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 International Center for Insurance Regulation (ICIR) Goethe-University Frankfurt Assicurazioni Generali S.p.A. Frankfurt, May 24, th Talk on Insurance and Regulation Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 0/13

2 Disclaimer The findings, views and interpretations expressed herein are those of the authors and should not be attributed to Assicurazioni Generali S.p.A. Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 0/13

3 Motivation Since 2009, esp. German life insurers struggle with low interest rates: Large annual guaranteed rates vs. small return on assets In the EU: 59% of legacy contracts with guarantees between 2% and 4% Deteriorating solvency (Berdin and Gründl (2015)) 2016: Solvency II came into force Market-consistent valuation + risk-based capital Low discount rates + high capital requirement for guarantees Rise in interest rates beneficial for solvency level? Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 1/13

4 Rates are currently increasing... Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 2/13

5 Our Approach Simulate HGB + Solvency II balance sheet of average German life insurer in 2015 Interest rates: (1) low (10Y rf rate = 0.5%), (2) sudden increase to 6% in 2 years, (3) gradual increase by 0.3% p.a. Assets: Mainly sovereign + corporate bonds; calibrated according to EIOPA Stress Test 2014 Liabilities: Portfolio of endowment life (saving) contracts with guaranteed interest rate (=Höchstrechnungszins, 1.25% in 2015) and 30 yrs to maturity Lapse risk: Policyholders can lapse contracts and receive surrender value (=99% of accumulated funds); calibrated to German market Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 3/13

6 Benchmark Interest Rates 1 8% 6% 4% 2% (1) Low interest rates Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 4/13

7 Rising Interest Rates 1 8% 6% 4% 2% (2) Sudden increase 1 8% 6% 4% 2% (3) Gradual increase Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 5/13

8 Calibration Parameter Initial Value Solvency ratio (standard model; no transitionals) 12 Average guarantee in force 3.4% HGB Equity / Assets 1 Modified duration (Assets) 8.3 Modified duration (Liability; scaled to assets) 11.4 Calibration matches representative German life insurer in 2015 Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 6/13

9 Increasing lapse rates % 3 25% 2 15% 1 5% (2) Sudden increase. 4 35% 3 25% 2 15% 1 5% (3) Gradual increase. Figure: Lapse rate across cohorts in each year. Median lapse rate increases from 2.7% (2015) to 7.5% upon sudden increase High surrender payments to policyholders Note: 7.5% much more conservative than 2018 EIOPA stress test (lapse rate = 2) Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 7/13

10 ...result in liquidity need (1) Low (2) Sudden Increase (3) Gradual Increase Figure: Free cash flow / Assets 0. Roughly 2 of initial assets sold over time in case of sudden increase (2) ( total debt security holdings of German life insurers in 2017) Substantial market impact Fire sales + liquidity spirals? Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 8/13

11 HGB Own Funds Niederstwertprinzip: Assets but not liabilities depreciate under HGB (1) Low (2) Sudden Increase (3) Gradual Increase (a) HGB own funds / total assets. 2 15% 1 5% (1) Low (2) Sudden Increase (3) Gradual Increase (b) ZZR / Liabilities. Interest rate rise worse than low interest rates on HGB balance! Zinszusatzreserve exacerbates adverse effect and increases even after interest rate rise! Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 9/13

12 SII Own Funds and Surrender Payments Solvency II: market-consistent valuation Assets + Liabilities depreciate Own Funds / Assets increase due to duration gap BUT: Best estimate might fall below surrender value Each contract lapsed can cost own funds Reduction of own funds MCV Figure: Surrender return upon a gradual increase (3): Relative difference between best estimate and surrender value. Best estimate < surrender value if interest rates are high Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 10/13

13 SII Own Funds (1) Low (2) Sudden Increase (3) Gradual Increase Figure: SII own funds / total assets. a) Interest rate rise generally positive b) Surrender payments make (2) sudden rise less favorable than (3) gradual rise in first years Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 11/13

14 Solvency Ratio (1) Low (2) Sudden Increase (3) Gradual Increase Figure: Solvency II ratio: OF/SCR. SCR increases as absolute interest rate shock increases with rates (r down = (1 δ)r) Sudden increase detrimental for solvency Gradual increase beneficial Berdin, Gründl, Kubitza - Rising interest rates, lapse risk, and the stability of life insurers 12/13

15 Conclusion Rising interest rates... result in liquidity need of up to 2 of total assets fire sales (?) are beneficial on SII but not HGB balance sheet accounting frictions! jeopardize solvency if increase is too fast.

16 Thank you.

17 References Berdin, E. and Gründl, H. (2015). The Effects of a Low Interest Rate Environment on Life Insurers. Geneva Papers on Risk and Insurance - Issues and Practice, 40: European Insurance and Occupational Pensions Authority (EIOPA) (2014). Technical specification for the solvency ii preparatory phase. available at insurance/solvency-ii/solvency-ii-technical-specifications.

18 Appendix

19 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 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 2015 (model) < ε, increase d 2 and go to 1). Else: Return. ) N ( µ t, σt 2 )

20 Calibration (1/2) Asset weights based on avg German insurer in 2015 (EIOPA (2016)): 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 20 sovereign bonds, 10 corporate bonds that mature in t = 0, 1, 2,... Duration = 8.26 years ( GDV (2013), EIOPA (2016))

21 Calibration (2/2) Back book with contracts that mature at times t = 0, 1,..., 29 Liability duration = 11.4 ( GDV (2013), EIOPA (2016)) Average guarantee outstanding at t = 0: 3.4% ( EIOPA (2016)) Lapse penalty 1 ϑ = 1%

22 Solvency Capital Requirements Standard model of Solvency II: SCR = OF t OF shocked Market risk: interest rate, equity, property, spread Lapse risk: down/up/mass shock of lapse rates Solvency ratio: OF/SCR (without LTGM or ERM) Initial Solvency Ratio = 12 ( BaFin (2016)) OF /MV (Assets) 8% ( EIOPA (2016))

23 Bonds FV Coupons Premiums Bonds FV Coupons Premiums Bonds FV Coupons Premiums (1) Low interest rates. 0 (2) Sudden increase. 0 (3) Gradual increase. Figure: Composition of median cash inflows over time scaled by the market value of assets at time t = 0. Bonds FV are face-value payments of maturing bonds. Coupons consists of bond coupon, rent, and dividend payments. Premiums are the annual premiums of policyholders.

