How to customize photo cover and dividers

Chasing our Tails With our Risk Models 2017 Willis Towers Watson. All rights reserved. Fat Tails Many risks taken by insurers have Fat Tails 2017 Willis Towers Watson. All rights reserved. 2 Fat Tails So Why is that a Problem? 1. 2. 3. 4. 5. We model risks We have no data to fit to tails So we extrapolate And we validate our models by validating our extrapolation process We also explain our models with a process description 6.

That leaves non-modelers in the dust 7. Which may be a problem 2017 Willis Towers Watson. All rights reserved. 3 Todays Talk Chasing our Tails with Risk Models How different people make decisions How we might bridge the gap between modelers and non-modelers regarding Fat Tails Suggest using a new/old metric Coefficient of Risk (COR)

Provide a variety of examples of COR values and use 2017 Willis Towers Watson. All rights reserved. 4 Decision Making Models of the World Natural Decision Making From the Gut Newtonian Logical Statistical Future as Multiverse Systems Analysis Complex Independencies 2017 Willis Towers Watson. All rights reserved. 5 Natural Decision Making (NDM) Gut Pragmatic / Reactive

Trial and Error Heuristics and Biases Behavioral Economics 2017 Willis Towers Watson. All rights reserved. 6 Natural Decision Making Heuristics and Gut Reactions Advantages Disadvantages Fast and Frugal (Gigerenzer)

The more you trust your gut the better your intuition gets Natural process of developing Heuristics Decision making requires emotion 2017 Willis Towers Watson. All rights reserved. Hard to distinguish between luck and skill Hard to know Humans tend to make systematic and predictable mistakes Luck vs. Skill

Trust your Gut Our brains automatically sort through thousands of factors and identify just a few that are actually needed to make a good decision. Biases When your gut doesnt have a clue Tend to like Out of the money puts 7 My Favorite Biases Anchoring Availability

heuristic Confirmation bias Endowment effect Framing effect Gambler's fallacy Hindsight bias Illusion of control Overconfidence effect Status quo bias Survivorship bias Ostrich Effect 2017 Willis Towers Watson. All rights reserved.

8 Actuaries Guts While early actuarial work usually didnt fall under NDM Actuarial assumptions almost universally incorporated what came to be called Provisions for Adverse Deviation For the longest time, PADs were totally from the actuarys gut But only very experienced actuaries had guts Eventually, Australians replaced the gut with the 75%tile 2017 Willis Towers Watson. All rights reserved. 9 Newtonian Logical Deterministic World Maximum Likely Scenario Cause effect Risk Reward Single Frequency/Severity view of risk

2017 Willis Towers Watson. All rights reserved. 10 Newtonian Scientific Cause and Effect Advantages Disadvantages Scientific Method Can be applied to complex problems

Provides a clear path to proceed with decision making Eliminates guesswork and subjectivity Reduces errors Usually by breaking a big problem up into smaller more tractable problems Decision making without emotion 2017 Willis Towers Watson. All rights reserved. Requires high analytical competence To break a problem up into the right pieces that can be solved Can be slow and painstaking

Need to examine many parts to solve a problem Only deals with one possible outcome at a time The whole may be different from the sum of the parts! Decision making without emotion 11 Rational Decision Making 1. Study the problem 2. Develop a list of possible solutions

3. Evaluate the effectiveness of each possible solution 4. Choose the best alternative 2017 Willis Towers Watson. All rights reserved. 12 Expert Problem Solving Uses Natural Decision Making Klein, Naturalistic Decision Making, 2008 2017 Willis Towers Watson. All rights reserved. 13 Statistical The Future as Multiverse Risk and Uncertainty Risk as probability distribution Expected value Rational Expectations Value at Risk

Statistical Inference ??? 2017 Willis Towers Watson. All rights reserved. 14 Statistical Probability Distributions Advantages Disadvantages Takes many possibilities into account all at once Our computer models sort through

thousands of factors and determine the full range of outcomes. Fit models to experience or modify to reflect trends Complexity Lack of Data Experience varies so model varies Hard to calibrate Biases apply to how we react to areas with low data Hard to know

2017 Willis Towers Watson. All rights reserved. Biases apply to model assumptions as well as to NDM May scare away some users May cause over reliance by others When your model doesnt have a clue 15 We consider every possibility And somehow we know the likelihood of every possibility Two broad approaches to that The future is assumed to be some minor variation on the past Observed frequency = Likelihood May apply expert judgment to make minor adjustments to that The collective wisdom of the market is correct about the future Likelihood is inferred from prices of various securities Any variation from that infers that arbitrage opportunities exist 2017 Willis Towers Watson. All rights reserved.

