Selecting among Alternative Investments

268 Part IV: Anticipating Surprises: Risk and Uncertainty

Given the information in Figure 15-1, Global Airlines uses the mini-max regret criterion to determine what fare to set given it doesn’t know what’s going to happen to the price of oil. To apply the mini-max regret criterion, Global takes the following steps:

1. Determine the regret for a 10-percent decrease in the price of oil.

For a 10-percent decrease in the price of oil, the best payoff is $52 million with same fares. The regret for reducing fares is $2 million, $52 – $50, and the regret for raising fares is $10 million, $52 – $42. The maximum regret is $10 million.

2. Determine the regret for no change in the price of oil.

For no change in the price of oil, the best payoff is $56 million with reduced fares. The regret for keeping the same fares is $5 million, $56 – $51, and the regret for raising fares is $8 million, $56 – $48. The maximum regret is $8 million.

3. Determine the regret for a 10-percent increase in the price of oil.

For a 10-percent increase in the price of oil, the best payoff is $49 million with the same fares. The regret for reducing fares is $6 million, $49 – $43, and the regret for raising fares is $2 million, $49 – $47. The maximum regret is $6 million.

4. Determine the regret for a 20-percent increase in the price of oil.

For a 20-percent increase in the price of oil, the best payoff is $44 million with raising fares. The regret for reducing fares is $9 million, $44 – $35, and the regret for keeping the same fares is $3 million, $44 – $41. The maximum regret is $9 million.

5. Choose the action with the minimum or smallest maximum regret.

Figure 15-2 summarizes the regrets for each action. The maximum regret associated with reducing fares is $9 million. The maximum regret in the same-fares column is $5 million, and the maximum regret you see with raising fares is $10 million. Global Airlines should charge the same fares because its maximum regret of $5 million is smaller than the maximum regret associated with any other action.

The primary advantage of the mini-max regret decision criterion is its relative simplicity. This criterion’s disadvantages include its emphasis on the worst possible outcome, and it ignores risk as represented by an outcome’s probability of occurring.

Chapter 15: Risk Analysis: Walking Through the Fog

269

Figure 15-2:

Regret matrix.

Calculating the expected value

Hope for the best but expect the worst. That’s in essence what the maxi-min and mini-max regret criteria are all about. Both of those decision-making criteria focus upon the worst possible outcome, and if you’re like Eeyore, the extremely pessimistic donkey in the Winnie-the-Pooh books, they’re probably the criteria you should use.

But I like at least some of my perspective to be based on a “hope for the best” attitude. I don’t want to ignore the worst-case scenario, but I don’t want it to be the exclusive basis for my decision.

The expected monetary value decision-making criterion overcomes the pessimistic approach by incorporating all possible outcomes in the decisionmaking process. Each state of nature is assigned a probability of occurrence. This probability can be determined from historical data, subjective criteria, or theory. In determining probabilities, however, the sum of the probabilities for all states of nature must equal 1. In other words, you have to specify all possible situations.

After you determine probabilities, calculate the expected monetary value (EMV) of a specific action, aj, through the following formula: