LIABILITY PORTFOLIO MANAGEMENT Diversification of Longevity and Mortality Risk Stuart Silverman, FSA, MAAA, CERA Longevity 12 September 29-30, 2016

LIFE INSURANCE MORTALITY VS. ANNUITY/PENSION LONGEVITY Commonly Held Beliefs: Increased life insurance claims offset by reduced annuity payouts Increased longevity increases annuity payouts but reduces insurance death claims Therefore, a balanced portfolio of life insurance and annuity/pension liabilities may be “immunized” against changes in mortality experience. Yes, but how do we quantify it? 2

LIFE INSURANCE MORTALITY VS. ANNUITY/PENSION LONGEVITY 5/19/2018 8:52 PM LIFE INSURANCE MORTALITY VS. ANNUITY/PENSION LONGEVITY Historical Mortality Improvement Experience – US Population 1960-2010 Male Age 35 vs. Male Age 75 Correlation Coefficient = 1.8% 3

LIFE INSURANCE MORTALITY VS. ANNUITY/PENSION LONGEVITY 5/19/2018 8:52 PM LIFE INSURANCE MORTALITY VS. ANNUITY/PENSION LONGEVITY Historical Mortality Improvement Experience – US Population 1960-2010 5-Year Moving Average Average Male Ages 30-39 vs. Average Male Ages 70-79 From 1960-2010 Correlation = 26.3% BUT from 1985-2010, Correlation = -38.1% 4

LIFE INSURANCE MORTALITY VS. ANNUITY/PENSION LONGEVITY From our analyses, there is some offset, but it is by no means perfectly matched. It may be in the best interest of a company to understand the diversification of mortality and longevity risk for the following areas: Pricing Products Setting Economic Surplus Determining Appropriate Levels of Margins Mix of Business Considerations Including allocation of resources 5

PROJECTING MORTALITY/LONGEVITY USING STOCHASTIC MODELS Milliman REVEAL is a proprietary software tool that generates stochastic mortality scenarios reflecting volatility of Trend Risk Basis Risk Long-Term Underwriting Risk Extreme Long-Term Event Risk Catastrophic Short-Term Event Risk Provides insight into liability risks previously covered by fixed margins applied to the mortality and longevity assumptions. 6

ADDING VOLATILITY TO MORTALITY ASSUMPTIONS TREND RISK (Changes in Mortality Improvement) May develop assumptions from US Population Experience or Company-Specific Data, reflecting three factors: Long term mortality improvement trends Short-Term (annual) mortality improvement volatility Correlation in mortality improvement trend volatility 7

ADDING VOLATILITY TO MORTALITY ASSUMPTIONS BASIS RISK (variations from base mortality table) Assumed mortality based on standard industry tables but business placed with any given insurer may reflect different characteristics from the those underlying standard tables. Annuity example – The risks associated with annuitant lives may vary by occupation, size of policy, or region. Life insurance example – The underwriting process assigns each life to discrete underwriting classes, each of which may cover a range of expected mortality. 8

ADDING VOLATILITY TO MORTALITY ASSUMPTIONS LONG TERM UNDERWRITING RISK (Life Insurance Only) Effect of underwriting wears off  Select and Ultimate Mortality Tables preferred or substandard selection risk may wears off That produces uncertainty: around the length of the initial selection period, around years over which preferred or substandard rating takes to wear off around ultimate level of mortality after the completion of the wearing off. 9

ADDITIONAL SOURCES OF VOLATILITY Extreme Long Term Events Events that cause mortality rates to change faster and more abruptly than anticipated in the other sources. Examples: Effective new treatments for specific diseases Evolution of drug-resistant infections Catastrophic Short Term Events Abrupt temporary deviations in mortality trends. Terrorism Flu epidemic Natural Disaster 10

ADJUSTING MIX OF BUSINESS TO MAXIMIZE PROFITABILITY Company’s risk management includes the decision whether to grow, acquire, or divest different types of business. Analysis of interaction between different business types important information For example: Insight into managing economic capital. Interaction of business types  Determining if block of business should be divested or de-emphasized. Offering more competitive pricing on particular product Increased sales Shift product portfolio mix 11

RECONSIDERING FIXED MARGIN USING STOCHASTIC ANALYSIS Expected Results With Fixed Margin Consider company’s objective to add a margin sufficient to achieve results comparable to 90th percentile of Best Estimate? ≈  Stochastic Best Estimate (No Margin) between 95th and 99th Percentiles Modify Pricing Margins for Targeted Risk Metric Risk metrics are those presented in Recent Case Study: “Diversification of longevity and mortality risk” http://www.milliman.com/uploadedFiles/insight/2016/Diversification-longevity-mortality-risk.pdf 12

