Quantitative business analysis by i lindner and j r van den brink

Decision TreeRain Ruined refreshments Unhappines No Rain Very pleasant party 1 Rain Crowded but dry Proper feeling of being sensible g No Rain Crowded, hot Regrets about what might have

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Quantitative Business Analysis

(QBA)

I Lindner and J.R van den Brink

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Q tit ti B i A l i

• T torials: T esda s and Wednesda s

• Prepare exercises beforehand!

• Program for the first two weeks: Exercises from chapter “Topic E1 –

Exercises Decision Analysis”:

week 1: 1.1, 1.2, 1.3, 1.5, 1.8

week 2: 1.4, 1.6, 1.7, 1.9

Quantitative Methods (QBA) 3

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Contents of the Course

Week 1-2 (Ines Lindner)

1 Decision Analysis using Decision Trees

Week 3-6 (René van den Brink)

2 Strategic Thinking - Noncooperative Games

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• Book “Quantitative Business Analyses”

by C van Montfort and J.R van den Brink:

chapter T1 T2 E1 and E2;

• Book is available at Aureus

• Sheets of lectures (on Blackboard)

• Relevant sections for decision theory: 8.1-8.3, 8.5 (except “Using Excel ”), 8.6, 8.8- , ( p g ), ,

8.10

• We don’t discuss software applications in this

course!

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Two efficient strategies to pass

the exam!

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Facts:

• You have to read the text material in You have to read the text material in

order to pass the exam

you already know 50 percent

Conclusion: Read text material before

lecture and take lecture as revision

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enough for exam.

Conclusion: Try to do the exercises yourself and take tutorial as a feedback on your

8

and take tutorial as a feedback on your

performance

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→ Answers to exercises decision theory will

be available at the end of week 2

9

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Decision Theory

Central question: What is the best decision to take?

Assumptions:

• We have some information

• We are able to compute with perfect accuracy

• We are fully rational

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What kinds of decisions need a

theory?

Optimization – examples

• What is the best product mix?

• What is an optimal way to spend my money p y p y y

(intertemporal choice)?

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theory?

Choice under risk – examples

• Should I play the lottery? p y y

• What kind of insurrence should I buy?

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(depends on your boss)?

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theory?

Game theory: y

• Additional difficulty: the need to take into

account how other people in the situation will act

• Presence of several “players” (strategically acting agents)

• Requires strategic analysis (week 3-6).

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Decision Theory

Central question: What is the best decision to take?

• Absence of strategic considerations

• Can be seen as a one-player game.

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Decision Analysis using Decision Trees

Dilemma: organize party indoors or in

garden? What if it rains?

g

Events and Results

but content

Regrets

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g

but content

Regrets

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g

but content

Regrets

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Decision Tree Components

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Decision Tree

Rain

Ruined refreshments

Unhappines

No Rain

Very pleasant party

1

Rain

Crowded but dry

Proper feeling of being sensible g

No Rain

Crowded, hot Regrets about what might have been

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Decision Tree

Rain

Unhappines

No Rain

1

P ff ?

1

Rain

Crowded but dry

Proper feeling of being sensible

Payoffs ?

g

No Rain

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Decision Tree

Rain

Unhappines

No Rain

1

Hi h

1

Rain

Crowded but dry

Highest payoff

g

No Rain

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Decision Tree

Rain

Unhappines

No Rain

1

L

1

Rain

Crowded but dry

Lowest payoff

g

No Rain

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1

100

1

Rain

Crowded but dry

50

g

No Rain

Crowded, hot Regrets about what

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Possible Interpretation of Payoffs: p y

How much is this outcome worth to me?

1

100

1

Rain

Crowded but dry

50

g

No Rain

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Example: Having a party outdoors with no rain is

i.e this is my maximum willingness to pay for it if it

1

100

1

Rain

Crowded but dry

50

g

No Rain

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Example: Having a party outdoors with rain is worth

i.e a hypothetical someone would have to pay me at

1

100

1

Rain

Crowded but dry

50

g

No Rain

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1

100

1

Rain

Crowded but dry

50

g

No Rain

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1

Rain

Crowded but dry

No Rain

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1

0.6

1

Rain

Crowded but dry

No Rain

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1

0.6

1

Rain

Crowded but dry

0.4

No Rain

0.6

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1

100

1

Rain

Crowded but dry

50

g

No Rain

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Crowded but dry

No Rain

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Crowded but dry

50 0

50

g

No Rain

0

- 50

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Decision Tree

Partial Cashflows, Payoffs and Probabilities

Payoffs

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Solving a Decision Tree

Wh t i th b t d i i ?

What is the best decision?

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Consider decision “Outdoors”

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Use Expected Value:

Probability(Rain) = 40% Value = -100

Probability(No Rain) = 60% Value = 100

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Use Expected Value:

Probability(Rain) = 40% Value = -100

Probability(No Rain) = 60% Value = 100

Expected or average value:

0.4×(-100) + 0.6×100 = 20

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Expected Value

• Event node with n mutually exclusive

events (exactly one of the events will

occur)

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Expected Value

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Expected Value

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Expected Value

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Decision Tree

20

-10

= 0.4*50+0.6*(-50)

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Decision Tree

20

-10

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Decision Tree

20

-10

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EV(Outdoors) > EV(Indoors)

20

-10

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Decision Tree

0.4 Rain

-100 Unhappy Outdoors -100 -100

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Evaluation of Decision Tree

0.4 Rain

0 20 0.6

No Rain

100 Pleasant

100 100 1

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E l ti f D i i T

Evaluation of Decision Tree

Roll back method: start at terminal nodes and

work from right to left

Compute Expected Value of Event Nodes

Choose Event Node with maximum (or

minimum) EV in Decision Nodes

The value of the tree is the EV in the root of the tree (if values are money it is called the

EMV or Expected Money Value)

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Exercise 1 1:

Exercise 1.1:

Investment in a new product?

