An unavoidable opportunity loss is the cost associated with uncertainty. Therefore, the expected opportunity loss associated with a decision provides a measure of the expected monetary gain from the removal of all uncertainty about future events. From the opportunity loss or regret matrix, the cost of uncertainty is measured by the minimum expected opportunity loss. From the payoff matrix, the cost of uncertainty is measured by the difference between the expected payoff associated with choosing the correct alternative under each state of nature (which will be known only after the fact) and the highest expected payoff available from among the decision alternatives. The cost of uncertainty is the unavoidable economic loss that is due to chance. Using this concept, it becomes possible to judge the value of gaining additional information before choosing among decision alternatives.

The previous gasoline-pricing problem can illustrate this use of opportunity loss. On the basis of the data in Table 14.5, the expected opportunity loss of each decision alternative can be calculated as shown in Table 14.6. Here it is assumed that U-Pump projects a 50/50, or 50 percent, chance of a competitor price reduction. The minimum expected opportunity cost in this case is $750 and represents U-Pump's loss from not knowing its competitor's pricing reaction with certainty. This cost of uncertainty represents the $750 value to U-Pump of resolving doubt about its competitor's pricing policy. U-Pump would be better off if it could eliminate this uncertainty by making an expenditure of less than $750 on information gathering.

Firms often engage in activities aimed at reducing the uncertainty of various alternatives before making an irrevocable decision. For example, a food-manufacturing company will employ extensive marketing tests in selected areas to gain better estimates of sales potential before going ahead with the large-scale introduction of a new product. Manufacturers of consumer goods frequently install new equipment in a limited number of models to judge reliability and customer reaction before including the equipment in all models. Similarly, competitors often announce price changes well in advance of their effective date to elicit the reaction of rivals.

Risk analysis plays an integral role in the decision process for most business problems. This chapter defines the concept of economic risk and illustrates how the concept can be dealt with in the managerial decision-making process.

• Economic risk is the chance of loss due to the fact that all possible outcomes and their probability of occurrence are unknown. Uncertainty exists when the outcomes of managerial decisions cannot be predicted with absolute accuracy but all possibilities and their associated probabilities of occurrence are known.

• Business risk is the chance of loss associated with a given managerial decision. Many different types of business risk are apparent in the globally competitive 1990s. Market risk is the chance that a portfolio of investments can lose money because of swings in the stock market as a whole. Inflation risk is the danger that a general increase in the price level will undermine real economic values. Interest-rate risk stems from the fact that a fall in interest rates will increase the value of any agreement that involves a fixed promise to pay interest and principal over a specified period. Credit risk is the chance that another party will fail to abide by its contractual obligations. Corporations must also consider the problem of liquidity risk, or the difficulty of selling corporate assets or investments that have only a few willing buyers or that are otherwise not easily transferable at favorable prices under typical market conditions. Derivative risk is the chance that volatile financial derivatives could create losses in underlying investments by increasing rather than decreasing price volatility.

• Cultural risk is borne by companies that pursue a global rather than a solely domestic investment strategy. Product market differences due to distinctive social customs make it difficult to predict which products might do well in foreign markets. Currency risk is another important danger facing global businesses because most companies wish to eventually repatriate foreign earnings back to the domestic parent. Finally, global investors also experience government policy risk because foreign government grants of monopoly franchises, tax abatements, and favored trade status can be tenuous. Expropriation risk, or the risk that business property located abroad might be seized by host governments, is another type of risk that global investors must not forget.

• The probability of an event is the chance, or odds, that the incident will occur. If all possible events or outcomes are listed, and if a probability of occurrence is assigned to each event, the listing is called a probability distribution. A payoff matrix illustrates the outcome associated with each possible state of nature. The expected value is the anticipated realization from a given payoff matrix.

• Absolute risk is the overall dispersion of possible payoffs. The smaller the standard deviation, the tighter the probability distribution and the lower the risk in absolute terms. Relative risk is the variation in possible returns compared with the expected payoff amount. Beta is a measure of the systematic variability or covariance of one asset's returns with returns on other assets.

• A normal distribution has a symmetrical distribution about the mean or expected value. If a probability distribution is normal, the actual outcome will lie within ±1 standard deviation of the mean roughly 68 percent of the time. The probability that the actual outcome will be within ±2 standard deviations of the expected outcome is approximately 95 percent; and there is a greater than 99 percent probability that the actual outcome will occur within ±3 standard deviations of the mean. A standardized variable has a mean of 0 and a standard deviation equal to 1.

• Risk aversion characterizes individuals who seek to avoid or minimize risk. Risk neutrality characterizes decision makers who focus on expected returns and disregard the dispersion of returns (risk). Risk seeking characterizes decision makers who prefer risk. At the heart of risk aversion is the notion of diminishing marginal utility, where additional increments of money bring ever smaller increments of marginal utility.

• Under the certainty equivalent approach, decision makers specify the certain sum that they regard comparable to the expected value of a risky investment alternative. Any expected risky amount can be converted to an equivalent certain sum using the certainty equivalent adjustment factor, a, calculated as the ratio of a certain sum divided by an expected risky amount, where both dollar values provide the same level of utility. The risk-adjusted valuation model reflects both time value and risk considerations.

• The risk-adjusted discount rate k is the sum of the risk-free rate of return, RF, plus the required risk premium, Rp. The difference between the expected rate of return on a risky asset and the rate of return on a riskless asset is the risk premium on the risky asset.

• A decision tree is a map of a sequential decision-making process. Decision trees are designed for analyzing decision problems that involve a series of choice alternatives that are constrained by previous decisions. Decision points represent instances when management must select among several choice alternatives. Chance events are possible outcomes following each decision point.

• Computer simulation involves the use of computer software and workstations or sophisticated desktop computers to create a wide variety of decision outcome scenarios. Sensitivity analysis focuses on those variables that most directly affect decision outcomes, and it is less expensive and less time-consuming than full-scale computer simulation.

• Game theory is a useful decision framework employed to make choices in hostile environments and under extreme uncertainty. A variety of auction strategies are based on game theory principles.

• The most familiar type of auction is an English auction, where an auctioneer keeps raising the price until a single highest bidder remains. A winner's curse results when overly aggressive bidders pay more than the economic value of auctioned items. In a sealed-bid auction, all bids are secret and the highest bid wins. A relatively rare sealed-bid auction method is a Vickrey auction, where the highest sealed bid wins, but the winner pays the price of the second-highest bid. Another auctioning method is the so-called reverse or Dutch auction. In a Dutch auction, the auctioneer keeps lowering a very high price until a winning bidder emerges. The winning bidder is the first participant willing to pay the auctioneer's price.

• A game-theory decision standard that is sometimes applicable for decision making under uncertainty is the maximin criterion, which states that the decision maker should select the alternative that provides the best of the worst possible outcomes. The minimax regret criterion states that the decision maker should minimize the maximum possible regret (opportunity loss) associated with a wrong decision after the fact. In game theory, opportunity loss is defined as the difference between a given payoff and the highest possible payoff for the resulting state of nature. From the opportunity loss or regret matrix, the cost of uncertainty is measured by the minimum expected opportunity loss.

Decision making under conditions of uncertainty is greatly facilitated by use of the tools and techniques discussed in this chapter. Although uncertainty can never be eliminated, it can be assessed and dealt with to minimize its harmful consequences.

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