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# Risky Models

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Risk models are a normal part of decision making.

This presentation suggests that most people are poor at judging probabilities, and that risk and loss aversion are strong behavioral modifiers which affect decisions.

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### Risky Models

1. 1. Risky Models Palisade EMEA 2012 Risk Conference London1 © 2012 Captum Capital Limited
2. 2. Modelling RiskEstimate probability of future eventsProbabilities based on: Statistical analysis of historic data Expert opinion Wisdom of crowds Subjective best guessRisk models used to make decisions2
3. 3. Subjective Risk PerceptionDecision makers: Have a poor appreciation of probabilities Are risk averse Are loss averse3
4. 4. US Masters 2012 Sudden Death Play-off Final 10th Hole – Camilla Par 4 Augusta National4
5. 5. 10th Hole Playoff Louis Oosterhuizen (South Africa) Reached green in 3 shots 15 feet from pin Bubba Watson (United States) Reached green in 2 shots 8 feet from pin5
6. 6. Bubba Wins! Oosterhuizen – Bogey 5 Watson – Par 46
7. 7. Toss a coin... H T 0.5 + 0.5 = 17
8. 8. Risk Perceptions1. 2. 0.75 £300 P=1.0 £100 0.25 - £5003. 4. £500 £700 0.5 0.25 0.5 0.75 - £100 - £3008
9. 9. 650 Perceptions1. 2. £300 P=1.0 0.75 £100 0.25 14% 26% - £5003. £500 4. £700 0.5 0.25 0.5 0.75 - £300 - £100 35% 26%© Dr. Kelvin Stott9
10. 10. Loss Aversion Utility £100 Loss Profit Prospect Theory - £100 Kahneman & Tversky (1974)10
11. 11. Multiple Milestones11
12. 12. TAMIX Option Value12
13. 13. Tamix Option Cash FlowYear 0 1 2 3 4Cash Flow -1.00 0 -12.55 0 157.35P 1 0.5 0.5x0.9NPV -1.00 -10.00 100.00Cash Flow in £000sDiscount Rate R = 12% rNPV = -1 + 0.5 x -10 + 0.45 x 100= £39,000,00013
14. 14. @Risk Option Value14
15. 15. TAMIX Model Output15
16. 16. What does it mean? Probability of rNPV \$million) Happening -1.00 50% -6.00 5% 39.00 45%16
17. 17. Risk Impact Matrix Insignificant Minor Moderate Major Catastrophic 1 2 3 4 5Rare 1 1 2 3 4 5Unlikely 2 2 4 6 8 10Possible 3 3 6 9 12 15Likely 4 4 8 12 16 20Certain 5 5 10 15 20 2517
18. 18. NHS Risk AssuranceAll NHS Trusts are required to have a Risk Assurance FrameworkHow useful is it? Different people assign different risk probabilities & impacts Non-quantifiable risks18
19. 19. NHS Risk ExamplesRisk Risk Real Risk RatingService demand exceeds contractbudget 20 25Likely 4 Impact 5 [Finance Director]EWTD limits availability of juniordoctors 20 10Certain 5 Impact 4 [Medical Director]19
20. 20. The Monty Hall ProblemOriginally proposed by:Steve Selvin in theAmerican Statistician 1975 Named after: Monty Hall, host Let’s Make a Deal20
21. 21. The Game  Three doors; one hides a car, the others hide goats  You choose one of the 3 doors  The host opens a door you haven’t chosen to reveal a goat  Should you stick with your original choice – or swap?21
22. 22. Monty Hall @ Risk Model22
23. 23. The logic of the problem Stick Swap £ 0 0 £ 0 0 0 £ 0 0 £ 0 0 0 £ 0 0 £ 1:3 chance 2:3 chance to win to win23
24. 24. Decision Tree Solution Car Host Total Stay SwitchPlayerpicks Location opens PDoor 1 1/2 Door 1/6 Car Goat 2 Door 1 Door 1/2 1/6 Car Goat 3 1 Door Door 2 1/3 Goat Car 3 1 Door Door 3 1 /3 Goat Car 2 24
25. 25. A Controversial GameA newspaper column received several thousand complaints about this solutionExperiments show ~80% think there is no difference between staying or switchingEven after training in probability, ~70% still choose the wrong answer25
26. 26. St Petersburg paradox Presented the problem and its solution in Commentaries of the Imperial Academy of Science of Saint Petersburg (1738) The problem was invented by Daniels cousin Nicolas Bernoulli who first stated it in a letter to Pierre Raymond de Montmort of 9 September 1713 The paradox is a classic problem in Daniel Bernoulli probability and decision theory, based on a lottery game 1700 -178226
27. 27. The gameYou start with £1A coin is tossed: Heads – your stake is doubled Tails – game overKeep tossing the coin as long it comes up heads27
28. 28. Some plays Payout 1 T £1 2 H–H-T £4 3 H–H–H-T £8 4 H–H–H–H–H-T £3228
29. 29. What’s the problem?The Expected Value of the game is unlimited!29