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:
1. Increased life insurance claims offset by reduced annuity payouts
2. Increased longevity increases annuity payouts but reduces
insurance death claims
3. 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
Historical Mortality Improvement Experience – US Population 1960-2010
10.000%
Male Age 35 vs. Male Age 75
8.000%
6.000%
4.000%
2.000%
0.000%
-2.000%
-4.000%
-6.000%
-8.000%
-10.000%
Male Age 35
Male Age 75
Correlation Coefficient = 1.8%
3
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
10.000%
8.000%
6.000%
4.000%
2.000%
0.000%
-2.000%
-4.000%
-6.000%
-8.000%
-10.000%
Male Ages 30-39
From 1960-2010 Correlation = 26.3%
BUT
Male Ages 70-79
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:
1.Long term mortality improvement trends
2.Short-Term (annual) mortality improvement volatility
3.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:
1) around the length of the initial selection period,
2) around years over which preferred or substandard rating takes to wear off
3) around ultimate level of mortality after the completion of the wearing off.
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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.
Examples:
- 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
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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
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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)
6.89%
8.89%
8.21%
7.56%
7.01%
IRR
9.00%
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
FIXED MARGIN
TERM LIFE INSURANCE:
PAYOUT ANNUITY:
• 105% of best estimate annual
mortality rates, and
• 95% of best estimate annual
mortality rates, and
• Best estimate annual mortality
improvement rates reduced
0.50%
• Best estimate annual mortality
improvement rates increased
0.50%
REVISED FIXED MARGIN
(to achieve 90th percentile target)
TERM LIFE INSURANCE:
PAYOUT ANNUITY:
• 103% of best estimate annual
mortality rates, and
• 97% of best estimate annual
mortality rates, and
• Best estimate annual mortality
improvement rates reduced
0.40%
• Best estimate annual mortality
improvement rates increased
0.40%
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RECONSIDERING THE FIXED MARGIN FROM
CASE STUDY
Table 22 from Case Study
Deterministic vs. Fixed Margin vs Stochastic Results
Discount Deterministic
Rate
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)
6.89%
7.55%
8.21%
7.56%
7.01%
6.33%
IRR
9.00%
Revised fixed margin
produced IRRs
th
equivalent to 90 percentile stochastic projection.
15
RECONSIDERING MARGINS USING STOCHASTIC ANALYSIS
IRR of Annuity and Term Portfolios
14.00%
12.00%
2
Original Margins ≈ 97th percentile
10.00%
8.00%
IRR
6.00%
1
Expected (No Margins) ≈ 50th Percentile
4.00%
3
Revised Margins ≈ 90th Percentile
2.00%
0.00%
Percentile Rank
Stochastic (1000 Scenarios)
Expected (Zero Margins)
Original Margins
Revised Margins
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.
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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
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
IRR
9.00%
6.70%
7.43%
7.57%
100% Baseline Term and 1000% Baseline Annuities
IRR
9.00%
6.53%
7.32%
7.40%
Therefore, optimal mix allowed for significantly more annuity business, and
the deterministic margins need to be revisited as the mix of business changes.
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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
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Stuart Silverman, FSA, MAAA, CERA
Principal & Consulting Actuary
[email protected]
+1-646-473-3108