Lecture 4 Risk Analysis

1
1.040/1.401Project ManagementSpring 2006Risk
AnalysisDecision making under risk and
uncertainty

Department of Civil and Environmental
Engineering Massachusetts Institute of Technology
2
Preliminaries

• Announcements
• Remainder
• email Sharon Lin the team info by midnight,
  tonight
• Monday Feb 27 - Student Experience Presentation
• Wed March 1st Assignment 2 due
• Today, recitation Joe Gifun, MIT facility
• Next Friday, March 3rd, Tour PDSI construction
  site
• 1st group noon 130
• 2nd group 130 300
• Construction nightmares discussion
• 16 - Psi Creativity Center, Design and Bidding
  phases

3
Project Management Phase
DESIGN PLANNING
DEVELOPMENT
OPERATIONS
FEASIBILITY
CLOSEOUT
4
Risk Management Phase
RISK MNG
DESIGN PLANNING
DEVELOPMENT
OPERATIONS
FEASIBILITY
CLOSEOUT

• Risk management (guest seminar 1st wk April)
• Assessment, tracking and control
• Tools
• Risk Hierarchical modeling Risk breakdown
  structures
• Risk matrixes
• Contingency plan preventive measures, corrective
  actions, risk budget, etc.

5
Decision Making Under Risk Outline

• Risk and Uncertainty
• Risk Preferences, Attitude and Premiums
• Examples of simple decision trees
• Decision trees for analysis
• Flexibility and real options

6
Decision making
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Uncertainty and Risk

• risk as uncertainty about a consequence
• Preliminary questions
• What sort of risks are there and who bears them
  in project management?
• What practical ways do people use to cope with
  these risks?
• Why is it that some people are willing to take on
  risks that others shun?

8
Some Risks

• Weather changes
• Different productivity
• (Sub)contractors are
• Unreliable
• Lack capacity to do work
• Lack availability to do work
• Unscrupulous
• Financially unstable
• Late materials delivery
• Lawsuits
• Labor difficulties
• Unexpected manufacturing costs
• Failure to find sufficient tenants

• Community opposition
• Infighting acrimonious relationships
• Unrealistically low bid
• Late-stage design changes
• Unexpected subsurface conditions
• Soil type
• Groundwater
• Unexpected Obstacles
• Settlement of adjacent structures
• High lifecycle costs
• Permitting problems

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Importance of Risk

• Much time in construction management is spent
  focusing on risks
• Many practices in construction are driven by risk
• Bonding requirements
• Insurance
• Licensing
• Contract structure
• General conditions
• Payment Terms
• Delivery Method
• Selection mechanism

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Outline

• Risk and Uncertainty
• Risk Preferences, Attitude and Premiums
• Examples of simple decision trees
• Decision trees for analysis
• Flexibility and real options

11
Decision making under riskAvailable Techniques

• Decision modeling
• Decision making under uncertainty
• Tool Decision tree
• Strategic thinking and problem solving
• Dynamic modeling (end of course)
• Fault trees

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Introduction to Decision Trees

• We will use decision trees both for
• Illustrating decision making with uncertainty
• Quantitative reasoning
• Represent
• Flow of time
• Decisions
• Uncertainties (via events)
• Consequences (deterministic or stochastic)

13
Decision Tree Nodes
Time

• Decision (choice) Node
• Chance (event) Node
• Terminal (consequence) node
• Outcome (cost or benefit)

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Risk Preference

• People are not indifferent to uncertainty
• Lack of indifference from uncertainty arises from
  uneven preferences for different outcomes
• E.g. someone may
• dislike losing x far more than gaining x
• value gaining x far more than they disvalue
  losing x.
• Individuals differ in comfort with uncertainty
  based on circumstances and preferences
• Risk averse individuals will pay risk premiums
  to avoid uncertainty

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Risk preference

• The preference depends on decision maker point of
  view

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Categories of Risk Attitudes

• Risk attitude is a general way of classifying
  risk preferences
• Classifications
• Risk averse fear loss and seek sureness
• Risk neutral are indifferent to uncertainty
• Risk lovers hope to win big and dont mind
  losing as much
• Risk attitudes change over
• Time
• Circumstance

