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# Chap16 decision making

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### Chap16 decision making

1. 1. Statistics for Managers Using Microsoft® Excel 4th Edition Chapter 16 Decision Making Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-1
2. 2. Chapter Goals After completing this chapter, you should be able to:  Describe basic features of decision making  Construct a payoff table and an opportunity-loss table  Define and apply the expected value criterion for decision making  Compute the value of perfect information Describe utility and attitudes toward risk Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.  Chap 16-2
3. 3. Steps in Decision Making  List Alternative Courses of Action   List Uncertain Events   Possible events or outcomes Determine ‘Payoffs’   Choices or actions Associate a Payoff with Each Event/Outcome combination Adopt Decision Criteria Evaluate Criteria for Selecting the Best Course of Action Statistics for Managers Using Microsoft Excel, 4e © 2004 Chap 16-3 Prentice-Hall, Inc. 
4. 4. List Possible Actions or Events Two Methods of Listing Payoff Table Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Decision Tree Chap 16-4
5. 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 Large factory 200 Statistics for Managers Using Average factory 90 Microsoftfactory 4e © 2004 Small Excel, 40 Prentice-Hall, Inc. Stable Economy 50 120 30 Weak Economy -120 -30 20 Chap 16-5
6. 6. Sample Decision Tree Strong Economy 90 Stable Economy 120 -30 Strong Economy Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. -120 Weak Economy Small factory 50 Strong Economy Average factory Stable Economy Weak Economy Large factory 200 40 Stable Economy 30 Weak Economy 20 Payoffs Chap 16-6
7. 7. Opportunity Loss Opportunity loss is the difference between an actual payoff for an action and the optimal payoff, given a particular event Investment Choice (Action) Payoff Table Profit in \$1,000’s (Events) Strong Economy Stable Economy Weak Economy Large factory 200 50 -120 Average factory 90 120 -30 Small factory 40 30 20 The action “Average factory” has payoff 90 for “Strong Economy”. Given “Strong for Managers Using Statistics Economy”, the choice of “Large factory” would have given a payoff of 200, or 110 higher. Opportunity loss = 110 for this cell. Microsoft Excel, 4e © 2004 Chap 16-7 Prentice-Hall, Inc.
8. 8. Opportunity Loss (continued) Investment Choice (Action) Large factory Average factory Small factory Payoff Table Profit in \$1,000’s (States of Nature) Strong Economy 200 90 40 Stable Economy 50 120 30 Investment Choice (Action) Statistics for Managers Using Microsoft Excel, 4e © Large factory 2004 Average factory Prentice-Hall, Inc. Weak Economy Opportunity Loss Table -120 -30 20 Opportunity Loss in \$1,000’s (Events) Strong Economy 0 110 Stable Economy 70 0 Chap Weak Economy 140 50 16-8
9. 9. Decision Criteria  Expected Monetary Value (EMV)   Expected Opportunity Loss (EOL)   The expected profit for taking action Aj The expected opportunity loss for taking action Aj Expected Value of Perfect Information (EVPI)  The expected opportunity loss from the best decision Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-9
10. 10. Expected Monetary Value Solution Goal: Maximize expected value  The expected monetary value is the weighted average payoff, given specified probabilities for each event N EMV( j) = ∑ x ijPi i=1 Where EMV(j) = expected monetary value of action j xij = payoff for action j when event i occurs Statistics for Managers Using P = probability of event i Microsoft Excel, 4e ©i 2004 Prentice-Hall, Inc. Chap 16-10
11. 11. Expected Monetary Value Solution (continued)  The expected value is the weighted average payoff, given specified probabilities for each event Profit in \$1,000’s (Events) Investment Choice (Action) Strong Economy (.3) Stable Economy (.5) Large factory 200 50 Average for Managers Using 120 90 Statisticsfactory Small factory 40 30 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Weak Economy (.2) -120 -30 20 Suppose these probabilities have been assessed for these three events Chap 16-11
12. 12. Expected Monetary Value Solution (continued) Goal: Maximize expected value Payoff Table: Profit in \$1,000’s (Events) Investment Choice (Action) Large factory Average factory Small factory Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) 200 90 40 50 120 30 -120 -30 20 Expected Values (EMV) 61 81 31 Maximize expected value by choosing Average factory Example: EMV (Average factory) = 90(.3) + 120(.5) + (-30)(.2) Statistics for Managers Using = 81 Microsoft Excel, 4e © 2004 Chap 16-12 Prentice-Hall, Inc.
