Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap 17-1 Statistics for Managers Using Microsoft® Excel 5th Edition Chapter 17 Decision Making

Statistics for Managers Using Microsoft Excel, 5e © 2008 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

Statistics for Managers Using Microsoft Excel, 5e © 2008 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

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap 17-4 Payoff Table Profit in $1,000’s (Events) Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy A payoff table shows alternatives, states of nature, and payoffs

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap 17-5 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, 5e © 2008 Prentice-Hall, Inc.Chap 17-6 Opportunity Loss Profit in $1,000’s (Events) Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy 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, 5e © 2008 Prentice-Hall, Inc.Chap 17-7 Opportunity Loss Opportunity Loss in $1,000’s (Events) Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy Payoff Table Opportunity Loss Table Profit in $1,000’s (Events) Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy Stable Economy Weak Economy

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap 17-8 Decision Criteria  Expected Monetary Value (EMV)  The expected profit for taking action A j  Expected Opportunity Loss (EOL)  The expected opportunity loss for taking action A j  Expected Value of Perfect Information (EVPI)  The expected opportunity loss from the best decision

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap 17-9 Expected Monetary 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 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, 5e © 2008 Prentice-Hall, Inc.Chap Expected Monetary Value  The expected value is the weighted average payoff, given specified probabilities for each event Suppose these probabilities have been assessed for these three events Profit in $1,000’s (Events) Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy (0.3) Stable Economy (0.5) Weak Economy (0.2)

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap Expected Monetary Value  Example: EMV (Average factory) = 90(.3) + 120(.5) + (-30)(.2) = 81 Payoff Table: Profit in $1,000’s (Events) Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy (0.3) Stable Economy (0.5) Weak Economy (0.2) EMV (Expected Values)

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap Expected Opportunity Loss  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 = opportunity 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, 5e © 2008 Prentice-Hall, Inc.Chap Expected Opportunity Loss  Example: EOL (Large factory) = 0(.3) + 70(.5) + (140)(.2) = 63 Opportunity Loss Table Opportunity Loss in $1,000’s (Events) Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy (0.3) Stable Economy (0.5) Weak Economy (0.2) Expected Opportunity Loss (EOL)

Statistics for Managers Using Microsoft Excel, 5e © 2008 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, 5e © 2008 Prentice-Hall, Inc.Chap Expected Profit Under Certainty  Expected profit under certainty = expected value of the best decision, given perfect information Example: Best decision given “Strong Economy” is “Large factory” Value of best decision for each event: Profit in $1,000’s (Events) Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy (0.3) Stable Economy (0.5) Weak Economy (0.2)

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap Expected Profit Under Certainty Profit in $1,000’s (Events) Investment Choice (Action) Large Factory Average Factory Small Factory Strong Economy (0.3) Stable Economy (0.5) Weak Economy (0.2)  Now weight these outcomes with their probabilities to find the expected profit under certainty: 200(.3)+120(.5)+20(.2) = 124

Statistics for Managers Using Microsoft Excel, 5e © 2008 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, 5e © 2008 Prentice-Hall, Inc.Chap Accounting for Variability Percent Return (Events) Stock Choice (Action) Stock AStock B Strong Economy (.7) Weak Economy (.3) Expected Return (EMV) Consider the choice of Stock A vs. Stock B Stock A has a higher EMV, but what about risk?

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap Accounting for Variability Calculate the variance and standard deviation Example: Percent Return (Events) Stock Choice (Action) Stock AStock B Strong Economy (.7) Weak Economy (.3) Expected Return (EMV) Variance Standard Deviation

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap Accounting for Variability Calculate the coefficient of variation for each stock: Stock A has much more relative variability

Statistics for Managers Using Microsoft Excel, 5e © 2008 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, 5e © 2008 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, 5e © 2008 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, 5e © 2008 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, 5e © 2008 Prentice-Hall, Inc.Chap Revised Probabilities Example Revised Probabilities (Bayes’ Theorem)

Statistics for Managers Using Microsoft Excel, 5e © 2008 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, 5e © 2008 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, 5e © 2008 Prentice-Hall, Inc.Chap Accounting for Variability with Revised Probabilities Calculate the variance and standard deviation Example: Percent Return (Events) Stock Choice (Action) Stock AStock B Strong Economy (.875) Weak Economy (.125) Expected Return (EMV) Variance Standard Deviation

Statistics for Managers Using Microsoft Excel, 5e © 2008 Prentice-Hall, Inc.Chap Accounting for Variability with Revised Probabilities The coefficient of variation for each stock using the results from the revised probabilities:

Statistics for Managers Using Microsoft Excel, 5e © 2008 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, 5e © 2008 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, 5e © 2008 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, 5e © 2008 Prentice-Hall, Inc.Chap Three Types of Utility Curves Utility $$$ Risk Averter Risk SeekerRisk-Neutral

Statistics for Managers Using Microsoft Excel, 5e © 2008 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, 5e © 2008 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 In this chapter, we have