DECS 433Winter 2011Decision Making under UncertaintyProfessor: Ronen Gradwohl

This is a tentative draft of the syllabus: October 2010

Description

This course introduces basic concepts and tools for decision making under un-certainty and imperfect information. These concepts and tools are essential bothfor your course work at Kellogg and in your future career as a business leader.

Within the Kellogg curriculum, the material introduced in this course is usedin core and elective courses in economics, statistics, finance, operations, and ac-counting. Mastering the material of this course will help you get the most out ofthese courses.

More important is this course’s relevance for your future career. As a futurebusiness leader, you will constantly face problems in which you lack the informa-tion necessary to make the “perfect” decision. Companies price without knowingperfectly the demand for their product; pharmaceutical companies commit con-siderable resources without knowing whether their products will succeed or fail;global companies face exchange rate risk; hedge funds face interest rate risk; in-vestors in emerging markets cannot perfectly assess the full spectrum of economicand political risks they will face. The list is endless. In fact, it is hard to thinkof a significant business decision that does not entail some measure of imperfectinformation and, therefore, uncertainty.

While perfect decisions are unattainable, better decisions are. This course willprovide you with models, tools, and concepts to help you make better use of theinformation available in situation like the ones listed above, and many more. Theideas of this course will be presented along three axes:

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• Models: These represent stylized environments often encountered in practice.The models we introduce lend themselves to the applications of batteries ofpowerful tools that can help you quantify uncertainty, guide your decisionmaking process, and reveal hidden connections that you might otherwisemiss.

• Tools: While models provide ways to frame problems, tools will help us crackthem. The course introduces powerful tools from probability theory, riskanalysis, and Monte Carlo simulations to help us do just that.

• Principles and Concepts: Tools and models help us get concrete answers toconcrete questions. Just as important are the principles and concepts of de-cision making that generalize to broader contexts. They are the qualitativeinsights we learn from the models and tools. For example, concepts of “flawof averages,” risk aversion, value of information, option value, adverse se-lection, and herd behavior, are fundamental to all aspects of modern riskmanagement, even in contexts not covered in this course.

Bringing it all together. The first half of the course builds fundamental compo-nents in depth. The second half shifts to a different challenge: how to creativelyintegrate the models, tools, and concepts of the first half to deal with richer, in-creasingly multi-faceted issues of central importance in modern business. Theseinclude such topics as insurance, selection bias, herd behavior, and cost uncertainty,among others.

Grading

Homework assignments: Some homework assignments are individual, whileothers are to be done in groups. This is clearly noted in the syllabus.

Answers should be handed in at the beginning of class on the due date. Home-work solutions should be printed. No late submissions.

Groups: The class will be divided into study groups for the purpose of grouphomework assignments. Please submit one answer per group for group homeworkassignments.

Homework Honor Code Policy:In completing individual homework assignments, you may not discuss the ques-

tions with other students (in any section) currently taking this course or that have

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taken it in the past. Exceptions: You may discuss the course topics, concepts, andgeneral Excel skills with others.

The policy for group homework assignments is similar: group members may notdiscuss the homework questions with students outside the group currently takingthis course or having taken it in the past. The exceptions noted above apply.

Grade distribution:

• Homework (15%, divided equally between homework assignments).

• Midterm (in-class; 30%; optional—see below).

• Final (cumulative and in-class; 55%).

Optional midterm: The midterm will count only if it improves your overallgrade. I determine the final grade by first calculating the higher of:

• The score based on the percentages above; and

• The score with the same weights for homework assignments, but where thefinal exam counts for 85% and the midterm carries no weight.

This means that if you decide not to take the midterm, or you take it but youdo better in the final exam, only the final exam grade will count. The midtermwill count only if it can help you improve your overall position. This being said,you are strongly encouraged to take the midterm and invest the time and effort todo well in it.

Class participation and attendance: Attendance, class participation, prepa-ration, and contribution to group work are important components of your learningexperience in this course. Attendance is therefore expected unless there is a validbusiness or health condition. Your course score may be adjusted, up or down, bya maximum of 10% to reflect attendance, class participation and contribution togroup work. This adjustment will primarily be used in borderline cases betweenletter grades (A/B, etc). Your final letter grade in this course will be based on thisadjusted score.

Final letter grade: These are determined according to the guidelines set by theOffice of the Dean.

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Weekly Deliverables• Homework assignments. To be handed in at the beginning of class in hardcopy. Do not send homework assignments electronically. For group home-work assignments, submit only one copy per group. Students are responsiblefor answering questions and participating in class discussion of homeworkquestions, especially group homework assignments.

