Transcript Teaching Spreadsheet Simulation

Teaching (Monte-Carlo)
Spreadsheet Simulation
Roger Grinde, [email protected]
University of New Hampshire
Files: http://pubpages.unh.edu/~rbg/TMS/TMS_Support_Files.html
7/7/2015
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Simulation in Spreadsheets
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Do you teach simulation?
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In which courses?
With spreadsheets? Add-Ins?
Monte Carlo? Discrete Event?
Do you use simulation to help teach other
topics?
Do other courses (not taught by you) use
simulation?
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Session Overview
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Learning Goals
Motivations
Examples that Work Well
Examples Posing Difficulties
Foundations of Simulation
Concept Coverage Through Examples
Learning Goals (Revisited)
Issues to Consider
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Learning Goals
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What are your learning goals when
teaching simulation?
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Concept Coverage Through
Examples
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Philosophy: Expose students to a number of
application areas, “sneaking” in the
concepts along the way.
Counter to the way many of us were
taught.
Key: We need to clearly understand which
concepts we’re trying to convey with each
example.
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Games/Tournaments
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Personal Financial
Planning
Multiple Project
Selection
Stock Price
Modeling, Option
Pricing
Inventory (multiperiod)
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Queuing
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Capital Project NPV
Extension of other analaysis tools
Is simulation needed?
Variety of probability distributions
Model-building issues (where a simulation model would be
different than a deterministic model)
Output distribution as function of input distributions
Historical/empirical data
Summary statistics
Alternate decision criteria & risk measures
Sources of error
Correlation and/or relationships among input variables
Optimization concepts in simulation
Portfolio Allocation
Learning Goal/Objective
Inventory (singleperiod)
Mapping: Goals to Examples
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Motivations
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Two investment alternatives
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A: Invest $10,000.
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B: Invest $10,000
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Probability of a $100,000 gain is 0.10
Probability of a $10,000 loss is 0.90
Probability of a $500 gain is 1.0
Which would you choose?
Why?
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Motivations (continued)
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On Average, “A” is twice as good as “B”!
Do we ever actually receive the
average?
Decisions made based only on the
average can be very poor.
Other examples
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Motivations: Simulation and Risk
Analysis
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Simulation allows us to evaluate the risk of a
particular situation.
Risk: Typically defined as the uncertainty associated
with an undesirable outcome (such as financial loss).
Risk is not the same as just being uncertain about
something, and is not just the possibility of a bad
outcome.
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Risk considers the likelihood of an undesirable outcome
(e.g., the probability) as well as the magnitude of that
outcome.
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Simulation Model Schmatic
Fixed (Known) Inputs
Random (Uncertain) Inputs
Simulation Model
Outputs &
Performance Measures
Decision Variables
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Same basic schematic throughout
course
Concept of an output “distribution.”