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Decision Rules

• The pessimistic rule (maximin minimax)
• The conservative decisionmaker seeks to
• maximize the minimum gain (if outcome payoff)
• or minimize the maximum loss (if outcome loss,
  risk)
• The optimistic rule (maximax)
• The risklover seeks to maximize the maximum gain
• Compromise (the Hurwitz rule)
• Max (a min (1- a) max) , 0 a 1
• a 1 pessimistic
• a 0.5 neutral
• a 0 optimistic

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The bridge case unknown probties
1.09 million
replace
1.61 M
0.55
1.43
repair
Investment PV

• Pessimistic rule
• min (1, 1.61) 1 replace the bridge
• The optimistic rule (maximax)
• max (1, 0.55) 0.55 repair and hope it works!

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The bridge case known probties
1.09 million
replace
1.61 M
0.55
1.43
0.25
repair
0.5
Investment PV
0.25
Expected monetary value E (0.25)(1.61)
(0.5)(0.55) (0.25)(1.43) 1.04 M
Data link
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The bridge case decision

• The pessimistic rule (maximin minimax)
• Min (Ei) Min (1.09 , 1.04) 1.04 repair
• In this case optimistic rule (maximax)
• Awareness of probabilities change risk attitude

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Other criteria

• Most likely value
• For each policy option we select the outcome with
  the highest probability
• Expected value of Opportunity Loss

22
To buy soon or to buy later
-100
Buy soon
-100-305 -125
-1005 -95
-100530 -65
Buy later
Current price 100 S1 30 S2 no price
variation S3 - 30 Actualization 5
23
To buy soon or to buy later
-100
Buy soon
-125
-95
-65
Buy later
0. 5
0.25
0.25
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The Utility Theory

• When individuals are faced with uncertainty they
  make choices as is they are maximizing a given
  criterion the expected utility.
• Expected utility is a measure of the individual's
  implicit preference, for each policy in the risk
  environment.
• It is represented by a numerical value associated
  with each monetary gain or loss in order to
  indicate the utility of these monetary values to
  the decision-maker.

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Adding a Preference function
1.35
1
.7
100
125
65
Expected (mean) value E (0.5)(125)
(0.25)(95) (0.25)(65) -102.5 Utility
value f(E) ? Pa f(a) 0.5 f(125) 0.25
f(95) .25 f(65) .50.7 .251.05
.251.35 0.95 Certainty value -102.50.975
-97.38
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Defining the Preference Function

• Suppose to be awarded a 100M contract price
• Early estimated cost 70M
• What is the preference function of cost?
• Preference means utility or satisfaction

utility

70
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Notion of a Risk Premium

• A risk premium is the amount paid by a (risk
  averse) individual to avoid risk
• Risk premiums are very common what are some
  examples?
• Insurance premiums
• Higher fees paid by owner to reputable
  contractors
• Higher charges by contractor for risky work
• Lower returns from less risky investments
• Money paid to ensure flexibility as guard against
  risk

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Conclusion To buy or not to buy

• The risk averter buys a future contract that
  allow to buy at 97.38
• The trading company (risk lover) will take
  advantage/disadvantage of future benefit/loss

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Certainty Equivalent Example

• Consider a risk averse individual with preference
  fn f faced with an investment c that provides
• 50 chance of earning 20000
• 50 chance of earning 0
• Average money from investment
• .520,000.5010000
• Average satisfaction with the investment
• .5f(20,000).5f(0).25
• This individual would be willing to trade for a
  sure investment yielding satisfactiongt.25 instead
• Can get .25 satisfaction for a sure
  f-1(.25)5000
• We call this the certainty equivalent to the
  investment
• Therefore this person should be willing to trade
  this investment for a sure amount of moneygt5000

Mean satisfaction with investment
.50
.25
Certainty equivalent of investment
Mean value Of investment
5000
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Example Contd (Risk Premium)

• The risk averse individual would be willing to
  trade the uncertain investment c for any certain
  return which is gt 5000
• Equivalently, the risk averse individual would be
  willing to pay another party an amount r up to
  5000 10000-5000 for other less risk averse
  party to guarantee 10,000
• Assuming the other party is not risk averse, that
  party wins because gain r on average
• The risk averse individual wins b/c more satisfied