• Investment costs €10 000Investment costs €10.000

• Market research

=> 60% success, €80.000 profit

40% failure, - €30.000 loss

• Investment cost not yet included in profit

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Exercise 1 1:

Exercise 1.1:

0.6 Product is success

70000 Invest 80000 70000

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Exercise 1 1:

Exercise 1.1:

70000 Invest 80000 70000

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Exercise 1 1:

Exercise 1.1:

70000 Invest 80000 70000

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• Note that we have not yet discussed risk attitude!

with a 40% chance

70000 Invest 80000 70000

-10000 10000 26000 26000 0.4 0.4

Product is failure

-40000

1 -30000 -40000 26000

Don't invest

0

0 0

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We will talk about risk attitude (risk averse – risk loving) when we discuss the concept of “utility”

70000 Invest 80000 70000

-10000 10000 26000 26000 0.4 0.4

Product is failure

-40000

1 -30000 -40000 26000

Don't invest

0

0 0

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Implicit assumption in analysis below:

we are risk indifferent

70000 Invest 80000 70000

-10000 10000 26000 26000 0.4 0.4

Product is failure

-40000

1 -30000 -40000 26000

Don't invest

0

0 0

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Possible Justifications:

(1) We are risk indifferent

(2) We make these kinds of decisions a lot

( )

70000 Invest 80000 70000

-10000 10000 26000 26000 0.4 0.4

Product is failure

-40000

1 -30000 -40000 26000

Don't invest

0

0 0

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Multistage Decisions

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• Multistage problem: involves sequence of

decision alternatives and outcomes

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Multistage Decisions - Example

development on cancer treatment

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of €85 000?

of €85,000?

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of €85 000?

of €85,000?

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prepare product 1,2 or 3?

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be fully predicted

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be fully predicted

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be fully predicted

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Best Case Worst Case

Product Equipment

costs

R&D costs

ability

Prob-R&D costs

ability

Prob-Best Case Worst Case

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Multistage Decision Tree

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-5000

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-5000 + 85000

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-5000 + 85000 – 4000

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-5000 + 85000 – 4000 -60000

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-5000 + 85000 – 4000 -60000

= 16000

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Find best decision byFind best decision by roll back method

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Start at terminal nodes and work from right to left.

Compute expected value

of event nodes

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Start at terminal nodes

and work from right to

left

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left

28000

of event nodes

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Choose event node with

maximum (or minimum)

EV in decision nodes

28000

29000

32000

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EV in decision nodes

28000

29000

32000

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Next step: Again work

from right to left

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from right to left

= 13500

32000

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from right to left

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13500

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Sensitivity Analysis

• Sensitivity Analysis: how sensitive is the result for changes in

values of parameters?

• Why is this an interesting question?

• E.g the probability to get the grant is usually a rough

estimation.

estimation

• We estimated it to be 0.50

• Do we get a complete different result if it is 0 49 or 0 51?

• Do we get a complete different result if it is 0.49 or 0.51?

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S i h f hi i

Systematic approach of this question:

• We came to the conclusion that it makes sense to submit the proposal if chance to get it is 0 5

proposal if chance to get it is 0.5

• What is the minimum probability for which it still makes

sense to submit the proposal (possibly losing €5000)?

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0.6 High R&D

16000 Prepare product 1 -60000 16000

-4000 28000 0 4 -4000 28000 0.4

Low R&D

46000 -30000 46000

0.1 High R&D

Prepare product 3 -80000 -4000 -5000 13500

-4000 32000 0.9

Low R&D

36000 -40000 36000

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0.6 High R&D

16000 Prepare product 1 -60000 16000

-4000 28000 0 4 -4000 28000 0.4

Low R&D

46000 -30000 46000

0.1 High R&D

Prepare product 3 -80000 -4000 -5000 13500

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0.6 High R&D

16000 Prepare product 1 -60000 16000

-4000 28000 0 4 -4000 28000 0.4

Low R&D

46000 -30000 46000

0.1 High R&D

p *32000+(1-p)*(-5000)

Prepare product 3 -80000 -4000 -5000 13500

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0.6 High R&D

16000 Prepare product 1 -60000 16000

-4000 28000 0 4 -4000 28000 0.4

Low R&D

46000 -30000 46000

0.1 High R&D

p *32000+(1-p)*(-5000)

Prepare product 3 -80000 -4000 -5000 13500

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37000*p=5000 p Divide both sides by 37000

=> p = 5/37 = 0 1351

> p 5/37 0.1351

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Interpretation:

• For p = 0.1351, we are indifferent between submitting For p 0.1351, we are indifferent between submitting

the proposal or not since it gives us the EMV of zero in

not sensitive to small changes around 0.5.

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Value of Information

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Recall Dilemma: organize party

indoors or in garden?

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Recall Dilemma: organize party

indoors or in garden?

0.4 Rain

0 20 0.6

No Rain

100 Pleasant

100 100 1

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