Week 7 AGSM 2006 Page 1. ATaxonomy ofdecisions
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1 Week 7 AGSM 2006 Page 1 ATaxonomy ofdecisions cer tainty uncer tainty attribute single multiple FA CBA Multi- Attribute Decisions Decision Analysis? decisions Decision Analysis: decision making under uncertainty >
2 Week 7 AGSM 2006 Page 2 Decision Analysis Introduction 1. Basic Concepts Atechnique for helping make decisions, and avoiding pitfalls. We discuss: Formulating the issue. Identifying the alternative actions. Valuing the possible outcomes. (Not merelyinmonetar y terms.) Encoding uncertainty. probabilities Cer tainty Equivalent (C.E.). The Value of Perfect Information. (VPI) The value of imperfect information.
3 Week 7 AGSM 2006 Page 3 Beginning Principles: The best you can do is to integrate in a logical manner: What you can do. What you know.(such asprobabilities, and values) What you want or value. (Such aspreferred outcomes) What you can do What you know What you want Decision model
4 Week 7 AGSM 2006 Page 4 2. The Simplest Decision Case 1 The simplest decision under uncertainty calling a coin toss: you win $10 or nothing. Highlights some concepts which are useful in more complex decisions. Let s star t with a volunteer ( )and ask some questions: 1. Would you pay$2for a ticket to play the game? 2. What sthe minimum you d sell the ticket for? 3. What sthe maximum you d pay for perfect information about the toss (from a clair voyant)? 4. And forimperfect information? Ever yone write down your answers toquestions 2 and 3.
5 Week 7 AGSM 2006 Page 5 The Coin Toss values this game at. values perfect information at $ values imperfect information at < $
6 Week 7 AGSM 2006 Page 6 ConsistencyCheck 1. You sell the Ticket to the Lottery for your Certain Equivalent, or minimum selling price $X. Youwalk awaywith $X for cer tain. 2. You buy Perfect Information about the coin toss for a maximum of $Y.You then correctly call the toss and win the $10. Youwalk awaywith $10 $Y for cer tain. 3. So, to be consistent: $X =$10 Y
7 Week 7 AGSM 2006 Page 7 ConsistencyCheck Minimum selling price (The Certainty Equivalent) + Value of Perfect Information = Maximum Payoff But why? So the Value of Imperfect Information must be less than the Maximum Payoff minus Minimum selling price (The Certainty Equivalent)
8 Week 7 AGSM 2006 Page 8 Calling the Toss Concepts: Uncer tainty and probability Profit lotteries Decisions as allocations of resources Sunk cost irretrievable allocations of resources Cer tainty Equivalent value of the lottery Information and probability Value of information Consistencyindecision making
9 Week 7 AGSM 2006 Page 9 Concepts (cont.) Decisions versus outcomes What is meant byagood decision? Individual decisions, corporate decisions Decision trees: Enter? Yes $2 Toss No $0 Wrong $0 Right $10
10 Week 7 AGSM 2006 Page 10 Insights? 1. The three elements of a decision: actions:here call Heads or Tails. events are Nature s possible moves: here Heads or Tails. outcomes:here either $10 for a correct call or nothing. 2. Her attitude to risk: the minimum she was prepared to sell the ticket for. 3. Her value of information: limited by the Value of Perfect Information, a function of the probabilities and payoffs.
11 Week 7 AGSM 2006 Page The Decision Analysis Process. Stage 1 Decision analysis is a three-stage, quality process. But if at any step in the process the decision becomes obvious, you should stop and make the decision. 1. Structuring: Frame the Right Problem Clarify the decision. Raise and sort issues. Generate creative alternatives. Model the problem.
12 Week 7 AGSM 2006 Page 12 The Decision Analysis Process Stages 2and Evaluation: Use Logical Thinking Discover what is important. Applyanappropriate risk attitude. Determine the value of new information. 3. Agreement: Have Commitment to Action Checkfor refinement. Agree on course of action. Implement course of action. Decision analysis is a normative process.
13 Week 7 AGSM 2006 Page Evaluation Making Difficult Decisions: How manydecisions with complete certainty have you ever made? Does a good decision always guarantee a good outcome? (Does Tiger Woods always win?)