24 Lump-sum benefit Surrender payments Lump-sum benefit Surrender payments Lump-sum benefit Surrender payments (1) Low interest rates. 0 (2) Sudden increase. 0 (3) Gradual increase. Figure: Composition of median cash outflows over time scaled by the market value of assets at time t = 0. Lump-sum benefit are payments to policyholders at contract end. Surrender payments are payments to policyholders lapsing their contract before maturity.

25 MCV 1 MCV 1 MCV (1) Low interest rates. (2) Sudden increase. (3) Gradual increase. MCV SV Figure: MCV surrender return, MCV lapse =, in different interest rate environments. MCV MCV lapse reflects the return on market-consistent value of a life insurance contract (MCV) that the insurer earns upon the contract lapsing. The figure shows the distribution of the median surrender return for each cohort over time. The straight and thick line depicts the median (across cohorts) median (within cohorts) lapse rate over time. If MCV lapse < 0, the insurer makes a loss on the MCV balance sheet upon contract s lapsing.

26 (1) Low (2) Sudden Increase (3) Gradual Increase (a) Market-consistent valuation (1) Low (2) Sudden Increase (3) Gradual Increase (b) Historical cost accounting. Figure: Own funds ratio: Own funds relative to total assets at (a) market-consistent values and (b) historical cost accounting values. Median and 9 confidence interval over time for the three interest rate environments (1) low interest rates, (2) sudden increase in interest rates, and (3) gradual increase in interest rates.

27 1 8% RoA (without depreciation) Depreciation 1 8% RoA (without depreciation) Depreciation 1 8% RoA (without depreciation) Depreciation 6% 6% 6% 4% 4% 4% 2% 2% 2% (1) Low interest rates. (2) Sudden increase. (3) Gradual increase. Figure: Insurer s return on assets and depreciation of HCA book values. The figures compare the book value of assets at time t with time t 1 with respect to the pure asset return (including coupon, dividend, and rent payments) and depreciation of book value (upon a decline of at least 1 of market values compared to face values). We show the median and 9 confidence at each point in time.

28 2 15% 1 5% (1) Low (2) Sudden Increase (3) Gradual Increase (a) Interest rate reserve (1) Low (2) Sudden Increase (3) Gradual Increase (b) HCA own funds - respective IRR. Figure: Impact of interest rate reserve. (a) Size of the German interest rate reserve (IRR; German: ZZR) relative to the book value of liabilities including the IRR, (L IRR t L BV t )/L IRR t. (b) HCA value of own funds when accounting for the IRR as a liability.

29 4% 4% 4% 3% 3% 3% 2% 2% 2% 1% rg (constant lapse) rg (sensitive lapse) (1) Low interest rates. 1% rg (constant lapse) rg (sensitive lapse) (2) Sudden increase. 1% rg (constant lapse) rg (sensitive lapse) (3) Gradual increase. Figure: Average guarantee in force (weighted by the MCV of insurance contracts). Sensitive lapse refers to the baseline situation with lapse rates being sensitive to interest rates and contract age. Constant lapse refers to a situation with constant probability of lapsing for each policyholder, λ =

30 Solvency Capital Requirement SCR Lapse SCR Interest Rates SCR Remaining Market + Div SCR Lapse SCR Interest Rates SCR Remaining Market + Div SCR Lapse SCR Interest Rates SCR Remaining Market + Div (1) Low interest rates (2) Sudden increase (3) Gradual increase. Figure: Solvency II capital requirement (SCR) / liabilities. Interest rate risk drives SCR SCR increases although guarantee decreases: Absolute shock is larger with higher interest rates: r down 10 = r 10 r

31 SCR Lapse SCR Interest Rates SCR Remaining Market + Div SCR Lapse SCR Interest Rates SCR Remaining Market + Div SCR Lapse SCR Interest Rates SCR Remaining Market + Div (1) Low interest rates (2) Sudden increase (3) Gradual increase. Figure: Solvency II capital requirement (SCR) as a share of the MCV of liabilities. SCR Lapse refers to the capital requirement for lapse risk; SCR Interest Rates refers to the capital requirement for interest rate risk; SCR Remaining Market + Div. to the capital requirement for remaining market risks (equity, property, and spread risk) and accounts for diversification effects between SCRs for different risks according to the correlation coefficients given by the European Insurance and Occupational Pensions Authority (EIOPA) (2014).

32 (1) Low (2) Sudden Increase (3) Gradual Increase Figure: Solvency II ratio as own funds to solvency capital requirement (SCR). Median and 9 confidence interval over time for the three interest rate environments (1) low interest rates, (2) sudden increase in interest rates, and (3) gradual increase in interest rates.

33 4.5 % 4.5 % Profit Participation 4 % 3.5 % 3 % 2.5 % 2 % (a) In year 9. Observedr P ˆr P : β t,1 = Profit Participation 4 % 3.5 % 3 % 2.5 % Observed r P ˆr P ; β t,1 = % (b) In year 20. Figure: Environment (2): Observed and predicted profit participation for calculating the market-consistent value (MCV) of life insurance contracts.