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Chapter 11– Structured Risk Management

Chapter 11– Structured Risk Management. Risk Management Expected Value of Perfect Control Sensitivity Analysis – Robustness – easy to do with Precision Tree Value Added structured approach - Individual random events Role of Information Expected Value of Imperfect Information

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Chapter 11– Structured Risk Management

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  1. Chapter 11– Structured Risk Management • Risk Management • Expected Value of Perfect Control • Sensitivity Analysis – Robustness – easy to do with Precision Tree • Value Added structured approach - Individual random events • Role of Information • Expected Value of Imperfect Information • Bayes Rule and EVII • Optimal Conditional decision • Sequential decisions with information delay • Real Options

  2. Risk Management Theme You cannot manage risk if you do not admit there is uncertainty Managing uncertainty also includes unrealized upsidepotential and not just downside losses You cannot allocate appropriate resources if you do not quantify the risk or uncertainty

  3. 40.0% 0 30% Take 9.9 1.9 FALSE Take Rate Low -8 5.86 60.0% 0 50% Take 16.5 8.5 How Much Automation Investment 6.32 40.0% 0.4 30% Take 13.8 0.8 TRUE Take Rate High -13 6.32 60.0% 0.6 50% Take 23 10 Figure 11.1: Decision tree Boss Controls automation investment

  4. Investment in Automation -Question: Robustness of Optimal Solution • The “High” investment alternative involves a new technology. • Management is concerned that the capital equipment estimate could be off by + 7%. • There is even more concern regarding the variable cost estimate that could be off by + 10% • The Low investment alternative is well tested and there is hope that continuous improvement could reduce the variable cost by 5%. • Because they did not know, they set the take rate probabilities at 0.6 and 0.4 respectively. However, there is a lot of uncertainty regarding this estimated probability.

  5. Investment in AutomationRobustness of Optimal Solution • Magnitude of Difference between two solutions • ($6.32M-$5.86M) = $460,000 • Investment(s) • How much increase in HIGH Investment fixed cost results in change in best decision? • Variable Cost(s) • How much would the variable cost for Low Investment have to decline to make it preferred? • Probability of 30% take rate: Increases? Decreases? • What else and why?

  6. Activate:Precision Tree & Sensitivity AnalysisOutput – Separate Worksheets • Sensitivity – one parameter at a time • One line –Objective function for optimal strategy: A change in optimal decision is usually bend in line • Multiple lines – Objective function for each decision. Crossing lines  change in optimal decision • Tornado diagram – more variables but less info • Spider Plot – more variables, more info, but limited to no more than 3 or 4 variables – too cluttered and confusing

  7. Review: Figure 10.23: Sensitivity analysis automation investment – fixed cost of high investment$13.48 million X axis – Fixed cost input as negative value (-13) Axis would be reversed if cost was stored as (13)

  8. Review: Figure 10.24: Expected value of the optimal decision for each value of fixed cost of high investment

  9. Review: Figure 10.25: Sensitivity analysis automation investment – low take rate probability Decision changes when probability approaches 0.6 (a 50% increase)

  10. List of Variable Ranges • Fixed investment: High Investment: ±7% of base • Price: 0 to –10% of base • Variable Cost of Low investment: ± 10 % of base • Variable Cost of High investment: 0 to 5 % of base • Probability of Low Take rate: ± 0.2 absolute • Low take rate (30%): 0 to –10% absolute • Volume: 0 to – 15% of base

  11. Precision Tree Sensitivity AnalysisTornado Diagram Many parameters: unlimited • Uses Min & Max values specified in the range and calculates Objective function. • Ranks the analysis in order of their range of impact on the objective  looks like tornado • Does NOT show changed decisions!!

