Asset Liability Management models in Prophet

1. Asset Liability Management models in Prophet ALS versus Global Strategy library Lenka Miczova Legal & General, UK October 2013

2. CONTENTS. • Introduction • ALM models • Prophet • Simple ALM models • Where (ALM) models enter MCEV, S2 formulas • Global & Asset library versus ALS • Future Model Improvements for MCEV, S2 • Questions

3. ALM models • Asset Liability Management models • The main aim of ALM is to derive an investment strategy. In practice it is developed in conjunction with other strategies e.g. Bonus strategy, Risk Management Strategy, New Business strategy. • Asset, Liability and all the interactions are brought into one model.

4. ALM models • Separate Liability and Asset model possible • Liability cash flows dependent on investment returns (A→L) • separate asset and separate liability model sufficient • e.g. Unit-linked products, Risk products • Liability and Asset modelled together • Both side interaction between asset and liability cash flows – e.g. additionally Investment strategy dependent on liability cash flows (L→A) • e.g. With Profit Life Assurance • Used for • MCEV, S2 • Fund modelling • Testing Management decisions • Deriving Investment Strategy L L A A X

5. ALM models • What’s in? • Liability cash flows • Asset cash flows • Fund (Balance Sheet) • Profit, Tax (Revenue account) • Management decisions • Investment strategy • Reversionary bonus(UK) • Terminal bonus (UK) • Profit Sharing (Europe) • Shareholder Transfers • Dividends, Capital Injections Balance sheet Assets Liabilities Surplus Reported Value of Assets Fund Reserves

6. Liability model • Decrements • Liability Cash flows • PROFITt = Premium Incomet+Investment Returnt • – Benefit Outgot– Expensest • – Change in Statutory reservest • – Taxt • Value Of Liabilitiest = Benefit Outgot +Expensest – Premium Incomet • For more details about modelling liabilities see PetrKeblusek’s presentation (11.10.)

7. Introduction to Prophet • source: • PwC (Delivering your model • expectations, July 2011) • 49 Insurance companies • EU, Middle East and USA • Prophet • One of the most common software for actuarial models • Being developed by Sungard • Code stored in Libraries • Variable – basic block of code stored in Library, e.g. Number of in force policies, Premium income, Initial expenses, ... • Standard variable – simple code, IF/ELSE • Extended variable – more complex coding • Products– functionality selected from Library using system of Indicators (e.g. 500 variables) • Model points – policy/asset data, usually 1mp = 1 policy • Tables – other input data (mortality rates, lapse rate, expenses, economic assumptions, ...)

8. Introduction to Prophet Liability product L1 • Development – company specific changes made in library • Calculation – liability product code evaluated for each mp, assumptions read from tables • Results – accumulated values from all mps, stored per (sub) product, standard variable, time Library Liability product L2 Set of Indicators used to choose variables and their definitions L1 L2 Tables L1 mps L2 mps

9. Prophet Stochastic ALM libraries 1990 Asset (A) Global Strategy (G) ALM above existing liability models Assets (A) – complex assets Global Strategy (G ) – simple assets, fund, management decisions, ... 2001 DFA (Dynamic Financial Analysis) Fast stochastic ALM runs Focus on fund level Asset, Fund & Liability Development concept 2006 ALS (Asset Liability Strategy) Best of A+G and DFA New functionalities

10. Simple ALM model • Example of ALM model with G+A Libraries • 1 Liability product with(part of the ALM model to enable whole fund modelling) • 1 Global product for calculating investment return, inflation, ... for this product (no asset product, only simple assets) • 2 With Profit Liability products • 1 Asset product for assets covering L2 and L3 reserves • 1 Global for interaction between A1 and L2, L3 and for fund modelling • Management decisions passed down (red arrows on the next slide, liability and asset cash flows recalculated): • Investment strategy to assets • Bonus rates to liabilities L L A A L1 G1 L2 L3 A1 G2 X

11. PVFP Simple ALM model PV of Liabilities Fund level calculations 2013 fund L L A A Not In Memory G2 L2, L3 mps L2, L3 NB mps ∑ L2+L3 cf ∑ A1 cf L1 NB mps L1 mps ∑ L1 cf Dynamic A1 NB mps A1 asset mps A1 Memory In L2 L3 Dynamic Not In Memory L1 non Inv. Return, Inflation for L1 G1 2013 2014 2015 3rd loop 2nd loop X (Animation recommended)

12. Simple ALM model • Projection e.g. 40yrs, 60yrs • Calculation repeated e.g. 2000 times for each simulation • Stochastic • Many runs on different assumptions • Results per Simulation + Mean value, Quantiles • Economic scenarios (Barrie & Hibbert, TSM, …): • ZCB • Prices or • Spot yield curve (SPOT_RATE_PC) or • Par yield curve • Equity • Total return index(RET_IDX) • Dividend yield(RNY_PC) • Inflation index(INFLN_IDX) • Deflator(DEF)