13. 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 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-13
14. 14. Add Probabilities and Payoffs (continued) Strong Economy (.3) Large factory 200 Stable Economy (.5) 50 Weak Economy (.2) -120 Strong Economy (.3) Average factory 90 Stable Economy (.5) 120 Weak Economy (.2) -30 Strong Economy (.3) Decision Small factory Statistics for Managers Using Uncertain Events Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. 40 Stable Economy (.5) 30 Weak Economy (.2) 20 Probabilities Payoffs Chap 16-14
15. 15. Fold Back the Tree EMV=200(.3)+50(.5)+(-120)(.2)=61 Large factory Strong Economy (.3) 200 Stable Economy (.5) 50 Weak Economy EMV=90(.3)+120(.5)+(-30)(.2)=81 Average factory Small factory Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. -120 Strong Economy (.3) 90 Stable Economy (.5) 120 Weak Economy EMV=40(.3)+30(.5)+20(.2)=31 (.2) (.2) -30 Strong Economy (.3) 40 Stable Economy (.5) 30 Weak Economy (.2) 20 Chap 16-15
16. 16. Make the Decision EV=61 Large factory Strong Economy (.3) 200 Stable Economy (.5) 50 Weak Economy EV=81 Average factory Strong Economy (.3) Stable Economy (.5) Weak Economy EV=31 Small factory Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. (.2) (.2) -120 90 120 -30 Strong Economy (.3) EMV=81 40 Stable Economy (.5) Maximum 30 Weak Economy (.2) 20 Chap 16-16
17. 17. Expected Opportunity Loss Solution Goal: Minimize expected opportunity loss  The expected opportunity loss is the weighted average loss, given specified probabilities for each event N EOL( j) = ∑ L ijPi i =1 Where EOL(j) = expected monetary value of action j Lij = Using Statistics for Managers opp. loss for action j when event i occurs Microsoft Excel, 4e © 2004 Pi = probability of event i Chap 16-17 Prentice-Hall, Inc.
18. 18. Expected Opportunity Loss Solution Goal: Minimize expected opportunity loss Opportunity Loss Table Opportunity Loss in \$1,000’s (Events) Investment Choice (Action) Large factory Average factory Small factory Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) 0 110 160 70 0 90 140 50 0 Expected Op. Loss (EOL) 63 43 93 Minimize expected op. loss by choosing Average factory Statistics for Managers Using Example: EOL (Large factory) = 0(.3) + 70(.5) + (140)(.2) Microsoft Excel, 4e © 2004 = 63 Chap 16-18 Prentice-Hall, Inc.
19. 19. 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) Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-19
20. 20. Expected Profit Under Certainty  Expected profit under certainty = expected value of the best decision, given perfect information Profit in \$1,000’s (Events) Investment Choice (Action) Strong Economy (.3) Large factory 200 Average factory 90 Small factory Value of best decision 40 for each event: 200 Stable Economy (.5) Weak Economy (.2) 50 120 30 -120 -30 20 120 20 Example: Best decision given “Strong Statistics for Managers Using Economy” is “Large factory” Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-20
21. 21. Expected Profit Under Certainty (continued) Profit in \$1,000’s (Events) Investment Choice (Action) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Now weight Large factory 200 50 -120 these outcomes Average factory 90 120 -30 with their Small factory 40 30 20 200 120 20 probabilities to find the 200(.3)+120(.5)+20(.2) Expected expected value: Statistics for Managers Using = 124 profit under Microsoft Excel, 4e © 2004 certainty Chap 16-21 Prentice-Hall, Inc. 
22. 22. 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 Statistics for Managers Using would be willing to spend to obtain (EVPI is the maximum you Microsoft Excel, 4e © 2004 perfect information) Chap 16-22 Prentice-Hall, Inc.
23. 23. Accounting for Variability Consider the choice of Stock A vs. Stock B Percent Return (Events) Stock Choice (Action) Strong Economy (.7) Weak Economy (.3) Stock A 30 -10 Stock B 14 8 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Expected Return: 18.0 12.2 Stock A has a higher EMV, but what about risk? Chap 16-23
24. 24. Accounting for Variability (continued) Calculate the variance and standard deviation for Stock A and Stock B: Percent Return (Events) Stock Choice (Action) Strong Economy (.7) Weak Economy (.3) Stock A 30 -10 Stock B 14 8 N Expected Standard Return: Variance: Deviation: 18.0 Example: σ = ∑ ( Xi − Using Statistics for Managers μ) P( Xi ) = (30 − 18) i=1 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. 2 A 2 2 336.0 18.33 7.56 12.2 2.75 (.7) + ( −10 − 18 )2 (.3) = 336.0 Chap 16-24
25. 25. Accounting for Variability (continued) Calculate the coefficient of variation for each stock: CVA = σA 18.33 × 100% = × 100% = 101.83% EMVA 18.0 CVB = Stock A has much more relative variability σB 2.75 × 100% = × 100% = 22.54% EMVB 12.2 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-25
26. 26. Return-to-Risk Ratio Return-to-Risk Ratio (RTRR): EMV(j) RTRR(j) = σj Expresses the relationship between the return (expected payoff) and the risk (standard deviation) Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-26
27. 27. Return-to-Risk Ratio RTRR(j) = EMV(j) σj RTRR(A) = EMV(A) 18.0 = = 0.982 σA 18.33 RTRR(B) = EMV(B) 12.2 = = 4.436 σB 2.75 You might want to consider Stock B if you don’t like risk. Although Stock A has a higher Expected Statistics for Managers has a much larger return to risk Return, Stock B Using Microsoft Excel, a much smaller CV ratio and 4e © 2004 Chap 16-27 Prentice-Hall, Inc.
