sda 3e chapter 10

8/4/2019 SDA 3E Chapter 10

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2007 Pearson Education

Chapter 10: Decisions andRisk


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Types of Business DecisionsAccepting or rejecting a proposal or

project

Selecting from a set of non-mutuallyexclusive alternatives

Selecting the best decision from a set of

mutually exclusive alternatives Choosing a best decision strategy when

a sequence of choices and chancesevents may occur


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Structuring Decision Problems Potential alternative decisions

Factory locations

Products to introduce

Investments

Criteria by which to evaluate decisions

Net profit Cost

Environmental impact


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Decisions Involving a Single

Alternative Net present value (NPV)

NPV =

Internal rate of return (IRR)

IRR is the discount rate that makesthe total present value of all cashflows zero:

n

tt

t

i

F

0 )1(

0

)1(0

n

t

t

t

IRR

F


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Example


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Decisions Involving Non-

Mutually Exclusive Alternatives Ranking criteria

Return on investment (ROI)

Cost/benefit ratios

investmentinitial

tsannualrevenueAnnualROI

cos


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Example


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Decisions Involving Mutually

Exclusive Alternatives

Scoring model - a

quantitativeassessment of adecision alternativesvalue based on a setof attributes.


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Decisions Involving

Uncertainty and Risk Identify decision alternatives

Identify possible outcomes or chance events

Evaluate the payoff associated with eachalternative and outcome (payoff table)

The decision depends on how risk is valued.

Decision/Event Market rises Market falls Market stable

Aggressive fund $1000 -$1500 $0Balanced fund $600 -$500 $200

Bond fund $200 $300 $100


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Risk The chance of an undesirable outcome.

Decision/Event Market rises Market falls Market stable

Aggressive fund $1000 -$1500 $0

Balanced fund $600 -$500 $200

Bond fund $200 $300 $100

Little risk Highest risk


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Decision StrategiesAverage payoff

Aggressive

Conservative

Opportunity loss


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Average PayoffDecision/Event Market rises Market falls Market stable Average

Aggressive

fund

$1000 -$1500 $0 -$166.67

Balancedfund

$600 -$500 $200 $100

Bond fund $200 $300 $100 $200

Choose Bond fund


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Aggressive StrategyDecision/Event Market rises Market falls Market stable Best Return

Aggressive

fund

$1000 -$1500 $0 $1000

Balancedfund

$600 -$500 $200 $600

Bond fund $200 $300 $100 $300

Choose Aggressive fund


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Conservative StrategyDecision/Event Market rises Market falls Market stable Worst Return

Aggressive

fund

$1000 -$1500 $0 -$1500

Balancedfund

$600 -$500 $200 -$500

Bond fund $200 $300 $100 $100

Chose Bond fund


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Opportunity LossDecision/

Event

Market rises Market falls Marketstable

MaximumOpportunityLoss

Aggressivefund

$1000$0

-$1500$1800

$0$200

$1800

Balancedfund

$600

$400

-$500

$800

$200

$0

$800

Bond fund $200$800

$300$0

$100$100

$800

Choose either Balanced or Bond fund


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Understanding Risk Average payoffs never occur!

Decision/Eve

nt

Market

rises

Market falls Market

stable

Average

Aggressivefund

$1000 -$1500 $0 -$166.67

Balancedfund

$600 -$500 $200 $100

Bond fund $200 $300 $100 $200

Less variation More variation


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Measuring Risk Standard deviation

Measures variation, but does not

account for magnitude of return orloss

Return to risk the ratio of mean

return to the standard deviation

Similar to the Sharpe ratio in finance


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Which Project is Riskier?Quantitative measures:

Standard deviation

Project A: $993.7

Project B: $1414.2

Return to Risk

Project A: 7.80

Project B: 5.656


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Expected Value Decision MakingAverage payoff strategy is appropriate

for repeated decisions

Real estate development

Day trading

Pharmaceutical research


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Expected Monetary Value Select the alternative with the best

expected payoff

n

j

jiji SDVSPDE1

),()()(

where P(Sj) = the probability that event Sjoccurs and n = the number of events.


