Risk analysis Chapter

LOGO

Chapter 13 Risk Analysis

Your Site Here

Presented By:Singhzee and Group

Economics

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

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

Hazard or a chance of loss

Bigger the chance of loss/Greater the size of loss = the more risky the action

Risk and Probability

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…

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…

Subjective Definition of Probability

Risk and Probability Ctd…

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

75%

25%

Both equally likely

50%- 50%

Probability Distributions

A Table listing All possible outcomes Probability of their occurrence

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

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 Unsuccessful

-$600,000 0.5 -$300,000

Do not increase price

$200,000

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

Alternative 1

Alternative 2

Event 1

Event 2

EVPI

Expected Value of Perfect Information(EVPI)

How much would you pay to gain access to perfect information?

CompletelyAccurate

Information

About Future

Outcomes

Increase in Expected

Profit

ToReduce

Uncertainty

EVPI Continued…

EVPI=Expected Profit with Perfect Information- Expected Profit without Perfect

Information Example:

Research Survey ReportSurvey says Prob Decision Profit Prob*Profit

Campaign Successful 0.5 Increase $800,000 $400,000

CampaignUnsuccessful 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

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

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

Constructing a Utility Function

Utility Function=Level of satisfaction

Expected Utility

Sum of utility of each outcome times probability of

the outcome’s occurrence

Constructing a Utility Function Example: Tomco Oil Corporation

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

Attitudes towards Risk

Three Types

Risk Averter

Risk Lover

Risk-Neutral

Risk Averter

Choice: Certain outcome

Risk Lover

Choice: Uncertain outcome

Risk-Neutral

Maximization of expected wealth

Regardless of risk

Measures of Risk

2.

•Example:

•Jones Corporation

•Investment Decision

for a new plant

1. •Dispersion of Probability Distribution

• Profit from the Decision

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

(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

(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

(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

Adjusting the Valuation Model for Risk

Effects of managerial decision

PV of future profits

Certainty Equivalent Approach

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

Click to Edit Title

Sub Title Sub Title

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

A

B

C

D

1 2 3 4

Click to Edit Title

r=8+4=12%

LOGO

Thank You!