28. 28. Decision Making in PHStat  PHStat | decision-making | expected monetary value  Check the “expected opportunity loss” and “measures of valuation” boxes Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-28
29. 29. Decision Making with Sample Information Prior Probability  Permits revising old probabilities based on new information New Information Revised Probability Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-29
30. 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. F1 = strong forecast F2 = weak forecast E1 = strong economy = 0.70 E = Managers Using Statistics2forweak economy = 0.30 Microsoft Excel, 4e © 2004 P(F1 | Inc. P(F1 | E2) = 0.30 Prentice-Hall,E1) = 0.90 Prior probabilities from stock choice example Chap 16-30
31. 31. Revised Probabilities Example (continued) P(F1 | E1 ) = .9 , P(F1 | E 2 ) = .3 P(E1 ) = .7 , P(E 2 ) = .3  Revised Probabilities (Bayes’ Theorem) P(E1 )P(F1 | E1 ) (.7)(.9) P(E1 | F1 ) = = = .875 P(F1 ) (.7)(.9) + (.3)(.3) P(E 2 )P(F1 | E 2 ) P(E 2 | F1 = = .125 Statistics for Managers )Using P(F1 ) Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-31
32. 32. EMV with Revised Probabilities Pi Event Stock A xijPi Stock B xijPi .875 strong 30 26.25 14 12.25 .125 weak -10 -1.25 8 1.00 Revised probabilities Σ = 25.0 Σ = 11.25 EMV Stock B = 11.25 EMV Stock A = 25.0 Statistics for Managers Using Maximum Microsoft Excel, 4e © 2004 EMV Prentice-Hall, Inc. Chap 16-32
33. 33. EOL Table with Revised Probabilities Pi Event Stock A xijPi Stock B xijPi .875 strong 0 0 16 14.00 .125 weak 18 2.25 0 0 Σ = 2.25 Revised probabilities Σ = 14.00 EOL Stock B = 14.00 EOL Stock A = 2.25 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Minimum EOL Chap 16-33
34. 34. Accounting for Variability with Revised Probabilities Calculate the variance and standard deviation for Stock A and Stock B: Percent Return (Events) Stock Choice (Action) Strong Economy (.875) Weak Economy (.125) Stock A 30 -10 Stock B 14 8 N Expected Standard Return: Variance: Deviation: 25.0 Example: σ = ∑ ( Xi − μ) P( Xi ) = Statistics for Managers Using (30 − 25) i=1 Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. 2 A 2 2 175.0 13.229 3.94 13.25 1.984 (.875 ) + ( −10 − 25 )2 (.125 ) = 175.0 Chap 16-34
35. 35. Accounting for Variability with Revised Probabilities (continued) The coefficient of variation for each stock using the results from the revised probabilities: CVA = σA 13.229 × 100% = × 100% = 52.92% EMVA 25.0 CVB = σB 1.984 × 100% = × 100% = 14.97% EMVB 13.25 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-35
36. 36. Return-to-Risk Ratio with Revised Probabilities EMV(A) 25.0 RTRR(A) = = = 1.890 σA 13.229 EMV(B) 13.25 RTRR(B) = = = 7.011 σB 1.984 With the revised probabilities, both stocks have higher expected returns, lower CV’s, and larger return to risk ratios Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-36
37. 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. Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-37
38. 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. Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-38
39. 39. Utility Utility Utility Three Types of Utility Curves \$ Risk Averter \$ Risk Seeker Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. \$ Risk-Neutral Chap 16-39
40. 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 Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-40
41. 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 Statistics for Managers Using  Addressed Microsoft Excel, 4e the concept of utility © 2004  Prentice-Hall, Inc. Chap 16-41