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PHStatTool: Expected

Monetary Value


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Example


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EVPI Expected opportunity loss - the average addi-

tional amount the investor would haveachieved by making the right decision insteadof a wrong one

Expected value of perfect information (EVPI)- the maximum improvement in the expectedreturn that can be achieved if the decisionmaker is able to acquirebefore making adecisionperfect information about thefuture event that will take place.


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ExampleEVPI = expected valueof perfect information

= minimum expectedopportunity loss =360. That is, byhaving perfect

information, we canincrease our expectedreturn by at most$360


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Portfolio Risk Analysis Portfolio - a collection of assets, such as stocks,

bonds, or other investments, that are managed as agroup.

Objective: maximize expected return whileminimizing risk

Expected return = wE[X] + (1-w)E[Y]

w= fraction of portfolio for asset X

1w= fraction of portfolio for asset Y

Standard deviation

XYYXP

wwww )1(2)1(2222


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PHStatTool: Covariance and

Portfolio Analysis

Change weight to

evaluate differentscenarios

Data table forrisk evaluation

Expected Portfolio

Return RiskX-Weight 230 685.6380 200$ 953.939

0.1 206$ 900.269

0.2 212$ 846.6030.3 218$ 792.941

0.4 224$ 739.2860.5 230$ 685.6380.6 236$ 632.000

0.7 242$ 578.3740.8 248$ 524.763

0.9 254$ 471.1731 260$ 417.612


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The Newsvendor Problem Single period purchase decision

Purchase goods for $c

Sell goods for $r Unsold goods sold for $s

d = Demand during period

x = number purchased How many goods should be purchased to

maximize the expected profit?


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General Model

Case 1: x d

Profit = rd + s(x - d) cx

Case 2: x < d

Profit = rx - cx = (r - c)x

Expected Profit =

x

d xd

dpxcrdpcxdxsrd0 1

)(])[()(])([


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Example and Spreadsheet

Solution

Maximum expected profit


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The Flaw of Averages If y = f(x) represents a generic decision

model, then E[y] is not necessarily

equal to f(E[x]). In other words, you cannot use the

average value of an input in a model to

determine the expected output.


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Decision Trees Decision trees model a sequence of decisions and

chance events.

Nodes points in time at which events take place

Decision (choice) nodes Event (chance) node

Branches choices or outcomes

Adecision strategy is a specification of an initial

decision and subsequent decisions that arecontingent on the occurrence of events.

A decision strategy has an associated payoffdistribution, called a risk profile, that shows possiblepayoffs and their probabilities.


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TreePlan: Excel Decision Tree

Add-In


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Sensitivity Analysis in Decision

Trees


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Utility and Decision Making Utility theory an approach or

assessing risk attitudes quantitatively by

quantifying a decision makers relativepreferences for particular outcomes.


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ExampleDecision/Event Rates rise Rates stable Rates fall

Bank CD $400 $400 $400

Bond fund -$500 $840 $1000Stock fund -$900 $600 $1700

Using expected values, the stock fund is best,but this does not account for risk. Convertmonetary payoffs into utility measures.


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Process Rank payoffs from highest

to lowest For each payoff x, Suppose

you have the opportunity ofachieving a guaranteedreturn of x, or taking achance of receiving $1,700(the highest payoff) withprobability por losing $900

(the lowest payoff) withprobability 1 - p. Whatvalue ofp(the utility) wouldmake you indifferent tothese two choices?


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Decision Tree Lottery for $1000

Payoff


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Utility Function and Decision

Use utilities to compute expected values of each decision

On the basis of expected utility, the Bank CD is now the best decision.


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Risk Averse Utility Function


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Exponential Utility Functions Often used to approximate risk-averse

utility functionsRxexU /1)(


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Finding R Find the maximum payoff $P for which

the decision maker is willing to take an

equal chance on winning $P or losing$P/2. This is the value of R.


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Example Suppose R = 400

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