16 Expected Values were the focus Actuarial work focused on reviewing statistical data to determine best estimate Which may or may not be close to Expected Value Actuarial Cost came to be the term for the present value without PADs Even when actuaries worked with full loss distributions Tended to focus on expected values for a part of the loss distribution 2017 Willis Towers Watson. All rights reserved. 17 Statistical inference Used extensively for medical decision making

Used by consumer product companies But rarely used by insurers or actuaries 2017 Willis Towers Watson. All rights reserved. 18 Advent of Risk Management and Enterprise Risk Modeling Focus on Risk contingent future events Quantifying risk usually in terms of an amount of loss for a particular frequency (VaR) or average loss for a range of frequencies (CTE) High focus on Extreme Values 99.5% Everyone acts as if they can know what a 99.5% loss is

The statistical models that were developed for other purposes (Pricing, Hedging, Reinsurance) are adapted to create 99.5% values We all then try very, very hard not to think of what Statistical inference would say about our results! 2017 Willis Towers Watson. All rights reserved. 19 Systems Analysis Interdependencies Homeostasis and adaptability Positive and negative feedback loops Systems capacity Complex adaptive systems Fragility 2017 Willis Towers Watson. All rights reserved. 20 Systems Analysis Interdependencies Advantages

Disadvantages Systems Model more closely resembles real world That can be shared with users Systems Models can reveal things that can happen in the tails

Even if they have never happened before 2017 Willis Towers Watson. All rights reserved. Humans will tend to bring their biases into systems analysis Complicated Builds a story Everything is not extrapolation Many systems cannot be understood properly by taking them apart Biases While you do not take system

apart you need to identify pieces, their interaction and how/when they break May scare away some users May cause over reliance by others Hard to know When your systems model is wrong 21 Equity Market Risk In many seasons, the equity performs the expected random walk with some noticeable long term alpha On occasion, the markets break down Positive feedback loops cause market prices to rise far ahead of fundamentals (Internet Boom in late 1990s) Negative feedback loops cause market prices to fall so far that they invalidate market valuations before the fall (2001, 2008)

These excesses on the upside and downside suggest that Gaussian model of stock market that is associated with Random Walk paradigm is insufficient Stock Market has Fat Tails that are due to systems effects 2017 Willis Towers Watson. All rights reserved. 22 Credit Market Risk Minsky Financial Instability Hypothesis Hedge Finance Borrowing levels are supportable by cash flows. Businesses can afford to repay both interest and principle from cash flows. Speculative Finance Borrowing is not fully supportable by cash flows. Businesses can afford to repay interest from cash flows. Expect to refinance principle. Ponzi Finance Borrowing is totally unsupportable from cash flows. Businesses cannot afford to repay interest or principle from cash flows. Expect to increase borrowing to fund future interest payments. 1998 Asian Credit Crunch 12 economies impacted, sharp contraction of credit

availability 2001 US Credit event default losses were twice the level of other post WWII credit events 2008 Global Financial Crisis Minsky cycle hits US/UK housing markets 2017 Willis Towers Watson. All rights reserved. 23 Natural Catastrophes Earthquakes, Hurricanes, Typhoons, Tsunamis, Floods are all the end stage of a system that has exceeded its capacity When capacity is exceeded, things are thrown into a different system where great deals of energy are released, rather than being dampened within the system. 2017 Willis Towers Watson. All rights reserved. 24 Why do big complex systems fail A Bias of many systems analysts

Some believe that complex systems are inherently fragile The bigger systems get the more complex they get And the more fragile they get Natural systems usually develop natural control systems Dynamic balance of predators and prey for example Very complex natural systems can become fragile when humans eliminate major parts of the natural control systems Big complicated human systems are sometimes fragile Humans mash together smaller systems that are minimally controlled and fail to realize that the new larger, more complex systems needs more controls Ashbys Law the Law of Requisite Variety 2017 Willis Towers Watson. All rights reserved. 25 Fat Tails What do they mean to each type of thinker?

