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Monte Carlo Analysis for Policy Making: Managing Uncertainty in Financial Modeling

Learn how Monte Carlo Analysis combines distributions and impacts policy setting, its history, and why it's essential for managing risk. Explore examples, analytical results, software use, and sensitivity analysis in financial modeling. Understand how correlated distributions and generating valid distributions affect policy implementation.

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Monte Carlo Analysis for Policy Making: Managing Uncertainty in Financial Modeling

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  1. Monte Carlo Analysis A Technique for Combining Distributions

  2. Purpose of lecture • Introduce Monte Carlo Analysis as a tool for managing uncertainty • To demonstrate how it can be used in the policy setting • To discuss its uses and shortcomings, and how they are relevant to policy making processes. FIN 591: Financial Modeling, Spring 2004

  3. What is Monte Carlo Analysis? • It is a tool for combining distributions, and thereby propagating more than just summary statistics • It uses a random number generation, rather than analytic calculations • It is increasingly popular due to high speed personal computers. FIN 591: Financial Modeling, Spring 2004

  4. Background/History • “Monte Carlo” from the gambling town of the same name (no surprise) • Limited use because time consuming • Much more common since late 80’s • Too easy now? FIN 591: Financial Modeling, Spring 2004

  5. Why do Monte Carlo Analysis? • Combining distributions • With more than two distributions, solving analytically is very difficult • Simple calculations lose information • Mean  mean = mean • 95% %ile  95%ile  95%ile! • Gets “worse” with 3 or more distributions. FIN 591: Financial Modeling, Spring 2004

  6. Monte Carlo Analysis • Takes an equation • Example: Risk = probability  consequence • Draws randomly from defined distributions • Multiplies, stores • Repeats this over and over and over… • Results displayed as a new, combined distribution. FIN 591: Financial Modeling, Spring 2004

  7. Simple Example • Skin cream additive is an irritant • Many samples of cream provide information on concentration: • mean 0.02 mg chemical/application • standard dev. 0.005 mg chemical/application • Two tests show probability of irritation given application • low p(effect per mg exposure)=0.05 / mg • high p(effect per mg exposure)=0.10 / mg. FIN 591: Financial Modeling, Spring 2004

  8. Skin cream additive data FIN 591: Financial Modeling, Spring 2004

  9. Analytical Results • Risk = Exposure  potency • Mean risk = 0.02 mg  0.075 / mg = 0.0015 or 0.15% probability that someone using the cream will be irritated. FIN 591: Financial Modeling, Spring 2004

  10. Analytical results • “Conservative estimate” • Use upper 95th %ile Risk = 0.03 mg  0.0975 / mg = 0.0029 or p(irritation|application) = 0.29%. FIN 591: Financial Modeling, Spring 2004

  11. Monte Carlo: Visual example Exposure = normal (mean 0.02 mg, s.d. = 0.005 mg) Potency = uniform (range 0.05 / mg to 0.10 / mg) FIN 591: Financial Modeling, Spring 2004

  12. Random Draw One p(irritate) = 0.0165 mg × 0.063 / mg = 0.0010 FIN 591: Financial Modeling, Spring 2004

  13. Random Draw Two p(irritate) = 0.0175 mg × 0.089 / mg = 0.0016 Summary: {0.0010, 0.0016} FIN 591: Financial Modeling, Spring 2004

  14. Random Draw Three p(irritate) = 0.152 mg × 0.057 / mg = 0.0087 Summary: {0.0010, 0.0016, 0.00087} FIN 591: Financial Modeling, Spring 2004

  15. Random Draw Four p(irritate) = 0.0238 mg × 0.085 / mg = 0.0020 Summary: {0.0010, 0.0016, 0.00087, 0.0020} FIN 591: Financial Modeling, Spring 2004

  16. After Ten Random Draws Summary {0.0010, 0.0016, 0.00087, 0.0020, 0.0011, 0.0018, 0.0024, 0.0016, 0.0015, 0.00062} Mean = 0.0014 Standard deviation = (0.00055). FIN 591: Financial Modeling, Spring 2004

  17. Using software • Could write this program using a random number generator • But, several software packages exist • I use @Risk • User friendly • Customizable • RNG good up to about 10,000 iterations. FIN 591: Financial Modeling, Spring 2004

