GBUS 8900 Management Decision Models
Course Description |
Schedule | Software Resources |
Templates |
References
Assignments
- Fall Late Week, 11:45-1:10 PM,
Room 280.
In the first week we will begin to create
models of dynamics that develop over time.
1.
Assignment for Creating a Dynamic Model
Reference: Background
reading about influence diagrams is contained in Structuring Assumptions in
Decision Making (UVA-QA-0499), page 1 thru top of page 8, and page 15 to end.
If you desire extra reading for the first four
sessions of the course, or another slant on developing a model, see
chapter 2 (and perhaps other chapters) of Management
Science: The Art of Modeling With Spreadsheets, Second Edition,
Powell, Stephen G., and Kenneth R. Baker, John Wiley and Sons, 2007, on reserve for the course in the Darden Library.
Prepare:
Internet Rapide (UVA-QA-0617)
Assignment Questions:
1. What would be your recommendation on the basis of a
single period? Is it necessary to do more than a single period
model? Why?
2. How would you structure a multi-period model?
- what is the performance measure (or value criterion)
you wish to maximize?
- what are the decision variables?
- what are the core intermediate variables? An influence diagram
to draw the relationships among these core intermediate variables--if a
variable is influenced by the previous value of a variable, label the
influence arrow with PREVIOUS
- complete the influence diagram including relationships among all
variables (decision variables, intermediate variables and the
performance measure). Do not let this get too complicated--a dozen
variables should be plenty to capture the model. Use references to
previous
3. Prepare an Excel spreadsheet model on which to
develop a multi-period recommendation (let's all take the model out 21
quarters for starters; at period 0 all 1 million customers are type A).
Check that your influence diagram matches
your model.
4. Use a guided trial and error search to find a
reasonable
recommendation. Your own trial and error search for the best plan will be
sufficient, optimization is not necessary. Spend your time on a
spreadsheet model that captures the essential elements without being fancy. AVOID SOLVER--YOUR
MODEL IS NONLINEAR AND YOU'D NEED TO START IT AT A HUGE NUMBER OF STARTING
POSITIONS TO GET ANY ASSURANCE OF A GLOBAL OPTIMUM. The adventurous may want to try using Optquest on their model (a
User's Guide for Optquest is available in the course packet for class 12).
5. Please submit your Excel file for Internet Rapide to me
for use in class discussion no later than 8 a.m. on the day of class. You
are allowed to work together on this.
(Optional) You may care to include your influence diagram in
an Excel worksheet in your workbook, or not.
Name your file so that the first three letters indicate the
case (INT), the next 6 are the first six
letters of your surname, and the next 6 are the first six letters of your
given name. Thus the spreadsheet of the student Juan Zapata Tyme for Internet Rapide would be
saved as:
INTTyme__Juan__.XLS .
If you work together concatenate all additional names to
the file name, e.g. INTSurnamGivenm SurnamGivenm SurnamGivenm. Submit your file
to the course assignment drop box located at the
MDM Course
Folder using the instructions for uploading files that you will receive by email.
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Objectives:
Introduction to structuring spreadsheet
relationships
§
Using influence
diagrams
§
Building
dynamic models
Alternate time horizons for decisions
§
Snapshot
one-period
§
Short- a few
periods
§
Long-term
Decision interactions and guided search
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2.
Assignment for MNB One
Read: "Markov
Brand-Switching Models," Section 13.1 of Management Spreadsheet Modeling and
Analysis, by Rick Hesse, Irwin, Chicago, 1997.
Reference: The following link gives
examples of Markov chains, including a weather example and a link to the
underlying page-rank approach of Google, which is based essentially on a
Markov process, where the states are url's on the internet.
http://en.wikipedia.org/wiki/Examples_of_Markov_chains
Prepare:
MNB One Credit Card Portfolio (UVA-QA-0613)
Assignment Questions:
1. What is the
valuation of the portfolios based on current contribution?