• Items to prepare for class discussion. These are problems that are usually,but not always, part of the homework assigned for that week. They are clearlymarked in the syllabus as “prepare for class discussion” and will be the focusof class discussion. Every student is expected to be thoroughly familiar withthem.

• Required readings. These are readings on key concepts in the course; students’familiarity with them is expected.

• Optional readings. These are interesting readings on topical issues or eventsof historical interest. Something to broaden our horizons and enrich under-standing of the subject. They are not formally required.

References

• Sandholm, W. and B. Saraniti: Chapters 2, 3 and 4 of Vital Statistics: Proba-bility and Statistics for Economics and Business Decisions, 2007, Manuscript.

• Kirkwood, G. W.: Decision Tree Primer, Arizona State University, 2002.

• McKeon, Scott: Excel Basics, Kellogg School of Management.

All three readings above will be available for download, free of charge, on thecourse Blackboard site.

Optional Reading:

• Savage, S.: The Flaw of Averages, Wiley, 2009.

This book has many nice examples and intuitive explanations. It is also a fun read.Some of the examples will be mentioned in class. But the book is not formal, andno substitute for the more rigorous treatment in this course. A copy of the booksells for about $15.

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Course Outline

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Week 1

SESSION 1: Probability and Decision Making

Topics: Frequentist and subjective interpretations of probability. Basic defini-tions: states, events, and outcomes. Basic laws of probability. Probability trees.

Examples: The conjunction fallacy.

Reference: Sandholm & Saraniti, Ch. 2.2, 2.3.

Session Plan: After a course introduction, the main goal is to introduce some key definitions

and concepts. At this stage, the definitions can be overwhelming! Do not worry, they will be

repeated and illustrated as we move further in the course.

SESSION 2: Stopping Problems

Topics: Stopping problems; geometric distribution.

Examples: Coincidences; Surviving a Russian Roulette; a simple simulation.

Session Plan: Stopping problems are our first non-trivial probability model. They are simple

enough to be easily and thoroughly analyzed, yet rich enough to accommodate many important

applications. We introduce a special class of distributions extensively used in practice, the

geometric distribution. In the context of stopping problems, we introduce numerous examples

and the concepts of conditional probability, Bayes rule. Time permitting, we may also start

discussing random variables, their expectations and distributions.

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Week 2

SESSION 3: Incorporating Information in Decisions

Homework 1 due (individual)

Topics: Bayes’ rule, independence and conditional probability.Examples: The base-rate fallacy, or how not to spot a terrorist.Reference: Sandholm & Saraniti, Ch. 2.4.Optional Reading:

• Jack Zlotnick: “A Theorem for Prediction,” secret CIA document, declassi-fied 9/18/1995.

Session Plan: We introduce the concepts of conditional probability and Bayes rule. These are

the tools we need to understand how probability judgments change in light of new evidence. We

will first look back at stopping problems introduced earlier and see that we were already using

conditional probabilities and Bayes rule without being explicit about it. We then introduce the

general definitions and apply them to the problem of how the probability of a major earthquake

changes if decades pass without one. Intuitively, we want to understand what people mean when

they say we are due for a big one. Finally, as another illustration of these tools we discuss a

common error known as the base-rate fallacy.

SESSION 4: Measuring Variability

Topics: Random variables, their distributions and expectations. Bernoulli andbinomial random variables.Examples: Churning mortgages; Cat Bonds.

References: Sandholm & Saraniti, ch. 2.5.

Optional Reading:

• Michael Lewis: “Nature’s Casino,” The New York Times, 8/26/2007.

Session Plan: We introduce the concepts of random variables and their distributions. To

make a decision under uncertainty means that we do not know all the facts needed to predict

the consequences of our decisions. We quantify what we mean by: “consequences vary due to

unknown factors” using the concepts of variance and standard deviation. Time permitting, we

also introduce the binomial distribution, a central concept in modern risk management, finance,

insurance, and operations, among others. The session ends with examples of Catastrophe (Cat)

bonds, which are instruments used to spread the risk of major insurance disasters.

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Week 3

SESSION 5: “The Flaw of Averages”

Homework 2 due (groups) The homework uses:

• “Union Carbide-Butane Transport,” HBS 9-180-017, 1979.

Topics: Maximizing the expectation of payoff; maximizing the payoff of theexpectation.

Examples: Discussion focuses on the Union Carbide case.

Session Plan: This class centers on the idea that tailoring one’s plans to the mean is often

misleading and can lead to flawed decisions. Formally, one should maximize expected payoff

rather than the payoff of the expectation. This will turn out to be one of the most important

concepts in this course. This session will focus on the Union Carbide case as an illustration.