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Examples that Work Well
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Fundamentals: Dice Roller, Interactive Simulation
Tool
Personal Decisions: Car Repair/Purchase Decision,
Portfolio (single period, based on CB Model), College
Funding (based on Winston & Albright)
Capital Project Evaluation: Truck Rental Company
(based on Lawrence & Weatherford), Project
Selection/Diversification (CB Model), Product
Development & Launch (CB Model)
Finance: Stock Price Models, Option Pricing,
Random Walks, Mean Reverting Processes
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Examples (continued)
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Inventory: DG Winter Coats (NewsVendor),
Antarctica (multi-period, based on Lapin & Whisler)
Queuing: QueueSimon (Armonn Ingolfsson)
Games/Tournaments: NCAA Tourney (based on
Winston & Albright)
Simulation in Teaching Other Topics: Revenue
Management Illustration
Crystal Ball Features: CB Macros, CB Functions
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Examples Posing Difficulties
for Spreadsheets
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Multi-server queues and queue
networks
Most production systems
Business process redesign
However, some add-ins do exist for
simple discrete-event models (e.g.,
SimQuick by David Hartvigsen)
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Foundations of Simulation
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Randomness, Uncertainty
Probability Distributions
Tools
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Dice Roller (John Walkenbach: http://www.jwalk.com/ss)
Die Roller (modified)
Die Roller (modified for investment “game”)
Interactive Simulation Tool
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From “What If” to “Wow”
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Simulation as an Extension of Other
Methodologies
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Spreadsheet Engineering, Base Case
What-If Analysis
Sensitivity Analysis
Scenario Analysis
Simulation
Comparison of Analysis Methodologies
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Extending Other
Methodologies
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Familiar Example/Case
Students provided with some probability
distribution information
Develop comfort with mechanics of
simulation
See the “value added” of simulation
Provides entry point for discussion of
important questions
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Example: Watson Truck
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Adapted from Lawrence & Weatherford
(2001)
Students have built base-case model,
and have done sensitivity analysis
Examples
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Base Case
Sensitivity Analysis
Simulation
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Watson Truck: Inputs
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
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B
C
D
E
F
G
Watson Truck Rental
Parameters/Uncontrollable Inputs
Purchase Price
Property Tax
Var Cost/Truck
# Trucks
Prop Tax Growth
Truck Cost Growth
Base Truck Rental Rate
% Trucks Rented @ $1000
Rental Rate Slope
Rental Rate Inflation
Business Sale Multiplier
Discount Rate
$1,000,000
$35,000
$4,800
50
4%
7%
$1,000
60%
7%
9%
3
10.0%
Decision Variable
Rental Rate (decision variable)
$1,000
Intermediate Calculations
Rental Rate Slope
% Trucks Rented
-0.07%
60.0%
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per year
per year
per month
per $100 reduction in rental rate
Sales price assumed to be 3*(year 3 revenues)
per $1 increase in rental rate
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Watson Truck: Base Case
Model
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25
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27
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29
30
31
32
33
34
35
36
37
38
39
40
A
B
Primary Output
Net Present Value (@ discount rate)
C
D
E
F
G
H
C25: =NPV(C15,D40:F40)+C40
$209,769
Cash Flow Model
0
Cash Inflows
Truck Rental Income
Business Sale
Total Inflows
Cash Outflows
Purchase Price
Property Tax
Truck Var Cost
Total Outflows
1
2
3
$360,000
$392,400
$360,000
$392,400
$427,716
$1,283,148
$1,710,864
$1,000,000
$35,000
$240,000
$275,000
$36,400
$256,800
$293,200
$37,856
$274,776
$312,632
($1,000,000)
$85,000
$99,200
$1,398,232
F30: =E30*(1+$C13)
$0
$1,000,000
F31: =C14*F30
F32: =SUM(F30:F31)
F36: =E36*(1+$C8)
F37: =E37*(1+$C9)
F38: =SUM(F35:F37)
F40: =F32-F38
Net Cash Flow
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Watson Truck: Sensitivity
Analysis
Tornado Sensitivity Chart
Output Measure
$0
$50,000 $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000
Base Truck Rental Rate
% Trucks Rented @ $1000
# Trucks
Parameter
Purchase Price
Business Sale Multiplier
Var Cost/Truck
Discount Rate
Rental Rate Inflation
Rental Rate Slope
Property Tax
Truck Cost Growth
Prop Tax Growth
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-10 Pct
+10 Pct
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Watson: Simulation
Forecast: Net Present Value (@ discount rate)
1,000 Trials
Frequency Chart
1,000 Displayed
.035
35
.026
26.25
.018
17.5
.009
8.75
Mean = $232,119
.000
0
($525,250)
($139,570)
$246,111
$631,792
$1,017,472
Certainty is 82.00% from $0 to +Infinity Dollars
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Learning Goals Addressed (at
least partially)
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Linkage with other course/functional area
What inputs should we simulate?
Useful probability distributions. Choice of
parameters.
Concept of an output distribution
Simulation in context with other tools
What results are important?