13. Simple ALM model • Comments to the previous picture • Future Asset New Business • New assets always bought to cover reserves of existing liabilities • Future Liability New Business • Not included in MCEV, S2 • Included for e.g. Appraisal Value, Balance Sheet projection • Model point grouping inevitable • Not grouped mps: 1 policy represented by 1 mp in Prophet in deterministic runs (non stochastic, non dynamic) • Grouping: e.g 500 000 mps replaced by weighted 2000 mps with (reasonably) equivalent cash flows • Reasons for grouping • Run time • stochastic runs, dynamic looping • Liability NB created for each month of selling • Memory(dynamic only) – all mps in memory due to dynamic looping • Validation of accuracy needed

14. Where (ALM) models enter S2 • Assets = BEL + RM+SCR+Surplus • Assets – Present value of assets (Accounting value used for Base BEL) • BEL (Best Estimate Liabilities) • Mean PV of Liabilities • RM (Risk Margin) • Compensation for the risk of future experience being worse than the best estimate assumptions used for BEL • Calculated as Cost of holding capital to support non hedgeable risks → Projection of Non Hedgeable SCR required • See next slide for calculation of SCR • See last chapter of presentation for projection of SCR • Cost of Capital method used: • Values calculated in (ALM) actuarial models

15. Where (ALM) models enter S2 • Assets = BEL + RM+SCR+Surplus • SCR (Solvency Capital Requirement) • Value at Risk measure on a 99.5% confidence interval of the variation over one year of the amount of (assets minus (BEL + RM)) • In Prophet(ALM) modelsStandard formula: all delta NAV approach:In Practice (bottom components before aggregation):→ unstressed BEL(Base BEL) run and manystressed BEL runscalculatedfor SCR in actuarial models. • Values calculated in (ALM) actuarial models

16. Where (ALM) models enter MCEV • MCEV = NAV – FCRC + PVFP – TVFOG – CRNHR • NAV (Net Asset Value) • (basically) Accounting value of Equity • Further split to: NAV = RC + FS • RC (Required Capital) – MV of assets attributed and required to back liabilities for covered business whose distribution to shareholders is restricted • MAX(Solvency I capital requirement, SCR) • Or Company specific calculation e.g. to allow for company credit rating • FS (Free Surplus) = NAV – RC • FCRC (Frictional Cost of Required Capital) • Frictional costs should reflect the taxation and investment cost on the assets backing RC • Cost of capital method used • Projection of RC required → Projection of SCR required again

17. Where (ALM) models enter MCEV • MCEV = NAV – FCRC + PVFP – TVFOG – CRNHR • PVFP (Present Value of Future Profit) • certainty equivalent projection – in practice 1 economic scenario where all assets earn forward rate derived from relevant yield + liquidity premium if applicable • TVFOG (Time Value of Financial Options and Guarantees) • Must be based on stochastic techniques • PVFP lessStochastic PVFP(Mean Present Value of Future Profit e.g. 2000 simulations) • CRNHR (Cost of Residual Non Hedgeable Risks) • Cost of non hedgeable risks not already allowed for in TVFOG e.g. Mortality risk, morbidity risk, ... (Cost of capital method) • SII approach used for determining capital (SCR) • Projection of SCR required • Note: all components evaluated not only for the main MCEV result but also for all MCEV Sensitivies, AoC (Analasis of Change), VNB (Value of New Business) • Values calculated in (ALM) actuarial models

18. G+A versus ALS • Main differences • Company structure • Internal / External / Flexing liabilities • Development concept • Type of Assets • Investment strategy • Profit Sharing • Non YE Start of projection

19. G+A versus ALS – Company Structure G+A L1 Seg 4 Seg 1 Seg 2 Seg 3 Seg 5 Seg 6 Seg 8 Seg 9 Seg 10 Seg 11 Seg 12 Seg 7 Equities Cat 1 Bonds Cat 1 Bonds Cat 2 Bonds Cat 1 Equities Cat 2 G3 G1 A3 A1 G2 A2 G3 L2 A3 F u n d G1 G2 A1 A2 L3 L1 L2 L3

20. G+A versus ALS – Company Structure ALS L1 Seg 12 Seg 8 Seg 7 Seg 11 Seg 10 Seg 9 Seg 2 Seg 3 Seg 4 Seg 5 Seg 6 Seg 1 Equities Cat 1 Bonds Cat 2 Bonds Cat 1 Bonds Cat 1 Equities Cat 2 Fund Pool 3 Pool 2 Pool 1 Seg3 Seg2 Seg1 Reserves L2 ALS1 F u n d part 1 L3 part 2 L1 L2 L3