Natural Decision Making From the Gut Newtonian Logical Statistical Future as Multiverse Systems Analysis Complex Independencies 2017 Willis Towers Watson. All rights reserved. 26 Fat Tails In Risk Models 2017 Willis Towers Watson. All rights reserved. Fat Tails Definition:

A Fat Tail means that high severity/low probability events are more severe/ more likely than would be predicted by a Gaussian distribution Why is this an issue? Many risk models had assumed Gaussian distribution of one or all risk drivers Many risks actually have Fat Tails Solution: Use Fat Tailed Model 2017 Willis Towers Watson. All rights reserved. 28 Fat Tails So are we done with this talk already?

Perhaps not. Questions: How Fat are the Tails of your Model? Why should anyone believe what your model says about the tail values? Are they Fat enough? Or Too Fat? How do they compare with the Tails of other Models? How Fat should the Tails be? Who should be involved in deciding? Can you explain your answer to any of the above questions to anyone who is not a modeler? 2017 Willis Towers Watson. All rights reserved. 29 Four Models How do they each see the world? Natural Decision Making From the Gut Newtonian Logical Statistical Future as Multiverse

Systems Analysis Complex Independencies 2017 Willis Towers Watson. All rights reserved. 30 Fat Tail Incidents 2017 Willis Towers Watson. All rights reserved. 31 Coefficient of Riskiness Use 1 in 1000 loss as a proxy for the tail of the distribution of gains and losses With CLT assumed Extreme Loss is quick and easy to determine Tail is 3.09 standard deviations worse than the mean For simplicity, round to 3

Call that the Coefficient of Riskiness (CoR) .9 99 = 2017 Willis Towers Watson. All rights reserved. 32 Chebyshevs Inequality CoR is the k factor in Chebyshevs Inequality 1 Pr (| | ) 2 k Percentile 10.00 99.00% 14.14

99.50% 15.81 99.60% 22.36 99.80% 31.62 99.90% 2017 Willis Towers Watson. All rights reserved. 33 Preliminary Tests of COR The following slides show some preliminary tests of the COR calculation applied to hundreds and thousands of insurance risk models that were developed by Willis Re actuaries for our clients These tests show that in many cases the insurance blocks have much higher

CORs than 3.09 2017 Willis Towers Watson. All rights reserved. 34 Test of Coefficient of Riskiness COR was calculated for 3400 insurance models that were created by Willis Re actuaries over 2011-2014 This is a plot of all of those 3400 mixed insurance risk models. Next step will be to stratify those 3400 models by type. For instance, we note that the model with the highest COR is a Homeowner only model for a single state company in a Nat Cat zone.

2017 Willis Towers Watson. All rights reserved. Note: COR 4 indicates value is 3 4, etc 35 Stratification of Models This plot looks at 400 models of Property Risk Natural Catastrophe (Windstorm &/or Earthquake) losses 2017 Willis Towers Watson. All rights reserved. 36 Insurance Models with and without cat risk 2017 Willis Towers Watson. All rights reserved. 37 COR over time Willis Re Insurance Models 2017 Willis Towers Watson. All rights reserved.

