Risk and Uncertainty

Strategic planning and management often is concerned with future events that are inevitably characterized by uncertainty. It is important to recognize such uncertainty and to explicitly deal with it from the outset. Strategic decisions should involve an assessment of uncertainty and risk based on available estimates of alternative payoffs or gains. A risk is taken no matter what the decision. Even the decision to do nothing involves the risk of lost opportunity. An effective manager, whether in the public or private sector, must be aware of how opportunity, innovation, and risk are interrelated and must be willing to take risks appropriate to his or her level of responsibility.

Converting Uncertainty to Risk

One manager's uncertainty may be another's acceptable risk. What one manager may interpret as an uncertain situation to be avoided, another may see as an opportunity, albeit involving some risk. Although the two terms often are mistakenly used interchangeably, the distinction between uncertainty and risk is important in fiscal management.

Certainty can be defined as a state of knowledge in which the specific and invariable outcomes of each alternative course of action are known in advance. The key to certainty is the presence of only one state of nature (although under some circumstances, numerous strategies maybe applied to achieve that state). This condition enables the manager to predict the outcome of a decision with 100 percent probability.

Uncertainty can be defined as a state of knowledge in which one or more courses of action may result in a set of possible specific outcomes. The probabilities of these outcomes, however, are neither known or meaningful. As Archer has observed, uncertainty involves a range of conditions in which probability distributions vary from a condition of relative confidence, based on objective probabilities, to a condition of extreme uncertainty, with little or no information as to the probable relative frequency of particular events. [6]

If a manager is willing to assign objective or subjective probabilities to the outcome of uncertain events, then such events may be said to involve risk. Risk is a state of knowledge in which each alter-native leads to one of a set of specific outcomes, each outcome occurring with a probability that is known to the decision maker. More succinctly, risk is reassurable uncertainty. Risk is measurable when decision expectations or outcomes can be based on statistical probabilities. The event of a Republican or Democratic victory in any given election is an uncertain outcome. The event of drawing a red card from a well-shuffled deck is an example of a risky outcome with a probability of 50 percent.

Uncertainty, Risk, and Probability Functions

Risk and uncertainty must be confronted from two primary sources: (1) statistical uncertainty, and (2) uncertainty about the state of the real world in the future. The first type of uncertainty is usually less troublesome to handle. It arises from chance elements in the real world and would exist even if the second type of uncertainty were zero. Monte Carlo and related probability techniques can be used to deal with statistical uncertainty when it is encountered. [7]

Establishing a probability function can bring problems within more manageable bounds by reducing uncertainty to some level of risk that may be tolerable, depending on the risk threshold of the manager or organization. Probabilities can be established either a posteriori (by induction or empirical measurement) or a priori (by deduction or statistical inference).

The basic conditions necessary to establish a posteriori probability are: (1) the number of cases or observations must be sufficiently large to exhibit statistical stability; (2) the observations must be repeated in the appropriate population or universe; and (3) the observations must be made on a random basis. The inductive approach offers the maximum opportunity for applied decision theory, because the number and range of situations in which such objective probabilities can be applied are increasing significantly.

Under the deductive, or a priori approach, a probability statement is not intended to predict a particular outcome for a given event. Rather, it asserts that in a large number of situations with certain common characteristics, a particular outcome is likely to occur. In short, a statistical inference is made regarding the probable outcome of an uncertain event or series of events.

Uncertainty and Cost Sensitivity

The second type of uncertainty--uncertainty about the future state of the real world--is more troublesome for fiscal management. In such cases, the use of sophisticated statistical techniques may be little more than expensive window dressing. When the environment is uncertain, an expected value approach often must be applied. Expected value is deter-mined by multiplying the value products across all possible outcomes. In mathematical terms, expected value (EV) can be expressed as:

EV = P1$1 + P2$2 + . . . Pn$n.

where P stands for probability, $ stands for the value of an outcome, and

P1 + P2 + . . . Pn = 1.

Several techniques utilizing the concept of expected value have been developed to analyze uncertainty about the future state of events. These techniques include: (1) sensitivity analysis, (2) contingency analysis, and (3) a fortiori analysis. Each of these techniques is applicable in cost analysis under varying circumstances. The purpose here is not to present a "how-to" approach, but rather to identify the conceptual framework underlying these methods.

Sensitivity analysis is designed to measure (often quite crudely) the possible effects that variations in uncertain decision elements (for example, costs) may have on the alternatives under analysis. In most strategic decisions, a few key parameters exhibit considerable uncertainty. The analyst must determine a set of expected values for these parameters (as well as other parameters). Recognizing that these expected values may be, at best, "guesstimations," the analyst may use several values (optimistic, pessimistic, and most likely) in an attempt to ascertain how sensitive the results might be to variations in the uncertain parameters.