14 Week 7 AGSM 2006 Page 14 Decisions with Certainty: Good Decision Good Outcome Bad Decision Bad Outcome
15 Week 7 AGSM 2006 Page 15 Decisions with Uncertainty: Good Outcome Good Decision? Bad Outcome Bad Decision? Bad Outcome Good Outcome implies a Decision Node implies a Chance Node A decision:anirrevocable allocation of resources.
16 Week 7 AGSM 2006 Page Evaluation A Second Example: Youhavethe opportunity to win $100 if you correctly call the roll of adie as even or odd. The opportunity is not costless you must pay $35 for the oppor tunity. Youwill call the die roll odd oreven. There is only one chance to invest. Would you accept this opportunity?
17 Week 7 AGSM 2006 Page 17 Howwould you evaluate this opportunity? Typical answersare: Ican affordtolose $35 Icould reallyuse $100 Iwould toss a coin Ineed to ask mypar tner or spouse Idon t gamble My internal rate of return is...
18 Week 7 AGSM 2006 Page 18 Do you think $35 is a good deal for this opportunity? How did you evaluate this opportunity? Yes/No? Is this a good or bad decision? If you were able to negotiate, what price would you pay for this oppor tunity?
19 Week 7 AGSM 2006 Page 19 We need to think logically about the decisions we make. Should I take this opportunity? What is a good decision? What would someone else do? e.g., mybrother,etc. Can I affordtolose the $35? What do I think are my chances of a good outcome? Decision trees help us structure decisions in a logical manner.
20 Week 7 AGSM 2006 Page 20 Probability is a state of mind, not things. The Bayesian approach allows us to assign probabilities in once-off situations. What is the value to you of a single toss of a coin: $100 if heads, nothing if tails? Define the expected return from the single toss to be the average return of a hypothetical series of many tosses: $100 ½+$0 ½= $50. Treat unique events as if they were played over many times. All prior experience must be used in assessing probabilities. (Coins are almost always fair; it s warm enough to go to the beach most weekends in March in Sydney.)
21 Week 7 AGSM 2006 Page 21 Values plus probabilities. Decision making requires the assessment of values as well as probabilities. Would you payasmuch as$50 to play inthe once-off coin toss? Few people would; most people would pay apremium to reduce their risk: theyare risk averse, and would sell their lottery ticket at something less than $50; the lowest selling price is their Cer tainty Equivalent (C.E.). The risk premium equals the expected return less the Certainty Equivalent, when selling. Risk aversion can be defined and measured using utility theory.
22 Week 7 AGSM 2006 Page 22 The utility of a lottery... Decisions can onlybemade when a criterion is established for choosing among alternatives. The utility of a lottery isits expected utility. (by the definition of utility) The implications of the present for the future must be considered. What discount rate to use? Must distinguish between a good decision and a good outcome. Prudent decision-making doesn t guarantee the desired outcome invariably,but should improve the odds.
23 Week 7 AGSM 2006 Page 23 The Value of Perfect Information? Often we can, at a cost, reduce our uncertainty about Nature s future events (using market research, forecasting, statistical analysis). There must be a limit to what we should spend in these endeavours howmuch isit? The Value of Perfect Information. (VPI) The value of imperfect information is less. Often we can, at a cost, buy more certainty about the future (pay an insurance premium, buy a hedge against future outcomes). What is a fair price to pay?
24 Week 7 AGSM 2006 Page Using Decision Trees to Evaluate Decisions Adecision tree is a flow diagram that shows the logical structure of a decision problem. It is a visual aid to lay out all the elements of a decision. It contains four elements: Decision nodes,,which indicate all possible courses of action open to the decision maker; Chance nodes,,which show the intervening uncertain events and all their possible outcomes; i.e., Nature plays Probabilities foreach possible outcome of a chance event; and Payoffs, whichsummariz e the consequences of each possible combination of choice and chance.
25 Week 7 AGSM 2006 Page 25 The decision tree for this opportunity ($100 on calling a roll): The decision is whether or not to invest $35 for the opportunity to receive $100 or $0 as the outcome on the call of a die roll as odd or even. Decision Invest $35 Don t invest Chance $0 Correct Incorrect $100 $0 What else is needed to evaluate this opportunity?
