Question

One of Mary’s investments is going to mature, and she wants to determine how to invest the proceeds of $50,000. Mary is considering three new investments: a business startup fund (BSF), a one-year certificate of deposit (CD) with a guarantee of 4.5% return, or a communication technology stock called New 5 G Technology(N5G). Mary estimates the return on BSF as 15%, 9%, -3% or -12%, and the return on N5G as 33%, 28%, -13% or -22%, depending on whether market conditions are excellent, good, average, or poor, respectively. Mary also has been collecting financial market information daily and estimates the probabilities of an excellent, good, average, and poor market to be 0.23, 0.20, 0.47, and 0.10, respectively. (B-1) Construct a payoff matrix (in dollars) for this problem. (B-2) What decision should be made according to Expected Value Approach? (B-3) Create a regret table and explain what decision should be made according to Minimax Regret Approach. (B-4) What is the EVPI?

Answer 1

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EVPI is  expected value of perfect information.

EVPI helps to determine the worth of an insider who possesses perfect information. The expected value with perfect information is the amount of profit foregone due to uncertain conditions affecting the selection of a course of action. Given the perfect information, a decision-maker is supposed to know which particular state of nature will be in effect. Thus, the procedure for the selection of an optimal course of action, for the decision problem given in example 18, will be as follows:

If the decision-maker is certain that the state of nature S₁ will be in effect, he would select the course of action A₃, having maximum payoff equal to Rs 200.

Similarly, if the decision-maker is certain that the state of nature S₂ will be in effect, his course of action would be A₁ and if he is certain that the state of nature S₃ will be in effect, his course of action would be A₂. The maximum payoffs associated with the actions are Rs 200 and Rs 600 respectively.

The weighted average of these payoffs with weights equal to the probabilities of respective states of nature is termed as Expected Payoff under Certainty (EPC).
Thus, EPC = 200 * 0.3 + 200 * 0.4 + 600 *0.3 = 320

The difference between EPC and EMV of optimal action is the amount of profit foregone due to uncertainty and is equal to EVPI.

Thus, EVPI = EPC - EMV of optimal action = 320 - 194 = 126