3. Risk Analysis

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1.040/1.401Project Management

Spring 2006

Risk AnalysisDecision making under risk and uncertainty

Department of Civil and Environmental EngineeringMassachusetts Institute of Technology


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Project Management Phase

FEASIBILITY DESIGN

PLANNING

CLOSEOUT DEVELOPMENT OPERATIONS

Financing&Evaluation

Risk Analysis&Attitude


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Risk Management Phase

• 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.

FEASIBILITY DESIGNPLANNING

CLOSEOUT DEVELOPMENT OPERATIONS

RISK MNG


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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


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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 onrisks that others shun?


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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 sufficienttenants

• Community opposition

• Infighting & acrimoniousrelationships

• Unrealistically low bid

• Late-stage design changes

• Unexpected subsurfaceconditions – Soil type

– Groundwater

– Unexpected Obstacles

• Settlement of adjacentstructures

• High lifecycle costs

• Permitting problems

• …


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Importance of Risk•

Much time in construction management isspent focusing on risks

• Many practices in construction are driven byrisk

– Bonding requirements – Insurance

– Licensing

– Contract structure

• General conditions• Payment Terms

• Delivery Method

• Selection mechanism


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Outline


Risk Preferences, Attitude and Premiums

• Examples of simple decision trees• Decision trees for analysis



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Decision making under risk

Available 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)


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Decision Tree Nodes

• Decision (choice) Node

• Chance (event) Node

• Terminal (consequence) node – Outcome (cost or benefit)

Time


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Risk Preference

• People are not indifferent to uncertainty

– Lack of indifference from uncertainty arises fromuneven preferences for different outcomes

( Sự giảm của Sự không khác biệt từ sự không chắc chắn bắt nguồn từ sự ưu thích không bằng nhau về các kết quả khác nhau)

– 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 uncertaintybased on circumstances and preferences

• Risk averse individuals will pay “risk premiums” to


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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 riskpreferences

• Classifications

– Risk averse fear loss and seek sureness – Risk neutral are indifferent to uncertainty

– Risk lovers hope to “win big” and don’t mindlosing 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)

• A{( 0.4,100) (0.2, 50) (0.3,-100) (0.1, -50)}• B{( 0.4,80) (0.2, 60) (0.3,-80) (0.1, -50)}

• The optimistic rule (maximax)

– The risklover seeks to maximize the maximum gain

•Compromise (the Hurwitz rule): – Max (α min + (1- α) max) , 0 ≤ α ≤ 1

• α = 1 pessimistic

• α = 0.5 neutral

• α = 0 optimistic


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The bridge case – unknown prob’ties

$1.61 M

$0.55

$1.43

replace

repair

$ 1.09 million

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 prob’ties

$1.61 M

$0.55

$1.43

replace

repair

$ 1.09 million

Investment PV

Expected monetary value

E = (0.25)(1.61) + (0.5)(0.55) + (0.25)(1.43) = $ 1.04 M

0.25

0.5

0.25

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


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To buy soon or to buy later

Buy soon

Current price = 100

S1 = + 30%

S2 = no price variation

S3 = - 30%

Actualization = 5

-100-30+5 = -125

-100+5 = -95

-100+5+30 = -65

Buy later

-100


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To buy soon or to buy later

Buy soon

-125

-95

-65

Buy later

-100

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 witheach 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

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) =

= .5*0.7 + .25*1.05 + .25*1.35 = ~0.95

Certainty value = -102.5*0.975 = -97.38

100125 65

1

.7

1.35


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Defining the Preference Function

• Suppose to be awarded a $100M contractprice

• 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 (riskaverse) individual to avoid risk

• Risk premiums are very common – what are

some examples? – Insurance premiums

– Higher fees paid by owner to reputablecontractors

– 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 = – .5*$20,000+.5*$0=$10000

• Average satisfaction with the investment= – .5*f($20,000)+.5*f($0)=.25

• This individual would be willing to trade fora sure investment yielding satisfaction>.25instead

– 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 tradethis investment for a sure amount ofmoney>$5000

.25

Mean value

Of investme

Mean satisfaction with

investment

Certainty equivale

of investment

$ 5 0 0 0

.50


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Example Cont’d (Risk Premium)

• The risk averse individual would be willing totrade the uncertain investment c for any

certain return which is > $5000

•Equivalently, the risk averse individual wouldbe 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: E[X] is the mean (expected value) operator

• The mean outcome of uncertain investment c is E[c] – In example, this was .5*$20,000+.5*$0=$10,000

• The mean satisfaction with the investment is E[f(c)]

– In example, this was .5*f($20,000)+.5*f($0)=.25

• We call f -1(E[f(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(.5*20,000+.5*0)=$5,000


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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(E[f(c)])>E[c]

• They want Certainty equivalent > mean outcome

– For risk neutral individuals, f -1(E[f(c)])=E[c]

– For risk averse individuals, f -1(E[f(c)])


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Motivations for a Risk Premium

• Consider

– Risk averse individual A for whom f -1(E[f(c)]) f -1(E[f(c)])

– B gets average monetary gain of r


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.25

Mean value

Of investment

Mean satisfaction with

investment

Certainty equivalent

of investment

$ 5 0 0 0

.50


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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(E[f(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 differentattributes comparable


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The bridge case - Multiple tradeoffs

MTTF = mean time to failure

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


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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


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Decision Making Under Risk



• Examples of simple decision trees

• Decision trees for analysis



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Multiple objective

The student’s dilemma


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Examples of simple decision trees

• Decision trees for analysis



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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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Bidding Decision Tree with

Stochastic Costs, Competing Bids


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Selecting Desired Electrical Capacity

l


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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 trees for representing uncertainty

Decision trees for analysis



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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


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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 valuesbut an uncertain value for any particular time or event.

• For each uncertain variable, you define the possible valueswith a probability distribution.

• Distribution types include:

• A simulation calculates multiple scenarios of a model byrepeatedly sampling values from the probability distributions

• Computer software tools can perform as many trials (orscenarios) as you want and allow to select the optimalstrategy

…


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Monetary Value of $6.75M Bid


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Monetary Value of $7M Bid


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With Risk Preferences: 6.75M


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With Risk Preferences: 7M

L U t i ti i C t


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Larger Uncertainties in Cost

(Monetary Value)

L U t i ti II


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Large Uncertainties II

(Monetary Values)

With Risk Preferences for Large


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With Risk Preferences for Large

Uncertainties at lower bid

With Risk Preferences for


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With Risk Preferences for

Higher Bid


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Optimal Strategy


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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

Ways to Ensure of Flexibility


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Ways to Ensure of Flexibility

in Construction

• Alternative Delivery

• Clear spanning (to allowmovable 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


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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, explicitlyplan to adapt as events unfold

– Typically we delay a decision into the future


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Real Options

• Real Options theory provides a means ofestimating financial value of flexibility

– E.g. option to abandon a plant, expand bldg

• Key insight: NPV does not work well withuncertain costs/revenues

– E.g. difficult to model option of abandoninginvest.

• Model events using stochastic diff. equations

– Numerical or analytic solutions

– Can derive from decision-tree based framework


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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 offw/greater flexibility!

• Frequently retrofitting $ > up-front $


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Flexibility and real options


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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 : aconstructively simple approach to decision making

• Bedford, Probabilistic risk analysis: foundations and methods

• … and a lot more!

3. Risk Analysis

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