The Dynamics of Annuity Pricing, Credit, Mortality Risk & Capital Management for UK Life Offices

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1 The Dynamics of Annuity Pricing, Credit, Mortality Risk & Capital Management for UK Life Offices John Hibbert 23 rd June 3 Finance & Investment Conference 2 Overview Some background on the annuity market. What policy questions do we want to answer? A stochastic model of annuity business: Interest rates Credit behaviour & credit spreads Mortality uncertainty A basic case study.

2 UK Annuity Rates Analysis at March 2 3 Scottish Widows Prudential Legal & General Friends Provident Canada Life AMP NPI Sun Life Standard Life Norwich Union GE Life Annuity Based on Gilt Rate Annuity Based on Swap Rate Approx 2 basis Approx 65 basis Annuity Rate Per, (Male Age 65) Source: Annuity Direct, Man aged 65, Single Life, No guarantee, level annuity. Assumes 5% expense loading, and 9% PxA92 with CMI 7 improvements. UK Annuity Rates Analysis at May 3 4 AMP NPI Friends Provident Prudential Canada Life Scottish Widows Standard Life Clerical Medical Legal & General Norwich Union AXA Sun Life Annuity Based on Gilt Rate Annuity Based on Swap Rate Approx 2 basis Annuity Rate Per, (Male Age 65) Source: Annuity Direct, Man aged 65, Single Life, No guarantee, level annuity. Assumes 5% expense loading, and 8% PxA92 with CMI 7 improvements.

3 Implied rates of return vs Mortality assumption 5 5.% Internal Rate of Return 4.5% 4.% 3.5% AMP NPI Prudential Swap rate Gilt yield Scottish Widows 3.% 7% 75% 8% 85% 9% 95% % 5% % 5% 2% % of PMA92 (with CMI imps.) Source: Annuity Direct, Man aged 65, Single Life, No guarantee, level annuity. Assumes 5% expense loading, Annuity rates at 25 th May 3. 6 Background Highly competitive annuity market. Increasing exposure among issuers to credit-risky bonds. Heightened awareness of mortality risk due to past errors in forecasting. Scarcity of capital. Regulator s focus on risk management.

4 7 Policy Issues # How much capital is required to support annuity business? Statutory basis? Economic basis ~ Probability of capital exhaustion limited below some threshold level. What ROC is achieved? How do credit risk & mortality risk fit together? How can credit & mortality hedges be evaluated? How much of the bond spread is lost through (expected) default? 8 Policy Issues #2 Portfolio management: How much diversification is required within the bond portfolio? Is it appropriate to re-balance to maintain a minimum rating level in the bond portfolio? How likely are we to experience default rates above a specified level?

5 9 A Model For Annuity Business Aim to combine models for: Liabilities (& Mortality uncertainty) Asset model Term structure behaviour Credit behaviour (issuer credit states & credit spreads) Valuation rules Model choice What sort of model? Closed-form? Historic simulation? Monte-Carlo Simulation? There is an array of choices for each component of the model Parsimony Transparency Evolution

6 Model Components: Liabilities Analysis of 4 cohorts : Cohort # Age Sex (=Male, =Female) Annuity Payment Per Life Start Date (Deferral) Guarantee Period Type Smoker Non- Smoker Number of Lives in Cohort FALSE FALSE FALSE 4 75 FALSE Model Components: Liabilities 2 8,, Outflow ( ) 7,, 6,, 5,, 4,, 3,, Age= Age=55 Age=65 Age=75 2,,,, Term (Years)

7 Model Components: Liabilities 3 25,, Outflow ( ) 2,, 5,,,, Age=75 Age=65 Age=55 Age= 5,, Time (Years) Model Components: Default-Free Term Structure Model 4 Spot Rate, R(t,T) 8% 6% 4% 2% % 8% 6% 4% 2% % Term (Years) Note: α =.2, α 2 =.75, σ =., σ 2 =.2, µ=.96, g=-.5

8 Model Components: Credit Behaviour & Credit Spreads We have used a modified version of the (CreditMetrics-style) framework of Jarrow-Lando-Turnbull. Provides a method to describe rating changes and defaults. Provides a potential method for modelling the behaviour of credit spreads. 5 A sample -year credit transition matrix 6 -Year Credit & Default Transition Matrix Rating at End of Period AAA AA A BBB BB B CCC Default AAA 88.%.6%.9%.2%.3% AA 3.9% 88.% 6.7%.9%.3%.3% A.2% 5.4% 87.8% 5.3%.8%.4% -.% 4 BBB.%.6% 9.6% 82.5% 5.3%.3%.2%.4% 5 BB.%.3%.% 9.7% 79.2% 7.2%.9%.7% 6 B -.2%.4%.8% 6.3% 85.4% 2.7% 4.2% 7 CCC - -.5%.5% 2.6% 9.6% 7.4% 4.5% Default % Rating at Start of Period

9 7 Implied default rates Cum Probability of Default (%) % 9% 8% 7% 6% % 4% 3% 2% % % Time (Years) AAA AA A BBB BB B CCC Bond Yields Analysis at st March 2 8 Government Bond Swap Contract AA-rated Bond Prudential Annuity () Scottish Widows () A-rated Bond BBB-rated Bond BB-rated Bond B-rated Bond Default-Free Yield Risk / Liquidity Premium Expected Credit Loss Implied Spread Over Gilt Basis Points 9

