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Chap 19-1 Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall On Line Topic Decision Making Basic Business Statistics 12 th Edition

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Chap 19-2 Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Learning Objectives In this topic, you learn: To use payoff tables and decision trees to evaluate alternative courses of action To use several criteria to select an alternative course of action To use Bayes’ theorem to revise probabilities in light of sample information About the concept of utility

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Chap 19-3 Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Steps in Decision Making List Alternative Courses of Action Choices or actions List Uncertain Events Possible events or outcomes Determine ‘Payoffs’ Associate a Payoff with Each Choice/Event combination Adopt Decision Criteria Evaluate Criteria for Selecting the Best Course of Action

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Chap 19-4 Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall List Possible Actions or Events Payoff TableDecision Tree Two Methods of Listing

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Chap 19-5 Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall A Payoff Table A payoff table shows alternatives, states of nature, and payoffs States of Nature (Events) Profit in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy

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Chap 19-6 Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Sample Decision Tree Large factory Small factory Average factory Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy Payoffs

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Chap 19-7 Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Opportunity Loss State Of Nature (Events) Profit in $1,000’s (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy The action “Average factory” has payoff 90 for “Strong Economy”. Given “Strong Economy”, the choice of “Large factory” would have given a payoff of 200, or 110 higher. Opportunity loss = 110 for this cell. Opportunity loss is the difference between an actual payoff for an action and the highest possible payoff, given a particular event Payoff Table

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Chap 19-8 Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Opportunity Loss States of Nature (Events) Profit in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy (continued) States of Nature (Events) Opportunity Loss in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy Payoff Table Opportunity Loss Table

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Chap 19-9 Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Decision Criteria Maximax An optimistic decision criteria Maximin A pessimistic decision criteria Expected Monetary Value (EMV(j)) The expected profit for taking action j Expected Opportunity Loss (EOL(j)) The expected opportunity loss for taking action j Expected Value of Perfect Information (EVPI) The expected opportunity loss from the best decision Return-to-Risk Ratio Takes into account the variability in payoffs

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Maximax Solution States of Nature (Events) Profit in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy Maximum payoff for Large Factory is 200 Maximum payoff for Average Factory is 120 Maximum payoff for Small Factory is 40 Maximax Decision: Build the Large Factory because 200 is the maximum

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Maximin Solution States of Nature (Events) Profit in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy Minimum payoff for Large Factory is -120 Minimum payoff for Average Factory is -30 Minimum payoff for Small Factory is 20 Maximin Decision: Build the Small Factory because 20 is the maximum

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Expected Monetary Value Solution The expected monetary value is the weighted average payoff, given specified probabilities for each event Where EMV(j) = expected monetary value of action j x ij = payoff for action j when event i occurs P i = probability of event i Goal: Maximize expected value

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall The expected value is the weighted average payoff, given specified probabilities for each event States of Nature (Events) Profit in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Suppose these probabilities have been assessed for these three events (continued) Expected Monetary Value Solution

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall States of Nature (Events) Profit in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Example: EMV (Average factory) = (90)(.3) + (120)(.5) + (-30)(.2) = 81 Expected Value (EMV) Maximize expected value by choosing Average factory (continued) Payoff Table: Goal: Maximize expected value Expected Monetary Value Solution

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Decision Trees Are Another Way To Display & Analyze The Same Information A Decision tree shows a decision problem, beginning with the initial decision and ending will all possible outcomes and payoffs. Use a square to denote decision nodes Use a circle to denote uncertain events

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Add Probabilities and Payoffs Large factory Small factory Decision Average factory Uncertain Events Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy (continued) PayoffsProbabilities (.3) (.5) (.2) (.3) (.5) (.2) (.3) (.5) (.2)

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Fold Back the Tree Large factory Small factory Average factory Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy (.3) (.5) (.2) (.3) (.5) (.2) (.3) (.5) (.2) EMV=200(.3)+50(.5)+(-120)(.2)= 61 EMV=90(.3)+120(.5)+(-30)(.2)= 81 EMV=40(.3)+30(.5)+20(.2)= 31

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Make the Decision Large factory Small factory Average factory Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy (.3) (.5) (.2) (.3) (.5) (.2) (.3) (.5) (.2) EV= 61 EV= 81 EV= 31 Maximum EMV= 81

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Expected Opportunity Loss Solution The expected opportunity loss is the weighted average loss, given specified probabilities for each event Where: EOL(j) = expected opportunity loss of action j L ij = opportunity loss for action j when event i occurs P i = probability of event i Goal: Minimize expected opportunity loss

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Expected Opportunity Loss Solution States of Nature (Events) Opportunity Loss in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Example: EOL (Large factory) = 0(.3) + 70(.5) + (140)(.2) = 63 Expected Op. Loss (EOL) Minimize expected op. loss by choosing Average factory Opportunity Loss Table Goal: Minimize expected opportunity loss

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Expected Opportunity Loss vs. Expected Monetary Value The Expected Monetary Value (EMV) and the Expected Opportunity Loss (EOL) criteria are equivalent. Note that in this example the expected monetary value solution and the expected opportunity loss solution both led to the choice of the average size factory.