  12. Figure 11.2: Tornado diagram Boss Controls automation investment Range of parameter Prob of Low Take (0.2 to 0.6) Vehicles (850 K to 1 million) Price ($54 to $60) Low take rate (20% to 30%) High Invest. ($13 m + 910K)

  13. Precision Tree Sensitivity Analysis Spider Diagram practical limit of 4 parameters • More detailed than Tornado but harder to include many variables. • X axis – change input (percent) • Y axis – change in expected value • Aggregation of many one-way sensitivity analyses but scaled to a common percentage. • Shows the slope of the impact on the objective function and non-linearities. • Shows changes in decisions  bends in line graph

  14. List of Variable Ranges • Fixed investment: High Investment: ±7% of base • Price: 0 to –10% of base  one sided (lower value) • Range of Change in input % from a negative % to 0% • Probability of Low Take rate: ± 0.2 absolute • Decision does not change except at the very highest value – slight bend in line at end • Volume: 0 to – 15% of base  one sided (lower value) • Range of Change in input % from a negative % to 0%

  15. Spider Graph of Decision Tree 'Automation Investment' Expected Value of Entire Model 8.5 8 Expected Value 7.5 7 6.5 Prob. (D13) 6 Vehicles (Mil.) (C10) 5.5 Price (C4) 5 High_Investment (D6) 4.5 4 3.5 0% 20% 40% 60% -60% -40% -20% Change in Input (%) Figure 11.3: Spider plot for Boss Controls automation investment Decision changes: bend

  16. Manage RiskImpact of Strategies to Change Risk Profile • Cut off the downside risk Figure ‎11-4c • Move outcomes to some guaranteed level. • Minimum purchase quantity in a contract • increase the mean and remove the most disastrous possibilities. • Insurance cuts off the downside risk (costs money)  leftward shift in the whole risk profile but reduce the overall expected value • Shift the risk profile to the right Figure ‎11-4b. • add value to all possible outcomes  eliminate altogether an operating cost in a project.

  17. Figure 11.4: Impact of risk management actions on risk profile

  18. Change Risk Profile – Manage Risk • Reduce but not eliminate extremely negative outcomes: Figure ‎11-4e • Magnitude reduction” consistent with the way managers view risk • Probability reduction not as well understood • Centrally concentrate uncertainty: Figure ‎11-4d • Risk sharing: sell half of a risky opportunity for a price equal to half of its expected value

  19. Figure 11.4: Impact of risk management actions on risk profile

  20. Make or Buy Decision: Non-strategic (strictly cost) Decision Context: Manufacture a component yourself or contract with a supplier to manufacture it. There is a design for a component but you are not sure when it comes time to manufacture, that the design will be feasible as is. If not, there will need to be a quick major redesign of the component. If you manufacture it, you expect that with the redesign it will cost 8% more than the original estimate. The decision to make or buy must be made now before you have time to fully check out the design. The demand for the product is also uncertain. If you sign a contract with the supplier for a specific piece price, if the current design turns out to be infeasible, you know the supplier will use the design change as an excuse to increase the price 15%.

  21. Make or Buy Data: Random Events Random Events 1.Design Feasibility Prob. Current Design will Work 0.4 Need a Major Redesign 0.6 2.DemandVolumeProb. Low 1.0 million 0.3 Medium 1.25 million 0.5 High 1.5 million 0.2

  22. Make or Buy Data: Cost Data Costs: Make In-House Facility investment fixed Cost - $55M Variable Cost/ per part If current design works - $100/part If new Design is needed - $108/part Costs: Buy from Supplier Facility investment fixed Cost - $0 Variable Cost/ per part If current design works - $140/part If new Design is needed - $161/part

  23. Design Feasibility Probability Make Costs Buy Costs Works 0.4 100 140 Does NOT 0.6 108 161 Premium 8% 15% Demand Prob. 30.0% 0.12 Low 1 0.3 1 155 40.0% 1.25 0.5 Demand 1.5 0.2 100 177.5 0.2 50.0% Medium 180 Fixed Costs 1.25 Make 55 20.0% 0.08 High Buy 0 1.5 205 TRUE Current Design 55 183.38 30.0% 0.18 Low 1 163 60.0% Demand 108 187.3 0.3 50.0% Medium 190 1.25 20.0% 0.12 High 1.5 217 Decision 183.38 30.0% 0 Low 1 140 40.0% Demand 140 171.5 0 50.0% Medium 175 1.25 20.0% 0 High 1.5 210 FALSE Current Design 0 186.935 30.0% 0 Low 1 161 60.0% Demand 161 197.225 0 50.0% Medium 201.25 1.25 20.0% 0 High 1.5 241.5 Complex calculation & NOT sum of values on branches Figure 11.8: Western Co. make or buy decision E(X) Works E(X) Make Minimize Cost Does NOT work Make or Buy Works Buy Does NOT work

