Stochastic Modelling & Internal Capital Management. Prudential (Hong Kong) Prudential (Hong Kong) Patrick Li

Transcription

1 Stochastic Modelling & Internal Capital Management Prudential (Hong Kong) Patrick Li Prudential (Hong Kong) 4, November, 2008

2 Agenda 1. Introduction 2. Stochastic modelling High level introduction Asset Economic Scenario Generator (ESG) Liabilities and management actions Interpretation of results 3. Internal Capital Management Realistic Balance Sheet (RBS) Economic capital assessment (EC) Internal capital assessment (ICA) 4. Other applications Strategic Asset Allocation (SAA) Stochastic pricing 5. Challenges & conclusion

3 Introduction Why do we need stochastic modelling? Managing and understanding the inter-relationship between asset and liability is crucial to maintain the financial soundness of insurance company. A well-functioning stochastic model enables the company to: Evaluate the Economic Capital Assess the current credit rating of the company Project results stochastically and satisfy various reporting requirements, e.g. RBS, ICA Assess the appropriateness of investment strategy Assess the appropriateness of policy charges (e.g. guarantee charges) Understand future liquidity needs of the business Propose management actions to mitigate potential financial risks

4 History (Prudential HK) History of applying stochastic modelling for capital analysis European Embedded Value starting from 2004 Stochastic model was developed Aimed to integrate the assets and liabilities cash flows with appropriate management actions Prudential Group started to report EEV from 2004YE, which satisfies the reporting requirement of the CFO Forum Benefited from a stable and audited stochastic model, Prudential HK has extended the functionality of the model to Realistic Balance Sheet (required by UK FSA) Internal capital Assessment (required by UK FSA) Economic capital calculation Market Consistent Embedded Value, which is a newly required reporting basis required by the CFO Forum Strategic Asset Allocation Stochastic pricing report profit margin on MCEV basis and assess cost of significant embedded guarantee in products 4

5 Flow in stochastic model Information flow in stochastic model Asset Data / Simulations Asset strategies Determines investment mix and return Fund level calculation Liability cash-flows from model point level Management actions - Bonus / dividend actions Non- Economic Assumptions Model point level calculation Liability model point data Aggregation of results Output 1. Investment returns 2. Asset mix 3. Bonus / dividend rates 4. Liability cash flow information 5. Solvency position 5

6 Asset - considerations Asset strategies and key modelling considerations Economic scenario generator (ESG) To simulate returns on asset classes (equities, bonds, cash, properties, etc) Correlations between returns of different asset classes Correlations between inflation, interest rates and exchange rates across different economies Types of scenarios - risk neutral and real world Different scenarios for various purposes Verifications on produced simulations (e.g. martingale test for risk neutral scenarios) Management actions related to asset strategies Rebalance to long term investment strategy over time Apply de-risking strategies under extreme scenarios (e.g. when solvency is threatened) 6

7 Asset verifications of ESGs The following checks can be performed to ensure the appropriateness of ESGs. (Take MCEV risk neutral scenarios as an example.) Consistency of investment return with swap curve Martingale test : ensures all asset classes are with the same average returns Value conservation : ensures no leakage of value in the projection Consistency check: price a sample bond with the simulation set and compare the average bond value with the certainty equivalent scenario. 7

8 Example verification (2) Example 2 Investment return of assets Vs swap curve Purpose: to verify different assets are earning the same return as swap Investment Return by Asset Class - CE scenario Cash Return Bond Return Equity Return Investment return Swap rate

9 Example verification (1) Example 1 Martingale tests Purpose: to verify the risk neutrality of returns of different assets Martingale Test Definition: Verify if the discounted prices of all asset classes are the same as today s prices (ie the average projected returns of any asset should be very close to the average return on cash over the same time horizon) Problem: Assets, other than Cash deviate from intial price (1 dollar) Explanations and challenges: 1. Degree of randomness - the graph above demonstrates average of 1000 simulations. The more simulations provided, the higher degree of convergence. However, a balance should be considered between accuracy and model run-time 2. Asset volatility - Magnify effect of point 1 Equities Overseas Equities Domestic Government Bonds Corporate Bonds Cash 9

10 Example verification (3) Example 3 Value conservation test Purpose: to check internal consistency of ESG and model PV of all cash flows should be zero (0) Starting asset + ΣPV of premium - ΣPV of all expenses and outgoes - ΣPV of SH transfer PV ending asset = 0 Table below illustrates an example. Insignificant mismatch of asset and liability (0.04%) is due to the investment income leakage as mentioned in last slide Starting assets PV Premium Distribution Impact PV Miscellaneous surplus PV benefit outgo PV expense and commission PV Tax PV Shareholder transfers Ending assets TOTAL Assets 112,245 2,557,494 4,087 2,673,826 % Diff (Asset/ Liab-1) Liabilities (1,321,896) (376,197) (21,873) (40,800) Insignificant! (912,010) (2,672,776) 0.04% 10