38 COR Values for ESG output Fat Tails 12/31/2016 Mean Sigma CoV 0.001 COR.001 Rate of Price Inflation 1.25% 0.76% 0.609 0.07 7.59 US Commodities

2.46% 9.47% 3.845 -0.604 6.64 US Mortgages_ABS_CMBS 2.71% 5.40% 1.994 -0.24 4.95 US Hedge_Fund 3.44% 6.53%

1.899 -0.257 4.46 US Property_Equity 4.91% 14.18% 2.89 -0.567 4.34 US Rate of Medical Inflation 3.57% 1.61% 0.451 0.10 4.07

HY_Global 4.18% 10.20% 2.438 -0.364 3.98 US Unemployment Rate 5.15% 0.89% 0.172 0.09 3.91 JPM_EM_Global 6.77%

10.79% 1.594 -0.326 3.65 Global_Equity 6.37% 17.72% 2.78 -0.559 3.51 US Infrastructure 5.88% 16.49% 2.803 -0.507

3.43 2017 Willis Towers Watson. All rights reserved. 39 COR Values Not Fat Tails 12/31/2016 Mean Sigma CoV 0.001 COR.001 US_HY 5.79% 9.96% 1.721

-0.279 3.38 Private_Equity, European 6.21% 22.15% 3.567 -0.683 3.36 Commodities_Gold 2.11% 13.06% 6.184 -0.415 3.34 Rate of Wage Inflation

1.82% 1.14% 0.626 0.05 3.21 GDP 2.98% 2.38% 0.799 -0.05 3.20 US Equity_Total_Return 5.80% 18.00%

3.10 -0.508 3.14 Equities_GlobalSmallCap 6.49% 20.60% 3.176 -0.580 3.13 US HighYield_BB 6.95% 20.72% 2.98 -0.555 3.01

Change in Property Value Total Return 4.21% 9.58% 2.272 -0.23 2.85 UK Structured Credit 2.89% 6.71% 2.322 -0.158 2.79 Emerging Market Equity 7.86%

25.25% 3.213 -0.619 2.76 Emerging Equities_Small Cap 9.12% 26.22% 2.876 -0.633 2.76 US Real Assets Timberland 10.60% 11.66% 1.1 -0.065

1.47 US Real Assets Agricultural Land 10.53% 8.21% 0.78 -0.003 1.32 2017 Willis Towers Watson. All rights reserved. 40 US Equities Mean Sigma CV 1 in 1000

CoR Equity Total Return Jump Diffusion 5.80% 18.00% 310% 50.81% 3.14 DJIA 7.53% 15.71% 209% 48.03% 3.54 S&P 500

7.96% 16.02% 201% 47.96% 3.49 Equity Returns Regime Switching 10.68% 19.92% 187% 59.25% 3.51 2017 Willis Towers Watson. All rights reserved. 41 Distributions 2017 Willis Towers Watson. All rights reserved.

42 What about 99.5%tile? All of this discussion applies equally to 99.5%tile 2017 Willis Towers Watson. All rights reserved. 43 What about 99.5%tile? All of this discussion applies equally to 99.5%tile 2017 Willis Towers Watson. All rights reserved. 44 Relationship between 99.9 and 99.5%tile 2017 Willis Towers Watson. All rights reserved. 45

Historical Coefficient of Riskiness (HCOR) COR is, of course, always an extrapolation HCOR however can be calculated in any cases where there is a good sized set of observations Define HCOR as the historical worst observation less the sample mean divided by the standard deviation Where the historical worst observation is excluded from the calculation of the sample mean and standard deviation 2017 Willis Towers Watson. All rights reserved. 46 Actual Insurance Company HCOR20 2017 Willis Towers Watson. All rights reserved. 47 Risk Tic Tac Toe (From insurers point of view) Volatility

(CoV) High Reinsured (Type A) Trouble X Medium Not reinsured Reinsured (Type B) Trouble Low Not insured Not reinsured Reinsured

(Type C) Low Medium High Fat Tail (CoR) 2017 Willis Towers Watson. All rights reserved. 48 Insurance Models CV vs. COR plot 2017 Willis Towers Watson. All rights reserved. 49 Empty Region X 2017 Willis Towers Watson. All rights reserved. 50 Pareto Distribution

Some risks are modeled with Pareto Distributions Really fat tails Pareto Distributions can have infinite variances Alpha 1 2 And can have infinite Mean Alpha <1 Which makes calculating CoR impossible for those models 2017 Willis Towers Watson. All rights reserved. 51 Wild and Extreme Randomness

