Chap16 decision making
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This document provides an overview of key concepts in decision making covered in Chapter 16 of the textbook "Statistics for Managers Using Microsoft Excel". It begins by listing the chapter goals, which include describing decision making processes, constructing decision tables, applying expected value criteria, and accounting for risk attitudes. It then outlines the typical steps in decision making, such as listing alternatives and possible outcomes. Key decision making criteria are defined, like expected monetary value, expected opportunity loss, and value of perfect information. Examples are provided to demonstrate how to apply these concepts to make optimal decisions under uncertainty.
Chap16 decision making
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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