11 Liability Liabilities strategies and key modelling considerations Modelling of liability cash flows Capture product specific cash flows Reflect appropriate charges (e.g. guarantee charges) and expenses Include reserve calculations Aim to estimate the profits / loss / solvency position at each future projection period Verifications Correctness of liability cash flows Perform deterministic run in ALM model to check against with the deterministic model Value conservation (as shown above) 11

12 Management actions Management actions in stochastic models usually relate to the following areas Dynamic bonus / dividend actions Bonuses and dividends will be increased / decreased based on investment performance and portfolio experience Policyholders behaviour Dynamic lapse for products with lapse being sensitive to investment returns / bonus rates Stochastic mortality predict the timing of pandemic risks However, most of the policyholders behaviours are developed based on professional judgement and HK lacks sound experience to conclude any material relationship relating to policyholders behaviour Dynamic Investment strategy De-risking action when solvency level is low Drifting investment strategy to reduce the cost of option and guarantee 12

13 Management Action Bonus Action (1) Bonus action is one of the key management actions which allows the company to pass through experiences (e.g. investment returns) to policyholders under a wide range of scenarios. Considerations when designing the bonus rule: Aims to mimic real life practice Frequency of bonus changes in stochastic model is similar to real life practice Obtains commitment from management team Not easy since management needs to commit their actions under extreme scenarios Tests the management rule under a range of scenarios To gain comfort in the stochastic model An example is shown in the next several slides to reveal the validation that we had performed when designing the bonus rules. 13

14 Management Action Sample Bonus Action (1) Example: Sample bonus rate - mechanics Bonus decision is driven by comparison between asset share (AS) and gross premium valuation (GPV) of the business When AS > 140% GPV, bonus rate will increase When AS < GPV, bonus rate will reduce; Otherwise bonus rate will remain the same Validation is required to gain comfort of the mechanics to trigger bonus actions. Sample validation procedures are shown as below. 14

15 Management Action Sample Bonus Action (2) Validation 1 general mechanism of bonus movements Mechanism for Bonus rate determination % Asset Share < Liability -> Bonus cut % Original Currency 'm Asset Share Gross Premium Reserve (Liability) Bonus Rate 100% < Asset Share / liability < 140% -> Bonus rate remains the same 3.00% 1.00% -1.00% Bonus rate Asset Share > 140% of liability -> Bonus increase -3.00% % YEAR 15

16 Management Action Sample Bonus Action (3) Verification 2-1. Check against government bond yield 2. Verify the margin withheld mechanism Relationship between Investment return and Bonus rate (a sample simulation) Bonus rate moves in tandem with investment return, which validates the bonus declaration mechanism. 2. Bonus rate is less than investment return, which is intuitive since some investment return is used to fund policy expenses. 3. Bonus rate is not increased until asset share exceeds 140% of liability, bonus is more stable when the margin is in place. 7 Percentage Bonus rate - no margin in bonus decision Bonus rate - with 140% margin in bonus decision Investment return YEAR 16

17 Management action De-risking strategy (1) Management actions related to asset strategies can reduce investment risk under certain scenarios, e.g. de-risking actions. The following example aims to depict how the de-risking strategy can work in stochastic model. The sample de-risking strategy is illustrated below. Set 2 boundaries of solvency ratio to trigger the de-risking strategy If solvency ratio > 200%, asset mix follows the predefined asset mix If solvency limit < 120%, equity proportion is set as zero; all investment will be shift to bonds in that case If solvency limit is in between 120% and 200%, asset mix is interpolated 17

18 Management action De-risking strategy (2) Graphical illustration how de-risking strategy works? Illustrative asset mix with de-risking strategy 100.0% 250% 90.0% 80.0% 200% 70.0% Solvency Ratio 150% 100% Lower than L Greater than U 60.0% 50.0% 40.0% Equity Proportion Upper boundary (U) 30.0% 50% In between U and L Lower boundary (L) 20.0% 0% Solvency Ratio Equity proportion Year 10.0% 0.0% 18

19 Results The following results can be obtained from the stochastic model at each projection period. Asset returns - Investment mix and Returns of each asset class Liability information Liability cash flow / solvency position Bonus rates Relationship between guarantee costs and charges Projection results can be aggregated to product level and fund level to drive different management decisions. Validation can be performed at various levels. Bonus rates bonus series level Sensitivity to check the reasonableness of movements company level Analysis of movement to validate the run results in various runs company level 19