Sources of error in simulation
Simulation mechanics
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Sources of Error in Simulation
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What are some of the sources of error
in a spreadsheet simulation
model/analysis?
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Example: Single-Period
Portfolio
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Simple example, but helps address a number
of learning goals
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Do we need to simulate?
Precision of estimates from simulation
Confidence vs. Prediction (certainty) intervals
Effect of correlation among input quantities
Quantification of risk, multiple decision criteria
Optimization concepts within simulation context
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Spreadsheet
B
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
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C
D
E
Portfolio Allocation Model
Investments
Money Market fund
Income fund
Growth and Income fund
Aggressive Growth fund
Total amount available
Decision variables
Money Market fund
Income fund
Growth and Income fund
Aggressive Growth fund
Total expected return
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Annual
return
3.0%
5.0%
7.0%
11.0%
$100,000
Amount
invested
$25,000
$25,000
$25,000
$25,000
$6,500
Lower
bound
$0
$10,000
$0
$10,000
Upper
bound
$50,000
$25,000
$80,000
$100,000
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Do we need simulation?
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Assuming we know the distributions for the
returns, do we need simulation to compute
the
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expected return of the portfolio?
variance of the portfolio?
tail probabilities?
What if the returns of the securities are
correlated?
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What is the effect of correlation?
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Correlation of Returns
Large Stocks
Large Growth Stocks
Large Value Stocks
Small Stocks
Small Growth Stocks
Small Value Stocks
Foreign Stocks
Bonds
Large
Stocks
Large
Growth
Stocks
Large
Value
Stocks
1
0.958411
0.901159
0.720036
0.755265
0.507037
0.391551
0.366054
1
0.74063
0.606356
0.720758
0.322101
0.294704
0.267404
1
0.776748
1
0.678815 0.921266
1
0.715396 0.875155 0.618755
1
0.454882 0.275857 0.325624 0.140232
1
0.465424 0.28663 0.164181 0.369522 0.112362
Small
Stocks
Small
Growth
Stocks
Small
Value
Stocks
Foreign
Stocks
Bonds
1
Based on Standard & Poor Micropal, via Franklin/Templeton Investor Topics Update, Winter 2001
(Asset Returns from 1980-2000)
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Results (n=1000)
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No Correlation
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Mean = $6842
Standard Deviation = $5449
5% VaR = ($2165)
Positive Correlation
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Mean = $6409
Standard Deviation = $7386
5% VaR = ($5655)
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Decision Criteria
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What criteria are important for making
decision as to where to invest?
Measures of risk.
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Simulation gives us the entire output distribution.
Entry point for optimization within simulation
context
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Alternate scenarios, efficient frontier, OptQuest,
RiskOptimizer, etc.
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Crystal Ball Functions and
Simple VBA Control
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Crystal Ball provides built-in functions
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Control through VBA
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Distribution Functions (e.g., CB.Normal)
Functions for Accessing Simulation Results (e.g.,
CB.GetForeStatFN)
For some students, can be a “hook.”
Allows one to prepare a simulation-based model
for someone else who doesn’t know Crystal Ball.
Example
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Precision of Results:
Confidence Intervals
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Students can calculate a confidence
interval for the mean?
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Do they know what it means?
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Sample Results (Portfolio
Problem)
Statistics:
Trials
Mean
Median
Mode
Standard Deviation
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90% Confidence Interval
$233.56
Standard Error
1.645
Z
$6,025
Lower Limit
$6,794
Upper Limit
What does that confidence interval mean?
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Value
1000
$6,409
$6,531
--$7,386
Common (student) error
What does this imply about an individual outcome?
For example, from any single year?
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Sample Results (cont)
Percentile
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
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dollars
($16,088)
($5,655)
($3,052)
($1,008)
$271
$1,277
$2,498
$3,484
$4,307
$5,365
$6,531
$7,695
$8,349
$9,310
$10,386
$11,419
$12,431
$13,896
$15,689
$18,659
$30,330
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What do these results
mean?
What is the 90%
“prediction” (or “certainty”)
interval?