2. Which portfolio
should Duguid recommend for purchase?
3. What insight can a
Markov model provide into the value of a customer:
- Which would you prefer, a Current or a 30-Day Markus
Nayman customer? Why?
- Compare the value of a randomly selected Sirtem customer with a Markus
Nayman
customer. Why is one better than the other?
4. How much should
Duguid be willing to spend on the educational program?
5. What are some
situations where Markov processes would be appropriate to capture the
dynamics of a system?
Use the spreadsheet
MNB One.xls in your preparation.
See the optional material in the course folder (Interfaces
Vol. 35, No. 5, Sept-Oct. 2005) with my highlights and notes:
Merrill Lynch used Monte Carlo simulation of a Markov process (where the
states relate to client credit ratings) to save $4 billion dollars of
liquidity. Doing this in your finance job would make you a big
hero.
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Objectives:
Introduction to Markov processes
§
Initial state
distributions
§
Transition
matrices
§
Payoffs
§
Steady-state
probabilities
Initial states versus transition probabilities
§
Comparative
value
§
Tradeoffs
Summary of dynamic models
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3.
Assignment for Risk Preference Class
Read: pages 120-128 of
"Risk Preference and Utility," (the first 9 pages of) chapter 9 of Quantitative Business Analysis:
Text and Cases (QBA), by Bodily, Carraway, Frey, and Pfeifer.
Prior to this class:
Complete levels 1 and 2 of the Risk_Preference_Utility_Math quiz, located at
http://it.darden.virginia.edu/BTN/
You may need to self-register for the quiz using the register link on
the main page. The quiz begins at level 1 (easiest problems) and you
will work your way up in difficulty levels as you answer questions
correctly. Correspondingly, missing questions will cause your difficulty
level to drop. This is similar to the GMAT format.
Prepare:
1. Exercises 1 and 2 at the end of chapter 9, page 133.
2. (Optional) Assessing Your Own Utility
to Compare Signup Bonuses (attached in hardcopy).
Use the spreadsheet
Bonus Dollars.xls in your
preparation. This spreadsheet makes use of TreePlan, a spreadsheet add-in for decision tree analysis. The tree is already developed in Bonus Dollars.xls for you to use.
You need only enter your risk tolerance in the appropriate cell.
Software Resource:
ASSESS is an Interactive Program for
Utility Assessment from Philippe Delquié of Insead. Click
here to download <ASSESSinstall.zip>,
a zip file containing ASSESS for Windows. After downloading, extract all
files to a temporary folder and run Setup.exe.
Assignment Questions:
While you can use a calculator or a
spreadsheet to do exercises 1 and 2 at the end of the chapter, you may wish to use TreePlan
to develop a decision tree. Documentation for downloading and using
TreePlan
is in a PDF on the course folder (open Treeplan.xla with Excel to use it). Note that to use
a constant risk-averse utility function with Treeplan, you must choose "Use Exponential
Utility" in the Options dialog box (which comes up in the dialog window in Excel
when you hit CTRL+Shift+T), and you must place a risk tolerance number in a cell that
has a range name RT. In Excel, find Define Name on the
Formula ribbon to create a range
name.
After reading the chapter and preparing the
exercises above, consider how risk preference should be used in practice in the
corporation.
Objectives:
Introduction to risk preference
§
Certainty
equivalent
§
Risk premium
§
Utility
function
§
Expected
utility captures it all
Using expected utility
§
in a decision
tree
§
for insight
about diversification.
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4.
Assignment for Risk Preference Utility
Exercises
Prepare:
1.
Risk Preference Utility Caselets (UVA-QA-0703).
Reference:
1. "Risk Preference and
Utility," chapter 9 of
QBA.
Read: Deal or No Deal
paper (to be distributed)
Assignment Questions:
1. Make use of
TreePlan to prepare caselets I and III.
