Economic Capital Based on Stress Testing

Transcription

1 Economic Capital Based on Stress Testing ERM Symposium 2007 Ian Farr March 30, 2007

2 Contents Economic Capital by Stress Testing Overview of the process The UK Individual Capital Assessment (ICA) Experience 2

3 Economic Capital by Stress Testing: Overview of the Process

4 OVERVIEW OF THE PROCESS A stress testing approach is becoming most common method to calculate EC Economic Capital is measured as the difference in market consistent net assets between normal conditions and stressed conditions Stress tests are applied for each material risk, calibrated to a probability level over a one-year time horizon, consistent with the company s financial strength rating Separate stresses are applied to cover a variety of market, credit and insurance risks that might occur over the projected one-year time horizon Normal Conditions MV Assets Net assets MCV Liabs Stressed Conditions MV Assets Net assets MCV Liabs Results are aggregated using a correlation matrix Net assets Net assets Economic Capital Normal Stressed Commonly used in Europe, increasingly used in North America 4

5 OVERVIEW OF THE PROCESS There are four stages in the process Step 1 Develop an economic view of the business Economic assessment of assets and liabilities Step 2 Identify key risks and determine levels of stress to be applied List of stress events to quantify key risks Step 3 Apply stresses to the economic balance sheet EC requirement for each key risk Step 4 Aggregate individual risk capital results, allowing for correlation effects Total EC requirement for your business 5

6 OVERVIEW OF THE PROCESS STEP 1: DEVELOP AN ECONOMIC VIEW OF THE BUSINESS An economic view of the business is essential to the derivation of economic capital requirements SAP/GAAP Balance Sheet Economic Balance Sheet Assets Liabilities Assets Liabilities Excess assets EC Mix of market and book values Margins amortized over contract duration At market value Best estimate basis Margins removed 6

7 OVERVIEW OF THE PROCESS STEP 2: IDENTIFY KEY RISKS; DETERMINE STRESSES TO BE APPLIED Stress tests are determined for each of your key risks and at a level consistent with your target financial strength rating Your key risk exposures are identified within four major risk categories: Market Credit Insurance Operational For example: market risk equity price fall, fixed interest yield move, For each risk, a level of stress test(s) is chosen, consistent with your target financial strength rating (illustrative figures): Target Financial Strength Rating Equivalent Risk of Ruin Over 1 Year Equity Price Stress Fixed Interest Yield Stress AAA 0.05% -50% +/- 200bps AA 0.1% -40% +/- 150bps A 0.2% -35% +/- 120bps BBB 0.5% -30% +/- 100bps 7

8 OVERVIEW OF THE PROCESS STEP 3: APPLY STRESSES TO THE ECONOMIC BALANCE SHEET The EC required for each risk is derived by applying the corresponding stress test(s) to the economic balance sheet The impact of each stress test on the economic value of both assets and liabilities is assessed The EC requirement for the underlying risk is determined by the change in economic net assets as a result of the stress tests, measured over a one-year period Normal Conditions MV Assets Net assets Normal Net assets BE Liabs Net assets Stressed Stressed Conditions MV Assets Net assets BE Liabs Economic Capital 8

9 OVERVIEW OF THE PROCESS STEP 4: AGGREGATE RESULTS, ALLOWING FOR CORRELATION Capital requirements for each risk are aggregated formulaically, using a matrix of correlation factors Aggregate capital = Where Ci is the capital required for the ith risk at the required confidence level and is the correlation coefficient between ith and jth risk ρ ij Correlation factors are based on historical data analysis, combined with expert judgment (illustrative figures): Market risk Credit risk Insurance risk Operational risk ρ ij C i j i Market Credit Insurance Operational 100% 40% 0% 40% 100% 0% 0% 100% 0% 100% Choice of correlation factors is weighted towards the higher correlations that typically arise in more extreme scenarios C j The results of the FastTrack EC approach can be used to help identify estimated capital requirements and provide a basis for further stochastic work 9