20 Internal capital management A developed stochastic model can enable the company to perform the following reporting that requires stochastic projections. Realistic Balance Sheet (RBS) Economic Capital Internal Capital Assessment (ICA) 20

21 Realistic Balance Sheet Realistic balance sheet (RBS) is part of the UK FSA requirement that ensures the financial health of with-profits business. Definitions: Surplus Asset Total asset of the fund Realistic liabilities valued based on market consistent ESGs Risk Capital Margin Capital required under prescribed economic shocks and persistency shock Realistic surplus surplus on RBS basis Total Asset Realistic Liabilities (including Cost / Charge of Guarantee and smoothing) Risk Capital Margin Key Considerations: Initial yield curve is based on government gilt instead of swap curves Shocks are prescribed by FSA and such shocks may not be applicable to HK. 21

22 Economic capital (1) Question: What is our ruin probability in the next 5 years? What credit rating can we achieve? If we wish to achieve Aaa credit rating in 5 years, how much capital do we need now? Stochastic technique is required to provide an answer to the questions. 1. Ruin probability can be obtained by running through 5000 simulations. 2. The required capital to achieve Aaa rating can be obtained by iterating the run with various level of capital (Aaa in 5 years -> the ruin probability <= 0.17% according to Moody s data) Through these stochastic analysis, we can understand our current financial position (in terms of credit rating) and obtain the economic capital required for the company. 22

23 Economic capital (2) 23

24 Internal Capital Assessment Internal Capital Assessment (ICA) is part of the UK FSA requirement that calculates the required margin to sustain a 1-in-200 shocks. Definitions: Asset Total asset of the fund Realistic liabilities valued based on market consistent ESGs Internal Capital Assessment Economic and non-economic events are 1-in-200 (99.5% VaR) and they are integrated. Total Asset Realistic Liabilities (including Cost / Charge of Guarantee and smoothing) Internal Capital Assessment Excess Surplus Key Considerations & Challenges: 1-in-200 events are not prescribed and company needs to derive their specific events Approach to derive the 1-in-200 events is very complex (using copulas) and difficult to determine Events are country specific. The derived excess surplus is under close scrutiny of UK FSA. 24

25 Stochastic model applications Stochastic model can also be applied in the following tasks. Strategic Asset Allocation (SAA) Stochastic pricing Others 25

26 Stochastic Model Applications - SAA Aim of the analysis: To derive the optimal investment strategy that provides the best return to policyholders and lowest volatility / risk. The following graphs show the sample analysis which conclude the risk / return of 28 sets of investment strategy. Efficient Frontier - determined by assuming 28 sets of investment strategy 5.0% E(PH 7yr IRR) [Geom] 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% Varying geographic location of equity Varying bond duration 19 W3 20 W2 W Base W1 W5 Each short yellow trail represents different asset mix within the prescribed asset allocation. (1) Equity mix is of different geographic locations (2) Bonds are held until maturity and with different durations. 1.0% Points lying on efficient frontier provide the highest return with a given level of risk 0.5% 0.0% 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% Im plied Volatility 26

27 Stochastic Model Applications Stochastic Pricing Stochastic pricing - areas that need stochastic modelling skills Propose appropriate strategic asset allocation Probability of ruin across 1000 simulations Taking account of volatility of asset returns Determination of guarantee charges Asset strategies in extreme situations Normal deterministic pricing procedures still apply when the above decisions are fixed from stochastic modelling. 27

28 Challenges Before enjoying the advantages of a well-functioning asset and liability model, let s see the challenges. Management actions and implementation To get management commitment on deciding the dynamic actions and implementation Development of management actions on policyholders behaviour is difficult due to lack of industry-wide experience studies Resources Asset and liability management is new in the HK market. Shortage of actuarial talents that are equipped with ALM knowledge. The model is complex, coding can be tedious and training cycle is long. The model requires intensive computing power. A dedicated team with high quality actuarial talent is required to maintain the stochastic model. 28

29 Conclusions Conclusions With a sophisticated stochastic model, financial position can be better reflected in different reporting bases, e.g. EEV, MCEV. More advanced analyses can be performed in-house, e.g. SAA and Economic Capital determination, which aids management to understand the financial position. Through performing stochastic analyses, company can better understand its own risks. This further stimulate the management to decide more appropriate management rules and investment strategies. Company needs to face a number of challenges, e.g. human resources and hardware issues. Moreover, getting commitment from management to these new actuarial concepts and execution of management actions could also be a challenge for the chief actuary. 29