Exhibit 8 illustrates how sensitivity analysis can be used to determine the variations in rankings among several alternatives, based on anticipated costs. First, the analyst sets the expected values for all costs that are certain (for which some reliable basis exists for establishing an estimated cost). Three values for the uncertain costs are then determined. The optimistic cost represents an assessment of cost based on the assumption that everything will go right with the project--that all of the uncertainty is resolved favorably. The pessimistic cost represents the opposite assumption. The most likely cost figure falls somewhere in between these two extremes.

Two points concerning uncertainty are illustrated in Exhibit 8. First, the range of uncertainty may vary from alternative to alternative (for alternative A, the uncertain range is $10,000 to $110,000; for alternative B, $30,000 to $115,000; and for alternative C, $20,000 to $90,000). Second, uncertain costs may not always be the critical factor in determining the "best" alternative. For example, although uncertain costs for alternative C vary over the narrowest range, this alternative still ranks third except under conditions of high, or pessimistic, uncertain costs.

Probability theory also can be applied in connection with sensitivity analysis. Assume, for example, that the probability of the most likely costs being realized is 50 percent; the most pessimistic costs, 30 per-cent; and the most optimistic costs, 20 percent. The composite expected values for all costs are shown at the bottom of Exhibit 8. Given these probability assumptions, alternative B is clearly the preferred alternative.

Contingency analysis is designed to examine the effects on alternative choices when a relevant change is postulated in the evaluation criteria. This approach can also be used to determine the effects of a major change in the general decision environment, or "ground rules," within which the problem situation exists. In short, contingency analysis is a "with and without" approach. In the field of public health, for ex-ample, alternative approaches to environmental health might be evaluated with and without a major new code enforcement program. In a more local context, a public service organization might evaluate various sites for the location of its headquarters under existing conditions of client distribution and access routes. Additional evaluations might then be made, assuming different client distributions and other route configurations.

A fortiori analysis (from the Latin, meaning "with stronger reason") is a method of deliberately "stacking the deck" in favor of one alternative to determine how it might stand up in comparison to other approaches. Suppose that, prior to analysis, the governing board strongly favors alternative C. In performing the analysis on C in comparison to the other feasible alternatives, a deliberate choice is made to resolve any major uncertainties in favor of C. The analyst would then determine how each of the other alternatives compared under these circumstances. If some alternative other than C looks good (that is, if C does not show up "with stronger reason" to be the best alternative), there may be a very strong case for dismissing the initial intuitive judgment in favor of C. This type of analysis can be carried out in a series of trials, with each alternative, in turn, being favored in terms of the major uncertainties.

These three techniques for dealing with uncertainty may be useful not only in a direct analytical sense; they may also contribute indirectly to the resolution of problem situations. Through sensitivity and contingency analyses, for example, it may be possible to gain a better understanding of the really critical uncertainties of a given problem. With this knowledge, a new alternative might be formulated that would provide a reasonably good hedge against a range of more significant uncertainties. This is often difficult to do. When it can be accomplished, however, it may offer one of the best ways to offset the uncertainties of a problem situation.

Uncertainty, Risk, and Expected Utility

The assumption that people actually behave rationally in the manner suggested by the mathematical notion of expected value often is contradicted by observable behavior in risky situation. People are willing to buy insurance, for example, even though they know that the insurance company makes a profit. People are willing to buy lottery tickets even though the chances of winning are minimal.

Consideration of the problem of insurance and the so-called "St. Petersburg paradox" led Daniel Bernoulli, an eighteenth-century mathematician to propose that these apparent contradictions could be resolved by assuming that people act so as to maximize their expected utility, rather than expected value. Thus, people buy insurance because the consequences against which they are insured are significant in view of the costs. People are willing to invest small amounts of money in lottery tickets, even though the probability outcome is highly uncertain, because the payoff is so high relative to their expected utility.

Extensive research has been performed in the area of risk and uncertainty because the behavior of decision makers often appears to violate commonly accepted axioms of rational behavior. Although no exact probabilities may exist for the success or failure of a particular event, has observed that an individual with "clear-cut, consistent preferences over a specified set of strategies. . . will act as if he has assigned probabilities to various outcomes." [8] The values for the probabilities will be unique for each individual and not unlike the values of utility that might be assigned to an individual through a study of his or her social preferences. The obverse of social preferences, of course, is risk aversion, a subject on which opinions vary. [9]

As most economists will now admit, utility theory alone cannot resolve the disputes over social preference and/or aversion to risk. There are numerous situations in which fiscal managers will have to obtain a more careful reading of the various utility functions or preferences of their clientele and the organization as a whole. As Stokey and Zeckhauser explain, strategic choice under uncertainty is a threefold process: [10]

(1) Alternatives must be assessed to determine what probabilities and payoffs are implied for individual members of the organization and its clientele.