SESSION 6: “The Flaw of Averages” continued; Catch-up

Topics: Continue with examples emphasizing the difference between maximizingthe expectation of payoff vs. maximizing the payoff of the expectation.

Examples: Airline overbooking problem; price problem; valuing an option.

Session Plan: Confusing expected payoff maximization with maximizing the payoff of theexpectation is a common flaw in decision making. It appears in numerous contexts, from supplychain management and financial options, to pricing and deciding how early one should leave tocatch a flight at a busy airport! We provide a framework to detect the “flaw of averages” andbetter understand how to correct for it.

By now the course should be moving at a fast pace, so this is a good time to slow down a

little and catch up in the event that we have fallen behind relative to the syllabus. We will use

any time remaining to review some concepts as needed and go over a few problems.

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Week 4

SESSION 7: Diversification and the Risk-Reward Tradeoff

Homework 3 due (individual)

Topics: Variance, covariance, and the efficient risk-reward frontier.

Examples: Portfolio choice; uses and abuses of probability: the case of structuredfinance.

References: Sandholm & Saraniti, ch. 3.1, 3.2, 3.3, 4.2.

Session Plan: We continue exploring the notions of “risk” and variability by considering sit-

uations where a decision maker is exposed to the sum (or averages) of two or more random

variables. The key concept here is that of covariance. We explain the impact of covariance on

the variability of a portfolio of two stock and derive the mean-variance frontier. We conclude

with an example inspired by the 2008 financial crisis illustrating the impact of covariance on the

valuation of structured finance products.

SESSION 8: Risk Aversion

Topics: Risk, risk aversion and certainty equivalents. Logarithmic utility. In-creasing risk via mean-preserving spreads.

Examples: Deal-or-no-deal; drill-baby-drill.

Prepare for class discussion:

• Al-Najjar, N.I.: “Deal or No Deal,” Kellogg School of Management.

Reference: Kirkwood, ch. 2.

Session Plan: We explore the concept of “risk,” perhaps the most fundamental and ubiquitous

force in all business decisions. We distinguish between risk and variability and introduce the

concept of risk aversion, a personalistic-subjective measure of how people respond to risk. We

introduce the notion of utility for money and operationalize it with logarithmic utility.

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Week 5

SESSION 9: Normal Distribution & The CLT

Homework 4 due (individual)

Topics: The normal distribution; the Central Limit Theorem; relationship withbinomial probabilities.

Example: Demand and the distribution of values in a market.

References: Sandholm & Saraniti, ch.

Session Plan: We introduces two of the most important concepts in all of probability: the

normal distribution (also known as the bell curve) and the central limit theorem (CLT). We

motivate this by modeling the distribution of values in a market, deriving a probabilistic model

of the demand curve in a market and discuss some implications on pricing—pricing, of course,

is a central topic in future courses in economics, so this gives you a foretaste and preparation,

rather than substitution, for future work.

SESSION 10: Risk and Insurance

Topics: Insurance, Value-at-Risk.

Example: Six Sigma quality control systems; uses and abuses of probability: thecase of LTCM.

Prepare for Class Discussion:

• Al-Najjar, N.I.: “Insuring Against Freak Accidents.”

• “Value-At-Risk,” HBS 9-297-069, 1997.

Optional Reading:

• “The Gods Strike Back,” The Economist, February 13, 2010. Pages 1-8.

Session Plan: We apply the CLT to understand the idea of diversifying risk in an insurance

context. We derive the “law of averages,” also known as the law of large numbers (LLN). We then

introduce the concept of Value-at-Risk, a measure of riskiness widely used by many companies.

We examine the assumptions on which it is based and provide an example of one of the largest

collapses of a financial institution, LTCM.

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Week 6

SESSION 11: Decision Trees and Cost Concepts

Topics: Decision trees; Sunk cost; Fixed vs. variable costs.

Examples: Sunk cost; thinking through exit decisions.

Prepare for Class Discussion:

• Al-Najjar, N.I. and D. Besanko: Exercise on Relevant Costs, Kellogg Schoolof Management, 2009.

• Dan Saligman: “Of Mice and Economics,” Forbes, August 24, 1998.

Reference: Kirkwood, ch. 1.4.

Session Plan: We introduce basic ideas underlying decision trees, a basic tool for analyzing

sequential decision making. We use decision trees to illustrate different cost concepts, in particular

the notion of sunk cost.

SESSION 12: Midterm Review

Coverage: Will be confirmed in class, but usually the exam covers all materialfrom Sessions 1-10. Exact coverage will depend on the pace of the course.

