Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-1 Chapter 16 Decision Making Statistics for Managers Using Microsoft ® Excel 4 th Edition

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-2 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 16-3 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-4 List Possible Actions or Events Payoff TableDecision Tree Two Methods of Listing

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-5 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-6 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-7 Opportunity Loss Investment Choice (Action) Profit in $1,000’s (Events) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-8 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 (continued) Investment Choice (Action) Opportunity Loss in $1,000’s (Events) Strong Economy Stable Economy Weak Economy Large factory Average factory Small factory Payoff Table Opportunity Loss Table

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 16-9 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap  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 Suppose these probabilities have been assessed for these three events (continued) Expected Monetary Value Solution

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap Investment Choice (Action) Profit in $1,000’s (Events) Strong Economy (.3) Stable Economy (.5) Weak Economy (.2) Large factory Average factory Small factory Example: EMV (Average factory) = 90(.3) + 120(.5) + (-30)(.2) = 81 Expected Values (EMV) Maximize expected value by choosing Average factory (continued) Payoff Table: Goal: Maximize expected value Expected Monetary Value Solution

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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 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)

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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 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 Example: Best decision given “Strong Economy” is “Large factory” Value of best decision for each event:

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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 (continued)  Now weight these outcomes with their probabilities to find the expected value: 200(.3)+120(.5)+20(.2) = 124 Expected profit under certainty

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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)

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap Accounting for Variability Stock Choice (Action) Percent Return (Events) Strong Economy (.7) Weak Economy (.3) Stock A Stock B 148 Consider the choice of Stock A vs. Stock B Expected Return: Stock A has a higher EMV, but what about risk?

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap Stock Choice (Action) Percent Return (Events) Strong Economy (.7) Weak Economy (.3) Stock A Stock B 148 Variance: Calculate the variance and standard deviation for Stock A and Stock B: Expected Return: Example: Standard Deviation: Accounting for Variability (continued)

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap Calculate the coefficient of variation for each stock: (continued) Stock A has much more relative variability Accounting for Variability

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap Return-to-Risk Ratio Return-to-Risk Ratio (RTRR):  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 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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 Decision Making with Sample Information  Permits revising old probabilities based on new information New Information Revised Probability Prior Probability

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap Revised Probabilities Example  Revised Probabilities (Bayes’ Theorem) (continued)

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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.875strong weak Σ = 25.0 Σ = Maximum EMV

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap Stock Choice (Action) Percent Return (Events) Strong Economy (.875) Weak Economy (.125) Stock A Stock B 148 Variance: Calculate the variance and standard deviation for Stock A and Stock B: Expected Return: Example: Standard Deviation: Accounting for Variability with Revised Probabilities

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap The coefficient of variation for each stock using the results from the revised probabilities: (continued) Accounting for Variability with Revised Probabilities

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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 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 Three Types of Utility Curves Utility $$$ Risk Averter Risk SeekerRisk-Neutral

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 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 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