Scenario Analysis Strict Uncertainty

Scenario Analysis Strict Uncertainty We take the term 'strict uncertainty' from French (1986, p. 32), as it aptly conveys the limiting nature of this approach. In decisions of this type, we assume that the outcome of an option is known with certainty, given that we know the outcome of an uncertain event. An event commonly chosen is the state of the market; equivalent terms are 'states of nature' and scenarios'. In Table, we examine the cash flows that would result from actions A to E, given various market conditions. First, the reader might wish to examine the data and consider which action to choose. Option E can be rejected, as all other options are better in all states of the market. Each of the other options, as we shall see, is preferred by one of a number of selection models. Maximin returns. This is probably the most popular of the selection criteria, being simply the action with the highest minimum returns. Action B fulfils this requirement; though lack-lustre in other respects, it does at least offer a minimum return of 40, and may therefore be considered a relatively safe return. Maximax returns. By contrast, this is possibly the least popular method. It advocates selecting the action with the promise of the highest return irrespective of other possible outcomes; this is, of course, action A. The outcome under bad market conditions would, we suspect, discourage most. Although maximax is rather reckless, maximin is perhaps rather too cautious. A middle way is the optimism-pessimism index (French 1986, p. 37). For this method, we choose a weight for the best and worst outcomes of a decision such that the weights add up to 1 (again, it is the relative importance of weights rather than their absolute value that matters). In Table 3.3 we might weight the worst outcome by 0.7 and the best outcome by 0.3, showing that we consider bad outcomes to be relatively more significant. Action A would score 33.5, B and C score 44.5 and D 46.5, so D would be chosen. As one might expect, D is not the action with the worst outcome, nor has it the The final approach is termed minimax regret. It is not the absolute value of return that matters here, but the difference between what was achieved and the best that might have been achieved in the conditions, i.e. the regret. For instance, if a manager chooses option A and the market is bad, his returns will be 5. Looking at the decision table he will realize that he should have chosen B, earning 40 under bad conditions. Hence his regret will be 40 - 5 = 35 There are many organizational settings where the concept of regret may be important. For example, one can imagine a manager's performance being subjected to a director's comment such as: 'If you had correctly anticipated that the market was going to be good, you could have achieved £100,000 profit. The trouble with you, Mr X, is that you don't know enough about the market!' The decision maker might find it difficult to explain that his actions were the best in view of the uncertainty that presented itself at the time. There is an important point at issue here, for a director will, in many situations, be unable to distinguish between uncertainty that afflicts the best of managers, and uncertainty due, in plain terms, to the manager's lack of ability. Would a better manager have been able to predict the market con-ditions? If so, then regret is indeed a measure of the loss. Table 3.3 shows that the maximum regret for A is 35, B 45, C 15 and D 25. Therefore C is to be preferred, as it minimizes the maximum regret. Each of the options, apart from E, is best by one of the criteria. Option A provides the best maximax returns, B would be chosen under the maximim criteria, C minimaxes regret and D has the best optimism-pessimism index. As decision rules these methods depend upon being able realistically to characterize uncertainty in this way. If the states of nature cannot be divided in this manner, or if we cannot be very sure of the outcome, given a particular state, then this approach is not suitable. The selection of a method depends upon one's attitude towards outcomes. If one above all wishes to avoid low returns, then maximin might be suitable. If, on the other hand, one is only concerned with achieving the highest results, then maximax is suitable, and so on. We will describe this later as a choice that is dependent upon risk attitude; from a reading of section 3.4.3, the reader will appreciate that maximin and the optimismpessimism index are forms of risk aversion and maximax is a form of risk seeing. It is clear that most significant decisions would benefit from a more realistic description of the problem, and a more precise measure of attitude towards the results. One particular development that seems desirable is to assess, in some way, the likelihood of the various states of nature. So far, we have been careful to make no assumption as to this likelihood. If we knew, for instance, that bad market conditions were extremely unlikely, we would probably view A more favourably and B less favourably. The extent of the change would depend upon our attitude towards the results. As this raises wider problems, we defer consideration to the next section. We conclude on a related issue. It is sometimes inferred that where no assumption is made about the likelihood of each state, it is an impartial judgement to assume that each state is equally likely. Although this was once a lashionable notion, we reject it along with most modern writers. The methods described above leave judgement on the states of nature in the realms of uncertainty. That is to say, no estimate is being made of the issue. This is clearly not the same as saying that one set of events is just as likely as another, and that the equal likelihood assumption represents some sort of impartial judgement. Yet such an approach is prevalent. For example, suppose a manager gave a high-low estimate of sales, we suspect that many would assume that the mid-point of the high-low represents an adequate single figure approximation, on the basis that, as nothing has been said about the probabilities within the range, we should assume that they are equally likely. But if the distribution is skewed or generally non-symmetrical, the mid-point may be a wholly unrealistic approximation (see Figure). Decision analysis is not the art of using data and making assumptions about which no opinion either direct or indirect has been expressed. Clearly, our probabilities must be meaningful.