1. © 2010 The Actuarial Profession  www.actuaries.org.uk Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52 * Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Value at Risk: Where did it all go wrong? Andrew D Smith Yorkshire Actuarial Society. 09 May 2012.

2. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only What is Value-at-Risk? Jorion (2007): “The worst loss over a target horizon Such that there is a low, pre-specified probability that the actual loss will be larger” Legislative references: Insurance Solvency II Directive: 1 © 2010 The Actuarial Profession  www.actuaries.org.uk The Solvency Capital Requirement... shall correspond to the Value-at- Risk of the basic own funds of an insurance or reinsurance undertaking subject to a confidence level of 99.5 % over a one-year period.

3. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Calculating VaR Using Percentiles 2 © 2010 The Actuarial Profession  www.actuaries.org.uk Basic Own Funds = Assets minus Technical Provisions t=0 “now” Opening own funds (t=0) mean own funds 0.5%-ile own funds VaR Own funds’ probability distribution in one year (ignoring shareholder dividends or capital raising) 0.5% probability (red region) Expected profit t=1 ”VaR horizon”

4. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Daily Value at Risk example: Barclays 3 © 2010 The Actuarial Profession  www.actuaries.org.uk Source: http://www.barclaysannualreports.com/

5. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Examples of Extreme Losses & Percentiles (calculations based on Normal distributions) 4 © 2010 The Actuarial Profession  www.actuaries.org.uk 05101520 Fortis AIG Number of Standard Deviations VaR 31/12/2007 Loss 2008 €17.6bn 99.97% $19.5bn 99.95% €28.0bn 99.9999976% $99.3bn 99.999999999999999999999999999999 99999999999999999999999999999974%

6. © 2010 The Actuarial Profession  www.actuaries.org.uk Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52 * Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Calculating VaR: A Worked Example 5 © 2010 The Actuarial Profession  www.actuaries.org.uk

7. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only VaR Calculations: Our Abstraction Our thought experiment 100 years of clean annual data Taken from a stationary process Data is historic company profits No evidence available besides 100 data points More realism Between 10 and 100 years of data, maybe high frequency Early data of questionable accuracy and relevance Data describes “risk drivers” (eg equity levels, interest rates, credit defaults, mortality assumptions etc) Profit is a complicated function of risk drivers. Relevant knowledge from related problems 6 © 2010 The Actuarial Profession  www.actuaries.org.uk

8. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Based on Excel Example Examine historic profit: annual and cumulative Method #1 (through the cycle) –Fit a distribution to observed profits (normal, Gumbel) –Check distribution fit Method #2 (pro-cyclical) –Regress Profit(t) against Profit(t-1) –Fit distribution of residual –Estimate percentile profit as regression formula + percentile residual Method #3 (conditional) –Examine situations leading to largest residuals –Estimate percentiles for Profit(t) conditional on Profit(t-1) 7 © 2010 The Actuarial Profession  www.actuaries.org.uk

9. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52 * Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Perfect knowledge: What if we knew the “true” model? 8 © 2010 The Actuarial Profession  www.actuaries.org.uk

10. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Longitudinal and Cross-Sectional Analysis Inside a Scenario File 9 © 2010 The Actuarial Profession  www.actuaries.org.uk Scenario # Time period History Same for each scenario Forecast Varies by Scenario Longitudinal Cross-sectional

11. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only How I Generated the Data Warning: this is an example of a “non-guessable” model –Unless you have huge volumes of data I do not claim your profits follow such a process! Let T be the end of the projection Use the backwards autoregressive (order 1) model: U, U 1, U 2 independent uniform(0,1), Excel Rand() function. Stationary distribution = Gumbel (proof next slide) 10 © 2010 The Actuarial Profession  www.actuaries.org.uk

12. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only The Maths Joint CDF of Profit(t-1) and Profit(t) Can read off –Stationary distribution (Gumbel), –Conditional distribution of Y given X (Wald) –Conditional distribution of X given Y (AR1 process on previous slide) 11 © 2010 The Actuarial Profession  www.actuaries.org.uk

13. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only How I Generated the Numbers Markov Process Conditional Percentiles 12 © 2010 The Actuarial Profession  www.actuaries.org.uk -5 0 5 10 15 -5051015 99.95% 99.5% 95% 50% 5% 0.5% 0.05% Profit(t-1) Profit(t)

14. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only PP – Plot: Non-normality detectable for large data sets so model risk reduces 13 © 2010 The Actuarial Profession  www.actuaries.org.uk 0 0.2 0.4 0.6 0.8 1 00.20.40.60.81 normal-Gumbel y=x Gumbel cdf Normal cdf: μ = Euler’s constant; σ = π /√6

15. © 2010 The Actuarial Profession  www.actuaries.org.uk Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52 * Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Validation and Back-Testing VaR 14 © 2010 The Actuarial Profession  www.actuaries.org.uk

16. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Longitudinal Validation under Basel How do you know your model is right? Bank regulation:10 day VaR at 99% Confidence –Look back over last year (250 trading days, overlapping periods each looking 10 days back) in which both VaR and profit are updated What does this process test? –The “back test” includes implicit tests of model and parameter error as well as outcomes –Although it won’t test risks that didn’t materialise in the last year 051015 Green zone unbiased (2.5 = 250 * 1%) Number of exceptions in a year Amber zone Red zone 15 © 2010 The Actuarial Profession  www.actuaries.org.uk

17. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Which of the Three VaR Methods is right? Method #1 (through the cycle aka unconditional aka stationary aka longitudinal) –Fit a distribution to observed profits (normal, Gumbel) Method #2 (pro-cyclical) –Regress Profit(t) against Profit(t-1) –Fit distribution of residual –Estimate percentile profit as regression formula + percentile residual Method #3 (conditional aka point in time aka cross- sectional) –Estimate percentiles of P(t) conditional on Profit(t-1) 16 Can you Defend your Model?

18. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Monte Carlo Back-test validity and Pro-cyclicality 17 © 2010 The Actuarial Profession  www.actuaries.org.uk -5 0 5 10 -505 Profit(t-1) Profit(t) VaR based on linear regression Stationary Var Conditional VaR Each VaR curve separates 0.5% of the dots from the other 99.5%

19. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Average Percentile Estimates over the Cycle Same exception rate / different mean VaR 18 © 2010 The Actuarial Profession  www.actuaries.org.uk -5 0 5 10 UnconditionalLinearConditional Mean estimated percentile over the cycle 99.95% 99.5% 95% median 5% 0.5% 0.05%

20. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only What is the best VaR Methodology? 19 © 2010 The Actuarial Profession  www.actuaries.org.uk StakeholderExample of possible concerns PolicyholderBenefit security Cost of insurance cover Corporate managerReported return on capital Management flexibility RegulatorMarket confidence Financial stability ShareholderShare price growth Dividends General publicAmplitude of economic cycle Bail-outs Actuaries?

21. © 2010 The Actuarial Profession  www.actuaries.org.uk Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52 * Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Sources of Error in VaR Calculations 20 Can you Defend your Model?

22. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Potential sources of error in VaR Calculations (the well-known examples) CategoryExampleBias RandomDraw from an experiment whose distribution is not in dispute. Textbook examples: coin toss, drawing coloured balls from an urn. Parameter error Estimation of parameters from finite samples Portfolio optimisation finds strategies where returns are over-stated or risks under- stated Model errorChosen mathematical model family does not contain the process that generated the data Complexity bias (eg use normal distribution instead of fat tails, linear AR1 instead of non-linear heterosecastic, dimension reduction, commercial pressure) 21 © 2010 The Actuarial Profession  www.actuaries.org.uk

23. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Monte Carlo Calibration Test 22 Model #1 Model #2 Model #50 Years 1-25 Fitted %-iles Yr26 Sim #1 Sim #2 Sim #200 10 000 runs in total Validator prepares 8 fitted percentiles (eg 0.5%, 1%, 5%, 10%, 90%, 95%,99%, 99.5%) 10 000 times Production team prepares Test Yr26 outcome against percentiles Robust Testing of VaR Across Multiple Distributions

24. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Less-discussed sources of error Did these contribute to AIG/Fortis Exceptions? 23 © 2010 The Actuarial Profession  www.actuaries.org.uk CategoryExampleBias Cyclical (point in time estimates) Mis-identification of hidden state variables, excluding “irrelevant” historic periods Symmetric dampeners, judgements about underlying investment value and correction of distorted or illiquid markets DataIncomplete or inaccurateFalsification or selective submission of data. Underwriting bias such as winners curse. Exaggerate benefit of lessons learns or effectiveness of recently imposed controls. Exposure (proxy model) Mis-statement of asset and liability sensitivity to combined moves in risk drivers Constructing hedges to minimise stated VaR; devising “easy” stress test that are known to pass. Lack of preparation for out- of-test stresses. ComputationRoundoff in floating point calculations; differential equation discretisation, simulation sampling error Debug effort focuses on commercially unacceptable output.

25. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only What does an auditor look for? A “True and Fair View” Error tolerance expressed in terms of “materiality” limits. Checking controls and calculations, and identifying any bungles. –Compare cumulative effect to materiality limits Are key management judgements reasonable.? –Comparable to statistical quality standards –Compare to common practice in the market. –Range for reasonable judgements may be narrower than parameter standard errors –Board retains responsibility for judgements The scope of materiality limits is limited to human bungles –Such as omitting a class of liabilities or calculating tax incorrectly. –Differences in judgement do not contribute to the materiality limit. Therefore, it is entirely possible for two reasonable judgements to produce results differing by many multiples of the stated materiality limit. 24 Can you Defend your Model?

26. © 2010 The Actuarial Profession  www.actuaries.org.uk Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52 * Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Does it Matter if the Model is Wrong? 25 © 2010 The Actuarial Profession  www.actuaries.org.uk

27. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52 * Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Robust Statistics Some firms’ VaR calculations rely on knowing the “right” model, but can you ever attain that knowledge? Many models could describe the data and not be rejected by statistical tests Robustness dictates that the methodology should work (produce at most 0.5% exceptions) for a range of possible models For example, through-the-cycle methods rely only on stationarity; our spreadsheet example showed how these tools can still work even if the “true” model is unknown. 26 © 2010 The Actuarial Profession  www.actuaries.org.uk

28. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Conclusions Many approaches to VaR can produce the right exception frequency over the cycle. These differ in –Average required capital over the cycle –Pro-cyclicalility –Robustness to mis-specification Errors in models, parameters, point-in-time, data, exposure and computations have contributed to excess exceptions Addressing biases requires detailed business process knowledge, not only statistics. Different stakeholders may not agree on what makes a “good” VaR calculation. 27 © 2010 The Actuarial Profession  www.actuaries.org.uk

29. Colour palette for PowerPoint presentations Actuarial Bright Green R148 G166 B31 Actuarial Slate R32 G44 B52* Secondary Olive Green R120 G162 B47 Secondary colour palette Primary colour palette Secondary Bottle Green R0 G147 B127 Secondary Turquoise R0 G138 B176 Secondary Aqua Blue R26 G160 B170 Secondary Pastel Green R126 G205 B195 Secondary Light Purple R123 G149 B174* Secondary Purple R97 G107 B156 Secondary Ecru R186 G163 B171 Secondary Yellow R215 G176 B18 Secondary Orange R213 G135 B43 Secondary Red R238 G52 B36 Secondary Rubine Red R226 G1 B119 *This colour reference is for screen presentations only Questions or comments? Further questions? My contact details: Disclaimer 28 © 2010 The Actuarial Profession  www.actuaries.org.uk Andrew D Smith Partner, Deloitte Hill House, 1 Little New Street London EC4A 3TR andrewdsmith8@deloitte.co.uk Any views or opinions in this presentation are those of the author alone and not of his employer or any other body with which he associates.