1. 8th July 2008
Living Longer – At What Price?
Incorporating Longevity Into A Risk Management Model

2. Longevity Risk
Practical Applications
Content
Longevity Risk Analysis
Contents
Risk Components 3
VaR Road Map 5
Risk Type Analysis 12
Hedging Ratios 15
LE01 Analysis 18
Redington Analysis 21
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3. Incorporating Longevity Into A Risk
Management Model
Risk Components
3

4. Longevity Risk
Practical Applications
Risk Components
 There has been major focus on
market risk in pension scheme
resulting a significant de-risking
actions including asset allocations
to bonds and LDI.
 However, a full approach to risks
should include analysis of
longevity risk and integration into
the whole risk budget.
 Having removed “unrewarded”
asset risks by hedging inflation and
interest risk typically leaves equity
and longevity risks as the principal
residual risks.
Longevity Risk Analysis
Risk Components
4

5. Incorporating Longevity Into A Risk
Management Model
VaR Road Map
5

6. Longevity Risk Analysis
VaR Definition
6
Value-at-Risk (VaR) – a Measurement of Market Risk
• Value-at-Risk (VaR) provides a single amount (the value) which one might expect to lose (at
risk) in a reasonable “worst case” scenario, i.e. in one year’s time. As a general rule,
Pension Schemes often use a figure which provides a 1-in-20 confidence level (95% VaR).
VaR 95

7. VaR Roadmap Without considering longevity risk
19.24%
8.49% 1.83%
7
Longevity Risk Analysis
VaR Roadmap

8. VaR Roadmap including Longevity Risk
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+0.68% (increased by 3.5%)
+3.66% (increased by 200%)+1.45% (increased by 17%)
Longevity Risk Analysis
VaR Roadmap

9. VaR Roadmap with Longevity Risk Hedged
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*Assumptions:
Longevity risk = 5.17% generic pension scheme
Longevity basis risk remaining = 1%
Longevity Risk Analysis
VaR Roadmap

10.  Adding longevity risk to VaR requires an assumption about correlation with other risk factors. We have assumed zero
correlation.
 By modelling longevity risk under the CBD model, and given 0 correlation with other risk factors, the total VaR
equates to
 As the total risk drops, longevity risk will dominates.
VaR Road Map
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Longevity Risk Analysis
VaR Roadmap

11. VaR Road Map
11
Longevity Risk
5.17%
Market Risk
19.24%
Total Risk
19.92%
Original Total Risk
19.92%
Longevity Risk
5.17%
Market Risk
8.49%
Total Risk
9.94%
Integrating longevity risk into overall risk analysis
increases the total risk by 3.5% of original market
risk.
But after hedging all interest and inflation risks,
the longevity component increases the total risk
by 17.1% of the original market risk.
Longevity Risk Analysis
VaR Roadmap

12. Incorporating Longevity Into A Risk
Management Model
Risk Analysis by Type
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13. Risk Type Analysis Without including Longevity Risk:
Longevity Risk Analysis
Practical Applications
• Typical risk analysis shows the contributions to total risk of portfolio by risk type.
•This graph shows risk contribution without considering longevity risk.
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14. Risk Type Analysis With Longevity:
Longevity Risk Analysis
Practical Applications
• Longevity risk on its own has 1-in-20 (VaR95) chance of increasing the liabilities by 5.17%.
• Assuming zero correlation between longevity risk and other risk types, total risk attributable to
longevity increases by 0.53%.
•Monte-Carlo simulation is not practicable as for other risk components. So general population
data from ONS is adopted to quantify model (CBD) volatility for our analysis.
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15. Incorporating Longevity Into A Risk
Management Model
Hedging Ratios
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16. Longevity Risk Analysis
Hedging Ratio
 The table below shows that changes in mortality assumptions can have a significant impact on
the PV and Duration of a pension scheme’s benefits.
*E.g. The PV for this specific scheme (calculated with a Long Cohort / 2% Underpin mortality table) is
13% greater than the PV calculated using “92” table. The duration increases by 13.5%.
Scenario Tests with Different Deterministic Mortality Tables
Active Deferred Pensioners Total
PV
(£ million)
Duration
(year)
PV
(£ million)
Duration
(year)
PV
(£ million)
Duration
(year)
PV
(£ million)
Duration
(year)
"92" 195 26.8 195 25.5 598 11.1 988 17.0
SC 196 26.9 197 25.6 605 11.2 998 17.1
SC 1% 201 27.5 201 26.1 613 11.4 1,015 17.5
SC 2% 216 29.3 218 27.8 641 12.3 1,075 18.9
MC 200 27.2 201 25.9 619 11.4 1,020 17.4
MC 1% 204 27.8 205 26.4 626 11.6 1,035 17.7
MC 2% 218 29.4 220 27.9 648 12.4 1,086 18.9
LC 209 28.0 210 26.6 648 12.0 1,067 18.0
LC 1% 212 28.5 214 27.1 652 12.2 1,078 18.3
LC 2% 223 29.8 225 28.3 666 12.7 1,115 19.3
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Accounting
basis
TPR new
proposal

17. Impact of Longevity Risk to Asset Liability Management:
•Consider generic pension scheme
with £1bn pensioner liabilities
whose duration is 11 years.
•Assume 100% interest rate and
inflation hedging on “Medium
Cohort” mortality assumptions.
• If actual mortality experience is
“Long Cohort”, present value and
duration of liabilities will increase.
• The liabilities’ PV01 will be around
13% higher than swap PV01 for
both interest rate and inflation. i.e.
Actual hedging ratio declines from
100% to 89%.
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Longevity Risk Analysis
Hedging Ratio

