DECISION CRITERIA

2.3 DECISION CRITERIA

The selection of a decision criterion is an essential part of DMUU, expressing decision-makers’ impatience and attitudes towards uncertain outcomes and valu- ing them. Below we shall discuss a few commonly used approaches.

2.3.1 The expected value (or Bayes) criterion

Preferences for decision alternatives are expressed by sorting their expected out- comes in an increasing order. For monetary values, the Expected Monetary Value (or EMV) is calculated and a choice is made by selecting the greatest EMV. For example, given an investment of 3 million dollars yielding an uncertain return one period hence (with a discount rate of 7%), and given in the returns in the table below, what is the largest present expected value of the investment? For the first, alternative we calculate the EMV of the investment one period hence and obtain: EMV = 4.15. The current value of the investment is thus equal to the present value of the expected return (EMV less the cost of the investment) or:

V (I ) = (1 + r) −1 EMV − I = 4.15 * (1 + 0.07) −1 − 3 = 0.878 Probability

0.10 0.20 0.30 0.15 0.15 0.10 Return

5 7 8 10 When there is more than one alternative (measured by the initial outlay and

forecasting of future cash flows), a decision is then reached by comparing the

27 economic properties of each investment alternative. For example, consider another

DECISION CRITERIA

investment proposal consisting of an initial outlay of 1 million dollars only (rather than 3) with a prospective cash flow given by the following:

Probability

0.10 0.20 0.30 0.15 0.15 0.10 Return

5 3 4 8 If we maintain the same EMV criterion, we note that:

V (I ) = (1 + r) −1 EMV − I = 1.95 * (1 + 0.07) −1 − 1 = 0.822 which clearly ranks the first investment alternative over the second (in terms of

the EMV criterion). In both cases the EMV is positive and therefore both projects seem to be economically worthwhile. There may be other considerations, for example, an initial outlay of 3 (rather than 1) million dollars for sure compared to an uncertain cash flow in the future (with prospective potential losses, albeit probabilistic, in the future). The attidude towards these losses are often important considerations to consider as well. Such considerations require the application of other criteria for decision making, as we shall briefly outline below. Note that it is noteworthy that such an individual approach does not deal with the market valuation of such cash flow streams and expresses only an individual’s judgement (and not market valuation of the cash flow, that is the consensus of judgements of participants on a market price). Financial analysis, as we shall see subse- quently, provides a market-sensitive discounting to these uncertain streams of cash.

2.3.2 Principle of (Laplace) insufficient reason

The Laplace principle states that, when the probabilities of the states of nature in a given problem are not known, we assume they are equally likely. In other words, a state of utmost ignorance will be replaced by assigning to each potential state the same probability! In this case, when we return to our first investment project, we are faced with the following prospect:

5 7 8 10 and its present EMV is,

V (I ) = (1 + r) −1 EMV − I = 5 * (1 + 0.07) −1 − 3 = 1.672 which implies that ‘not knowing’ can be worth money! This is clearly not the case,

since reaching a decision on this basis can lead to losses since the probability we have assumed are not necessarily the true ones. Gathering information in these cases may be useful, since it may be used to reduce the potential (miscalculated) expected losses.

28 MAKING ECONOMIC DECISIONS UNDER UNCERTAINTY

2.3.3 The minimax (maximin) criterion

The criterion consists in selecting the decision that will have the least maximal loss regardless of what future (state) may occur. It is used when we seek protection from the worst possible events and expresses generally an attitude of abject pessimism. Consider again the two investment projects with cash flows I and II specified below and for simplicity, assume that they require initially the same investment outlay. The flows to compare are:

Probability

0.10 0.20 0.30 0.15 0.15 0.10 Return I

8 10 Return II

5 7 8 10 The worst prospect in the first project is −7 million dollars while it is –8 million

dollars in the second project. The minimum of the maximum loss is therefore −7 million dollars, which provides a criterion (albeit very pessimistic) justifying the

selection of the first investment project. The minimax criterion takes the smallest of the available maximums. In this case, the projects have an equal maximum value and the investor is indifferent between the two. It is a second-best objective. Who cares about getting the gold medal as long as we get the silver! Honour is safe and the player satisfied. This criterion can be extended using this sporting analogy. A bronze is third best, good enough; while fourth best may be just participating, providing a reward in itself. Maximin is a loss-averse mindset. As long as we do get the best of all worst possible outcomes the investor is satisfied.

2.3.4 The maximax (minimin) criterion

This is an optimist’s criterion, banking on the best possible future, yielding the hoped for largest possible profits. It is based on the belief or the urge to profit as much as possible, regardless of the probability of desirable or other events. Again, returning to our previous example, we note that both projects have a maximal gain of 10 million dollars and therefore the maximum–maximum gain (maximax criterion) will indicate indifference in selecting one or the other project, as was the case for the minimax criterion. As Voltaire’s Candide would put it: ‘We live in the best of all possible worlds’ as he travelled in a world ravaged by man, as a prelude story to the French Revolution.

The minimin criterion is a pessimist’s point of view. Regardless of what hap- pens, only the worst case can happen. On the upside, such a point of view, leads only to upbeat news. My house has not burned today! Amazing!