Mandelbrot describes seven states of randomness Proper mild randomness (the normal distribution) Borderline mild randomness: (the exponential distribution with =1) Slow randomness with finite and delocalized moments Slow randomness with finite and localized moments (such as the lognormal distribution) Pre-wild randomness (Pareto distribution with =2 - 3) Wild randomness: infinite second moment (Variance is infinite. Pareto distribution with =1 - 2) Extreme randomness: (Mean is infinite. Pareto distribution with <=1) B. Mandelbrot, Fractals and Scaling in Finance, Springer,1997. 2017 Willis Towers Watson. All rights reserved. 52 Next Steps

Starting Asking about the COR of Risk Models Start looking at HCOR Then we can start to develop: Language for discussing model tail risk Processes for using it to validate models Procedure for estimating risk capital using companys own risk volatilities 2017 Willis Towers Watson. All rights reserved. 53 Coefficient of Risk How will our Four Thinkers use COR? Natural Decision Making From the Gut Newtonian Logical Statistical Future as Multiverse Systems Analysis Complex Independencies

2017 Willis Towers Watson. All rights reserved. 54 Dave Ingram Willis Towers Watson D +1 212 915 8039 E [email protected] 2017 Willis Towers Watson. All rights reserved. 55 Thank you! 2017 Willis Towers Watson. All rights reserved. Willis Re disclaimers This analysis has been prepared by Willis Limited and/or Willis Re Inc. and/or the Willis Towers Watson entity with whom you are dealing (Willis Towers Watson is defined as Willis Limited, Willis Re Inc., and each of their respective parent companies, sister companies, subsidiaries, affiliates, Willis Towers Watson PLC, and all member companies thereof) on condition that it shall be treated as strictly confidential and shall not be communicated in whole, in part, or in summary to any third party without written consent from Willis Towers Watson.

Willis Towers Watson has relied upon data from public and/or other sources when preparing this analysis. No attempt has been made to verify independently the accuracy of this data. Willis Towers Watson does not represent or otherwise guarantee the accuracy or completeness of such data nor assume responsibility for the result of any error or omission in the data or other materials gathered from any source in the preparation of this analysis. Willis Towers Watson shall have no liability in connection with any results, including, without limitation, those arising from based upon or in connection with errors, omissions, inaccuracies, or inadequacies associated with the data or arising from, based upon or in connection with any methodologies used or applied by Willis Towers Watson in producing this analysis or any results contained herein. Willis Towers Watson expressly disclaims any and all liability arising from, based upon or in connection with this analysis. Willis Towers Watson assumes no duty in contract, tort or otherwise to any party arising from, based upon or in connection with this analysis, and no party should expect Willis Towers Watson to owe it any such duty. There are many uncertainties inherent in this analysis including, but not limited to, issues such as limitations in the available data, reliance on client data and outside data sources, the underlying volatility of loss and other random processes, uncertainties that characterize the application of professional judgment in estimates and assumptions, etc. Ultimate losses, liabilities and claims depend upon future contingent events, including but not limited to unanticipated changes in inflation, laws, and regulations. As a result of these uncertainties, the actual outcomes could vary significantly from Willis Towers Watsons estimates in either direction. Willis Towers Watson makes no representation about and does not guarantee the outcome, results, success, or profitability of any insurance or reinsurance program or venture, whether or not the analyses or conclusions contained herein apply to such program or venture. Willis Towers Watson does not recommend making decisions based solely on the information contained in this analysis. Rather, this analysis should be viewed as a supplement to other information, including specific business practice, claims experience, and financial situation. Independent professional advisors should be consulted with respect to the issues and conclusions presented herein and their possible application. Willis Towers Watson makes no representation or warranty as to the accuracy or completeness of this document and its contents. This analysis is not intended to be a complete actuarial communication, and as such is not intended to be relied upon. A complete communication can be provided upon request. Willis Towers Watson actuaries are available to answer questions about this analysis.