  24. Structured Risk Management Step: Summary • Within optimal decision • Identify random paths with large downside risk • Large values that are negative or poor relative to the best paths • Probability associated with this sequence is not insignificant • Assess impact of • Increasing relative value of that path • Decreasing the probability of that path • Brainstorm strategies for making the above happen • Quantify these alternatives • Repeat for 2nd best decision

  25. Summary of Risk Management Alternatives: Table 11.4

  26. Summary of Risk Management Alternatives Table 11.4 Continued

  27. New topic: Information Value • Perfect Information • Imperfect Information • Sample Information • Expert Information • Accuracy of test (medical or engineering) • Delay decision until information unfolds Options

  28. Information Gathering • Traditional Approach – Gather information (surveys, tests, pilot plant, prototypes) until time or the budget runs out. • Most information is gathered to validate already made decision. • New Approach - Gather information if the cost of gathering it is less than the gain in expected value. • Process – Restructure the decision tree to determine the expected value with the information • Counterintuitive – How can you determine the value of information before you have even gathered the information?

  29. Expected Value of Perfect Information: EVPI • Goal: Determine the expected value of perfect information regarding an Uncertainty or Risk – Hire a Clairvoyant–Prophet Isaiah (Thomas) • This provides an upper bound on the value of all information including “imperfect” information. • If the information never changes the optimal decision then EVPI = 0. • Decision Tree Process: Move the random event in question to the front of the tree “before” the first decision is to be made. • Recalculate the overall expected value. • The NET Improvement is the EVPI.

  30. 60.0% 0.6 10.0 23 TRUE Take Rate 6.32 (=10*0.6 + 0.8*0.4) -13 40.0% 0.4 0.8 13.8 Decision 6.32 (MAX{6.32, 5.86}) 60.0% 0 8.5 16.5 FALSE Take Rate 5.86 (=8.5*0.6 + 1.9*0.4) -8 40.0% 0 1.9 9.9 Original Decision Tree – Automation InvestmentBoss Controls – Base Tree 50% Take Rate High Automation Investment 30% Take Rate Low 50% Take Rate 30% Take Rate

  31. TRUE 0.4 Low 1.9 1.9 EVPI = 6.76 - 6.32 = 0.44 40.0% How Much 1.9 FALSE 0 High 0.8 0.8 Take Rate Perfect Information 6.76 FALSE 0 Low 8.5 8.5 60.0% How Much 10 TRUE 0.6 High 10 10 Figure 11.7: EVPI tree for Boss Controls InvestmentTake rateevent moved to before decision 30% Take 50% Take Optimal decision depends on outcome of random event

  32. Expected Value of Perfect Information: Boss • Base strategy – High Investment & E(X) = $6.32M • If information indicates 30% take rate then “shift” to Low Investment with profit = $1.9M • If information indicates 50% take rate then stay with High Investment with profit = $10M • What is the probability the information will indicate a 30% take rate? Answer 0.4 • E(X) with perfect information = 1.9(.4) + 10 (.6) = 6.76 • EVPI = 6.76 – 6.32 = $0.44M • E(Perfect Control) = 10 – 6.32 = $3.86 M  much more valuable to exert control over uncertainty

  33. Review to contrast EVPC with EVPIMaximum value of risk management  Expected Value of Perfect Control: Not about obtaining information but rather exerting control over destiny • Goal: Determine the value of eliminating Uncertainty or Risk • This provides an upper bound on the value of risk management with regard to that uncertainty. • Process: • Assign probability of “1” to the best outcome of an uncertain event. • Recalculate the overall expected value. • The NET Improvement in expected value is the EVPC.

