EMV, EOL, EPPI, EVPI

2.5 EMV, EOL, EPPI, EVPI

EMV, EOL, EPPI and EVPI are terms associated with a decision; they will be elucidated through an application. Assume that data supplied by a Port Authority points to a number of development alternatives for the port. Uncertainty regard- ing the economic state of the country, geopolitical developments and so on, lead to a number of scenarios to be considered and against which each of these al- ternatives must be assessed. Each alternative can generate, ex-post, a sense of satisfaction at having followed the proper course of action as well as a sense that

a suboptimal alternative was taken. Four scenarios are assumed each to lead to the following results, summarized in the table below where entries are payoffs (losses):

34 MAKING ECONOMIC DECISIONS UNDER UNCERTAINTY

2.5.1 The deterministic analysis

An alternative is selected irrespective of the probabilities of forthcoming events. Given a number of alternatives and specified events, a decision can be taken. A number of criteria are used, such as maximax, maximin, minimax regret and the ‘equally likely’ (Laplace) criteria as stated earlier. Under these criteria, we see that alternatives 1 and 2 are always better than alternatives 3 and 4. Explicitly, the following results are obtained:

Criterion

Payoff Maximax

Alternative 2 −150 Minimax regret Alternative 1

700 Equally likely

Alternative 2

2.5.2 The probabilistic analysis

Probabilistic analysis characterizes the likelihood of forthcoming events by asso- ciating a probability with each event. It uses a number of potential criteria but we shall be concerned essentially with the EMV – expected monetary value index of performance. The results for our example are given by the following:

Probabilistic analysis: The Port Authority Expected value – Summary report Decision

Expected payoff Alternative 1 37.50 Alternative 2 217.50 Alternative 3 225.00 * Alternative 4 17.50

Calculations were made as follows: Alternative 1: 0.1(−200) + 0.15(−100) + 0.25(150) + 0.05(400) + 0.3(−300) + 0.15(700) = 37.50 Alternative 2: 0.1(300) + 0.15(−150) + 0.25(300) + 0.05(600) + 0.3(100) + 0 .15(500) = 217.50

Alternative 3: 0.1(−500) + 0.15(300) + 0.25(400) + 0.05(−100) + 0.3(400) + 0.15(100) = 225.00 Alternative 4: 0.1(400) + 0.15(600) + 0.25(−100) + 0.05(−2500) + 0.3(−300) + 0.15(100) = 17.50

35 The EMV (expected monetary value) consists of valuing each alternative by its

EMV , EOL , EPPI , EVPI

EMV. The ‘best’ choice (in an EMV context) is 225. In other words, ex-ante, the best decision we can take is alternative 3. By contrast, if a decision could be taken ex-post, once uncertainty is revealed and removed, the cost of each decision is given by its opportunity loss, whose expectation is the EOL (expected opportunity loss). This value is calculated explicitly through the opportunity loss table below:

Table of opportunity losses, calculations

Scenario 1 2 3 4 5 6 Probability

Table of opportunity losses

Scenario 1 2 3 4 5 6 Probability

Entries are calculated as follows. Say that scenario 1 realizes itself. The best alternative would then be alternative 4 yielding a payoff of 400. We replace in the table the entry 400 by 0 and then calculate in the first column corresponding to Scenario 1 the relative losses had we selected a suboptimal alternative. Now compute for each alternative the expected opportunity loss, which is the sum of columns for each row. Verify that the sums EMV + EOL are equal for each alternative, called the EPPI, or the Expected Profit under Perfect Information. Further, note that the recommended alternative under an EOL criterion is also alternative 3 as in the expected payoff (EMV) case. This is always the case and should not come as any surprise, since selecting the largest EMV is equivalent to the smallest EOL. Since,