Willis Towers Watson does not provide legal, accounting, or tax advice. This analysis does not constitute, is not intended to provide, and should not be construed as such advice. Qualified advisers should be consulted in these areas. Willis Towers Watson makes no representation, does not guarantee and assumes no liability for the accuracy or completeness of, or any results obtained by application of, this analysis and conclusions provided herein. Where data is supplied by way of CD or other electronic format, Willis Towers Watson accepts no liability for any loss or damage caused to the Recipient directly or indirectly through use of any such CD or other electronic format, even where caused by negligence. Without limitation, Willis Towers Watson shall not be liable for: loss or corruption of data, damage to any computer or communications system, indirect or consequential losses. The Recipient should take proper precautions to prevent loss or damage including the use of a virus checker. This limitation of liability does not apply to losses or damage caused by death, personal injury, dishonesty or any other liability which cannot be excluded by law. Willis Towers Watson does not guarantee any specific financial result or outcome, level of profitability, valuation, or rating agency outcome with respect to A.M. Best or any other agency. Willis Towers Watson specifically disclaims any and all liability for any and all damages of any amount or any type, including without limitation, lost profits, unrealized profits, compensatory damages based on any legal theory, punitive, multiple or statutory damages or fines of any type, based upon, arising from, in connection with or in any manner related to the services provided hereunder.

Acceptance of this document shall be deemed agreement to the above. This analysis is not intended to be a complete Financial Analysis communication. A complete communication can be provided upon request. Willis Towers Watson analysts are available to answer questions about this analysis. 2017 Willis Towers Watson. All rights reserved. 57

Recently Viewed Presentations

  • How to be Uncertain (and how to be less uncertain)

    How to be Uncertain (and how to be less uncertain)

    Tony O'Hagan. Outline. Language. Chinese whispers. The language of statistics. Probability 'The' or 'Your' ...
  • Marek Perkowski INTRODUCTION TO MODAL AND EPISTEMIC LOGIC

    Marek Perkowski INTRODUCTION TO MODAL AND EPISTEMIC LOGIC

    Example of Classical logic Syllogism. All hedgehogs are spiny. Matilda. is a . hedgehog. ∴ Matilda is spiny. You do not have to know the meanings of "hedgehog" or "spiny" or know anything about Matilda in order to know that...
  • The Risks of Tipping the Scales: Striking a Balance Between ...

    The Risks of Tipping the Scales: Striking a Balance Between ...

    Physical Resiliency. Push to the point of injury and beyond or quit when you feel tired. Emotional Resiliency. Take normal stressors in stride? or. Panic, exhaustion, and isolation or unable to tolerate minimal failures and negative feedback ... The Risks...
  • Why Do We - - - Try to Restore the Church? - Searcher&#x27;s Class

    Why Do We - - - Try to Restore the Church? - Searcher's Class

    What is the restoration movement seeking to do? Introduction. This is not a history lesson about the Restoration Movement. Our recent history (last 200+ years) is connected with this movement. Is this movement Biblical and valid? Focus on the Plea...
  • School Counseling, Plans of Study, and Individual Learning ...

    School Counseling, Plans of Study, and Individual Learning ...

    Wisconsin Comprehensive School Counseling Model: Delivery Definition of Individual Planning Assist students in planning, monitoring, and managing their academic, personal/social, and career development Purpose of Individual Planning Help students collect information for, develop, and use an Individual Learning Plan (ILP)...
  • Feature Writing - Professor Leach

    Feature Writing - Professor Leach

    Types of Feature Stories One thing to remember is Feature stories, while journalistic, are first and foremost stories With a Beginning Introduction Middle Rising action, climax, falling action End Conclusion There are two genres of feature stories News Feature (Less...
  • M Week: Lent Calendar T W Th F

    M Week: Lent Calendar T W Th F

    As part of the give it up challenge, this year you can create a display using the Lent poster. Write what you're giving up, or a message to Rabiul, or a prayer on the fish template and add to the...
  • Schwab PowerPoint template

    Schwab PowerPoint template

    The "Careers in the Independent Advisor Industry" presentation was developed for use in recruiting and outreach efforts. The customizable presentation will help tell the story of what an independent Registered Investment Advisor is, and why the work they do is...