1. Being Warren Buffett: a classroom simulation of the stock market
CAUSE webinar
Nicholas Horton
Being Warren Buffett: a classroom simulation of the stock market
March 24, 2009
Nicholas J. Horton
Department of Mathematics and Statistics
Smith College, Northampton, MA

2. Acknowledgements and references
Activity developed by Robert Stine and Dean Foster (Wharton School, University of Pennsylvania)
Published paper: “Being Warren Buffett: A classroom simulation of risk and wealth when investing in the stock market”, The American Statistician (2006), 60:53-60.
More information, the handout form and copy of the TAS paper can be found at:
A copy of these notes plus the R code to run the simulation and results from 5000 simulations can be found at:
Horton – Causeweb
Being Warren Buffett

3. Overview
The concepts of expected value and variance are challenging for students
A hands-on simulation can help to fix these ideas, in the context of the stock market
Allows students to experience variance first-hand
Can be implemented using dice (and calculators) in a classroom setting
Computer generation of results complements the analytic and hand simulations
Horton – Causeweb
Being Warren Buffett

4. Objectives
Understanding discrete random variables to model stock market returns
Calculate and interpret expectations for return from a given investment strategy
Calculate and interpret standard deviations of returns from a given investment strategy
Compare the risk and return for these strategies
Spark thinking about diversification and rebalancing of investments
Horton – Causeweb
Being Warren Buffett

5. Background information
Imagine that you have $1000 to invest in the stock market, for 20 years
Three investment possibilities are presented to students in groups of 2 or 3:
Question: Which of the three investments seems the most attractive to the members of your group?
Investment
Expected annual return
SD(annual return)
Green
8.3%
20%
Red
71%
132%
White
0.8% 4%
Horton – Causeweb
Being Warren Buffett

6. Dice outcomes
The investments rise or fall based on the outcomes of a 6-sided die:
Outcome
Green
Red
White 1
0.8
0.05
0.95 2
0.9
0.2 3
1.1 4 5
1.2 6
1.4
Horton – Causeweb
Being Warren Buffett

7. Example:
Suppose on the first roll your team gets the following outcomes (Green 2) (Red 5) (White 5), then on the second roll, you get (Green 4) (Red 2) (White 6)
Round
Green
Red
White
Start
$1000
Return 1
0.9 3 1
Value 1
$ 900
$3000
Return 2
1.1
0.2
Value 2
$ 990
$ 600
$1100
Horton – Causeweb
Being Warren Buffett

8. Repeat the process for 20 years
1 student to roll the dice (green, red and white)
1 student to determine the return and calculate the new value on the results handout
1 student to supervise and catch errant dice
At the end of class, each team enters their results on the classroom computer
Find out who are the “Warren Buffett’s” of the class
Horton – Causeweb
Being Warren Buffett

9. Group results form
Horton – Causeweb
Being Warren Buffett

10. Usually, red doesn’t do as well as green
Horton – Causeweb
Being Warren Buffett

11. But occasionally it wins big!
Horton – Causeweb
Being Warren Buffett

12. Expected returns for 20 years
Use property that the expectation of a product is the product of the expectation
GREEN: $1000*(1.083)^20= $ ,927
RED: $1000*(1.710)^20= $45,700,632
WHITE: $1000*(1.008)^20= $ ,173
We’d always want to pick RED, no?
Horton – Causeweb
Being Warren Buffett

13. Observed returns (using simulation)
Used R to simulate year histories, available as “res.csv”
Observed Q1, median, Q3
GREEN: $2,058 $3,621 $6,269
RED: $ $ $1,993
WHITE: $1,011 $1,141 $1,321
Percentage ending with less than initial investment ($1000)
GREEN: 5.9%
RED: %
WHITE: 25.0%
Horton – Causeweb
Being Warren Buffett

14. Another strategy (“pink”)
Consider a strategy where you balance investments between RED (dangerous) and WHITE (boring) each year
Call this “PINK”
Smaller average returns, but far less variable
Can be calculated using existing rolls (average returns), using space on the results form
Horton – Causeweb
Being Warren Buffett

15. How to implement PINK Pink $1000 3 1 2 $3000 $1000 $2000 0.05 1 0.525
$150
$1000
$1050
Horton – Causeweb
Being Warren Buffett

16. Connections to reality and thoughts on “pink”
GREEN performs like the US stock market (adjusted for inflation)
WHITE represents the (inflation adjusted) performance of US Treasury Bills
Quote from authors: “We made up RED. We don’t know of any investment that performs like RED. If you know of one, please tell us so we can make PINK!”
Horton – Causeweb
Being Warren Buffett

17. Boxplots of results (needs rescaling)
$80 billion!
Horton – Causeweb
Being Warren Buffett

18. Boxplots of results (where returns <=$50,000)
Horton – Causeweb
Being Warren Buffett

19. Teaching materials and checklist
Copies of handout describing the simulation (one per student)
Copies of results sheet (one per group)
Set of three die (though one will work in a pinch, one set per group)
Remind students to bring calculators (or run this in a lab rather than lecture)
Time requirements: between 50 and 80 minutes (depending in part on whether you calculate expected values, motivate the simulation parameters in terms of historical inflation and stock returns and whether “pink” is introduced)
Horton – Causeweb
Being Warren Buffett

20. Extensions and assessment
The activity was developed for use in both an MBA and PhD program
The paper introduces concepts of “volatility drag” and “volatility adjusted return” as more advanced topics (potentially applicable as a project at the end of a undergraduate probability class), as well as connections to calculus
Verifying the expected value and standard deviation of one of the investment strategies is a straightforward homework assignment (other assessments possible)
Students without formal exposure to expectations of discrete random variables can still fully participate in the simulation
Horton – Causeweb
Being Warren Buffett

21. Conclusions Hands-on activity is popular with students
Helps to reinforce important but often confused concepts in the context of a real world application
Small group work helps to address questions as they arise
Students turn in results to allow review of results (in addition to immediate display of summary and graphical statistics)
Horton – Causeweb
Being Warren Buffett

22. Being Warren Buffett: a classroom simulation of the stock market
Cal Poly Capstone Course
John Walker
Being Warren Buffett: a classroom simulation of the stock market
March 24, 2009
Nicholas J. Horton
Department of Mathematics and Statistics
Smith College, Northampton, MA