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Value of Information Expected Value of Perfect Information, EVPI Expected Value of Perfect Information EVPI = Expected profit under certainty – expected monetary value of the best alternative (EVPI is equal to the expected opportunity loss from the best decision)

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Expected Profit Under Certainty Expected profit under certainty = expected value of the best decision, given perfect information States of Nature (Events) Profit in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Example: Best decision given “Strong Economy” is “Large factory” Value of best decision for each event:

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Expected Profit Under Certainty States of Nature (Events) Profit in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) (continued) Now weight these outcomes with their probabilities to find the expected value. 200(.3)+120(.5)+20(.2) = 124 Expected profit under certainty

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Value of Information Solution Expected Value of Perfect Information (EVPI) EVPI = Expected profit under certainty – Expected monetary value of the best decision so: EVPI = 124 – 81 = 43 Recall: Expected profit under certainty = 124 EMV is maximized by choosing “Average factory”, where EMV = 81 (EVPI is the maximum you would be willing to spend to obtain perfect information)

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Accounting for Variability States of Nature (Events) Percent Return Stock Choice (Action) Stock AStock B Strong Economy (.7) 3014 Weak Economy (.3) Consider the choice of Stock A vs. Stock B Expected Return: Stock A has a higher EMV, but what about risk?

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall States of Nature (Events) Percent Return Stock Choice (Action) Stock AStock B Strong Economy (.7) 3014 Weak Economy (.3) Variance: Calculate the variance and standard deviation for Stock A and Stock B: Expected Return: Example Standard Deviation Accounting for Variability (continued)

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Calculate the coefficient of variation for each stock: (continued) Stock A has much more relative variability Accounting for Variability

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Return-to-Risk Ratio Return-to-Risk Ratio (RTRR): Expresses the relationship between the return (expected payoff) and the risk (standard deviation)

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Return-to-Risk Ratio You might want to consider Stock B if you don’t like risk. Although Stock A has a higher Expected Return, Stock B has a much larger return-to-risk ratio and a much smaller CV

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Decision Making with Sample Information Permits revising old probabilities based on new information New Information Revised Probability Prior Probability

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Revised Probabilities Example Prior probabilities from stock choice example F 1 = strong forecast F 2 = weak forecast E 1 = strong economy = 0.70 E 2 = weak economy = 0.30 P(F 1 | E 1 ) = 0.90 P(F 1 | E 2 ) = 0.30 Additional Information: Economic forecast is strong economy When the economy was strong (so the correct forecast is F 1 ), the forecaster was correct 90% of the time. When the economy was weak (so the correct forecast is F 2 ), the forecaster was correct 70% of the time.

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Revised Probabilities Example Revised Probabilities (Bayes’ Theorem) (continued)

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall EMV with Revised Probabilities EMV Stock A = 25.0 EMV Stock B = Revised probabilities PiPi EventStock Ax ij P i Stock Bx ij P i 0.875strong weak Σ = 25.0 Σ = Maximum EMV

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall EOL Table with Revised Probabilities EOL Stock A = 2.25 EOL Stock B = Revised probabilities PiPi EventStock Ax ij P i Stock Bx ij P i.875strong weak Σ = 2.25 Σ = Minimum EOL

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall States of Nature (Events) Percent Return Stock Choice (Action) Stock AStock B Strong Economy (.875) 3014 Weak Economy (.125) -108 Variance: Calculate the variance and standard deviation for Stock A and Stock B: Expected Return: Example Standard Deviation: Accounting for Variability with Revised Probabilities

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall The coefficient of variation for each stock using the results from the revised probabilities: (continued) Accounting for Variability with Revised Probabilities

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Return-to-Risk Ratio with Revised Probabilities With the revised probabilities, both stocks have higher expected returns, lower CV’s, and larger return-to-risk ratios

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Utility Utility is the pleasure or satisfaction obtained from an action. The utility of an outcome may not be the same for each individual.

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Utility Example: each incremental $1 of profit does not have the same value to every individual: A risk averse person, once reaching a goal, assigns less utility to each incremental $1. A risk seeker assigns more utility to each incremental $1. A risk neutral person assigns the same utility to each extra $1.

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Three Types of Utility Curves Utility $$$ Risk Averter Risk SeekerRisk-Neutral

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Maximizing Expected Utility Making decisions in terms of utility, not $ Translate $ outcomes into utility outcomes Calculate expected utilities for each action Choose the action to maximize expected utility

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Chap Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Topic Summary Described the payoff table and decision trees Opportunity loss Provided criteria for decision making Maximax and Maximin Expected monetary value Expected opportunity loss Return-to-risk ratio Introduced expected profit under certainty and the value of perfect information Discussed decision making with sample information Addressed the concept of utility

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