Note: TreePlan can be used for Caselet III only if the expected
utility calculation for each event branch is modified to use logarithmic
utility. Solver may be useful for question IIIc. What is the
valuation of the portfolios based on current contribution?
2.
How much additional value would be gained in
the "Deal or no Deal" game
a.
from using expected utility?
b.
from simply not being risk-seeking?
Suggest some business situations where you think additional value could
be obtained by using expected utility.
Recommended prior to class session 4,
especially if the use of expected utility for risk preference needs more
clarity:
Complete levels 3 and 4 of the Risk_Preference_Utility_Math quiz on the Darden BusinessMath site. This
is located at
http://it.darden.virginia.edu/BTN/
. A small portion (5%) of your grade is connected to completing
the four levels by Class 12, September 23.
Objectives:
Applying risk preference
§
in TreePlan
§
for portfolio
of investments
§
with
sensitivity to risk tolerance
§
for risk
sharing
Decreasing risk aversion, logarithmic utility model |
5.
Assignment for Real-time
Modeling ExerciseThere is no preparation in advance for this
class! In class, I will hand out a one-page problem situation. We'll work
through the analysis together during class time. This is an opportunity to
develop real-time problem solving skills. It is good preparation for some of the
problem-based interviews you will have later in the year. Since
there is no assignment for this class, use your excess preparation time
completing the Risk_Preference_Utility_Math tutorial or reviewing
previous material or preparing the following day's case.
6.
Assignment for Marsh and McLennan
Prepare: Marsh
& McLennan (A) (9-171-303, Rev 8/26/92)
Reference: "Risk
Preference and Utility," chapter 9 of Quantitative Business Analysis: Text and
Cases, by Bodily, Carraway, Frey, and Pfeifer, pages 126-131.
Assignment Questions:
1. Develop a simulation model for comparing the alternative
insurance plans, including the alternative to self-insure. You may use the
worksheet
MARSHMC.XLS in the MDM library.
2. Carry out a simulation of the two plans.
3. Which plan would you recommend to Eastern? What is the
best way to compare the plans?
4. Suppose
that Marsh and McLennan is decreasingly risk averse with a logarithmic utility
function
u(x) = ln (x+A) where x is the value of their losses, a negative number.
What plan would you select if A is $60 million? $150
million? Don't forget the self-insure alternative as you do this.
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Objectives:
Modeling of discrete event simulation
§
distribution
for events
§
calculation of
payoff
§
distribution
for payoff
Comparing risk profiles
§
expected value
and standard deviation
§
cumulative
distribution
§
expected utility in a simulation
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7. Assignment for Stars and Stripes
Prepare: Stars and Stripes: Quest to Bring Home
America's Cup, (UVA-QA-0563-M), student version 2.7 from this
URL:
http://it.darden.virginia.edu/intranet/case/starsstripes/darden/content/index.htm
Assignment Questions:
1. Which yacht do you recommend? Please
use the Your Decision link from the case to vote your recommendation
(while connected to the Internet).
2. Be prepared to offer supporting analysis.
You may make use of the spreadsheet
LVchallengerseriesmodel.xls
in the MDM library in your preparation.
Note: while the rules may be different now, at the
time of the case the challenger must use the same boat in the America's Cup
challenge that they used in the round robin and the Luis Vuitton Cup
semi-final and final. On the other hand the defender can pick a boat
after the Luis Vuitton Cup is finished and just before the America's Cup
final is raced. Use these assumptions from the time of the case in
your preparation.
Objectives:
Simulating an entire system for uncertain
conditions
§
race
§
series
§
tournaments
Using simulation for design
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8.
Assignment for Zeckendorf
Prepare: The Zeckendorf Company (9-186-135, Rev 3/29/94)
Assignment Questions:
1. Be prepared to discuss Zeckendorf's exposure to increases
in the commercial paper interest rate on this deal, depending on which of the
various financing alternatives they take (completely variable, completely
fixed, 9% cap, etc.).
