Rising interest rates, lapse risk, and the stability of life insurers

Transcription

1 Rising interest rates, lapse risk, and the stability of life insurers Elia Berdin, Helmut Gründl, Christian Kubitza Chair for Insurance and Regulation and International Center for Insurance Regulation (ICIR) Goethe-University Frankfurt Barcelona, October 23, 217 IAA Life Colloquium Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers /26

2 Motivation Since 29 life insurers have been struggling with low interest rates Large annual guarantees vs. small return on assets Deteriorating solvency (Berdin and Gründl (215)) Rise in interest rates beneficial for solvency? 216: Solvency II came into force Fair value-oriented valuation + risk-based capital Impact of rising interest rates on life insurers balance sheets? Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 1/26

3 Rise in interest rates A) Valuation benefit: Liabilities decrease faster than assets (duration gap) Own funds increase ( fair value BS) B) Liquidity risk: 9% of EU life contracts with lapse penalty < 15% (ESRB (215)) Rise in interest rates High lapse rate Large outflows (Recovery Value) but small inflows (RoA) Negative free cash flow ( book value BS) Own funds might decrease ( fair value BS) C) Lapse risk: Minimum return guarantee put option Rise in interest rates Lapse if guarantee small Policies with large guarantees remain in portfolio Riskier contracts Capital requirement Overall effect? Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 2/26

4 Literature Berdin and Gründl (215) and Berdin (216) study the impact of low interest rates on life insurers solvency Feodoria and Förstemann (215) show that it is rational for policyholders to lapse if interest rates rise too much Positive interest rate shocks relate to larger empirical lapse probabilities (Dar and Dodds (1989), Kim (25), Kuo et al. (23), Kiesenbauer (212), Russell et al. (213), Russo et al. (217)) Albizzati and Geman (1994) price the surrender option in case of volatile interest rates Le Courtois and Nakagawa (29) and Buchardt (214) establish a link between an insurer s PD and lapse risk Barsotti et al. (216) model lapse risk contagion Gap: Impact of interest rate rise in combination with lapse risk on an insurer s balance sheet. Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 3/26

5 Liabilities Accumulation phase of endowment life contracts (variable annuities) with fixed annual premiums and lump-sum benefit upon maturity Upon lapse: recovery value = ϑ accumulated funds, < ϑ < 1 Initial back book with contracts that mature at times t =, 1,..., 29 Liability duration = 15 Each cohort h of contracts features guaranteed rate of return rg h and profit participation rs,t h such that accumulated funds are ) Vt h = Vt 1 (1 h max + rg h, 1 + r S,t h r h G follows reference rate (=.6 MA 1(r rf )) in.5% steps r h S,t 9% RoA t ( German legislation) Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 4/26

6 Liabilities: Market-consistent valuation Market consistent (fair) contract value: PV (Liabilities) = V t PV (future guarantee + profit participation) Future profit participation, r S,t+s, is predicted by linear model estimated with average profit participation in previous 1 years: ˆr S,t+s = ˆβ t,1 + ˆβ t,2 log(s) 4.5 % Profit Participation 4 % 3.5 % 3 % 2.5 % Historical rs Fitted rs; beta 2 =.38 2 % Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 5/26

7 Liabilities: Lapse Risk Benchmark: λ 2.86% (average German lapse rate in 215) Interest-Rate Sensitive (IRS) Lapse: where λ h t ( rt h, Tt h ) = a + e c ed 1 rh t +d 2 T t h, r h t = r h G r rf (t) : excess guaranteed rate with sensitivity d 1 > Higher guarantee Smaller lapse rate T h t : current contract age with sensitivity d 2 > Older contracts Smaller lapse rate a = 1%: minimum lapse rate c N (µ c, σ 2 c ) : random effect across PH within cohort Calibration based on average lapse rates for in German endowment life business Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 6/26

8 Liabilities: Lapse Risk Calibration 5 % 4 % Average Lapse Rate 9% Confidence Interval 5 % 4 % Average Lapse Rate 9% Confidence Interval Lapse Rate 3 % 2 % Lapse Rate 3 % 2 % 1 % 1 % % 4 % 2 % % 2 % 4 % % 4 % 2 % % 2 % 4 % r G - r rf r G - r rf (a) T h t = 1 (b) T h t = 15 Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 7/26

