Module 2. lesson 3 Module 2. lesson 3 Module 2. lesson 3 Module 2. lesson 3 PDF

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Lesson 3Decision Making Under RiskDecision making under risk is a decision situation in which several possible states of nature may occur, and the probabilities of these states of nature are known. In this section we consider one of the most popular methods of making decisions under risk: selecting...

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Lesson 3

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Decision Making Under Risk

Decision making under risk is a decision situation in which several possible states of nature may occur, and the probabilities of these states of nature are known. In this section we consider one of the most popular methods of making decisions under risk: selecting the alternative with the highest expected monetary value (or simply expected value). Expected Monetary Value Given a decision table with conditional values (payoffs) that are monetary values, and probability assessments for all states of nature, it is possible to determine the expected monetary value (EMV) for each alternative. The expected value, or the mean value, is the long-run average value of that decision. The EMV for an alternative is just the sum of possible payoffs of the alternative, each weighted by the probability of that payoff occurring. This could also be expressed simply as the expected value of X, or E(X): ∑ where n = number of values of the random variable x or ∑ where

∑

=payoff for the alternative in state of nature i =probability of achieving payoff (i.e., probability of state of nature i) =summation symbol

If this were expanded, it would become: EMV (alternative)=

(payoff in 1st state of nature) x (probability of 1st state of nature) + (payoff in 2nd state of nature) x (probability of 2nd state of nature) + (payoff in last state of nature) x (probability of last state of nature)

Module 2. Decision Analysis

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The alternative with the maximum EMV is then chosen. Suppose that Mrs. Sheila Calica now believes that the probability of a favorable market is exactly the same as the probability of an unfavorable market; that is, each state of nature has a 0.50 probability. Which alternative would give the greatest expected monetary value? Table 8. Decision Table with Probabilities and EMVs for Itlog ni Mang Edwin State of nature Expected Decision Favorable Unfavorable Monetary market (P) market(P) Value (P Probabilities 0.5 0.5 Purchase L300 van 1,000,000.00 -500,000.00 250,000.00 Purchase multi-cab 700,000.00 -400,000.00 150,000.00 Do nothing 0.00 0.00 0.00 Purchase L300 van (0.5 x 1,000,000) + (0.5 x -500,000)=250,000 Purchase multi-cab (0.5 x 700,000) + (0.5 x -400,000)= 150,000 Do nothing (0.5 x 0) + (0.5 x 0) = 0 The largest expected value (250,000) results from the first alternative, “purchase a L300 van.” Thus, Mrs.Calica should proceed with the purchasing L300 Van. Note that when using the expected monetary value criterion with minimization problems, the calculations are the same, but the alternative with the smallest EMV is selected. Expected Value of Perfect Information It is often possible an investor or an entrepreneurs to purchase additional information regarding future events and thus make his decision better. For example, an investor could hire a market analyst to perform an analysis of the economy to more accurately determine which economic condition will occur in the future. However, the investor (or any decision maker/entrepreneur) would be foolish to pay more for this information than he or she stands to gain in extra profit from having the information. That is, the information has some maximum value that represents the limit of what the decision maker would be willing to spend. This value of information can be computed as an expected value—hence its name, the expected value of perfect information (also referred to as EVPI) To compute the expected value of perfect information, we first look at the decisions under each state of nature. If we could obtain information that assured us which state of nature was going to occur (i.e., perfect information), we could select the best decision for that state of nature. For example, in above example, if we know for sure that good economic conditions will prevail, then Mrs. Calica will decide to purchase L300 van. Similarly, if she knows for sure that poor economic conditions will occur, then she will decide to do nothing.

Module 2. Decision Analysis

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Table 9. Payoff table with decisions, given perfect information for Itlog ni Mang Edwin State of nature Decision Favorable market (P) Unfavorable market(P) Probabilities 0.5 0.5 1,000,000.00 Purchase L300 van -500,000.00 Purchase multi-cab 700,000.00 -400,000.00 Do nothing 0.00 0.00 The probabilities of each state of nature (i.e., .50 and .50) tell us that good economic conditions will prevail 50% of the time and poor economic conditions will prevail 50% of the time (if this decision situation is repeated many times). In other words, even though perfect information enables the investor/entrepreneur to make the right decision, each state of nature will occur only a certain portion of the time. Thus, each of the decision outcomes obtained using perfect information must be weighted by its respective probability: Expected Value Given Perfect Information = 1,000,000(.50) + 0(.50) =

500,000

The amount 500,000 is the expected value of the decision, given perfect information, not the expected value of perfect information. The expected value of perfect information is the maximum amount that would be paid to gain information that would result in a decision better than the one made without perfect information. Recall that the expected value decision without perfect information was to purchase a L300 van, and the expected value was computed as: EMV(Purchase L300 van)= (0.5 x 1,000,000) + (0.5 x -500,000) = 250,000 The expected value of perfect information is computed by subtracting the expected value without perfect information ( 250,000) from the expected value given perfect information (500,000): Expected Value of Perfect Information or EVPI = 500,000 - 250,000 = 250,000 The expected value of perfect information, 250,000, is the maximum amount that the Mrs. Calica would pay to purchase perfect information from some other source, such as marketing analyst. Of course, perfect information is rare and usually unobtainable. Typically, the decision maker/ entrepreneur would be willing to pay some amount less than $28,000, depending on how accurate (i.e., close to perfection) the decision maker believed the information was.

Module 2. Decision Analysis

21 Decision Trees A decision tree is a graphical diagram consisting of nodes and branches. In a decision tree, the user computes the expected value of each outcome and makes a decision based on these expected values. The primary benefit of a decision tree is that it provides an illustration (or picture) of the decision-making process. This makes it easier to correctly compute the necessary expected values and to understand the process of making the decision. We will use our example of the Itlog ni Mang Edwin case problem to demonstrate the fundamentals of decision tree analysis. The various decisions, probabilities, and outcomes of this example, initially presented in Table 10, are repeated in Table 9. The decision tree for this example is shown in Figure 4. The circles (●) and the square (■) in Figure 10 are referred to as nodes. The square is a decision node, and the branches emanating from a decision node reflect the alternative decisions possible at that point. Table 10. Payoff table with decisions for Itlog ni Mang Edwin State of nature Decision Favorable market (P) Unfavorable market(P) Probabilities 0.5 0.5 1,000,000.00 Purchase L300 van -500,000.00 Purchase multi-cab 700,000.00 -400,000.00 0.00 Do nothing 0.00

Figure 4. Itlog ni Mang Edwin Decision tree EMV1 (Purchase L300 van) (0.5 x 1,000,000) + (0.5 x -500,000)=250,000 EMV2 (Purchase multi-cab) (0.5 x 700,000) + (0.5 x -400,000)= 150,000 EMV3 (Do nothing) (0.5 x 0) + (0.5 x 0) = 0

Module 2. Decision Analysis...