  18. 100 iterations (less than two seconds) • Monte Carlo results • Mean 0.00161 • Standard Deviation 0.00048 • Compare to analytical results • Mean 0.0015 • standard deviation n/a. FIN 591: Financial Modeling, Spring 2004

  19. Summary chart - 100 trials FIN 591: Financial Modeling, Spring 2004

  20. Summary - 10,000 Trials • Monte Carlo results • Mean 0.00150 • Standard Deviation 0.000472 • Compare to analytical results • Mean 0.00150 • standard deviation n/a. FIN 591: Financial Modeling, Spring 2004

  21. Summary chart - 10,000 trials FIN 591: Financial Modeling, Spring 2004

  22. Issues: Sensitivity Analysis • Which input distributions have the greatest effect on the eventual distribution • Which parameters can both be influenced by policy and reduce risks • When better data can be most valuable (information isn’t free…nor even cheap). FIN 591: Financial Modeling, Spring 2004

  23. Issues: Correlation • Two distributions are correlated when a change in one is associated with a change in another • Example: People who eat lots of peas may eat less broccoli (or may eat more…) • Usually doesn’t have much effect unless significant correlation (||>0.75). FIN 591: Financial Modeling, Spring 2004

  24. Generating Distributions • Invalid distributions create invalid results, which leads to inappropriate policies • Two options • Empirical • Theoretical. FIN 591: Financial Modeling, Spring 2004

  25. Empirical Distributions • Most appropriate when developed for the issue at hand. • Example: local fish consumption • Survey individuals or otherwise estimate • Data from individuals elsewhere may be very misleading • A number of very large data sets have been developed and published. FIN 591: Financial Modeling, Spring 2004

  26. Empirical Distributions • Challenge: when there’s very little data • Example of two data points • Uniform distribution? • Triangular distribution? • Not a hypothetical issue…is an ongoing debate in the literature • Key is to state clearly your assumptions • Better yet…do it both ways! FIN 591: Financial Modeling, Spring 2004

  27. Which Distribution? FIN 591: Financial Modeling, Spring 2004

  28. Random number generation • Shouldn’t be an issue…@Risk is good to at least 10,000 iterations • 10,000 iterations is typically enough, even with many input distributions. FIN 591: Financial Modeling, Spring 2004

  29. Theoretical Distributions • Appropriate when there’s some mechanistic or probabilistic basis • Example: small sample (say 50 test animals) establishes a binomial distribution • Lognormal distributions show up often in nature, particular economics/business. FIN 591: Financial Modeling, Spring 2004

  30. Some Caveats • Beware believing that you’ve really “understood” uncertainty • Central tendencies are NOT “real risk” • Distributions are only PART of uncertainty • Beware misapplication • Ignorance at best • Fraudulent at worst. FIN 591: Financial Modeling, Spring 2004

  31. Example (after Finkel 1995) Alar “versus” aflatoxin Exposure has two elements Juice consumption Alar/UDMH residue Peanut butter consumption aflatoxin residue Potency has one element aflatoxin potency UDMH potency Risk = (consumption  residue  potency)/body weight FIN 591: Financial Modeling, Spring 2004

  32. Inputs for Alar & aflatoxin FIN 591: Financial Modeling, Spring 2004

  33. Alar and Aflatoxin Point Estimates • Aflatoxin estimates: • Mean = 0.028 • Alar (UDMH) estimates: • Mean = 0.046. FIN 591: Financial Modeling, Spring 2004

  34. Alar and Aflatoxin Monte Carlo • 10,000 runs • Generate distributions • (don’t allow 0) • Don’t expect correlation. FIN 591: Financial Modeling, Spring 2004

  35. Aflatoxin and Alar Monte Carlo Results (Point Values) FIN 591: Financial Modeling, Spring 2004

  36. FIN 591: Financial Modeling, Spring 2004

  37. FIN 591: Financial Modeling, Spring 2004

  38. FIN 591: Financial Modeling, Spring 2004

  39. FIN 591: Financial Modeling, Spring 2004

  40. End FIN 591: Financial Modeling, Spring 2004

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