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Certainty Equivalent

• More generally, consider situation in which have
• Uncertainty with respect to consequence c
• Non-linear preference function f
• Note EX is the mean (expected value) operator
• The mean outcome of uncertain investment c is
  Ec
• In example, this was .520,000.5010,000
• The mean satisfaction with the investment is
  Ef(c)
• In example, this was .5f(20,000).5f(0).25
• We call f-1(Ef(c)) the certainty equivalent of
  c
• Size of sure return that would give the same
  satisfaction as c
• In example, was f-1(.25)f-1(.520,000.50)5,00
  0

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Risk Attitude Redux

• The shapes of the preference functions means can
  classify risk attitude by comparing the certainty
  equivalent and expected value
• For risk loving individuals, f-1(Ef(c))gtEc
• They want Certainty equivalent gt mean outcome
• For risk neutral individuals, f-1(Ef(c))Ec
• For risk averse individuals, f-1(Ef(c))ltEc

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Motivations for a Risk Premium

• Consider
• Risk averse individual A for whom
  f-1(Ef(c))ltEc
• Less risk averse party B
• A can lessen the effects of risk by paying a risk
  premium r of up to Ec-f-1(Ef(c)) to B in
  return for a guarantee of Ec income
• The risk premium shifts the risk to B
• The net investment gain for A is Ec-r, but A is
  more satisfied because Ec r gt f-1(Ef(c))
• B gets average monetary gain of r

34
Gamble or not to Gamble
EMV (0.5)(-1) (0.5)(1) 0
Preference function f(-1)0, f(1)100 Certainty
eq. f-1(Ef(c)) 0 No help from risk analysis
!!!!!
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Multiple Attribute Decisions

• Frequently we care about multiple attributes
• Cost
• Time
• Quality
• Relationship with owner
• Terminal nodes on decision trees can capture
  these factors but still need to make different
  attributes comparable

36
The bridge case - Multiple tradeoffs
Computation of Pareto-Optimal Set For decision
D2 Replace MTTF 10.0000 Cost 1.00 C3
MTTF 6.6667 Cost 0.30 C4 MTTF 5.7738
Cost 0.00
Aim maximizing bridge duration, minimizing cost
MTTF mean time to failure
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Pareto Optimality

• Even if we cannot directly weigh one attribute
  vs. another, we can rank some consequences
• Can rule out decisions giving consequences that
  are inferior with respect to all attributes
• We say that these decisions are dominated by
  other decisions
• Key concept here May not be able to identify
  best decisions, but we can rule out obviously bad
• A decision is Pareto optimal (or efficient
  solution) if it is not dominated by any other
  decision

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03/06/06 - Preliminaries

• Announcements
• Due dates Stellar Schedule and not Syllabus
• Term project
• Phase 2 due March 17th
• Phase 3 detailed description posted on Stellar,
  due May 11
• Assignment PS3 posted on Stellar due date March
  24
• Decision making under uncertainty
• Reading questions/comments?
• Utility and risk attitude
• You can manage construction risks
• Risk management and insurances - Recommended

39
Decision Making Under Risk

• Risk and Uncertainty
• Risk Preferences, Attitude and Premiums
• Examples of simple decision trees
• Decision trees for analysis
• Flexibility and real options

40
Multiple objectiveThe students dilemma
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Decision Making Under Risk

• Risk and Uncertainty
• Risk Preferences, Attitude and Premiums
• Examples of simple decision trees
• Decision trees for analysis
• Flexibility and real options

42
Bidding

• What choices do we have?
• How does the chance of winning vary with our
  bidding price?
• How does our profit vary with our bidding price
  if we win?

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Example Bidding Decision Tree
Time
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Choosing Elevator Count
45
Bidding Decision Tree with Stochastic Costs,
Competing Bids
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Selecting Desired Electrical Capacity
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Decision Tree Example Procurement Timing

• Decisions
• Choice of order time (Order early, Order late)
• Events
• Arrival time (On time, early, late)
• Theft or damage (only if arrive early)
• Consequences Cost
• Components Delay cost, storage cost, cost of
  reorder (including delay)

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Procurement Tree
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Decision Making Under Risk

• Risk and Uncertainty
• Risk Preferences, Attitude and Premiums
• Decision trees for representing uncertainty
• Decision trees for analysis
• Flexibility and real options

