Dr. Chris Hornsby
Senior Consultant, RMS LifeRisks
The Life and Death Balance Mitigating solvency capital requirements through hedging
mortality and annuity exposure
Investigating Future Mortality: Blending Medical & Actuarial Science for Life & Longevity Risk Management
RMS LifeRisks Seminar l May 24, 2012
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Overview of the Longevity-Mortality Hedge
Example Portfolios
Hedging Trend Risk
Hedging Shock Risk
Combining Trend and Shock Risk
Risk Transfer Strategies
Conclusions
Agenda
2
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Overview of the Longevity-Mortality Hedge
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
An insurer writing both longevity and mortality business can
expect some degree of natural hedge:
– If life expectancy increases
Annuity losses (more pension payments)
Life gains (more premium income, less or more distant death benefit
payouts)
– If an excess mortality event occurs:
Life losses (increased / accelerated death benefit payouts and loss of
premium income)
Annuity gains (a certain number of pension contracts go away)
Overview of the Longevity-Mortality Hedge
4
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Example Portfolios
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Annuity Book
– Mean age: 68
– Liability: £1bn
Whole Life Book
– Mean age: 35
– Coverage: £10bn
Annuity Book is Older
6
0%
1%
2%
3%
4%
5%
6%
0 20 40 60 80 100 120
% o
f P
en
sio
n
Age
Males & Females
0%
1%
2%
3%
4%
5%
6%
0 20 40 60 80 100 120
% o
f C
overa
ge
Age
Males & Females
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Life book base mortality ~60% of annuitant mortality
Life Book Mortality Is Lighter
7
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 20 40 60 80 100 120 140
Lif
e m
x / A
nn
uit
y m
x
Age
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Annuity book duration: ~10 yrs
Life book duration: >20 yrs
Life Book Has Longer Duration
8
-20%
0%
20%
40%
60%
80%
100%
2012 2022 2032 2042 2052 2062 2072 2082 2092 2102
Exp
ect
ed
Cas
h F
low
PV
(%
of
firs
t ca
sh f
low
)
Year
Annuity Book Outflow
Life Book Inflow
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Increasing mortality with age sustains death benefit
payments over 4 decades
Premium income decays with policy lapses
Duration of Death Benefits > Duration of Premiums
9
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
2012 2022 2032 2042 2052 2062 2072 2082 2092 2102
Ca
sh
Flo
w P
V
Year
Death Benefits
Premiums
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Hedging Trend Risk
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Only death benefits sensitive to trend
Life Book Sensitive to Cumulative Mortality Improvement Over Longer Time Frame
11
-3.0%
-2.0%
-1.0%
0.0%
1.0%
2.0%
3.0%
4.0%
2012 2022 2032 2042 2052 2062 2072 2082 2092 2102 2112 2122
De
lta
Cas
h F
low
PV
un
de
r 1
% p
.a. M
I Sh
ock
Year
Annuity Outflow
Life OutFlow
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Change in liability under a 1% per-annum trend shock at
each age
Life Book Sensitive to Mortality Improvement over Wider Age Range
12
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0 20 40 60 80 100 120
Ch
an
ge in
£
Trend Shock Age
Annuity Book
Life Book
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Trend Risk Correlation in range of -25% to -50%
13
Risk Capital: p95 of run-off PV (£ million)
Annuity 30
Life 30
Life + Annuity 30
Saving 15
annuity £1bn :£7.5bn life annuity £1bn :£10bn life
-0.350
-0.325
-0.300
-0.275
-0.250
-0.225
-0.200
-0.175
-0.150
0.925 0.950 0.975 1.000 1.025 1.050 1.075
Life
Lia
bili
ty (
£ b
illio
n)
Annuity Liability (£ billion)
ρ=-25%
Risk Capital: p99.5 of best estate at t0+1 (£ million)
Annuity 25
Life 25
Life + