Managing Life Insurer Risk and Profitability: Annuity Market Development using Natural Hedging Strategies

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1 Managing Life Insurer Risk and Profitability: Annuity Market Development using Natural Hedging Strategies 1st CEPAR International Conference Analysing Population Ageing: Multidisciplinary perspectives and innovation Andy Wong, Michael Sherris and Ralph Stevens ARC Centre of Excellence in Population Ageing Research School of Risk and Actuarial Studies The University of New South Wales 2 July 2013 Michael Sherris (UNSW) Natural Hedging 2 July / 15

2 Introduction Population ageing and the need for post-retirement income products to manage longevity risk Costs of capital for life annuity products Natural hedging - offsetting of longevity risks in annuities with life insurance - potential to improve life annuity profitability Profit loadings, types of life insurance and regulatory capital requirements Michael Sherris (UNSW) Natural Hedging 2 July / 15

3 Natural Hedging Natural hedging involves managing longevity risk by sales of both life insurance and annuity business Products have different profit loadings Capital requirements can be reduced through diversification of risks Aims are to assess Effectiveness of natural hedging Impact of profit and policy type on product mix Solvency capital Michael Sherris (UNSW) Natural Hedging 2 July / 15

4 Previous studies Empirical evidence for natural hedging: Cox and Lin (2007). Value hedging approach Immunisation approach for natural hedging: Wang et al (2010). Delta gamma hedging natural hedging portfolios: Luciano et al (2012). Risk minimisation approaches CVaR minimising portfolio: Tsai et al (2010). Natural hedging on insurer surplus: Gatzert and Wesker (2012). Michael Sherris (UNSW) Natural Hedging 2 July / 15

5 Mortality and Interest Rate Models Affine mortality model based on Schrager (2006) Models mortality curve using Makeham mortality law µ x (t) = Y 1 (t) + Y 2 (t)c x Y1 and Y 2 follow Ornstein-Uhlenbeck process Calibrated to UK mortality Interest rates modelled using a CIR model (Cox Ingersoll Ross (1985)) dr(t) = κ(θ r(t))dt + σ r(t)dw 1 (t) Michael Sherris (UNSW) Natural Hedging 2 July / 15

6 Life insurer balance sheet Assets of insurer at time t denoted A(t) A(t) = A(t 1)(1 + r(t)) + n L (t) P L n A (t) a d L (t) DB (1) Liabilities of the insurer at time t denoted L(t) Surplus of insurer at time t is E(t) = A(t) L(t) Risk and Economic Capital VaR Solvency Michael Sherris (UNSW) Natural Hedging 2 July / 15

7 Results Factors considered Policy type Profit loading Dynamic pricing strategy Solvency capital Michael Sherris (UNSW) Natural Hedging 2 July / 15

8 Policy types and natural hedging Policy Combinations: annuity age 65 and Whole life insurance single premium age 35 Whole life insurance level premiums age year term life level premium age 35 Table : Risk levels of policy types Policy type 99% VaR Whole life insurance single premium 33.69% Whole life insurance level premiums 32.51% Term insurance level premiums 39.49% Whole life annuity 13.30% Michael Sherris (UNSW) Natural Hedging 2 July / 15

9 Michael Level Sherris premiums (UNSW) increases natural Natural Hedging hedging effect compared2 July to 2013 life 9 / 15 Policy types and natural hedging 99% VaR as percentage of liabilities (%) VaR by policy type Single premium whole life insurance Level premium whole life insurance Level premium 30 year term insurance Weight in annuities Figure : Life insurance policy types

10 Profit loading on natural hedging 99% VaR as percentage of liabilities (%) Profit loading on single premium whole life insurance 0% Loading 20% Loading life insurance 20% Loading annuities Weight in annuities Figure : Level premium 30 year term insurance with 20% profit loading Michael Sherris (UNSW) Natural Hedging 2 July / 15

11 Relative sensitivity to profit loading Table : Sensitivity profit loading Policy Relative VaR reduction Absolute VaR reduction Whole life single prem 30.54% 10.29% Whole life level prem 36.26% 11.79% Term life level prem 23.79% 9.39% Whole life annuity 79.04% 10.52% Profit loading shifts the distribution of losses Michael Sherris (UNSW) Natural Hedging 2 July / 15

12 Dynamic pricing reduces risk level for an insurer but also reduces natural hedge potential Michael Sherris (UNSW) Natural Hedging 2 July / 15 Dynamic pricing strategy Dynamic pricing strategy involves an insurers issuing a series of 1 year term insurance contracts 99% VaR as percentage of liabilities (%) Dynamic pricing and natural hedging 30 year term insurance 1 year term insurance renewed for 30 years Weight in annuities

13 Solvency Capital Table : Solvency reserves for single premium whole life insurance as a percentage of liabilities Annuity Weight 99% VaR 99% Solvency reserve % 36.04% % 32.56% % 28.63% % 24.43% % 22.12% % 17.99% % 14.99% % 12.34% % 11.32% % 11.63% % 14.70% 99% Solvency reserve is lower than VaR Michael Sherris (UNSW) Natural Hedging 2 July / 15

14 Solvency II capital Solvency II capital as percentage of liabilities (%) Solvency II capital by policy type Single premium whole life insurance Level premium whole life insurance Level premium 30 year term insurance Weight in annuities Figure : Solvency II capital by policy type Michael Sherris (UNSW) Natural Hedging 2 July / 15

15 Key Findings and Contributions Application of stochastic mortality model for pricing, valuation and risk management Natural hedging can reduce capital costs but requires a significant volume by premium of annuity business Level premium longer term life insurance more effective than renewable term insurance Higher relative loadings in life insurance reduce the volume of annuity business required Multiple period VaR more realistic measure of capital than Solvency II 1-year horizon Michael Sherris (UNSW) Natural Hedging 2 July / 15