26 Week 7 AGSM 2006 Page 26 The tree is missing the probability assessments for a good and a bad outcome. The tree does not yet incorporate the investor s judg ement of the probability of success and its complement, the probability of failure or loss. What information would help with this assessment? The number of sides on the die Any known bias the die might have Who gets to roll the die Correct p 1 p Incorrect $100 $0
27 Week 7 AGSM 2006 Page Evaluation Opportunities and Outcomes An important distinction is that between oppor tunities and outcomes. Oppor tunities are the sum of their possible outcomes. This is impor tant because you can onlychoose your opportunities not your outcomes. Opp A Opp B Outcomes fora Outcomes forb
28 Week 7 AGSM 2006 Page 28 How doweevaluate the opportunity? First, decide on the decision criterion. This can be any measure that allows the decision maker to evaluate deals in a quantitative manner. Expected MonetaryValue (EMV) provides the means to evaluate risky decisions consistently. EMV is the probability-weighted average:
29 Week 7 AGSM 2006 Page 29 Example: Calling the roll of the die. Invest $35 Don t invest $0 Correct ½ ½ Incorrect $100 $0 Probability Outcome 0.50 $100 = $ $0 = $0 EMV = $50 Investment = $35 Expected Net Profit = $15
30 Week 7 AGSM 2006 Page 30 Youhavedecided to take the opportunity. Youbelieve the probability of success of failure are equal, or 50/50. Youhavepaid the $35 investment, now sunk. Now what does the decision tree look like? Correct ½ ½ Incorrect $100 $0 How has the opportunity chang ed?
31 Week 7 AGSM 2006 Page 31 Beware the sunk-cost fallacy. Before deciding to pursue the investment, itisappropriate and impor tant to include the costs to enter the deal (the price of admission). But don t include what you ve already paid to get into an investment: that decision has already been made and the resources allocated, usually irreversibly. Let bygones be bygones. Evaluate future decisions for what they are wor th. Your selling price and the value you place on the investment oppor tunity should not depend on sunk costs.
32 Week 7 AGSM 2006 Page 32 The Certainty Equivalent of a lottery. Correct p Incorrect = $ 1 p $100 $0 adeal or oppor tunity C.E.: the minimum you d sell the ticket for. its Cer tain Equivalent
33 Week 7 AGSM 2006 Page Evaluation What is Your Risk Attitude? The difference between expected value (EMV) and the Certainty Equivalent (C.E.) is your risk premium. Values Risk Seeking C.E. EMV Risk Neutral C.E. Risk Averse C.E..... Risk
34 Week 7 AGSM 2006 Page 34 Risk profiles If you would paymore than EMV for a deal, then you are risk seeking. If you would payuptothe EMV for a deal, then you are risk neutral. If you would not payemv for a deal, then you are risk averse.
35 Week 7 AGSM 2006 Page 35 The event is set... The die has been rolled and the event is set. Youdon t knowthe outcome of the roll, so the outcome of the oppor tunity has not been determined. What would it be wor th to have perfect knowledg e about the roll of the die? What is the value of information?
36 Week 7 AGSM 2006 Page Evaluation The Value of Perfect Information Using the concept of a clair voyant, who knows all things past, present, and future,wecan structure a new deal: Current Info $?? Buy NewInfo Correct ½ ½ Incorrect p =1.0 $100 $0 $100
37 Week 7 AGSM 2006 Page 37 Consistencycheck: Minimum selling price? Value of perfect information? Are these consistent? Ask: What would I walk away with ($) in both cases?
38 Week 7 AGSM 2006 Page 38 Calculating the Value of Perfect Information: Value of the deal with perfect information $100 Your minimum selling price (CE) =Value of perfect information (VPI) $ $ Calculating the Value of Perfect Information (VPI) is not difficult, but finding a clair voyant, or source of perfect information, will be. Use the VPI as a guideline for spending time, effor t, and money on gathering newinformation before making a decision.
39 Week 7 AGSM 2006 Page 39 Sources of imperfect information: While there are no real clair voyants (alas), we can find new sources of information whichisimperfect: Experiments Exper ts Models Trial runs Market tests Forecasts
40 Week 7 AGSM 2006 Page 40 We must distinguish between good decisions and good outcomes. Decisions are what we can affect. Agood decision balances the probabilities of good and bad outcomes in accordance with our risk attitudes. Outcomes are what we get. Agood outcome is one we like.
41 Week 7 AGSM 2006 Page SummaryofEvaluation Adecision is an irrevocable allocation of resources. Probabilities, representing exper t judg ement, are based on experience, beliefs, knowledg e, and data. The value of a deal depends on the decision maker s risk attitude. The maximum value of gathering more information can be determined (using the Value of Perfect Information) before obtaining the actual information, in this framework. <
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