Chapter 17 Decision Making Basic Business Statistics 11th Edition Chapter 17 Decision Making Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.

Learning Objectives In this chapter, 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 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

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 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

List Possible Actions or Events Two Methods of Listing Payoff Table Decision Tree Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Investment Choice (Action) 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 200 50 -120 90 120 -30 40 30 20 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Sample Decision Tree Large factory Average factory Small factory Strong Economy 200 Large factory Stable Economy 50 Weak Economy -120 Strong Economy 90 Average factory Stable Economy 120 Weak Economy -30 Strong Economy 40 Small factory Stable Economy 30 Weak Economy 20 Payoffs Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Opportunity Loss Opportunity loss is the difference between an actual payoff for an action and the highest possible payoff, given a particular event Payoff Table State Of Nature (Events) Profit in $1,000’s (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy 200 50 -120 90 120 -30 40 30 20 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. Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

States of Nature (Events) Opportunity Loss (continued) Payoff Table States of Nature (Events) Profit in $1,000’s Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy 200 50 -120 90 120 -30 40 30 20 Opportunity Loss Table 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 70 140 110 50 160 90 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Decision Criteria Maximax Maximin Expected Monetary Value (EMV(j)) 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 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

States of Nature (Events) 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 200 50 -120 90 120 -30 40 30 20 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 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

States of Nature (Events) 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 200 50 -120 90 120 -30 40 30 20 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 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Expected Monetary Value Solution Goal: Maximize expected value The expected monetary value is the weighted average payoff, given specified probabilities for each event Where EMV(j) = expected monetary value of action j xij = payoff for action j when event i occurs Pi = probability of event i Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Expected Monetary Value Solution (continued) 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) 200 50 -120 90 120 -30 40 30 20 Suppose these probabilities have been assessed for these three events Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Expected Monetary Value Solution (continued) Goal: Maximize expected value Payoff Table: 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) 200 50 -120 90 120 -30 40 30 20 Expected Value (EMV) 61 81 31 Example: EMV (Average factory) = (90)(.3) + (120)(.5) + (-30)(.2) = 81 Maximize expected value by choosing Average factory Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

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 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Add Probabilities and Payoffs (continued) Strong Economy (.3) 200 Large factory Stable Economy (.5) 50 Weak Economy (.2) -120 (.3) Strong Economy 90 Average factory (.5) Stable Economy 120 (.2) Weak Economy -30 Decision (.3) Strong Economy 40 Small factory (.5) Stable Economy 30 (.2) Weak Economy 20 Uncertain Events Probabilities Payoffs Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Fold Back the Tree Large factory Average factory Small factory Strong Economy (.3) EMV=200(.3)+50(.5)+(-120)(.2)=61 200 Large factory Stable Economy (.5) 50 Weak Economy (.2) -120 (.3) Strong Economy EMV=90(.3)+120(.5)+(-30)(.2)=81 90 Average factory (.5) Stable Economy 120 (.2) Weak Economy -30 (.3) Strong Economy EMV=40(.3)+30(.5)+20(.2)=31 40 Small factory (.5) Stable Economy 30 (.2) Weak Economy 20 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Make the Decision Large factory Average factory Small factory Strong Economy (.3) EV=61 200 Large factory Stable Economy (.5) 50 Weak Economy (.2) -120 (.3) Strong Economy EV=81 90 Maximum EMV=81 Average factory (.5) Stable Economy 120 (.2) Weak Economy -30 (.3) Strong Economy EV=31 40 Small factory (.5) Stable Economy 30 (.2) Weak Economy 20 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Expected Opportunity Loss Solution Goal: Minimize expected opportunity loss The expected opportunity loss is the weighted average loss, given specified probabilities for each event Where: EOL(j) = expected opportunity loss of action j Lij = opportunity loss for action j when event i occurs Pi = probability of event i Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Expected Opportunity Loss Solution Goal: Minimize expected opportunity loss Opportunity Loss Table 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) 70 140 110 50 160 90 Example: EOL (Large factory) = 0(.3) + 70(.5) + (140)(.2) = 63 Expected Op. Loss (EOL) 63 43 93 Minimize expected op. loss by choosing Average factory Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