10 Economic Capital by Stress Testing: The UK ICA Experience

11 What is an ICA? The ICA is the Director s assessment of how much capital the company needs to hold to meet policyholder liabilities as they fall due. It is a requirement under UK regulation Firms must identify all major risks and quantify appropriate amounts of capital Based on a value at risk concept of covering (marketconsistent) liabilities after a 1 in 200 year event ( BBB ) Companies can alternatively look over a longer time horizon with a suitably adjusted ruin probability Requires stress testing and scenario analysis as a minimum; stochastic modelling is optional The regulator (FSA) will perform its own assessment and advise (Individual Capital Guidance) if they think the ICA is insufficient 11

12 Calibrating Stress Tests Market (e.g. equity, interest rate, implied volatility) Credit Insurance (e.g. persistency, mortality, longevity, morbidity) Operational Other (e.g. liquidity and group risk) 12

13 CALIBRATING STRESS TESTS Market risk: Equity and property stresses Industry typically uses around 40% equity fall and a 20 to 40% property fall Derived from historic analysis of market data (or from scenario generators which have been calibrated to historic data) How relevant is the older data to future conditions? 1000 real world scenarios Investment stress based on 99.5 percentile. Impact on capital of real world scenario over 1 year 13

14 CALIBRATING STRESS TESTS Market risk: Fixed income stresses Industry typically uses a stress of between 150bps and 250bps for fixed interest movements. Wide range of stress despite companies having access to the same set of calibration data Typically parallel shift only considered, sometimes modified by duration (greater shift in short rates) Changes in the shape of the yield curve also considered by companies with significant exposures 14

15 CALIBRATING STRESS TESTS Market risk: Volatility stresses Liabilities typically include optionality, valued on a market-consistent basis; companies need to consider implied volatility stresses Equity implied volatility: Fixed income volatility: Property implied volatility: Typical stresses have been in the range of an absolute increase of +20% to +25%. Typical stresses have been in the range of a relative increase of +20% to +30%. Either not considered or subjected to an equity volatility stress. 15

16 CALIBRATING STRESS TESTS Credit risk stresses Industry typically uses a stress of between 75bps and 150bps for credit stresses on a ( AA ) corporate bond Wide range of stress despite companies having access to the same set of calibration data Spread variation is major component; rating migration and default are secondary impacts in mark to market framework Changes in the shape of the credit stress have generally not been considered Reinsurance assets may be revalued assuming a higher discount rate to allow for default risk Some companies assume their largest reinsurance exposure defaults (typically allowing for significant recovery) 16

17 CALIBRATING STRESS TESTS Insurance risk stresses Insurance risks Mortality Persistency Expenses New business Capital should cover: Volatility on base experience Mis-estimation Trend Catastrophe Largest source of risk typically from annuitant longevity improvement Guaranteed Annuity Rates as well as immediate (payout) annuities For larger players, trend and cat risks dominate Calibration of key risks problematic 17

18 Approaches to operational risk Operational risk assessment approaches used In 2004 Bottom-up Benchmarks Basic HML Nothing Approach Formulaic HML Approach Top-down Stress & Scenario Tests Stress & Scenario Process Tests Modelling Simulation Modelling 10% 10% 20% 20% 15% 15% 5% 5% In % 10% 25% 5% 35% 5% 5% Source: Tillinghast analysis 18

19 Aggregation The correlation matrix approach has been the most popular approach to aggregation in ICAs to date Assumes risks are either normally or log-normally distributed Potentially ignores non-linearity of risks / tail correlations Correlation factors Typically fairly robust analysis of economic correlations More limited analysis of other correlations Tail correlations are key Non-linearity exists; the matrix approach Market and persistency (with profit) Interest rate and GAO take up rates Mortality and reinsurance counterparty (risk business) Significant diversification benefits are typically seen Range 25% - 60% (average around 35%) 19