50
Analysis Using Decision Trees

• Decision trees are a powerful analysis tool
• Example analytic techniques
• Strategy selection (Monte Carlo simulation)
• One-way and multi-way sensitivity analyses
• Value of information

51
Recall Competing Bid Tree
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Monte Carlo simulation

• Monte Carlo simulation randomly generates values
  for uncertain variables over and over to simulate
  a model.
• It's used with the variables that have a known
  range of values but an uncertain value for any
  particular time or event.
• For each uncertain variable, you define the
  possible values with a probability distribution.
• Distribution types include
• A simulation calculates multiple scenarios of a
  model by repeatedly sampling values from the
  probability distributions
• Computer software tools can perform as many
  trials (or scenarios) as you want and allow to
  select the optimal strategy

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Monetary Value of 6.75M Bid
54
Monetary Value of 7M Bid
55
With Risk Preferences 6.75M
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With Risk Preferences 7M
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Larger Uncertainties in Cost(Monetary Value)
58
Large Uncertainties II(Monetary Values)
59
With Risk Preferences for Large Uncertainties at
lower bid
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With Risk Preferences for Higher Bid
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Optimal Strategy
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Sensitivity Analysis I
63
Sensitivity Analysis II
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Decision Making Under Risk

• Risk and Uncertainty
• Risk Preferences, Attitude and Premiums
• Decision trees for representing uncertainty
• Examples of simple decision trees
• Decision trees for analysis
• Flexibility and real options

65
Flexibility and Real Options

• Flexibility is providing additional choices
• Flexibility typically has
• Value by acting as a way to lessen the negative
  impacts of uncertainty
• Cost
• Delaying decision
• Extra time
• Cost to pay for extra fat to allow for
  flexibility

66
Ways to Ensure of Flexibility in Construction

• Alternative Delivery
• Clear spanning (to allow movable walls)
• Extra utility conduits (electricity, phone,)
• Larger footings columns
• Broader foundation
• Alternative heating/electrical

• Contingent plans for
• Value engineering
• Geotechnical conditions
• Procurement strategy
• Additional elevator
• Larger electrical panels
• Property for expansion
• Sequential construction
• Wiring to rooms

67
Illustration of Flexibility
68
Illustration of Flexibility Selection of
Elevator Count

• More sophisticated model taking into account
• Initial costs
• Repair costs
• Loss due to lost conveyance

69
Sensitivity Analysis
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Outcome
71
Strategy Selection
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Adaptive Strategies

• An adaptive strategy is one that changes the
  course of action based on what is observed i.e.
  one that has flexibility
• Rather than planning statically up front,
  explicitly plan to adapt as events unfold
• Typically we delay a decision into the future

73
Real Options

• Real Options theory provides a means of
  estimating financial value of flexibility
• E.g. option to abandon a plant, expand bldg
• Key insight NPV does not work well with
  uncertain costs/revenues
• E.g. difficult to model option of abandoning
  invest.
• Model events using stochastic diff. equations
• Numerical or analytic solutions
• Can derive from decision-tree based framework

74
Example Structural Form Flexibility
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Considerations

• Tradeoffs
• Short-term speed and flexibility
• Overlapping design construction and different
  construction activities limits changes
• Short-term cost and flexibility
• E.g. value engineering away flexibility
• Selection of low bidder
• Late decisions can mean greater costs
• NB both budget schedule may ultimately be
  better off w/greater flexibility!
• Frequently retrofitting gt up-front

76
Decision Making Under Risk

• Risk and Uncertainty
• Risk Preferences, Attitude and Premiums
• Decision trees for representing uncertainty
• Examples of simple decision trees
• Decision trees for analysis
• Flexibility and real options

77
Readings

• Required
• More information
• Utility and risk attitude Stellar Readings
  section
• Get prepared for next class
• You can manage construction risks Stellar
• On-line textbook, from 2.4 to 2.12
• Recommended
• Meredith Textbook, Chapter 4 Prj Organization
• Risk management and insurances Stellar

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Risk - MIT libraries

• Haimes, Risk modeling, assessment, and management
• Mun, Applied risk analysis moving beyond
  uncertainty
• Flyvbjerg, Mega-projects and risk
• Chapman, Managing project risk and uncertainty
  a constructively simple approach to decision
  making
• Bedford, Probabilistic risk analysis foundations
  and methods
• and a lot more!