RECONSIDERING THE FIXED MARGIN FROM CASE STUDY Table 17 from Case Study Summary of Stochastic Results – Combined Discount Rate Deterministic Baseline Baseline with Fixed Margin 50th Percentile 75th Percentile 90th Percentile 95th Percentile 99th Percentile 4.00% $4,022,238 $2,093,713 $3,883,071 $3,296,649 $2,703,189 $2,270,528 $1,690,322 8.00% $525,466 ($537,499) $469,296 $112,191 ($219,509) ($494,029) ($826,082) 12.00% ($1,100,518) ($1,745,275) ($1,134,811) ($1,358,610) ($1,564,205) ($1,750,889) ($1,968,886) IRR 9.00% 6.89% 8.89% 8.21% 7.56% 7.01% 6.33% Fixed margin produces IRR comparable to 95th – 99th percentile stochastic projection. But what if company pricing measures targets for risk tolerance at the 90th percentile? 13

RECONSIDERING THE FIXED MARGIN FROM CASE STUDY TERM LIFE INSURANCE: 105% of best estimate annual mortality rates, and Best estimate annual mortality improvement rates reduced 0.50% PAYOUT ANNUITY: 95% of best estimate annual mortality rates, and Best estimate annual mortality improvement rates increased 0.50% REVISED FIXED MARGIN (to achieve 90th percentile target) TERM LIFE INSURANCE: 103% of best estimate annual mortality rates, and Best estimate annual mortality improvement rates reduced 0.40% PAYOUT ANNUITY: 97% of best estimate annual mortality rates, and Best estimate annual mortality improvement rates increased 0.40% 14

RECONSIDERING THE FIXED MARGIN FROM CASE STUDY Table 22 from Case Study Deterministic vs. Fixed Margin vs Stochastic Results Discount Rate Deterministic Baseline Baseline with Original Fixed Margin Baseline with Revised Fixed Margin 75th Percentile Baseline 90th Percentile Baseline 95th Percentile Baseline 99th Percentile Baseline 4.00% $4,022,238 $2,093,713 $2,648,076 $3,296,649 $2,703,189 $2,270,528 $1,690,322 8.00% $525,466 ($537,499) ($223,971) $112,191 ($219,509) ($494,029) ($826,082) 12.00% ($1,100,518) ($1,745,275) ($1,550,119) ($1,358,610) ($1,564,205) ($1,750,889) ($1,968,886) IRR 9.00% 6.89% 7.55% 8.21% 7.56% 7.01% 6.33% Revised fixed margin produced IRRs equivalent to 90th percentile stochastic projection. 15

RECONSIDERING MARGINS USING STOCHASTIC ANALYSIS 2 Original Margins ≈ 97th percentile 1 Expected (No Margins) ≈ 50th Percentile 3 Revised Margins ≈ 90th Percentile Risk metrics are those presented in the Case Study: “Diversification of longevity and mortality risk” http://us.milliman.com/uploadedFiles/insight/2016/Diversification-longevity-mortality-risk.pdf 16

ADJUSTING MIX OF BUSINESS TO MAXIMIZE PROFITABILITY A key aspect of a company’s risk management includes the decision whether to grow, acquire, or divest different types of business. Analysis of the direct risk interaction of the different types of business can provide vitally important information. For example, A type of business is significantly diversifying from the company’s existing portfolio; the company may want to offer more competitive pricing. Insight into underlying risk metrics can be helpful to managing economic capital. Understanding the interaction of these types of business may be useful in determining if a block of business should be divested or de-emphasized. As can be seen from the following table, using deterministic margins was not particularly helpful when considering business management. As the mix of business changed, the Revised Fixed Margins were no longer consistent with the desired risk metrics. 17

ADJUSTING MIX OF BUSINESS TO MAXIMIZE PROFITABILITY Selected Data from Tables 22-24 from the Case Study Comparison of IRR with Different Mixes of Business Therefore, optimal mix allowed for significantly more annuity business, and the deterministic margins need to be revisited as the mix of business changes. Discount Rate Deterministic Baseline Baseline with Original Fixed Margin Baseline with Revised Fixed Margin 90th Percentile 100% Baseline Term and 100% Baseline Annuities IRR 9.00% 6.89% 7.55% 7.56% 100% Baseline Term and 500% Baseline Annuities 6.70% 7.43% 7.57% 100% Baseline Term and 1000% Baseline Annuities 6.53% 7.32% 7.40% 18

TAKE-AWAYS Stochastic Modeling of Liability Risk can: Provide insight into the diversification of mortality and longevity risks Areas in which stochastic liability modeling can be helpful Pricing - Guide setting of fixed margins affecting profitability & competitiveness Economic Capital - Insight into underlying risk metrics for management of capital resources Mix of Business - Analysis may provide insight into managing the mix of business to optimize profitability 19

Stuart Silverman, FSA, MAAA, CERA Principal & Consulting Actuary stuart.silverman@milliman.com +1-646-473-3108