2. Use Crystal Ball to simulate future interest rates. A way
to generate future interest rates is by using a random walk relationship:
Next Month's Rate = This Month's Rate + CB.NORMAL(0,.5%)
How would you estimate the standard deviation to use in the
normal (.5% is just a first-try figure).
3. William Zeckendorf's risk preference was
assessed using lottery questions. This resulted in a utility curve for the
interest cost in this deal, as shown below. This curve doesn't fit any of the
standard utility models. However, the curve fits reasonably well with the
following piecewise linear curve in total interest cost (Cost):
If Cost is below 6 million, then Utility = 144 -
11*Cost/1,000,000
If Cost is between 6 and 7 million, then Utility = 372 -
49*Cost/1,000,000
If Cost is between 7 and 8 million, then Utility = 232 -
29*Cost/1,000,000
Note that the file
ZECENDO.XLS,
which contains the loan schedule, and
ZECINT.XLS,
which contains the interest rates in Exhibit 2, are in the MDM library.
(Optional) I would encourage individuals or, perhaps, pairs of students
to create Excel files with the results of their preparation and to please send me these
files by email by 8 a.m. before class.
I recommended
individuals to complete the following,
if you haven't done so and the use of expected utility for risk preference needs more
clarity:
• Complete levels 3 and 4 of the Risk_Preference_Utility_Math quiz on the Darden BusinessMath site. This
is located at <http://it.darden.virginia.edu/businessmath/>.
If you used it before, you may pick up where you left off before.
Objectives:
Compare fixed, floating, and capped alternatives
Introduction to random walk
§
what model
§
what standard
deviation
Experience using a general utility function
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9.
Lecture
on Simulation of Prices, Rates, and Cash flows
Prepare: Simulation of Prices, Rates and Cash Flows (A)
(9-203-056)
Assignment Questions:
Use the data for West Texas Intermediate crude oil spot prices in the
WTI worksheet of the file
CFETOOLS.XLS,
for the following questions, as you prepare the note.
1. Assuming oil prices follow a geometric random walk,
what are the appropriate drift and volatility? Is Xt+1/Xt
normally distributed?
2. Assuming oil prices follow a mean-reverting
process, what is the speed of mean reversion and the implied
long-run oil price? What is the volatility? Is the
empirical residual distribution normal?
3. For both processes, what is the probability that
oil prices will at least double in a year? Do these numbers
seem realistic?
4. Compare these two models oil prices for use in
short-term and long-term models.
Bring any questions regarding anything we have done so far in the course,
which we will consider as time allows.
Objectives:
Additive and multiplicative random walks
Drift
Mean-reversion
Estimation and tests of models
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10.
Assignment for
ChinaCarb
Prepare: ChinaCarb (UVA-QA-0759)
1 .
What does
ChinaCarb produce and how is it used in our daily lives? Why or why
not is this a good business for them to continue?
2.
Review the various approaches that you know
for modeling the simulation of the future price
per ton of
Catyl65SO
over time. Using
the data in case Exhibit 1, recommend a good model and estimate its
parameters.
3.
What are the
alternatives available to the owners of ChinaCarb?
Assume
that the owners of ChinaCarb are constantly risk-averse for the
purposes of this decision. What do you recommend they do? If the
success probability for transferring the technology to production
were lower, say 50%, what would you recommend to the owners?
4. How would
you make this a more attractive business with less risk?
What
ideas do you have for improving the set
of opportunities available to ChinaCarb?
Individually or in a group, prepare a
PowerPoint file containing 1 or 2 slides for each of questions 2,3,4
(maximum 6 slides). Please upload your PowerPoint file at the course
assignment drop box at
MDM Course
Folder and bring it to
class.
Please upload by 8:00 a.m. on the
class day your PowerPoint file using the standard upload procedure.
Name your file CHI followed by concatenated names of the members of
your group:
CHISurnamGivenm SurnamGivenm SurnamGivenm....,
where Surnam denotes the first six letters of a surname and Givenm
denotes the first six letters of a given name.
