l4risk_analysis

L4risk_analysis - Dealing with Uncertainty Concepts and Tools 1.040/1.401J System and Project Management Nathaniel Osgood Decision Making Under

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Unformatted text preview: Dealing with Uncertainty: Concepts and Tools 1.040/1.401J System and Project Management Nathaniel Osgood 2/17/2004 Decision Making Under Risk Decision trees for representing uncertainty Examples of simple decision trees Risk Preferences, Attitude and Premiums Decision trees for analysis Flexibility and real options Introduction to Decision Trees We will use decision trees both for Diagrammatically illustrating decision making w/uncertainty Quantitative reasoning Represent Flow of time Decisions Uncertainties (via events) Consequences (deterministic or stochastic) Learn well: Decision trees will reappear throughout the course Decision Tree Nodes Decision (choice) Node Time Chance (event) Node Terminal (consequence) node Decision Making Under Risk Decision trees for representing uncertainty Examples of simple decision trees Risk Preferences, Attitude and Premiums Decision trees for analysis Flexibility and real options Example Bidding Decision Tree Time Choosing Elevator Count Selecting Desired Electrical Capacity Bidding Decision Tree with Stochastic Costs, Competing Bids Decision Making Under Risk Decision trees for representing uncertainty Examples of simple decision trees Risk Preferences, Attitude and Premiums Decision trees for analysis Flexibility and real options 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 winning $x Individuals differ in comfort with uncertainty based on circumstances and preferences Risk averse individuals will pay "risk premiums" to avoid uncertainty Risk Preference Categories of Risk Attitudes Risk attitude is a general way of classifying risk preferences Risk averse fear loss and seek sure gains Risk neutral are indifferent to uncertainty Risk lovers hope to "win big" Risk attitudes change over Time Circumstance Preference Function Formally expresses a particular party's degree of preference for (satisfaction with) different outcomes ($, time, level of conflict, quality...) Can be systematically derived Used to identify best decision when have uncertainty with respect to consequences Choice with the highest mean preference is the best strategy for that particular party Risk Attitude in Preference Fns Identifying Preference Functions Simple procedure to identify utility value associated with multiple outcomes Interpolation between these data points defines the preference function Notion of a Risk Premium A risk premium is the amount paid by an individual to avoid risk Risk premiums are very common 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 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 for a sure investment yielding satisfaction>.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 amt of money>$5000 Example Cont'd (Risk Premium) The risk averse individual would be willing to trade the uncertain investment c for any certain return which is > $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 The other party wins because gain r on average The risk averse individual wins b/c more satisfied 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 For risk averse individuals, f-1(E[f(c)])<E[c] Motivations for a Risk Premium Consider Risk averse individual A for whom f-1(E[f(c)])<E[c] Less risk averse party B A can lessen the effects of risk by paying a risk premium r of up to E[c]-f-1(E[f(c)]) to B in return for a guarantee of E[c] income The risk premium shifts the risk to B The net investment gain for A is E[c]-r, but A is more satisfied because E[c] r > f-1(E[f(c)]) B gets average monetary gain of r 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 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" if it is not dominated by any other decision Decision Making Under Risk Decision trees for representing uncertainty Examples of simple decision trees Risk Preferences, Attitude and Premiums Decision trees for analysis Flexibility and real options Analysis Using Decision Trees Decision trees are a powerful analysis tool Addition of symbolic components to decision trees greatly expand power Example analytic techniques Strategy selection One-way and multi-way sensitivity analyses Value of information Recall Competing Bid Tree Optimal Strategy Monetary Value of $6.75M Bid Monetary Value of $7M Bid With Risk Preferences: 6.75M With Risk Preferences: 7M Larger Uncertainties in Cost (Monetary Value) Large Uncertainties II (Monetary Values) With Risk Preferences for Large Uncertainties at lower bid With Risk Preferences for Higher Bid Interactive 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) More Sophisticated Procurement Sensitivity Analysis I Sensitivity Analysis II Decision Making Under Risk Decision trees for representing uncertainty Examples of simple decision trees Risk Preferences, Attitude and Premiums Decision trees for analysis Flexibility and real options 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 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 Illustration of Flexibility Illustration of Flexibility: Selection of Elevator Count More sophisticated model taking into account Initial costs Repair costs Loss due to lost conveyance Sensitivity Analysis Outcome Strategy Selection 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 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 Example: Structural Form Flexibility 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 $ > up-front $ Decision Making Under Risk Decision trees for representing uncertainty Examples of simple decision trees Risk Preferences, Attitude and Premiums Decision trees for analysis Flexibility and real options ...
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This note was uploaded on 10/29/2008 for the course PM 1040 taught by Professor Dr.nathanielosgood during the Spring '04 term at MIT.

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