10 9 Sample credit spot spreads Spot Spread Over Risk-Free Rate 5% 4% 3% 2% % % AAA AA A BBB BB B CCC M aturity (Years) Note: B&H best estimate transition matrix,δ=.333, π=3 2 Variation in US Credit Spreads Spread over Government Bond (%) BBB minus Govt. AAA minus Govt

11 Model Components: Mortality Model CMI Tables estimate Stochastic Mortality Model Generates random fluctuations around this central estimate. q x (t) = q x (,t)exp[ Y t - σ Y2 /2 - tσ X2 /2 ] 2 Y t = X t +σ Y Z Yt X t = X t- +σ X Z Xt Stochastic Mortality The Basic Idea 22 6 Number of deaths per Year Note : Historical & predicted female population death rates in England & Wales (75 84 yr olds)

12 Stochastic Mortality Calibration A / 7-year-old Male q Year Note: σ X = 4% and σ Y = % Projected Payments Under Stochastic Mortality 24 2,, 9,, 8,, Total Outflow 7,, 6,, 5,, 4,, 3,, 2,,,,,, Time (Years) Barrie & Hibbert Note:Cohort size =, lives

13 Model Components: Valuation Rules Economic analysis Value assets and liabilities at their market values What is the MV of the liabilities? We assume here that they are defaultfree, i.e. discount at gilt yields. 25 Model Components: Valuation Rules Statutory basis Different practice among UK life offices Typical approach: Calc IRR on bond portfolio cash flows (promised cashflows) Make deduction for prudent default loss (typically -25 bp) Apply 97.5% haircut Generally results in statutory yield > gilt yield Does this reflect liquidity or is default allowance inadequate? Also results in statutory solvency position less volatile than economic one Credit spread volatility feeds through to liabilities 26

14 Model Components: Performance Criteria 27 Monte Carlo simulation exercises generate a vast amount of data. What criteria do we want to use to compare different management strategies? Probability of insolvency Statutory Economic Fix insolvency probability & estimate required capital support 28 Case # Expected cash outflows matched with default-free discount (zero-coupon) bonds. Single issue per year of annuity outflow. Mortality is known and deterministic according to the CMI tables. (Stochastic mortality model is switched OFF) All cash flows should be perfectly matched.

15 Case # Matched Govt Bonds; SMM=off 29 Economic Liability Value ( M) 2 Year 5 Portfolio Market Value ( M) 2 3 Case #2 Portfolio invested in (notional) credit-risky (AAA-rated) bonds. Same portfolio value as for case #. Diversified (notional) portfolio of issuers. Mortality is known and deterministic according to the CMI tables. (Stochastic mortality model is switched OFF) Potential mis-matching due to credit risks.

16 Case #2 AAA-rated Bonds; SMM=off 3 Economic Liability Value ( M) 2 Year 5 Portfolio Market Value ( M) 2 Simulated default experience ( AAA-rated issuers) 32 Cumulative Number of Defaults Time (Years) 4 5

17 Distribution of year-by-year portfolio delivered cash flows 33 2,, Portfolio Principal Payout 5,,,, 5,, AAA-rated issues. Buy & hold. Time (Years) Case #8 Year 5; A-rated Bonds; SMM=on; No Rebalance 34 Economic Liability Value ( M) 2 Year 5 Portfolio Market Value ( M) 2

18 35 Case #8 Year 5; A-rated Bonds; SMM=on; No Rebalance Portfolio Market Value ( M) Economic Liability Value ( M) Year 5 36 Case #8 Year 5; A-rated Bonds; SMM=on; No Rebalance Solvency Ratio Stochastic Mortality Factor Year 5

19 37 Case #8 Year 5; A-rated Bonds; SMM=on; No Rebalance Solvency Ratio Average Credit Status Year 5 38 Case #8 Year 5; A-rated Bonds; SMM=on; No Rebalance Solvency Ratio Cumulative Number of Defaults Year 5

20 39 Assessing risk-based capital What do we mean by risk-based capital? The capital required to fund the liabilities with a given level of confidence. Two components: Fair/realistic value Mis-match reserve Two approaches: run-off approach VAR-style percentile calculation Capital requirements to support various credit strategies 4 5% Fixed mortality Capital requirement (% realistic valuation) % 5% Stochastic mortality % GOVT AAA AA A Credit rating of bond portfolio

21 4 Summary Annuity providers are operating in an environment of intense competition. Liabilities are increasingly supported by credit-risky asset portfolios. Profitability hinges on a number of uncertain factors: The future realised credit experience The future realised mortality experience The level of anticipated cash flow matching Interest rate variability Stochastic models enable providers to investigate & quantify these factors providing a path towards: A better understanding of total portfolio exposure Better risk management & capital allocation 42 Copyright 3 Barrie & Hibbert Limited Barrie & Hibbert Limited is regulated by the Financial Services Authority The information in this report is believed to be correct but cannot be guaranteed. All opinions and estimates included in this report constitute our judgement as of the date indicated and are subject to change without notice. This report is intended for information purposes only and is not intended as an offer to buy or sell securities. 23 rd June 3

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