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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