2.3.5 The minimax regret or Savage’s regret criterion

The previous criteria involving maximums and minimums were evaluated ex-ante. In practice, payoffs and probabilities are not easily measured. Thus, these criteria

29 express a philosophical outlook rather than an objective to base a decision on. Ex-

DECISION CRITERIA

post, unlike ex-ante, decision-making is reached once information is revealed and uncertainty is resolved. Each decision has then a regret defined by the difference between the gain made and the gain that could have been realized had we selected the best decision (associated with the event that actually occurs). An expected ‘regret’ decision-maker would then seek to minimize the expectation of such a regret, while a minimax regret decision-maker would seek to select the decision providing the least maximal regret.

The cost of a decision’s regret represents the difference between the ex-ante payoffs that would be received with a given outcome compared to the maximum possible ex-post payoff received. Savage, Bell and Loomes and Sugden (see ref- erences) have pointed out the relevance of this criterion to decision-making under uncertainty by suggesting that decision makers may select an act by minimizing the regrets associated with potential decisions. Behaviourally, such a criterion would be characteristic of people attached to their past. Their past mistakes haunt their present day, hence, they do the best they can to avoid them in the future. Specifically, assume that we select an action (decision) and some event occurs. The decision/event combination generates a payoff table, expressing the condi- tional consequences of that decision when, ex-post, the event occurs. For example, the following table gives the payoff on a portfolio dependent on two different de- cisions on the portfolio allocation.

Event A Event B Event C Event D Event E Event F Probability

0.10 0.20 0.30 0.15 0.15 0.10 Return I

8 10 Return II

1 6 7 8 12 The decision/event combination may then generate a ‘regret’ for the decision –

for it is possible that we could have done better! Was decision 1 the better one? This is an opportunity loss, since a profit could have been made – had we known what events were to occur. If event B is the one that happens then clearly, based on an ex-post basis, decision 2 is the better one. If decisions were reversible then it might be possible to compensate (at least partially) for the fact that we took, a posteriori, a ‘wrong’ decision. Such a characteristic is called ‘flexibility’ and is worth money that decision makers are willing to pay for. What would I be willing to pay to have taken effectively decision 1 instead of 2 when event B happens? Options for example, provide such an opportunity, as we shall see in Chapter 6. An option would give us the right but not the obligation to make a decision in the future, once uncertainty is resolved. In most cases, these are decisions to sell or buy. But applications to real world problems have led to options to switch from one technology to another for example.

For example, say that we expect the demand for a product to grow significantly, and as a result we decide to expand the capacity of our plants. Assume that in fact, this expectation for demand growth does not materialize and we are left with

30 MAKING ECONOMIC DECISIONS UNDER UNCERTAINTY

a large excess capacity, unable to reduce it except at a substantial loss. What can we do then, except regret our decision! Similarly, assume that we expect peace to come on earth and decide to spend less on weapons development. Optimism, however much it may be wanted, may not, unfortunately, be justified and instead we find ourselves facing a war for which we may be ill-prepared. What can we do? Not much, except regret our decision. The regret (also called the Savage regret ) criterion, then, seeks to minimize the regret we may have in adopting

a decision. This explains why some actions are taken to reduce the possibility of such extreme regrets (as with the buying of insurance, steps taken to reduce the risks of bankruptcy, buying options to limit downside risk, in times of peace prepare for war – Sun-Tze and so on). Examples to this effect will be considered below using the opportunity loss table in the next section (Table 2.3).

Example: Regret and the valuation of firms

Analysts’ valuation of stocks are growing in importance. Analyst recommenda- tions have a great impact on investors, but their effects are felt particularly when analysts are ‘disappointed’ by a stock performance and revise their recommenda- tions downwards. In these cases, the effects can be disastrous for the stock price in consideration. In practice, analysts use a number of techniques that are based on firms’ reports. Foremost is the net return multiple factor. It is based on the ratio of the stock value of the firm to its net return. The multiple factor is then selected by comparing firms that have the same characteristics. It is then believed that the larger the risk, the smaller the multiple factor. In practice, analysts price stocks quite differently. A second technique is based on the firm’s future discounted (at the firm’s internal rate of return) cash flow. In practice, the future cash flow is based on forecasts that may not be precise. Finally, the third technique is based on assets value (which is the most conservative one). In other words, there is not

a uniform agreement regarding which objective to use in valuing a firm’s stock. Financial fundamental theory has made an important contribution by providing

a set of proper circumstances to resolve this issue. This will be considered in Chapter 6 in particular.

Example: The firm and risk management

Consider a firm operating in a given industry. Evidently, competition with other firms, as well as explicit (or implicit) government intervention through regulation, tax rebates for special environmental protection investments, grants or subsidized capital budgets in distress areas, etc., are instances where firms are required to

be sensitive to uncertainty and risk. Managers, of course, will seek to reduce and manage the risk implied by such uncertainty and seek ways to augment the market control (by vertical integration, acquisition of competition, etc.), or they may diversify risks by seeking activities in unrelated markets.

In the example Table 2.1 we have constructed a list of uncertainties and risks faced by firms and how these may be met. The list provided is by no means exhaus- tive and provides only an indication of the kind of problems that we can address. For example, competition can be an important source of risk which may be met by many means such as strategic M & A, collusion practices, diversification an so on.

31 Table 2.1 Sources of uncertainty and risks.

DECISION TABLES AND SCENARIO ANALYSIS

Uncertainty and risks

Protective actions taken

Long-range changes in market Research and development on new products, growth

diversification to other markets

Inflation Indexation of assets, and accounts receivable Price uncertainty of

Building up inventory, contract with suppliers input materials

(essentially futures), buying options and hedging techniques Competition

Mergers and acquisition, cartels, price-fixing, advertising and marketing effort, diversification