9 Asset Allocation Risk-free rate a la Hull and White (199) with mean reversion level ( ) 1 θ r (t) = γ + (β γ) e b(t h) dr(t) = α r (θ r (t) r(t))dt + σ r dw r (t) Calibration of initial yield curve: German bond yields in 215 Assets with aggregate duration 8.26 years and initial weights based on average German insurer in 215: Asset Portfolio Weights Sovereigns w sov 56.7% Corporate w corp 34.3% Stocks w stocks 5.6% Real Estate w real estate 3.4% Revolving portfolio with 2 sovereign bonds, 1 corporate bonds that mature in t =, 1, 2,... Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 8/26

10 Interest Rate Environments 8% 6% 4% 2% % Low Interest Rates 8% 6% 4% 2% % Sudden Upward Shock 8% 6% 4% 2% % Gradual Increase Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 9/26

11 Solvency Capital Requirements Capital requirements based on standard model of Solvency II Market risk: interest rate, equity, property, spread Lapse risk: down/up/mass shock of lapse rates up/mass shock: if recovery value > PV(liabilities), e.g. in times of small predicted profit participation down shock: if recovery value < PV(liabilities) e.g. in times of large predicted profit participation Solvency ratio: Own Funds/SCR Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 1/26

12 Environment (1): Interest Rates 8% 6% 4% 2% % Low Interest Rates 8% 6% 4% 2% % % 6% 4% 2% % Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 11/26

13 Environment (1): Liquidity 4 % 3 % 2 % 1 % % 6% 5% 4% 3% 2% 1% RoA RtP 1 % (a) Free Cash Flow / BV(Assets) (b) Return on Assets & to PH With interest rate sensitive lapses (dashed): Large guarantee contracts mature lapse rate FCF Large guarantee contracts lapse less average guarantee Low interest rates RoA declines Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 12/26

14 Environment (1): Solvency 8% 7% 6% 5% 4% 3% 2% (a) Own Funds / MV(Assets) 5% 4% 3% 2% 1% (b) Solvency Ratio With interest rate sensitive (IRS) lapses (dashed): Recovery values > PV(Liabilities) Own funds Average guarantee SCR Solvency ratio Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 13/26

15 Environment (2): Interest Rates 8% 6% 4% 2% % % 6% 4% 2% % Sudden Upward Shock 8% 6% 4% 2% % Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 14/26

16 Environment (2): Lapse Rates 4% 35% 3% 25% λt 2% 15% 5% Sharp increase in lapse rates Guarantees adjust very slowly Lapse rates high for long time Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 15/26

17 Environment (2): Liquidity 6% 5% 4% 3% 2% RoA RtP 6 % 4 % 2 % % 1% (a) Return on Assets & to PH 2 % (b) Free Cash Flow / BV(Assets) 1 st year: enormous asset depreciations Steady increase in RoA Decline in RtP due to slow adjustment of guarantees With IRS lapses (dashed): Substantial lapse rate of low-guarantee contracts RtP Enormous cash outflows Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 16/26

18 Environment (2): Liability Valuation 4.5 % 4.5 % Profit Participation 4 % 3.5 % 3 % 2.5 % Historical rs Fitted rs; beta 2= % (a) t = 9. Profit Participation 4 % 3.5 % 3 % 2.5 % Historical rs Fitted rs; beta 2=.7 2 % (b) t = 2. t = 1: Profit participation is predicted to increase for the first time PV(future benefits) substantially increases Recovery value << PV(liabilities) Own funds increase with lapse Sensitivity towards lapse changing from up- to down-shock Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 17/26

19 Environment (2): Solvency 8% 7% 6% 5% 4% 3% 2% (a) Own Funds / MV(Assets) 5% 4% 3% 2% 1% (b) Solvency Ratio Peak at t = 1: Change in extrapolation of r S Less sensitive with IRS lapses (smaller r S r G ) Average guarantee larger with IRS lapses SCR smaller Solvency Ratio In the long run: recovery values < PV(liabilities) Own funds with more lapse Solvency Ratio Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 18/26

20 Environment (3): Interest Rates 8% 6% 4% 2% % % 6% 4% 2% % % 6% 4% 2% % Gradual Increase Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 19/26

21 Environment (3): Lapse Rates λt 4% 35% 3% 25% 2% 15% 5% (a) Over time. λt 4% 35% 3% 25% 2% 15% 5% of Contract Begin (b) Over cohorts. Gradual increase in average lapse rates over time Large variation across but not within cohorts Increase in interest rates (lapse ) sets off increase in contract age (lapse ) Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 2/26

22 Environment (3): Liquidity 6% 5% 4% 3% RoA RtP 6 % 4 % 2 % 2% 1% (a) Return on Assets & to PH % 2 % (b) Free Cash Flow / BV(Assets) With IRS lapse (dashed): 1 years until RoA t RoA and RoA t RtP t small profit participation for substantial time Substantial liquidity need with IRS lapse Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 21/26

