Warren Buffy is an enormously wealthy investor who has built his fortune through his legendary investing acumen. He currently has been offered three major investments and he would like to choose one. The first one is a conservative investment that would perform very well in an improving economy and only suffer a small loss in a worsening economy. The second is a speculative investment that would perform extremely well in an improving economy but would do very badly in a worsening economy. The third is a countercyclical investment that would lose some money in an improving economy but would perform well in a worsening economy. Warren believes that there are three possible scenarios over the lives of these potential investments: (I) an improving economy. (2) a stable economy, and (3) a worsening economy. He is pessimistic about where the economy is headed, and so has assigned prior probabilities of 0.1, 0.5, and 0.4, respectively, to these three scenarios. He also estimates that his profits under these respective scenarios are those given by the following table: Which investment should Warren make under each of the following criteria? (a) Maximin payoff criterion. (b) Maximum likelihood criterion. (c) Bayes’ decision rule.

## Expert Answer

Economy Condition | ||||||

Investment | Improving | Stable | Worsening | Minimum Payoff | Average Payoff | |

E1 | E2 | E3 | ||||

Conservative | A1 | 30 | 5 | -10 | -10 | (30+5-10)/3 = 8.3 |

Speculative | A2 | 40 | 10 | -30 | -30 | 6.7 |

Countercyclical | A3 | -10 | 0 | 15 | -10 | 1.7 |

**Maximin Criterion or Conservative Approach:**

Under this approach decision maker will evaluate the decision alternatives, in terms of the worst payoff that can occur or the alternative that provides the best of all possible minimum payoffs of each alternative selected. Thus, management should use Maximin criterion to evaluate alternatives. Under maximin principle, take the smallest payoff under each alternative and then select the largest of those minimum payoffs. This criterion is also known as pessimistic approach

Minimum payoffs of A1, A2, and A3 alternatives are -10, -30, -10 respectively.

Maximum payoff among the alternative’s minimum payoff is -10 for both alternatives A1 and A3

Thus, according to Maximin principle, Warren can select either conservative or countercyclical investment alternatives.

**Maximum Likelihood criterion**:

This principle is based on a simple philosophy that if there is uncertainty about various events, then treat them as equally probable to occur, that is, each state of nature or chance event is assigned an equal probability. It is also known as equal probabilities criterion. In this assumption, the expected value (EV) or average payoff for each course of action or strategy is determined and the strategy with the highest mean value is adopted.

Average payoffs of A1, A2, and A3 alternatives are 8.3, 6.7, and 1.7 respectively.

Maximum payoff among the alternative’s average payoff is 8.3 for the alternatives A1.

Thus, according to Maximum likelihood principle, Warren should select conservative investment alternative.

**Bayes’ Decision rule**

This rule considers the prior probabilities for the state of natures and selects the alternative with the maximum expected payoff. Expected payoff is calculated as sum of product of probabilities and payoff of each alternative.

For example:

Expected payoff of alternative A1:

EP (A1) = 0.1 x 30 + 0.5 x 5 +0.4 x (-10) = 1.5

Similarly, EP (A2) = -3 and EP (A3) = 5

Maximum Expected Value = 5

The maximum EP is $5 for the alternative of countercyclical investment, thus Warren should select countercyclical investment according Baye’s decision rule.