  34. Review: Expected Value of Perfect Control: Automation Investment Assign probability of “1” to best outcome Net Change: $10 – 6.32 = $3.68 million 100% 1.0 50% 10.0 23 TRUE Take Rate High 10 =10*1 + 0.8*0) -13 0% 0 30% 0.8 13.8 Decision Automation Investment 10 (MAX(10, 8.5)) 100% 0 50% 8.5 16.5 FALSE Take Rate Low 8.5=8.5*1.0 + 1.9*0) -8 0% 0 30% 1.9 9.9

  35. 2nd example: EVPI – Western Make or Buy • Base strategy Make: E(X) = $183.38M • Uncertainties • Design works or not  Bound on Testing Design (Imperfect) • EVPI = $2.41 M • Demand  Bound on value of surveys (Imperfect) • EVPI = $2.16 M • Both uncertainties • EVPI = $3.16 M

  36. 0.12 Design Feasibility 30.0% Low Prob. Make Costs Buy Costs 1 155 Works 0.4 100 140 40.0% Demand Works 177.5 Does NOT 0.6 108 161 100 0.2 Premium 8% 15% 50.0% Medium 180 1.25 20.0% 0.08 High Demand Prob. 1.5 205 Current Design 1 0.3 TRUE Make 1.25 0.5 55 183.38 0.18 1.5 0.2 30.0% Low 1 163 Fixed Costs 60.0% Demand Does NOT work 187.3 Make 55 108 0.3 Buy 0 50.0% Medium 190 1.25 20.0% 0.12 Decision High 1.5 217 Make or Buy 183.38 0 30.0% Low 1 140 40.0% Demand Works 171.5 140 0 50.0% Medium 175 1.25 20.0% 0 High 1.5 210 Current Design FALSE Buy Make or Buy 0 186.935 0 30.0% Low 1 161 60.0% Demand Does NOT work 197.225 161 0 50.0% Medium 201.25 1.25 20.0% 0 High 1.5 241.5

  37. 0 30.0% Low Figure 11.9: Make-Buy EVPI: Design Feasibility Net Improvement 183.38-180.98 = $2.40M 155 155 FALSE Demand Make 177.5 0 50.0% Medium 180 180 20.0% 0 High Decision 205 205 40.0% Works 171.5 0.12 30.0% Low 140 140 TRUE Demand Buy 171.5 0 0.2 50.0% Medium 175 175 20.0% 0.08 High Current Design 210 210 Info Design 180.98 0.18 30.0% Low 163 163 TRUE Demand Make 187.3 0 0.3 Design uncertainty resolved before decision 50.0% Medium 190 190 20.0% 0.12 High Decision 217 217 60.0% Does NOT work 0 187.3 0 30.0% Low 161 161 FALSE Demand Buy 197.225 0 0 50.0% Medium 201.25 201.25 20.0% 0 High 241.5 241.5

  38. 0 40.0% Works 155 155 FALSE Current Design Make 159.8 0 0 60.0% Does NOT work 163 163 30.0% Decision Low 0 152.6 0.12 40.0% Works 140 140 TRUE Current Design Buy 152.6 0 0.18 60.0% Does NOT work 161 161 Demand Info Demand 0.2 181.22 40.0% Works 180 180 TRUE Current Design Make 0 186 0.3 60.0% Does NOT work 190 190 50.0% Decision Medium 0 186 0 40.0% Works 175 175 FALSE Current Design Buy 190.75 0 0 60.0% Does NOT work 201.25 201 40.0% 0.08 Works 205 205 TRUE Current Design Make 212.2 0 0.12 60.0% Does NOT work 217 217 20.0% Decision High 0 212.2 0 40.0% Works 210 210 FALSE Current Design Buy 228.9 0 0 60.0% Does NOT work 242 241.5 Figure 11.10: Make-Buy EVPI on Demand Net Improvement 183.38-181.22 = $2.16M Demand uncertainty resolved before decision

  39. Figure 11.11: Make-Buy Decision EVPI on Feasibility & Demand CombinedNet Improvement183.38-180.22 = $3.16MLess than the SUM of $2.16 (Demand EVPI) + $2.40 (Feasibility EVPI) Next slide: Schematic Trees

  40. Original Make or Buy Schematic Trees: EVPI EVPI Demand = $2.4 M Design Demand Make or Buy EVPI Design = $2.16M Demand Make or Buy Design Design Make or Buy Demand EVPI Combined: Design & Demand =$3.16M Make or Buy Demand Design

