The document discusses risk analysis and decision-making tools for managers, focusing on concepts such as expected value, probability distributions, and techniques to reduce uncertainty. It covers the definition and measurement of risk, including standard deviation and coefficient of variation, as well as the expected value of perfect information (EVPI). The text also explores attitudes toward risk using utility functions and the certainty equivalent approach to assess investment decisions.

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Chapter 13
Risk
Analysis
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Presented By:
Singhzee and Group
Economics

2. To study a variety of tools to help
managers improve decision making
To understand the concept of expected
value
To examine techniques to reduce
uncertainty
To understand the concept of expected
utility
Objectives

3.  Risk and Probability
 Probability Distributions and Expected Value
 Comparisons of Expected Profit
 Road Map to Decision
 The Expected Value of Perfect Information
 Measuring Attitudes towards risk
 The Standard Deviation and Coefficient of Variation Measures
of Risk
 Certainty Equivalence
Contents

4.  Hazard or a chance
of loss
 Bigger the chance
of loss/Greater the
size of loss = the
more risky the
action
Risk and Probability

5. Frequency Definition of Probability
 Proportion of times an outcome occurs
 Over the long run
 If the situation exists repeatedly
 E.g. A dice is thrown
 Probability of 1 = 1/6 or 0.167
Risk and Probability Ctd…

6. Subjective Definition of Probability
 Managers ‘ Degree of confidence or belief
 That event will occur
 Used when experiments cannot be repeated
 Use of Managers’ judgment
 High probability for higher degree of
confidence and vice versa
Risk and Probability Ctd…

7. Subjective Definition of Probability
Risk and Probability Ctd…

8. Subjective Definition of Probability
 For example:
 Introduction of a new product
Risk and Probability Ctd…
High
Demand is
more
likely
Low
Demand is
less likely
Both equally
likely

9. Probability Distributions
 A Table listing
 All possible outcomes
 Probability of their occurrence

10. Expected Value
 Weighted Average
 Of the profit of each outcome to its profit
 Weights = Probability of their occurrence
Events Probability Profit P*
New Robot
developed in 1 yr
0.6 $1,000,000 $600,000
New Robot not
developed in 1 yr
0.4 -$600,000 -$240,000
$360,000

11. Comparison of Expected Profit
 To decide the course of action
 For example: Jones Corporation
Decision
Alt
Events Profit P P* ExpProfit
Increase
price
Ad
Campaign
Successful
$800,000 0.5 $400,000
$100,000Ad
Campaign
Unsuccess
ful
-$600,000 0.5 -$300,000
Do not
increase
price
$200,000

12. Road Map to Decision
 Decision Tree
 Visualization strategic future
 Series of choices
 Decision Fork
o Choice/Decision Alternative
o Square/Decision Node
 Chance Fork
o Events influencing outcome
o Dotted or Circular Node

14. EVPI
Expected Value of Perfect Information(EVPI)
How much would you pay to gain access to perfect
information?
Completely
Accurate
Information
About
Future
Outcomes
Increase in
Expected
Profit
To
Reduce
Uncertainty

15. EVPI Continued…
EVPI=Expected Profit with Perfect Information-
Expected Profit without Perfect Information
Example:
 Research Survey Report
Survey says Prob Decision Profit Prob*Profit
Campaign
Successful
0.5 Increase $800,000 $400,000
Campaign
Unsuccessful
0.5
Do not
Increase
$200,000 $100,000
Total Expected Profit with Perfect Information $500,000
Total Expected Profit without Perfect Information $200,000

16. EVPI Continued…
EVPI=Expected Profit with Perfect
Information -Expected Profit without Perfect
Information
= $500,000 - $200,000
= $300,000
Access to Perfect
Information
Profit Increase
by $300,000

17. Measuring Attitudes toward risk: The Utility
Approach
Certain Profit
$2,000,000
Gamble(50/50)
$4,100,000
-$60,000
Expected profit =0.5($4100000)+0.5(-$60000)
= $2020000
Small Business
Managers
Large Business
Managers

18. Constructing a Utility Function
 Utility Function=Level of satisfaction
 Expected Utility
Sum of utility of each outcome times probability of
the outcome’s occurrence

19. Constructing a Utility Function Example: Tomco Oil Corporation

20. Constructing a Utility Function
Payoffs Utility(U)
$500,000 50
$300,000 10
$100,000 20
$0 10
-$90,000 0
 Example: Tomco Oil Corporation

22. Attitudes towards Risk
 Three Types
Risk Averter
Risk Lover
Risk-Neutral

23. Risk Averter
Choice: Certain outcome

24. Risk Lover
Choice: Uncertain outcome

25. Risk-Neutral
Maximization of expected wealth
Regardless of risk

26. Measures of Risk
2. •Example:
•Jones Corporation
•Investment
Decision for a new
plant
1. • Dispersion of Probability Distribution
• Profit from the Decision

27.  Magnitude of negative outcomes
 Dispersion of Probability distribution
Measures of Risk
 For Example:
 Jones Corporation
 Decision to invest in a
new plant
Panel A
Panel B

28. (1)Standard Deviation
 Most frequently used metric for dispersion
 Square root of the deviation of expected values
from payoffs
 Absolute measure of risk
 For Example:
 E(∏)=0.3(1)+0.2(0.4)+0.3(-0.6) = $0.2
$1 m
• 0.3
$0.2m
• 0.4
-$0.6
• 0.3

29. (1)Standard Deviation
Payoffs($) Probability
1 0.3 0.16 0.192
0.2 0.4 0 0
-0.6 0.3 0.16 0.192
0.384
Higher Standard Deviation Higher Risk

30. (2)Coefficient of Variation(V)
 Relative measure of risk
 Ratio of S.D(σ) to Expected Profit [E(∏)]
 Lower the V better the risk-return trade off

31. Adjusting the Valuation Model for Risk
 Effects of managerial decision
 PV of future profits
 Certainty Equivalent Approach

32. Certainty Equivalent
 A guaranteed return
 someone would accept,
 Instead of taking a chance on a higher, but
uncertain, return.
 Example: Job Vs Own Business
 Salary=Certainty equivalent
Certainty Equivalent Approach

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34.  Adjustment of Discount Rate
 Construction of Indifference Curve
 Estimation of Risk Premium
 r=sum of riskless rate of return+risk premium
Use of adjusted Discount rate

35. A
B
C
D
1 2 3 4
Click to Edit Title
r=8+4=12%

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