23 Environment (3): Solvency 8% 7% 6% 5% 4% 3% 2% (a) Own Funds / MV(Assets) 5% 4% 3% 2% 1% (b) Solvency Ratio PV(Liabilities) recovery values Own funds with IRS lapses (dashed) Average guarantee with IRS lapses SCR Solvency Ratio Long run: recovery values < PV(Liabilities) Own funds with lapse Solvency Ratio Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 22/26

24 Conclusion A sudden upward shock in interest rates jeopardizes a life insurer s liquidity for the next 2 years due to enormous recovery payments endangers the solvency situation for the next 5 years due to expensive guarantees A gradual increase in interest rates substantially worsens liquidity situation slightly reduces solvency cannot make up for small profit participation 2 main drivers: 1. More expensive liability portfolio as low-guarantee contracts lapse 2. PV(Liabilities) - Recovery Value : Increase vs. reduction in own funds upon lapse Up- vs. down-shock capital requirement for lapse Highly sensitive towards RoA forecast Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 23/26

25 Thank you for your attention Christian Kubitza Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 23/26

26 References Albizzati, M. O. and Geman, H. (1994). Interest rate risk management and valuation of the surrender option in life insurance policies. Journal of Risk and Insurance, pages Barsotti, F., Milhaud, X., and Salhi, Y. (216). Lapse risk in life insurance: Correlation and contagion effects among policyholders behaviors. Insurance: Mathematics and Economics, 71: Berdin, E. (216). Interest Rate Risk, Longevity Risk and the Solvency of Life Insurers. ICIR Working Paper Series (forthcoming). Berdin, E. and Gründl, H. (215). The Effects of a Low Interest Rate Environment on Life Insurers. Geneva Papers on Risk and Insurance - Issues and Practice, 4: Buchardt, K. (214). Dependent interest and transition rates in life insurance. Insurance: Mathematics and Economics, 55: Dar, A. and Dodds, C. (1989). Interest rates, the emergency fund hypothesis and saving through endowment policies: some empirical evidence for the uk. Journal of Risk and Insurance, 56(3): Feodoria, M. and Förstemann, T. (215). Lethal lapses - how a positive interest rate shock might stress german life insurers. Deutsche Bundesbank Discussion Paper, (12). Hull, J. and White, A. (199). Pricing Interest-Rate-Derivative Securitites. The Review of Financial Studies, 3(4): Kiesenbauer, D. (212). Main determinants of lapse in the german life insurance industry. North American Actuarial Journal, 16(1): Kim, C. (25). Modeling surrender and lapse rates with economic variables. North American Actuarial Journal, 9(4):45 7. Kuo, W., Tasi, C., and Chen, W. K. (23). An empirical study on the lapse rate: the cointegration approach. Journal of Risk and Insurance, 7(3): Le Courtois, O. and Nakagawa, H. (29). Surrender risk and default of insurance companies. Working Paper, EM Lyon Business School (France) and Hitotsubashi University (Japan). Russell, D. T., Fier, S. G., Carson, J. M., and Dumm, R. E. (213). An empirical analysis of life insurance policy surrender activity. Journal of Insurance Issues, pages Russo, V., Giacometti, R., and Fabozzi, F. J. (217). Intensity-based framework for surrender modeling in life insurance. Insurance: Mathematics and Economics, 72: Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 23/26

27 Backup Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 23/26

28 Calibration of lapse rates Average lapse rate in year t based on German environment: λ t = log (λ t a) = c + log ( 1 h nh t ) ( + log h n h t e ed 1 rh t +d 2 T h t ) N ( µ t, σt 2 ) Observations: Log excess average German lapse rates L 1,..., L n. 1) Repeat until convergence of µ c and σ c (c N (µ c, σc 2 ): a) d 1 = arg min ) 2 t ( λt L t b) Update µ c and σ c via ML estimators 2) If λ 215 (model) <.286 ε, increase d 2 and go to 1). Else: Return. Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 24/26

29 Environment (1): Lapse λt 4% 35% 3% 25% 2% 15% 5% (a) Over time. λt 4% 35% 3% 25% 2% 15% 5% of Contract Begin (b) Over cohorts. First: Large guarantee contract mature and lapse rates slightly increase Then: Lapse rates mainly depend on contract duration since r G r rf Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 25/26

30 Environment (2): Lapse λt 4% 35% 3% 25% 2% 15% 5% (a) Over time. λt 4% 35% 3% 25% 2% 15% 5% of Contract Begin (b) Over cohorts. Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 26/26