  41. Imperfect Information  Conditional Decision/ Probabilities P (High | Positive) Invest P(Positive) • Downstream values and/or probabilities are affected by an upstream random event • Decision made AFTER resolution of random event • Optimal decision path differs depending upon the outcome of a random event

  42. Expected Value of Imperfect InformationImperfect info partial resolution of uncertaintyTest or Sample Information • Few tests, experiments or surveys are perfect. • EVPI is an upper bound on the value of imperfect information. • EVII – without well documented test reliability: • Conditional probabilities based on judgment • EVII with Bayes Rule is used primarily in environments with extensive data on the reliability of tests – both false positives and false negatives. • Oil industry – Seismographic data. Test wells • Medical Applications • Weather forecasts

  43. EVII – without well documented test reliability • Conditional probabilities based on judgment • Expert understands the uncertain relationship between test data (performance, throughput, etc.) or market surveys and subsequent outcome. • Can the expert provide a probabilistic range of outcomes that have accompanied similar test results? • Understand concept of conditional probability – experience with both possible outcomes. • Need stable process environment – A priori probabilities are always in a narrow range, for example, of 0.40 to 0.60. • Not used to forecast rare events • Problem – people have invalid intuition. Cannot factor in “a priori” estimates that are updated with imperfect information.

  44. Boss Controls: Focus Groups & Imperfect Information based on Experience Boss Controls (BC) is gearing up to manufacture an option to be made available on 1 million new cars world-wide. Initial estimates are that the take rate for the option could be as low as 30% or as high as 50%. Assume for simplicity sake, these two take rates are equally likely. Experience with focus groups indicates that for options such as the one BC is considering, the results will either be Enthusiastic (E) or Good (G). In the past if the focus groups were Enthusiastic, the take rate ended up being at the HIGH end 70% time. However, if the focus groups’ reactions were just good, then 80% of the time the take rate was at the LOW end. Focus groups have an optimistic bias and tend to be enthusiastic 80% of the time.

  45. EVII & Decision Trees - Experience • Add an uncertain node at the front of tree to represent uncertain outcome of focus group • Insert the probabilities that reflect the likelihood of different responses: Here P(E) = .8 and P(G) = .2 • Probability of outcomes (Take rates) are now “Conditional” probabilities based on past experience (or Bayes Rule) • Insert the “conditional” probabilities into tree and calculate expected value.

  46. Figure 11.14: Decision tree of EVII for BC automation investment Expert estimates conditional probabilities Conditional Probabilities EVII = 6.436 – 6.320 = 0.116 Less than one third of EVPI was $400,000

  47. Conditional Probabilities Consistent with Original Estimates • A Priori Probability that Take Rate is 30% - Use Partition Formula P(A) = P(A|B)P(B) + P(A|B)P(B) • P(T=30%) = P(T=30% | G) P(G) + P(T=30% | E) P(E) • P(T=30%) = (3/4)(.4) + (1/3) (.6) = .5 “original estimate” • P(T=50%) = P(T=50% | G) P(G) + P(T=50% | E) P(E) • P(T=50%) = (1/4)(.4) + (2/3) (.6) = .5 “original estimate”

  48. Boss Control: Conditional Decision • If focus group’s reaction is ENTHUSIASTIC then HIGH investment in automation • If focus group’s reaction is GOOD then Low investment in automation

  49. INTUITION?Bayes’ Rule & Reliable Test • Rare Disease – How Rare: 1 in 1,000 • Probability of positive reading for a person with the disease – test is very reliable • P(Pos.| Disease) = P(P|D) = .99 • Probability of negative reading for a person without the disease – 4% false positives • P(Neg. | No Disease) = P(N|Dc) = .96 • Key Question: P(Disease | Pos) = P(D|P) = ?? • Let Dc = D complement, or D , or No disease

  50. Bayes’ Rule & Reliable Test - Results • Bayes’ Rule (General Formula): • with Bc = B complement or NOT B • Denominator uses partitioning (all ways that A can occur) to determine P(A) • Bayes’ Rule (Reliable Test): (Pos = Positive test result) • Intuitive  1000 tested yields 40 false positives (4% error rate) and 1 true positive

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