18. Incorporating Longevity Into A Risk
Management Model
LE01 Analysis
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19. Table 1: Sensitivity to 1 year rise in life expectancy for individual member
LE01 Analysis – Results – Which members represent the balance of risk?
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• This table shows the liability increase for a single member in each of these categories given an
increase in life expectancy of one year (LE01).
• LE01 analysis identifies the group of members with greatest longevity sensitivity and hence helps the
scheme to decide which group should be first candidate for buy-out or hedging.
• Members with highest age and final salary exhibit the greatest sensitivity.
• However, in order to be meaningful this data has to be measured against actual number of members
in scheme.
Longevity Risk Analysis
LE01 Analysis
Age/Salary 15K-30K 30K-45K 45K-60K 60K-75K 75K-90K 90K-105K 105K-120K 120K-135K 135K-150K 150K-165K 165K-180K 180-195
25-35 465 775 1,085 1,394 1,704 2,014 2,324 2,634 2,944 3,254 3,563 3,873
35-45 1,945 3,242 4,539 5,836 7,133 8,430 9,726 11,023 12,320 13,617 14,914 16,211
45-55 4,176 6,961 9,745 12,529 15,314 18,098 20,882 23,667 26,451 29,235 32,020 34,804
55-65 7,486 12,477 17,468 22,459 27,450 32,441 37,432 42,422 47,413 52,404 57,395 62,386
65-75 11,810 19,683 27,556 35,430 43,303 51,176 59,049 66,922 74,796 82,669 90,542 98,415
75-85 13,358 22,263 31,169 40,074 48,979 57,884 66,790 75,695 84,600 93,506 102,411 111,316
85-95 14,614 24,356 34,099 43,841 53,584 63,326 73,069 82,811 92,554 102,296 112,039 121,781
95-105 15,414 25,691 35,967 46,243 56,519 66,795 77,072 87,348 97,624 107,900 118,177 128,453
105-115 15,679 26,131 36,583 47,036 57,488 67,941 78,393 88,845 99,298 109,750 120,202 130,655

20. LE01 Table
LE01 Analysis – Results – Which members represent the balance of risk?
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• This table shows the increase in the value of the liabilities due to one year increase in life expectancy
for the entire group of members.
• The group of members aged between 55-75 receiving pensions of £45 – 90k p.a. is most sensitive to
longevity, which shows an increase of over £8m due to 1 year rise in life expectancy for the members
in this group.
• Therefore, the group with the highest age and pension does not necessarily exhibit the highest
LE01. That depends upon the age and benefit distribution of the scheme.
Longevity Risk Analysis
LE01 Analysis

21. Incorporating Longevity Into A Risk
Management Model
Redington Analysis
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22. Session Overview:
Solutions
Full Buyout Partial Buyout Partial Insurance
Standardized
Hedge
Customized
Hedge
Portfolio
Optimization
Asset Liability Modelling
Longevity Risk Integration Longevity VaR Roadmap Longevity Risk Impact Analysis
Stochastic Liability Analysis
Stochastic Model Calibration Stochastic Cashflow Analysis Quantify Longevity Risk
Deterministic Liability Analysis
Scenario Analysis LE01 Analysis
Socio Economic
Grouping
Scheme Specific
Mortality Analysis
Compliance
Longevity Risk Analysis
Redington Analysis

23. 23
Redington Analysis
Deterministic Review Stochastic Model Optimized Solutions
Longevity Risk Analysis
Redington Analysis

24. Bulk
Annuity/Purchase
Annuities e.g.
AIG/AEGON
• Equity
• Private Equity
• Properties
60% Equity 40% Bonds
>70 years old 50 – 70 years old < 50 years old
£X to reach
annuitization triggers
with 95% confidence
£Y to reach 110%
funding under
FRS17
LONGEVITY
ANALYSIS
60% fixed income +
Swaps overlay
40% alternatives
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Redington Partial Annuitisation Roadmap
Longevity Risk Analysis
Redington Analysis

25. Buyout Cost vs. Accounting Cost
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• Buy-out quotations vary greatly. This graph is an illustration of buyout cost breakdown.
Longevity Risk Analysis
Redington Analysis

26. Stochastic Mortality Analysis
Two-Factor CBD Model PV
(£’000,000)
Mean 1,002
S.d. 32
95% 1,054
5% 954
LVaR 52
As % of Total Liability 5.17%
Buyout Cost due to
Longevity
1,045
• Stochastic mortality models allow us to
• estimate the likelihood of a given longevity-related scenario.
• plot the distribution of liability values and quantify associated longevity risk.
• measure effectiveness of longevity hedging relative to other risk mitigation.
• calibrate buyout offer parameters.
Buyout
Cost due to
Longevity
Longevity Risk Analysis
Redington Analysis

27. Contacts
Dawid Konotey-Ahulu | Partner Direct: +44 (0) 207 250 3415
dawid@redingtonpartners.com
Robert Gardner | Partner Direct: +44 (0) 207 250 3416
robert.gardner@redingtonpartners.com
Redington Partners LLP
13 -15 Mallow Street London EC1Y 8RD
Telephone: +44 (0) 207 250 3331
www.redingtonpartners.com
THE DESTINATION FOR ASSET & LIABILITY MANAGEMENT
Contacts
Disclaimer
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