21. G+A versus ALS – Company Structure • Prophet Terminology • Liability Segment – one or more liability products or only part of liability product or external deterministic cash flows • Asset Pool – assets allocated to liability segment(s) to allow for different investment strategy and management decisions • Asset Category – user defined categories for Equities, Bonds, … e.g. foreign Equity, Short term bonds, Long Term Bonds • Asset Segment – one investment e.g. an equity, a bond or number of similar investments • Summary(modelling same structure in G+A versus ALS - example) • G+A: • 3 Assets products, 3 Global products needed to model three set of assets with different investment strategies • Only total results available, no split per Liability Segment • ALS: • 1 ALS product • More fundspossible – group purposes (1 fund for 1 company), transfers between funds • Results available per Liability Segment • → Simplified structure in ALS

22. G+A versus ALS – Modelling of liabilities • Modelling of liability cash flows – 3 approaches • External liabilities • (from G) • Internal liabilities • (from DFA) • Flexing • (from DFA) • Options • External liabilities + Flexing (Optional) or • Internal liabilities + Flexing (Optional) • No option for 1 ALS product to switch between Internal and External liabilities ALS1 L1 L2 L3 ALS1 L1, L2, L3, Assets, Fund ALS1 L1 L2 L3

23. G+A versus ALS – Modelling of liabilities • External liabilities • Bottom-up approach (ALM model on top of existing liabilities) • Full complexity of liability products • Same way of interaction in G+A and ALS • Monthly steps always G3 ALS1 A3 G1 G2 A1 A2 L1 L2 L3 L1 L2 L3

24. G+A versus ALS – Modelling of liabilities • Internal liabilities • Top-down approach (main focus on fund) • Faster models compare to external liabilities • 1 product only – No links between products (no slow reading)e.g. >50% faster • Annual steps of calculations possible instead of monthly (≈10x faster) • No Dynamic looping needed for Investment strategy or Management decisionsorder of liability cash flow calculation: external liability internal liability ALS1 L1 L2 L3 ALS1 L1, L2, L3, Assets, Fund decision decision mp1: t=0, t=1, t=2… mp2: t=0, t=1, t=2… mp1: t=1, t=2… mp2: t=1, t=2… (monthly loop) t=0: mp1, mp2 t=1: mp1, mp2

25. G+A versus ALS – Modelling of liabilities • Internal liabilities • Drawbacks • Liability cash flow simplification • Cash flows for all products on one place • No valuation before start of projection • Twoliability models for same liabilities • ALM model in ALS • Deterministic model for: • validation of liability cash flows in ALM model • some calculations with all model points and full complexity • High cost to develop even if liability model already exits

26. G+A versus ALS – Modelling of liabilities • Flexing • Principal: • Liability cash flows calculated by traditional liability model (no bonus, lapse behaviour, …) • Cash flows are then “flexed” in ALS with a system of multiplying ratios for each time and each simulation • Example of flexing • Fastest run time (e.g. 1 simulation in L*, 2000 sims only in ALS1) • Unmodelled business, Business with simpler guarantees A L1,L2,L3 ALS1: L1 L2 L3 Liability Math reserve: 1000 1200 1400 Bonus rate: 2% 3% Flexed Math reserve: 1200*(1+2%) 1400*(1+2%)* (1+3%) 2013 2014 2015

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28. G+A versus ALS – Development concept • Indicators x Table drive • G+A: Indicators – product functionality select from library using indicators → simpler products • ALS: more Table driven – general code in product, switches in tables • Custom codes • User defined code Indicators – simple idea to enable integration with future new functionalities in Prophet e.g. functionalities for S2 • Liability products too company specific→ no integration • ALM libraries – less company changesconsideration about future integration (less) Indicators Global Strategy library Indicators ALS1 ALS Library G1 Switches in tables New Sungard Liability library Sungard Liability library ?? Company Liability library

29. G+A versus ALS – Development concept • Extended variables • G+A: Standard variables • short simple formula, IF / ELSE statement only • ALS: extensive use of Extended variables • More complex – embedded variables, IF/ELSE, FOR loop, WHILE loop, … • Many calculations compressed into a single variable rather than being spread out over many standard variables • E.g. Reading liability cashflows: • Less memory needed but more complicated to test / debug / view results • results of extended formulas not always kept in memory nor saved • Prophet debugger needed G ALS Standard variable Extended variable t

30. G+A versus ALS – Type of Assets • Accounting options • MV (Market Value), ABV (Amortised Book Value), LV (Lowest Value) • Asset types (Common assets) • Cash – ((1 / 1 mth ZCB Price) – 1) used for cash return • Equity, Property • Dividends: • MV: • Bonds • ZCB, callable, index linked, floating, convertible • MV: • Bond cash flows projected from t on based on time t assumptions (coupons, NV) • ZCB Yield curve from time t used for discounting • ABV: • ABV without AI: Compound interpolation using IRR between starting ABV without Accrued Interest and NV • Plus Accrued Interest for time t

