Economic Analysis ofEconomic Analysis of International Solvency Regimes

for Life Annuity Markets

Maathumai Nirmalendran, Michael Sherris, Katja Hanewald

© University of New South Wales© University of New South Wales

OutlineOutline

M ti ti d Obj tiMotivation and Objectives

Comparison of Solvency RegimesComparison of Solvency Regimes

Economic Analysisy

Discussion of Findings

OutlineOutline

M ti ti d Obj tiMotivation and Objectives

Comparison of Solvency RegimesComparison of Solvency Regimes

Economic Analysisy

Discussion of Findings

MotivationMotivation• Longevity risk in societyLongevity risk in society• Enhance market participation in longevity

product marketsproduct markets• Effective regulation trade-off

Consumer AffordabilityPrudential 

Security

Research ObjectivesResearch Objectives

1. Comparison of International Solvency Regimes– Qualitative comparative framework

2. Economic Analysis of an insurer offering lifetime y gguaranteed annuities– Multi‐period value maximization insurer modelp

OutlineOutline

M ti ti d Obj tiMotivation and Objectives

Comparison of Solvency RegimesComparison of Solvency Regimes

Economic Analysisy

Discussion of Findings

Comparison of Solvency RegimesComparison of Solvency Regimes

1. Scope and Overview of existing regimes

2. Comparative framework

3. Regulatory issues for Insurers

Overview of Existing RegimesOverview of Existing Regimes

A t liAustralia

E

ScopeUnited States

European Union

Unitedl d United Kingdom

Switzerland

Comparative FrameworkComparative FrameworkHolzmüller (2009) – based on Cummins et al. (1994)

1. Giving the appropriate incentives

2. Formula should be risk sensitive

3. Formula should be appropriately calibrated

4. Focus on the highest insolvency costs for the economy as a whole

5. Focus on economic values

6. System should discourage misreporting

7. Formula should be as simple as possible

8. Adequacy in economic crises and anticipation of systemic risk

9. Assessment of management

10. Flexibility of framework over time

11. Strengthening of risk management and market transparency

Regulatory Issues for InsurersRegulatory Issues for Insurers

Shortcomings of ComparisonShortcomings of Comparison• Focus on general vs life insurersFocus on general vs life insurers

• Subjective assessment of the different solvency regimesregimes

• Does not consider the regulatory trade-off (bet een cost efficienc for cons mers and(between cost efficiency for consumers and prudential security of the insurer)

OutlineOutline

M ti ti d Obj tiMotivation and Objectives

Comparison of Solvency RegimesComparison of Solvency Regimes

Economic Analysisy

Discussion of Findings

Economic AnalysisEconomic Analysis

• A Life Insurer Value Maximising ModelObjective of the model– Objective of the model

– Model Components and Calibration

• Optimal Solvency levels and Premium Loadings

Life Insurer Value Maximizing ModelLife Insurer Value Maximizing Model• Objective: Assess the optimal capital and pricingObjective: Assess the optimal capital and pricing 

strategy for a life insurer offering life annuities 

d f— Maximising expected profit — Capital subscriptions — One‐year horizon— One‐year horizon— Different premium loadings (0%, 5%, 10%, 15%, 20%)— Different solvency levels (99.9%, 99.5%, 99%, 97%) y ( )

Life Insurer Value Maximizing ModelLife Insurer Value Maximizing ModelAssets and Investment Returns Expenses, 

Claims and Reserves

Term Structure Model

Insurer Model Initial CapitalDemand 

Curve

Frictional Costs

Stochastic Mortality  Costs

Insurer Profit, Enterprise Value Added

Model

Stochastic MortalityStochastic Mortality• Wills and Sherris (2008)

• Australian male mortality rates for ages 50 to 110

Demand CurveDemand Curve• Price‐default risk demand curve from Zimmer,Price default risk demand curve from Zimmer, 

Gründl and Schade (2011)

Term Structure ModelTerm Structure Model• Vasicek model ‐ one‐factor short rate modelVasicek model  one factor short rate model

Assets and Investment ReturnsAssets and Investment Returns• Bonds (86.8%), Stocks (7.7%) and Cash (5.5%)Bonds (86.8%), Stocks (7.7%) and Cash (5.5%)

• Bond returns ‐ short rates generated by the VasicekBond returns   short rates generated by the Vasicek model 

• Stock prices and cash rates are modeled as Geometric Brownian motionsGeometric Brownian motions

Premiums Capital and ExpensesPremiums, Capital and Expenses• Average retirement savings approximately $71,000Average retirement savings approximately $71,000 

for a 65 year old (Australian Bureau of Statistics, 2010)2010)

• Fixed A = $5, 149.70 (for single premium of $70,000, fitted mortality and yield models)$70,000, fitted mortality and yield models)

• Initial Capital subscribed from Shareholders• Expenses are 3.3% of the total annuity premiumExpenses are 3.3% of the total annuity premium 

(Challenger Life Company Ltd)

Claims and ReservesClaims and Reserves• Claims = total benefits paid at the end of the firstClaims   total benefits paid at the end of the first 

year (Q x A x probability of surviving one year).

• Policy liability reserves• net present value of future liabilitiesnet present value of future liabilities • premium loadings weighted by the proportion 

of survivorsof survivors

Frictional CostsFrictional Costs• 3 types from Yow and Sherris (2008)3 types from Yow and Sherris (2008)

— Taxation rate (0% ‐ imputation system)Taxation rate (0%  imputation system)— Total agency costs (2% x capital)— Bankruptcy costs (15%)Bankruptcy costs (15%)

Insurer Model ProfitInsurer Model - Profit

Insurer Model EVAInsurer Model - EVA

OutlineOutline

M ti ti d Obj tiMotivation and Objectives

Comparison of Solvency RegimesComparison of Solvency Regimes

Economic Analysisy

Discussion of Findings

Discussion of FindingsDiscussion of Findings

1. Case by case analysis

2. Sensitivity Testing

3. Final Conclusions3. Final Conclusions

99 5% Case99.5% Case

99 5% Case99.5% Case

Comparison of CasesComparison of Cases

Sensitivity TestingSensitivity Testing• Robustness of Demand ElasticitiesRobustness of Demand Elasticities

Sensitivity TestingSensitivity Testing• Frictional CostsFrictional Costs

ConclusionsConclusions• Positives of Existing Regulation:Positives of Existing Regulation:

• Principles‐based approaches 

• Risk management focusRisk management focus

• Two approaches for capital calculation

• Market valuation of assets and liabilities• Market valuation of assets and liabilities

• Business strategies with future focus and current risk management strategiesmanagement strategies

• Onsite examinations and offsite analysis

ConclusionsConclusions• Limitations and Improvements:Limitations and Improvements:

• Factor‐based calculations for more complex risks reduce the risk sensitivityy

• Use of similar internal models increase potential for more severe impacts from systemic risks

• Higher solvency levels maximized shareholder wealth and also satisfied consumer preferences for solvency

• Explicit prudential regulation which mandates public disclosure of financial reports

F th C t ?Further Comments?