living longer at what price- incorporating longevity into a risk management model

8th July 2008

Living Longer – At What Price?

Incorporating Longevity Into A Risk Management Model

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

2


Risk Components

3

Longevity Risk


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.


Risk Components

4


VaR Road Map

5


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

VaR Roadmap Without considering longevity risk

19.24%

8.49% 1.83%

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VaR Roadmap

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%)


VaR Roadmap

VaR Roadmap with Longevity Risk Hedged

9

*Assumptions: Longevity risk = 5.17% generic pension scheme Longevity basis risk remaining = 1%


VaR Roadmap

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

10


VaR Roadmap

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.


VaR Roadmap


Risk Analysis by Type

12

Risk Type Analysis Without including Longevity Risk:



• Typical risk analysis shows the contributions to total risk of portfolio by risk type.

•This graph shows risk contribution without considering longevity risk.

13

Risk Type Analysis With Longevity:



• 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. 14


Hedging Ratios

15


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


(year) PV


(year) PV


(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

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%. 17


Hedging Ratio


LE01 Analysis

18

Table 1: Sensitivity to 1 year rise in life expectancy for individual member

LE01 Analysis – Results – Which members represent the balance of risk?

19

• 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.


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

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.


LE01 Analysis


Redington Analysis

21

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


Redington Analysis

23

Redington Analysis

Deterministic Review Stochastic Model Optimized Solutions


Redington Analysis

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

24

Redington Partial Annuitisation Roadmap


Redington Analysis

Buyout Cost vs. Accounting Cost

25

• Buy-out quotations vary greatly. This graph is an illustration of buyout cost breakdown.


Redington Analysis

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


Redington Analysis

Contacts

Dawid Konotey-Ahulu | Partner Direct: +44 (0) 207 250 3415 [email protected] Robert Gardner | Partner Direct: +44 (0) 207 250 3416 [email protected] 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

Disclaimer For professional investors only. Not suitable for private customers.

The information herein was obtained from various sources. We do not guarantee every aspect of its accuracy. The information is for your private information and is for discussion purposes only. A variety of market factors and assumptions may affect this analysis, and this analysis does not reflect all possible loss scenarios. There is no certainty that the parameters and assumptions used in this analysis can be duplicated with actual trades. Any historical exchange rates, interest rates or other reference rates or prices which appear above are not necessarily indicative of future exchange rates, interest rates, or other reference rates or prices. Neither the information, recommendations or opinions expressed herein constitutes an offer to buy or sell any securities, futures, options, or investment products on your behalf. Unless otherwise stated, any pricing information in this message is indicative only, is subject to change and is not an offer to transact. Where relevant, the price quoted is exclusive of tax and delivery costs. Any reference to the terms of executed transactions should be treated as preliminary and subject to further due diligence .

Please note, the accurate calculation of the liability profile used as the basis for implementing any capital markets transactions is the sole responsibility of the Trustees' actuarial advisors. Redington Partners will estimate the liabilities if required but will not be held responsible for any loss or damage howsoever sustained as a result of inaccuracies in that estimation. Additionally, the client recognizes that Redington Partners does not owe any party a duty of care in this respect.

Redington Partners are investment consultants regulated by the Financial Services Authority. We do not advise on all implications of the transactions described herein. This information is for discussion purposes and prior to undertaking any trade, you should also discuss with your professional tax, accounting and / or other relevant advisers how such particular trade(s) affect you. All analysis (whether in respect of tax, accounting, law or of any other nature), should be treated as illustrative only and not relied upon as accurate.

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