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Confidence and Prediction
Intervals
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90% Confidence Interval for the Mean
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90% Prediction Interval (centered around
median)
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($6025, $6794)
(-$5655, $18,659)
Note: Crystal Ball uses the term “certainty”)
Students:
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Understand the difference?
Understand when one is more appropriate than
the other?
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Precision of Simulation Results
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Since we know the true value of the mean
(for the portfolio problem), this can be a good
example to look at precision and sample size
issues.
Crystal Ball: Precision control for mean,
standard deviation, and percentiles.
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Simulation stops when precision reached
Confidence interval for proportion or for a
given percentile sometimes makes more
sense.
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Crystal Ball: Precision Control
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Nice way to illustrate effect of sample
size.
Precision Control stops simulation based
on user-specified precision on the
mean, standard deviation, and/or a
percentile.
Example (Portfolio Allocation)
Example (Option Pricing)
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Learning Objectives
(Revisited)
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General
Probability Distributions
Statistics
Relationships Among Variables
Decision Making
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Possible Learning Goals
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General
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Use simulation as an extension of other analysis tools
Apply simulation to a variety of business problems
Identify when simulation is and is not needed to analyze a
situation
Probablilty Distributions
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Understand and use probability distributions to model
phenomena
Describe the output distribution, understanding this to be a
function of the input distributions
Use historical/empirical data and subjective assessments
appropriately in choosing distributions and parameters
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Possible Learning Goals (cont)
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Statistics
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Correctly interpret summary statistics, including
percentiles/histograms
Correctly interpret confidence and prediction (certainty)
intervals
Identify sources of error in simulation, apply to specific
situations
Relationships Among Variables
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Include appropriate correlation and/or other relationships
when model building
Describe the effect of correlation and/or other relationship
on simulation results
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Possible Learning Goals (cont)
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Decision Making
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Identify and correctly use different risk
measures
Use appropriate criteria in making
recommendations
Use optimization concepts in a simulation
application
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Difficult Issue (for me)
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Decide which learning goals are the
most important, and structure coverage
so those goals are attained.
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Student backgrounds
Time constraints
Overall course objectives
Mapping of learning goals to examples
that you will use.
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Mapping: Learning Goals to
Examples
Simulation, Statistidcal,
Spreadsheet Modeling,
Decision Making Concepts
Examples/Application Areas
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X
X
X
X
X
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X
X
X
X
Games/Tournaments
X
X
Personal Financial
Planning
Multiple Project
Selection
Stock Price
Modeling, Option
Pricing
Inventory (multiperiod)
X
X
X
X
Queuing
X
Capital Project NPV
Extension of other analaysis tools
Is simulation needed?
Variety of probability distributions
Model-building issues (where a simulation model would be
different than a deterministic model)
Output distribution as function of input distributions
Historical/empirical data
Summary statistics
Alternate decision criteria & risk measures
Sources of error
Correlation and/or relationships among input variables
Optimization concepts in simulation
Portfolio Allocation
Learning Goal/Objective
Inventory (singleperiod)
Mapping: Goals to Examples
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
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X
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Common Student Errors
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Thinking of simulation as the method of first choice.
Simulating too many quantities.
Too much focus on distribution/parameter selection or on
the numerical results, not enough on insights/decision.
Misinterpretation of results, especially confidence intervals
Modeling: Using same return, lead time, etc. for every time
period/order, etc. (difference between deterministic and
simulation models)
Choosing the assumptions, distributions, parameters, etc.
that give the “best” numerical results.
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Issues to Consider
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Teaching environment (lab setting or
not?)
Role of course in curriculum
Use add-ins for Monte-Carlo simulation?
Teach Discrete-Event simulation?
How much of the “quant” course should
be devoted to simulation?
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Conclusions, Discussion
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Files available at

7/7/2015
http://pubpages.unh.edu/~rbg/TMS/TMS_
Support_Files.html
46
Student Project Example
(MBA)
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PPT File
Excel File
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