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The Dangers of Extrapolation: A Case Study on WorldCom's Stock Market Performance, Exams of Mathematical Methods for Numerical Analysis and Optimization

The risks and limitations of extrapolation through a case study involving a student's investment decision in worldcom's stock based on historical data. The chapter emphasizes the importance of understanding the limitations of extrapolation and the potential consequences of relying on it for future predictions.

Typology: Exams

2012/2013

Uploaded on 04/16/2013

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05.07.1
Chapter 05.06
Extrapolation is a Bad Idea
After reading this chapter, you should be able to:
1. understand why using extrapolation can be a bad idea.
Example
(Due to certain reasons, this student wishes to remain anonymous.)
This takes place in Summer Session B – July 2001
Student: “Hey, Dr. Kaw! Look at this cool new cell phone I just got!”
Kaw: “That’s nice. It better not ring in my class or it’s mine.”
Student: “What would you think about getting stock in this company?”
Kaw: “What company is that?”
Student: “WorldCom! They’re the world’s leading global data and internet company.”
Kaw: “So?”
Student: “They’ve just closed the deal today to merge with Intermedia Communications,
based right here in Tampa!”
Kaw: “Yeah, and …?”
Student: “The stock’s booming! It’s at $14.11 per share and promised to go only one way—
up! We’ll be millionaires if we invest now!”
Kaw: “You might not want to assume their stock will keep rising … besides, I’m skeptical of
their success. I don’t want you putting yourself in financial ‘jeopardy!’ over some silly
extrapolation. Take a look at these NASDAQ composite numbers (Table 1)”
Student: “That’s only up to two years ago …”
Kaw: “That’s right. Looking at this data, don’t you think you should’ve invested back
then?”
Student: “Well, didn’t the composite drop after that?”
Kaw: “Right again, but look what you would’ve hoped for if you had depended on that trend
continuing (Figure 1).”
Student: “So you’re saying that …?”
Kaw: “You should seldom depend on extrapolation as a source of approximation! Just take
a look at how wrong you would have been (Table 2).”
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Chapter 05.

Extrapolation is a Bad Idea

After reading this chapter, you should be able to:

1_. understand why using extrapolation can be a bad idea._

Example (Due to certain reasons, this student wishes to remain anonymous.) This takes place in Summer Session B – July 2001

Student: “Hey, Dr. Kaw! Look at this cool new cell phone I just got!” Kaw: “That’s nice. It better not ring in my class or it’s mine.” Student: “What would you think about getting stock in this company?” Kaw: “What company is that?” Student: “WorldCom! They’re the world’s leading global data and internet company.” Kaw: “So?” Student: “They’ve just closed the deal today to merge with Intermedia Communications, based right here in Tampa!” Kaw: “Yeah, and …?” Student: “The stock’s booming! It’s at $14.11 per share and promised to go only one way— up! We’ll be millionaires if we invest now!” Kaw: “You might not want to assume their stock will keep rising … besides, I’m skeptical of their success. I don’t want you putting yourself in financial ‘jeopardy!’ over some silly extrapolation. Take a look at these NASDAQ composite numbers (Table 1)” Student: “That’s only up to two years ago …” Kaw: “That’s right. Looking at this data, don’t you think you should’ve invested back then?” Student: “Well, didn’t the composite drop after that?” Kaw: “Right again, but look what you would’ve hoped for if you had depended on that trend continuing (Figure 1).” Student: “So you’re saying that …?” Kaw: “You should seldom depend on extrapolation as a source of approximation! Just take a look at how wrong you would have been (Table 2).”

05.06.2 Chapter 05.

Table 1. End of year NASDAQ composite data End of year 1 NASDAQ 1 751. 2 1052. 3 1291. 4 1570. 5 2192. 6 4069.

0

5000

10000

15000

20000

25000

0 2 4 6 8 10 End of Year

NASDAQ

Actual Index

Polynomial Interpolation

Figure 1 Data from 1994 to 1999 extrapolated to yield results for 2000 and 2001 using polynomial extrapolation.

(^1) Range of years actually between 1994 (Year 1) and 1999 (Year 9). Numbers start from 1 to avoid round-off errors and near singularity in matrix calculations.

05.06.4 Chapter 05.

Kaw: “You’ve got a point, too—you’re brighter than you look … that is if you turn off the phone before coming to class.”


<One year later … July 2002> Student: “Hey, Dr. Kaw! Whatcha got for me today?” Kaw: “The Computational Methods students just took their interpolation test today, so here you go. Time to grade them!” Student: <Grunt!> “That’s a lot of paper! Boy, interpolation … learned that a while ago.” Kaw: “You haven’t forgotten my lesson to you about not extrapolating, have you?” Student: “Of course not! Haven’t you seen the news? WorldCom just closed down 93% from 83¢ on June 25 to 6¢ per share! They’ve had to recalculate their earnings, so your skepticism really must’ve spread. Did you have an “in” on what was going on?” Kaw: “Oh, of course not. I’m just an ignorant numerical methods professor.”

INTERPOLATION

Topic Extrapolation is a bad idea