editions, 1994 (in Portuguese)

• Trigeorgis, L. & S.P. Mason (1987): Valuing Managerial Flexibility
Midland Corporate Finance Journal, Spring 1987, pp.14-21

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