31. G+A versus ALS – Type of Assets • Asset types (More complex assets) • Corporate Bonds • Mortgages • Derivatives (incl. swaps, equity options, IR options, swaptions) - Black Scholes formula used for some of them • G+A versus ALS • Corporate Bonds improvements • G+A disadvantage – Limited communication between G+A usually ones a year only (December): • Only Cash and Equity possible in G products. A product needed for others • Small MV/ABV approximations needed in G between Decembers

32. G+A versus ALS – Investment Strategy • Asset pool defined in ALS by • Investment strategy • Liabilities through Segments • A product • Sub product • Set of products • Size of the pool: • Mathematical reserve • Free assets (1 pool per fund) • AS, Math res GAO, ... (not CZ) • Investment strategy • Target Mix (%) of asset categories in the pool (Long term strategy) (assets realigned according to this strategy) – options: • Deterministic – constant or different for each t • Dynamic – e.g. based on free asset ratio • % applied to all assets in the pool or to remaining assets according to the order of realignment • Boundaries for asset categories allowed instead of target mix % • Frequency of asset realignment (each month, annual, …) Seg 10 Seg 1 Seg 11 Seg 9 Seg 7 Seg 5 Seg 2 Seg 12 Seg 6 Seg 3 Seg 4 Seg 8 Equities Cat 1 Bonds Cat 1 Bonds Cat 2 Bonds Cat 1 Equities Cat 2 Pool 1 Pool 3 Seg3 Seg2 Seg1 Pool 2 Reserves F u n d

33. G+A versus ALS – Investment Strategy • ... Investment strategy • Buying and Selling (assets bought / sold each month to match reserves and when realigned): • Buying / Selling rules for an asset category: • Run off (no buying or selling) • Only buying allowed • Proportional selling • Asset segments sold in order • Different mix % for new assets possible (positive / negative) • Profile specified for new assets e.g. bonds, more terms allowed

34. G+A versus ALS – Profit Sharing • Profit Sharing formulain ALS • a%, ... e% - per liability segment • Profit Sharing is usually customised for a company both in G+A, ALS as the formula is not general enough • Asset turnover possible • To realise UCG (increase return) to reach required credit rate

35. G+A versus ALS – Non YE Start of Projection • Projections from other months than December required • First loop: from Start month till first December (e.g. 09/2013 – 12/2013) • Two complications (External liabilities only) • Time measurementG+A versus ALS • ALS (Start month) • G+A (Preceding Dec) • Liability (Start of policy) • No links between ALS and Liabilities (e.g. inflation %) before Start month • Attempts in ALS to read liability cash flows after 12/2015 – fix needed • Loop at Start functionality disabled • both G+A, ALS • bottom ALM product needed for the first calendar year of projection Start 09/2013, 3yr projection – real projection 09/2013 – 12/2015 2013 2014 2015 ALS2 L1 L2 L3 ALS1

36. Future Improvements – Current state • Current Prophet functionality • MCEV: • Each Prophet result reported separately. • S2: • Still quite a lot of “manual” (=xls) work. Further automation? Stoch PVFP sens1 Stoch PVFP sens2 Stoch PVFP PVFP sens1 PVFP sens2 PVFP Prophet results: MCEV report xls Stress1 BEL Stress2 BEL Stress3 BEL Stress4 BEL Stress5 BEL BEL Prophet results: SCR projection Allowance for contract boundaries RM SCR per component Aggregation

37. Future Improvements – S2 Protypes • S2 not implemented in Sungard libraries yet (all functionality developed by companies) • S2 Prototype models released in 2011 to open discussion about solutions: • Total SCR for Life risks shown • All stresses in one – all cash flows duplicated into array variables • e.g. DEATH_OUTGO represents Base BEL Death outgo • A_DEATH_OUTGO(1), A_DEATH_OUTGO(2) stress 1, stress 2 BEL Death outgo • This approach would mean replicating almost all liability model into array variables • Projection of SCR • Rebasing technique used to recalculate results • For SCRt stresses applied from t+1, array variables recalculated from t+1 on based on Base BEL value for t • Same approach can be used forallowing for contract boundaries • Not suitable for ALM (Dynamic) models! • No Nested Stochastic # IF policies

38. Future Improvements – Summary • Summary • Total SCR • Finalising in spreadsheet recommended for ALM models • Too expensive to implement into Prophet • Projection of SCR • Standard formula approach using risk carriers can be implemented as an additional Base BEL run with SCR from spreadsheet as an input • More sophisticated approach complicated • Nested Stochastic • Only 1 nested level possible and only for Internal liabilities in ALS • Improvements for Nested Stochastic functionality expected in ALS Release 2014

39. QUESTIONS? 39