Guidelines:

• The exam will be given out at the end of class, and will be due at the beginningof class the following week.

• The exam will be given out in an opaque envelope. You have 1.5 hours tocomplete the exam from the minute you take it out of the envelope. Oncethe 1.5 hours are up, you must return the exam to the envelope.

• The exam is open book and notes.

• You are permitted to use laptops to invoke EXCEL only.

• The exam will not require you to build simulations or elaborate spreadsheets.

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Week 7

SESSION 13: Decision Trees and Framing

Homework 5 due (groups)

Prepare for Class Discussion:

• “Weston Manufacturing Company,” HBS 9-111-047, 1967.

Reference: Kirkwood, ch. 1.4.

Session Plan: The focus of this session is to go over the Weston case. This involves constructing

a fairly non-trivial decision tree. We demonstrate the rolling back method of solving such decision

trees and conclude by discussing framing effects.

SESSION 14: Value of Information

Prepare for class discussion:

• Al-Najjar N.I.: “Blind Shear Rams,” Kellogg School of Management.

Reference: Kirkwood, ch. 3.

Session Plan: The focus of this session will be on the Blind Shear Ram case. This is our first

case on the value of information, both perfect and imperfect. That is, we ask how much are

you willing to pay of additional information that can reduce your uncertainty and improve your

decision.

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Week 8

SESSION 15: Options Value and Flexibility

Homework 6 due (group)

Topics: Real options; value of deferring decisions.

Prepare for class discussion:

• Besanko, D.: Scrapping an Oil Tanker, Kellogg School of Management, 2002.

Required Reading:

• A. Dixit and R. Pindyck: “The options approach to capital investment,”Harvard Business Review, 1995.

Session Plan: The focus of this session will be on the tanker homework. This involves a non-

trivial decision tree with a rich set of options to postpone the termination of a capital asset. We

conclude with a general discussion of the importance of the options logic in capital allocation.

SESSION 16: Selection Bias; Catch-up

Topics: Selection bias.

Prepare for class discussion:

• Al-Najjar N.I.: “Gaming Health Insurance,” Kellogg School of Management.

Example: Class will focus on the homework problem “Gaming Health Insurance”and the HBR article below.

Reading:

• J. Denrell: “Selection Bias and the Perils of Benchmarking,” HBR, 2005.

Session Plan: We go through the mechanics of the health insurance homework. We then

discuss issues surrounding the health care reform and, especially, mandatory participation. This

should leave us some time to devote to catching up and review.

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Week 9

SESSION 17: Market Entry with Cost Uncertainty

Homework 7 due (individual)

Topics: Entering a market with uncertain cost.

Prepare for class discussion:

• Besanko, D.: Exercise on Cost Uncertainty, Kellogg School of Management.

Example: Discussion will focus on the homework problem and the Dixit-Pindyckarticle from last week.

Required Reading:

• T. Horn, D. Lovallo, and S. Viguerie: “Learning to let go: Making better exitdecisions,” The McKinsey Quarterly, 2006.

Session Plan: We go through the homework problem. Our focus will be on using the tools of

the course to understand some of the problems arising in capital investment under uncertainty.

SESSION 18: Aggregating Information

Prepare for Class Discussion:

• “Wisdom of the Crowds,” Kellogg School of Management.

Topics: Information aggregation; wisdom of the crowds.

Session Plan: A critical function of firms, organizations, and markets is to aggregate dispersed

information and use it efficiently to make better decisions (OK, this is at least what the better

organizations and markets should strive to do). We will discuss two major models. The first

is based on the Wisdom of the Crowds problems, and will illustrate an efficient aggregation of

information; the second is a sequential choice model that gives rise to herd behavior.

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Week 10

SESSION 19: Aggregating Information (cont’d)

Homework 8 due (group)

Prepare for Class Discussion:

• Besanko, D.: “The Fable of ‘The Circle of Quality Management System,’ ”Kellogg School of Management.

Optional Reading:

• Surowiecki: Wisdom of the Crowds, Doubleday, 2004, Chapters 1 and 4.

These chapters are not included in your packet. The publisher charges $8 for the twochapters, even though the entire book is available at bookstores for about $10. This optionalreading will be briefly discussed in class; please buy a copy if you so prefer.

Session Plan: This session will introduce a simple model illustrating how markets may fail to

aggregate information.

SESSION 20: Integrative Topics and Course Conclusion

Homework 9 due (individual)

FINAL EXAM

See Student Affairs for date and time. Usually exam is in “Week 11,”same time and place as course. Rooms to be determined.

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