1. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-1 Chapter 17 Decision Making Basic Business Statistics 10 th Edition

2. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-2 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

3. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-3 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 Event/Outcome combination  Adopt Decision Criteria  Evaluate Criteria for Selecting the Best Course of Action

4. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-4 List Possible Actions or Events Payoff TableDecision Tree Two Methods of Listing

5. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-5 A Payoff Table A payoff table shows alternatives, states of nature, and payoffs Investment Choice (Action) Profit in $1,000’s (Events) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20

6. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-6 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 200 50 -120 40 30 20 90 120 -30

7. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-7 Opportunity Loss Investment Choice (Action) Profit in $1,000’s (Events) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 200 90 40 50 120 30 -120 -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. Opportunity loss is the difference between an actual payoff for an action and the optimal payoff, given a particular event Payoff Table

8. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-8 Opportunity Loss Investment Choice (Action) Profit in $1,000’s (States of Nature) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 (continued) Investment Choice (Action) Opportunity Loss in $1,000’s (Events) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 0 110 160 70 0 90 140 50 0 Payoff Table Opportunity Loss Table

9. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-9 Decision Criteria  Expected Monetary Value (EMV)  The expected profit for taking action Aj  Expected Opportunity Loss (EOL)  The expected opportunity loss for taking action Aj  Expected Value of Perfect Information (EVPI)  The expected opportunity loss from the best decision

10. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-10 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

11. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-11  The expected value is the weighted average payoff, given specified probabilities for each event Investment Choice (Action) Profit in $1,000’s (Events) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 Suppose these probabilities have been assessed for these three events (continued) Expected Monetary Value Solution

12. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-12 Investment Choice (Action) Profit in $1,000’s (Events) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 Example: EMV (Average factory) = 90(.3) + 120(.5) + (-30)(.2) = 81 Expected Values (EMV) 61 81 31 Maximize expected value by choosing Average factory (continued) Payoff Table: Goal: Maximize expected value Expected Monetary Value Solution

13. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-13 Decision Tree Analysis  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

14. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-14 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 200 50 -120 40 30 20 90 120 -30 (.3) (.5) (.2) (.3) (.5) (.2) (.3) (.5) (.2)

15. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-15 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 200 50 -120 40 30 20 90 120 -30 (.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

16. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-16 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 200 50 -120 40 30 20 90 120 -30 (.3) (.5) (.2) (.3) (.5) (.2) (.3) (.5) (.2) EV= 61 EV= 81 EV= 31 Maximum EMV= 81

17. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-17 Expected Opportunity Loss Solution  The expected opportunity loss is the weighted average loss, given specified probabilities for each event Where EOL(j) = expected monetary value of action j L ij = opp. loss for action j when event i occurs P i = probability of event i Goal: Minimize expected opportunity loss

18. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-18 Expected Opportunity Loss Solution Investment Choice (Action) Opportunity Loss in $1,000’s (Events) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory 0 110 160 70 0 90 140 50 0 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 Opportunity Loss Table Goal: Minimize expected opportunity loss

19. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-19 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.

20. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-20 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)

21. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-21 Expected Profit Under Certainty  Expected profit under certainty = expected value of the best decision, given perfect information Investment Choice (Action) Profit in $1,000’s (Events) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 Example: Best decision given “Strong Economy” is “Large factory” 200 120 20 Value of best decision for each event:

22. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-22 Expected Profit Under Certainty Investment Choice (Action) Profit in $1,000’s (Events) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory 200 90 40 50 120 30 -120 -30 20 200 120 20 (continued)  Now weight these outcomes with their probabilities to find the expected value: 200(.3)+120(.5)+20(.2) = 124 Expected profit under certainty

23. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-23 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)

24. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-24 Accounting for Variability Stock Choice (Action) Percent Return (Events) Strong Economy (.7) Weak Economy (.3) Stock A 30-10 Stock B 148 Consider the choice of Stock A vs. Stock B Expected Return: 18.0 12.2 Stock A has a higher EMV, but what about risk?

25. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-25 Stock Choice (Action) Percent Return (Events) Strong Economy (.7) Weak Economy (.3) Stock A 30-10 Stock B 148 Variance: 336.0 7.56 Calculate the variance and standard deviation for Stock A and Stock B: Expected Return: 18.0 12.2 Example: Standard Deviation: 18.33 2.75 Accounting for Variability (continued)

26. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-26 Calculate the coefficient of variation for each stock: (continued) Stock A has much more relative variability Accounting for Variability

27. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-27 Return-to-Risk Ratio Return-to-Risk Ratio (RTRR):  Expresses the relationship between the return (expected payoff) and the risk (standard deviation)

28. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-28 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

29. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-29 Decision Making with Sample Information  Permits revising old probabilities based on new information New Information Revised Probability Prior Probability

30. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-30 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. 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

31. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-31 Revised Probabilities Example  Revised Probabilities (Bayes’ Theorem) (continued)

32. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-32 EMV with Revised Probabilities EMV Stock A = 25.0 EMV Stock B = 11.25 Revised probabilities PiPi EventStock Ax ij P i Stock Bx ij P i.875strong3026.251412.25.125weak-10-1.2581.00 Σ = 25.0 Σ = 11.25 Maximum EMV

33. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-33 EOL Table with Revised Probabilities EOL Stock A = 2.25 EOL Stock B = 14.00 Revised probabilities PiPi EventStock Ax ij P i Stock Bx ij P i.875strong001614.00.125weak182.2500 Σ = 2.25 Σ = 14.00 Minimum EOL

34. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-34 Stock Choice (Action) Percent Return (Events) Strong Economy (.875) Weak Economy (.125) Stock A 30-10 Stock B 148 Variance: 175.0 3.94 Calculate the variance and standard deviation for Stock A and Stock B: Expected Return: 25.0 13.25 Example: Standard Deviation: 13.229 1.984 Accounting for Variability with Revised Probabilities

35. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-35 The coefficient of variation for each stock using the results from the revised probabilities: (continued) Accounting for Variability with Revised Probabilities

36. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-36 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

37. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-37 Utility  Utility is the pleasure or satisfaction obtained from an action.  The utility of an outcome may not be the same for each individual.

38. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-38 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.

39. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-39 Three Types of Utility Curves Utility $$$ Risk Averter Risk SeekerRisk-Neutral

40. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-40 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

41. Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 17-41 Chapter Summary  Described the payoff table and decision trees  Opportunity loss  Provided criteria for decision making  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