lecture 5 risk analysis

8/13/2019 Lecture 5 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 Engineering

Massachusetts Institute of Technology


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Preliminaries

Announcements

Remainder

email Sharon Lin the team info by midnight, tonight

Monday Feb 27 - Student Experience Presentation Wed March 1stAssignment 2 due

Today, recitation Joe Gifun, MIT facility

Next Friday, March 3rd, Tour PDSI construction site

1st group noon1:30 2nd group 1:303:00

Construction nightmares discussion

16 - Psi Creativity Center, Design and Bidding phases


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Project Management Phase

FEASIBILITY DESIGN

PLANNING

CLOSEOUTDEVELOPMENT OPERATIONS

Financing&Evaluation

Risk Analysis&Attitude


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Risk Management Phase

FEASIBILITY DESIGNPLANNING

CLOSEOUTDEVELOPMENT OPERATIONS

RISK MNG

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.


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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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Uncertainty and Risk

risk as uncertainty about a consequence

Preliminary questions

What sort of risks are there and who bears them inproject management?

What practical ways do people use to cope withthese 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 sufficient

tenants

Community opposition Infighting & acrimonious

relationships 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 is spentfocusing 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






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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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Risk Preference

People are not indifferent to uncertainty

Lack of indifference from uncertainty arises fromuneven 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 uncertaintybased 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 riskpreferences

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 (min + (1- ) max) , 0 1

= 1 pessimistic

= 0.5 neutral

= 0 optimistic


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The bridge caseunknown probties

replace

repair

$ 1.09 million

Investment PV

$1.61 M

$0.55

$1.43

Pessimistic rulemin (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 caseknown probties

replace

repair

$ 1.09 million

Investment PV

$1.61 M

$0.55

$1.43

Expected monetary valueE = (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 casedecision

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 withthe highest probability

Expected value of Opportunity Loss


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To buy soon or to buy later

Buy soon

Current price = 100S1 = + 30%S2 = no price variationS3 = - 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 makechoices as is they are maximizing a given criterion: theexpected utility.

Expected utility is a measure of the individual's implicitpreference, for each policy in the risk environment.

It is represented by a numerical value associated witheach monetary gain or loss in order to indicate theutility 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) = -102.5Utility 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 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 (riskaverse) individual to avoid risk

Risk premiums are very commonwhat aresome 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 takeadvantage/disadvantage of future benefit/loss


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Certainty Equivalent Example Consider a risk averse individual with

preference fnffaced with an investment cthat provides 50% chance of earning $20000

50% chance of earning $0

Average moneyfrom investment =

.5*$20,000+.5*$0=$10000 Average satisfactionwith the investment=

.5*f($20,000)+.5*f($0)=.25

This individual would be willing to trade for asureinvestment yielding satisfaction>.25instead Can get .25 satisfaction for a sure f-1(.25)=$5000

We call this the certainty equivalentto the investment

Therefore this person should be willing to tradethis investment for a sure amount of

money>$5000

.25

Mean valueOf investme

Mean satisfactionwithinvestment

Certainty equivaleof investment

$5000

.50


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Example Contd (Risk Premium)

The risk averse individual would be willing totrade the uncertain investment c for any certainreturn which is > $5000

Equivalently, the risk averse individual would bewilling to pay another party an amount rup to$5000 =$10000-$5000 for other less risk averseparty to guarantee $10,000

Assuming the other party is not risk averse, thatparty wins because gain ron 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 functionf

Note: E[X] is the mean (expected value) operator

The mean outcomeof uncertain investment c is E[c]

In example, this was .5*$20,000+.5*$0=$10,000

The mean satisfaction withthe 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 equivalentof 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 meanscan classify risk attitude by comparing thecertainty equivalent and expected value

For risk loving individuals, f-1(E[f(c)])>E[c]

They want Certainty equivalent > mean outcome

For risk neutralindividuals, f-1(E[f(c)])=E[c]

For risk averseindividuals, 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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Gamble or not to Gamble

EMV

(0.5)(-1) + (0.5)(1) = 0

Preference function f(-1)=0, f(1)=100Certainty 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 factorsbut still need to make differentattributes comparable


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The bridge case - Multiple tradeoffs

MTTF = mean time to failure

Computation of Pareto-Optimal SetFor decision D2

ReplaceMTTF 10.0000Cost 1.00

C3MTTF 6.6667Cost 0.30

C4MTTF 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 allattributes 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 Stellardue 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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Multiple objective

The students dilemma


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Bidding

What choicesdo we have?

How does the chance of winning vary with ourbidding price?

How does our profit vary with our bidding priceif we win?


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Example Bidding Decision TreeTime


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Bidding Decision Tree with

Stochastic Costs, Competing Bids


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Selecting Desired Electrical Capacity

T


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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 ofreorder (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 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 byrepeatedly sampling values from the probability distributions

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


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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 Ri k P f f L


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With Risk Preferences for Large

Uncertainties at lower bid

With Ri k Pr f r n f r


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With Risk Preferences for

Higher Bid


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Optimal Strategy


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Examples of simple decision trees




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Flexibility and Real Options

Flexibility isproviding 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 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


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Adaptive Strategies

An adaptive strategy is one that changes thecourse of action based on what is observedi.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 valueof 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 abandoning invest.

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 constructionactivities 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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Examples of simple decision trees




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Readings

Required More information:

Utility and risk attitudeStellar Readings section

Get prepared for next class:

You can manage construction risksStellar

On-line textbook, from 2.4 to 2.12

Recommended:

Meredith Textbook, Chapter 4 Prj Organization Risk management and insurancesStellar


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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!

lecture 5 risk analysis

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