Use the spreadsheet
ChinaCarb
Exhibits.xlsx in your preparation.
Objectives:
Estimating a random walk
§
What model?
§
Estimation of parameter sensitivity
Project analysis
§
Risk
§
Sensitivity
Creating value and reducing risk
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11. Assignment for Scor-eStore.com
Read: Real Options
(UVA-QA-0639)
Prepare: Scor-eStore.com
(UVA-QA-0581, Rev. 04/05)
Assignment Questions:
1. Using just paper, pencil,
and a calculator, determine the value of the first two ideas of
Bernard’s friends, over and above the base value of the opportunity already
calculated by Bernard.
2. Making use of Monte Carlo simulation, value
the last two ideas
offered by Bernard’s friends. Make use of the spreadsheet in Exhibit
2 of the case, which
can be found in the MDM library or downloaded by right-clicking this
link: ScoreStoreBase2cb.xls.
3. Does Bernard have reasonable cutoff levels to trigger action on
each of the ideas in question 2?
4.
Should Bernard invest in the business?
5. Test your option intuition--What would the addition
of more uncertainty (wider probability distributions or additional
uncertainties) do to the values found in questions 1 and 2?
6. Are there other contingent
opportunities that would add value to this business? Think of some
generic types of ideas that may be relevant here, without valuing
them.
Objectives:
Introduction to real option analysis
§
With decision
trees
§
With Monte
Carlo simulation
Triggers for downstream exercise decisions
§
What to use as
triggering quantity
§
How to find the
best trigger level
The value of options thinking
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12. Assignment for
John Carter: Hedging
Reading: Risk Exposure and Hedging
(UVA-QA-0595)
Using OptQuest (UVA-QA-0594)
Correlations in Crystal Ball (UVA-QA-0593)
Prepare: John Carter: Hedging
(UVA-QA-0596)
Reference: Risk
Preference and Utility (chapter 9 of Quantitative Business Analysis: Text
and Cases, by Bodily, Carraway, Frey, and Pfeifer).
Data Spreadsheet: The data in
Exhibit 1 of the case can be found in the MDM spreadsheet folder or downloaded by right-clicking this
link: John Carter Data.xls.
Assignment Questions:
1. Assume that the
production quantity of John Carter's farm is known with certainty. Is it a
good idea to hedge half of the production? How much should John Carter
hedge? Note: there are 2000 pounds in a ton.
2. Now assume that the
output quantity is uncertain. How does the correlation between output and
prices affect John Carter’s decision on how much to hedge? Please prepare your
analysis showing hedging decisions for correlations of -.99, 0, and .99.
3. Assuming output quantity
is uncertain, how much should John Carter hedge?
If you choose to run Optquest, for simplicity, run discrete levels
stepped 100 tons apart with a large number of trials in the simulations.
Please submit your Excel workbook file
for John Carter to me by 8 a.m. on the day of class. Please put in
separate worksheets of your workbook
a) the
basic model
b) statistics of hedged and unhedged simulation
runs (use "extract data" of Crystal Ball)
c) your recommendations for the questions, given the Optquest or other analysis you
did.
Name your file
CARSurnamGivenm, where
Surnam is the first six letters of your
surname and Givenm is the first six letters of your given name. Submit your file by
using the usual upload procedure to the course Assignment Drop Box at
MDM Course
Folder
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Objectives:
Understand hedging as a tool to reduce risk (and
maybe add value)
Hedging is meant to reduce exposure; knowing exposures is key
§
Depends on payoff interactions of variables
§
Correlations among quantities
Appeal of hedging depends on risk aversion |
13.