20 UK Experience Pros and cons of stress testing Pros Relatively quick and easy to compute Gives good insight into key sources of risk in isolation Easy to communicate at Board level and to rating agencies and regulators Highlights short term risks (which can be very real) Cons Aggregation by correlation matrix can be a significant approximation for complex business Sensitivity to business strategy can be insufficient for detailed decision-making Longer term view can give greater insight into business dynamics Overall experience very positive (from a sceptical start point) 20

21 Where next? From stress tests to (stochastic) scenarios Specific stress tests over year 1 Stochastic development over year 1 Net assets Stress 1 Stress 2 Market consistent stochastic liability at end of year 1 Net assets Stochastic, or approximated, market consistent liability end of year 1 (calibrated to adverse scenarios) 1 Time 1 Time Stochastic scenarios Allow more precise examination of impact of risk interactions and correlations Enables selection of the critical stress tests for your portfolio May need to approximate to market consistent liability at end year (eg option formulae; replicating portfolios) 21

22 Scenario Analysis Adopting a Structured Approach Diane Reynolds Algorithmics Inc. Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

23 Motivation Why? Why do scenario analysis? Correlations tend to be high during crises The board needs to envision catastrophic risk scenarios can help! Defining risk appetite / risk limits can be more intuitive when based on scenario analysis Heroic assumptions re: combining distributions can scenario analysis mitigate this? Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

24 Motivation How? Scenario analysis can quickly become unwieldy: Everyone always has something to contribute helpful or chaotic? How do you choose the right scenarios? When is a scenario too far-fetched to worry about? What do you do about scenarios whose impact is unknown? With all the bits of data, now what? Even if it s a great story, how to do quantify anything anyway? Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

25 A Coherent Framework 1. Set Objectives 2. Select Scenarios 3. Quantify Selected Scenarios 4. Impact Analysis Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

26 Setting Objectives Potential Objectives Establish target capital-to-risk ratio Meet rating agency expectations Inform capital management & funding strategies Improve capital allocation processes Manage portfolio composition & concentrations Uncover hidden correlations under stress conditions Identify, then Prioritize Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

27 Which Scenarios? Different Goals: Sensitivity vs. stress vs. extreme scenarios Revenue-impact vs. capital-impact scenarios Different Assumptions: Shocks vs. Shifts Different Sources: Historical, Hypothetical or Hybrid? Macroeconomic, market-based or catastrophe? Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

28 Creating a List of Scenarios Interviews Workshops Questionnaires Data mining experience is priceless! Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

29 Filtering the Scenarios List Key Questions What is the likely magnitude of the scenario? How plausible / conservative is the scenario? Are there any feasible courses of mitigation? Does the scenario add new information? Can the scenario be quantified for further analysis? Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

30 Quantifying a Scenario Four Steps 1. Establish the baseline MtM the portfolio Assess its current risk 2. Define the external scenario Example: Another large terrorist attack 3. Assess the internal scenario 4. Model financial position Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

31 Example: Covering all Risks Market Risks Interest Rates Exchange Rates Equity Values Operational Risks Legal / Litigation Own Business Continuity Credit Risks Bankruptcy Business Discontinuity Downgrades Reinsurance Insurance Risks Property Health Life Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

32 Example: Market & Credit Risks Evolution of USD spot rates Evolution of zero coupon rates on T-bills 110% 108% 105% CAD GBP EUR JPY day 6-mth 1-yr 103% % % % 0 1d 1w 1m 1q 6m 1y d 1w 1m 1q 6m 1y Post 9/11 evolution of key equity indices 120% 110% SPX Index DAX Index NKY Index 100% 90% Individual PD / Rating Changes 80% 70% 0 1d 1w 1m 1q 6m 1y Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