(2) Attitudes toward risk of these individuals must be evaluated to determine the certainty equivalents of these probabilities and payoffs.

(3) Having estimated the equivalent benefits that each alternative offers to different members of the organization/clientele, the decision maker must select the preferred outcome.

Although this process may sound simple, it often is very complex in application. Some basic tools been developed to aid in unraveling these complexities. [11] These techniques can be brought into play, however, only after the manager has a fairly good understanding of organizational and/or clientele preferences. Once the groundwork for approximating utility has been laid, the fiscal manager will be better prepared to address uncertainties in a more systematic fashion.

A basic objective of information management is to reduce uncertainty by bringing to light information that will clarify relationships among elements in the decision process. This reduction of uncertainty may cause the risk associated with a particular choice: (1) to remain unchanged; (2) to decrease (as in the case where a reduction in uncertainty permits the assessment of more definitive probabilities); or even (3) to increase (as happens when the additional information reveals risk factors that previously were unknown). Thus, although risk and uncertainty are interrelated, they must be treated independently in many situations.

Summary

Cost-benefit and cost-effectiveness analysis can be applied at two pivotal points in the evaluation of resource commitments. In the planning stage, cost-benefit analyses are based on anticipated costs and benefits. Such analyses are not necessarily empirically based. After a program or project has been implemented and shown to have a significant impact, cost-benefit and cost-effectiveness analyses can be used to assess whether the costs of the program are justified by the magnitude of net outcomes. Such after-the-fact analyses should be based on detailed studies of available empirical data.

Cost-benefit and cost-effectiveness models need not be adopted "whole cloth." A number of subroutines may be introduced into ongoing cost analysis procedures. Decision inputs can be developed to include considerations of time preference and marginal productivity of capital investment. The techniques of cost curve analysis can be applied to a variety of decision situations. The examination of expenditures in terms of program objectives and the evaluation of total benefits for alternative program expenditures can be important derivatives of cost-benefit techniques. The extended time horizon adopted in these analytical methods leads to a fuller recognition of the need for life-cycle costing and benefits analysis. The importance of incremental costing, sunk costs, and inheritable assets also is underlined by this extended perspective. Cost-goal and cost-constraint analyses add other important dimensions to the information available to the decision maker. As the complexity of the resource allocation problem becomes more evident, other subroutines may be adopted, depending on the availability of data and the capabilities of the analyst.

Uncertainty can be reduced and risk can be brought within tolerable limits through the generation of management information that clarifies critical relationships among elements in the decision process. Various methods have been formulated for converting uncertainty to risk --including the use of objective and subjective probabilities and the techniques of sensitivity analysis, contingency analysis, and a fortiori analysis. The concept of expected utility has been touched upon in this chapter in an effort to provide the reader with a broader understanding of the critical dimensions of strategic decisions.

Endnotes

[3] A.R. Prest and R. Turvey, "Cost Benefit Analysis: A Survey," The Economic Journal (1965), P. 583.

[4] Anatol Rapoport, "What Is Information" ETC: A Review of General Semantics 10 (Summer 1953), p. 252.

[5] Otto Eckstein, Water Resource Development (Cambridge, MA: Harvard University Press, 1958).

[6] Stephen H. Archer, "The Structure of Management Decision Theory," Academy of Management Journal 8 (December 1964), p. 283.

[7] For a discussion of Monte Carlo techniques, see: E.S. Quade, Analysis for Public Decisions (New York: American Elsevier, 1975).

[8] Sheen Kassouf, Normative Decision-Making (Englewood Cliffs, NJ: Prentice-Hall, 1970), p. 46

[9] For a broader discussion, see Jack Hirshleifer and David L. Shapiro, "The Treatment of Risk and Uncertainty," in Robert H. Haveman and Julius Margolis (eds.), Public Expenditures and Policy Analysis, 2nd ed. (Chicago, Ill.: Rand McNally, 1977), pp. 180-203.

[10] Edith Stokey and Richard Zeckhauser, A Primer for Policy Analysis (New York: Norton, 1978), p. 252.

[11] Howard Raiffa, Decision Analysis (Reading, MA.: Addison-Wesley, 1968). For an introductory discussion of Markov chains, see Stokey and Zeckhauser, A Primer for Policy Analysis, chap. 7.

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