Assignment
for McKinsey Guest Case
Optional Reading: Organizational
Use of Decision Analysis (UVA-QA-0655)
Prepare: Peregrine Steel Mill Case
Assignment Questions are at the end
of the Peregrine Steel Mill case
Objectives:
Use of external reseach (e.g.,on the
internet) to find appropriate supporting data
Experience with decision modeling in a consulting
framework
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14. Assignment for Enron Corporation's Weather Derivatives (A) and (B)
Prepare:
Enron Weather Derivatives digital case at this
URL:
http://it.darden.virginia.edu/intranet/case/enron1/weather/
Please view this while connected to the local
area network at the Darden School to ensure that the video streaming and
downloads are fast. Along with videos, this site also contains PDF (Acrobat) versions of the following cases,
which will are provided in hardcopy form:
1. Enron Corporation's Weather Derivatives (A)
(UVA-F-1299)
2. Enron Corporation's Weather Derivatives (B)
(UVA-F-1300)
Reference: Risk
Preference and Utility (chapter 9 of Quantitative Business Analysis: Text
and Cases, by Bodily, Carraway, Frey, and Pfeifer) (used in class 6)
Assignment Questions:
The primary task is to respond to the following questions
regarding the (B) case. In doing so, please prepare an Excel model and
(in a separate sheet of the same workbook file) prepare results from Crystal
Ball runs.
1. Which,
if any of the available contracts would you be willing to accept?
2. Which is the best contract for you?
3. If you could design your own
contract that would reduce your exposure to the greatest extent, what would it
be?
Make use of the data in Exhibit 1 of the (B) case which is
downloadable from the MDM spreadsheet library in the course folder, or by right clicking this link to
Weather.xls.
In your preparation, if you need to become more
familiar with derivatives in general to get started, think about these questions regarding
the (A) case:
1. What is the diagram of payoffs at
the end of the life
of the contract presented in Exhibit 1?
2. What are the pros and cons of weather protection from PNW’s perspective?
3. Why is Enron in this situation? What
does Enron stand to gain?
4. How should Mary Watts proceed to assess, and decide upon,
the use of weather protection for PNW?
What criteria should she use to make her decision?
Objectives:
Seeing
the relevant risk
Modeling the risk appropriately
The "ideal" hedge |
15. Assignment for Petrosupra Exploration
Prepare:
Petrosupra Exploration (UVA-QA-DRAFT)
Reference: Using OptQuest (UVA-QA-0594)
Assignment Questions:
1. First do a risk-neutral
analysis.
a) How do you model the
price of oil, based on the data in the case at the time of the case (not
hindsight)?
b) How do you model any
other uncertainties? What is the expected monetary value and risk
profile of the base opportunity without considering enhanced recovery? Be very clear about how your spreadsheet
model works. You may care to
include the influence diagram to document your decision model.
c) What is the expected
monetary value and risk profile of the total
opportunity including
enhanced recovery. Be clear about how you model the opportunity
represented by enhanced recovery and the decision whether to do it.
2. Now consider risk aversion
in your analysis. What would be the certainty equivalent for the
total opportunity including enhanced recovery.
3. a) Consider each of the
three deals with Claiborne Chemical, one by one, from a conceptual
standpoint. For each deal, do you think that deal would be preferable
to Petrosupra versus no arrangement with Claiborne, assuming Petrosupra
has no other exposure to oil price risk? Was it wise for Claiborne to be
willing to offer each of these deals, assuming they had no other use for
oil or exposure to the price of oil?
b) What should Petrasupra
do about the project in light of the Claiborne offer? If you wish to
simplify matters here by treating the decision about the enhanced
recovery the same way you did in question 1, that is fine. If you can
go beyond the 50-50 split to find what share of the Claiborne commitment
should be traded for what share of the LaFource opportunity, you will
earn the special title of supermodeler.
4. What suggestions do you have
for making the opportunity even better? How might you begin to model
and evaluate these ideas?
Please m ake
use of the spreadsheet OILPRICES.XLS
in your preparation.
Objectives:
Review random walk
Analyze multiple downstream decisions and options
Build intuition
Finding optimal decision variables using Optquest |
Thanks for your work in the class.
Happy Modeling!
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