33 Example: Input Details Scenario: 11th Sept 2001 attacks Risk Factor Category Relative value after event Risk Factor 0 1-d 1-w 1-m 1-q 6-m 1-yr Zero-Coupon Yield on Government Bonds CAD USD EUR GBP JPY MXN US Corporate Credit Spread (5-yr zero coupon rate) AAA AA A BBB BB B CCC CC C Japan Corporate Credit Spread (5-yr zero coupon rate) AAA AA A BBB BB B CCC CC C Exchange Rate vs USD CAD EUR GBP JPY MXN Equity Indices and Sub-Indices CAC DAX DJ Am Basic Materials DJ Am ConsumSrv DJ Am Financials DJ Am Healthcare DJ Am Industrials DJ Am Non-Cyclicals DJ Am Oil&Gas DJ Am Technological DJ Am Telecom DJ Am Utilities DJ Eu Basic Materials DJ Eu ConsumGds DJ Eu ConsumSrv DJ Eu Financials DJ Eu Healthcare DJ Eu Industrials DJ Eu Oil&Gas DJ Eu Technology DJ Eu Telecom DJ Eu Utilities FTSE HANG SENG NASDAQ NIKKEI mth LIBOR CAD USD CHF EUR GBP JPY Scenario: 11th Sept 2001 attacks Risk Factor Category Relative value after event Risk Factor 0 1-d 1-w 1-m 1-q 6-m 1-yr Zero-Coupon Yield on Government Bonds CAD USD EUR GBP JPY MXN US Corporate Credit Spread (5-yr zero coupon rate) AAA AA A BBB BB B CCC CC C Japan Corporate Credit Spread (5-yr zero coupon rate) AAA AA A BBB BB B CCC CC C Exchange Rate vs USD CAD EUR GBP JPY MXN Equity Indices and Sub-Indices CAC DAX DJ Am Basic Materials DJ Am ConsumSrv DJ Am Financials DJ Am Healthcare DJ Am Industrials DJ Am Non-Cyclicals DJ Am Oil&Gas DJ Am Technological DJ Am Telecom DJ Am Utilities DJ Eu Basic Materials DJ Eu ConsumGds DJ Eu ConsumSrv DJ Eu Financials DJ Eu Healthcare DJ Eu Industrials DJ Eu Oil&Gas DJ Eu Technology DJ Eu Telecom DJ Eu Utilities FTSE HANG SENG NASDAQ NIKKEI mth LIBOR CAD USD CHF EUR GBP JPY Scenario: 11th Sept 2001 attacks Risk Factor Category Relative value after event Risk Factor 0 1-d 1-w 1-m 1-q 6-m 1-yr Zero-Coupon Yield on Government Bonds CAD USD EUR GBP JPY MXN US Corporate Credit Spread (5-yr zero coupon rate) AAA AA A BBB BB B CCC CC C Japan Corporate Credit Spread (5-yr zero coupon rate) AAA AA A BBB BB B CCC CC C Exchange Rate vs USD CAD EUR GBP JPY MXN Equity Indices and Sub-Indices CAC DAX DJ Am Basic Materials DJ Am ConsumSrv DJ Am Financials DJ Am Healthcare DJ Am Industrials DJ Am Non-Cyclicals DJ Am Oil&Gas DJ Am Technological DJ Am Telecom DJ Am Utilities DJ Eu Basic Materials DJ Eu ConsumGds DJ Eu ConsumSrv DJ Eu Financials DJ Eu Healthcare DJ Eu Industrials DJ Eu Oil&Gas DJ Eu Technology DJ Eu Telecom DJ Eu Utilities FTSE HANG SENG NASDAQ NIKKEI mth LIBOR CAD USD CHF EUR GBP JPY Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

34 Example: Compute & Compare Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

35 Impact Analysis Metrics Time horizon Survival probability Communication: Frequency &Format Management Decisions Possible actions / mitigation Strategic planning Survival Probability = Pr(Loss < Capital Req d) = 55% Actual Capital Total Prob. 45% Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

36 Relating back to Objectives Potential Objectives Establish target capital-to-risk ratio Meet rating agency expectations Inform capital management & funding strategies Improve capital allocation processes Manage portfolio composition & concentrations Uncover hidden correlations under stress conditions Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.

37 Scenario Analysis Adopting a Structured Approach Algorithmics is a member of the Fitch Group, Inc Algorithmics Inc.