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. Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Value of Information Expected Value of Perfect Information, EVPI EVPI = Expected profit under certainty – expected monetary value of the best alternative (EVPI is equal to the expected opportunity loss from the best decision) Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

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) 200 50 -120 90 120 -30 40 30 20 Value of best decision for each event: 200 120 20 Example: Best decision given “Strong Economy” is “Large factory” Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Expected Profit Under Certainty (continued) 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) 200 50 -120 90 120 -30 40 30 20 200 120 20 Now weight these outcomes with their probabilities to find the expected value. 200(.3)+120(.5)+20(.2) = 124 Expected profit under certainty Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Value of Information Solution Expected Value of Perfect Information (EVPI) EVPI = Expected profit under certainty – Expected monetary value of the best decision Recall: Expected profit under certainty = 124 EMV is maximized by choosing “Average factory”, where EMV = 81 so: EVPI = 124 – 81 = 43 (EVPI is the maximum you would be willing to spend to obtain perfect information) Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Accounting for Variability Consider the choice of Stock A vs. Stock B States of Nature (Events) Percent Return Stock Choice (Action) Stock A Stock B Strong Economy (.7) 30 14 Weak Economy (.3) -10 8 Expected Return: 18.0 12.2 Stock A has a higher EMV, but what about risk? Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Accounting for Variability (continued) Calculate the variance and standard deviation for Stock A and Stock B: States of Nature (Events) Percent Return Stock Choice (Action) Stock A Stock B Strong Economy (.7) 30 14 Weak Economy (.3) -10 8 Example Expected Return: 18.0 12.2 Variance: 336.0 7.56 Standard Deviation 18.33 2.75 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Accounting for Variability (continued) Calculate the coefficient of variation for each stock: Stock A has much more relative variability Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Return-to-Risk Ratio Return-to-Risk Ratio (RTRR): Expresses the relationship between the return (expected payoff) and the risk (standard deviation) Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

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 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Decision Making with Sample Information Prior Permits revising old probabilities based on new information Probability New Information Revised Probability Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Revised Probabilities Example Additional Information: Economic forecast is strong economy When the economy was strong, the forecaster was correct 90% of the time. When the economy was weak, the forecaster was correct 70% of the time. F1 = strong forecast F2 = weak forecast E1 = strong economy = 0.70 E2 = weak economy = 0.30 P(F1 | E1) = 0.90 P(F1 | E2) = 0.30 Prior probabilities from stock choice example Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Revised Probabilities Example (continued) Revised Probabilities (Bayes’ Theorem) Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

EMV with Revised Probabilities Pi Event Stock A xijPi Stock B .875 strong 30 26.25 14 12.25 .125 weak -10 -1.25 8 1.00 Σ = 25.0 Σ = 13.25 Revised probabilities EMV Stock B = 13.25 EMV Stock A = 25.0 Maximum EMV Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

EOL Table with Revised Probabilities Pi Event Stock A xijPi Stock B .875 strong 16 14.00 .125 weak 18 2.25 Σ = 2.25 Σ = 14.00 Revised probabilities EOL Stock B = 14.00 EOL Stock A = 2.25 Minimum EOL Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Accounting for Variability with Revised Probabilities Calculate the variance and standard deviation for Stock A and Stock B: States of Nature (Events) Percent Return Stock Choice (Action) Stock A Stock B Strong Economy (.875) 30 14 Weak Economy (.125) -10 8 Example Expected Return: 25.00 13.25 Variance: 175.00 3.94 Standard Deviation: 13.23 1.98 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Accounting for Variability with Revised Probabilities (continued) The coefficient of variation for each stock using the results from the revised probabilities: Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

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 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Utility Utility is the pleasure or satisfaction obtained from an action. The utility of an outcome may not be the same for each individual. Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

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. Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Three Types of Utility Curves $ $ $ Risk Averter Risk Seeker Risk-Neutral Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

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 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Chapter 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 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..