Problem 1: Choosing an investment option under uncertainty

Jane is a small business owner. Her business is going well, and she has just received a payment of $200,000, which she wishes to invest. She is intending to choose between three investment options, and would like to choose the option which would yield the greatest return. Her decision is made difficult by the fact that the returns of the three options depend on the state of the economy. She has done some research, and has concluded that if the economy is good (i.e., in a period of growth), the expected returns (as percentages) from Options A, B, C and D will be respectively 4%, 12%, 15% and 4%; if the economy is in a state of stagnation, then the returns will be 4%, 5%, 2% and 6%; and if the economy is in a state of recession then the returns will be 4%, -1%, -5% and 7%.

Assume that Jane wishes to invest the entire $200,000 in just one of the three options (i.e., all in Option A, or all in Option B, or all in Option C).

Part 1: Decision Table

Decision tables are often an appropriate modelling technique to use when trying to find the best solution from a small number of alternatives. Enter the information for this problem in a decision table.

Part 2: Maximin and maximax decisions

Explain what is meant by the terms ‘maximim decision’ and ‘maximax decision’, and how these relate to optimistic and pessimistic outlooks.

What would the maximin and maximax decisions be in the above scenario?

In which decision scenarios would maximax or maximin decision usually be used?

Jane has a friend, George, who is an economist. George is very good at estimating the long-term probability of the economy being in each of the three states. For any year, has estimates that there is a 50% probability that the market will be a state of growth, a 30% probability that it will be in a state of stagnation, and a 20% probability that it will be in a state of recession.

Part 3: Expected value of return

Given the information that has been provided by George, calculate the expected value of the return from each option (make sure you show how you made your calculations), and state which option Jane should choose.

Jane has met a consultant, Frank, who claims to be able to predict, with certainty, what the state of the market will be in any year. Obviously, with this information, Jane would be able to make the optimal decision. However, Frank will only divulge this information for a fee.

1. Expected value of perfect information

Explain what is mean by the ‘Expected value of perfect information’, and calculate this for the given scenario.

What to submit

Submit a brief report presenting your answers and justifications to the above questions. Include the decision table in your report. Your submission will be marked according to the completeness and correctness of your response.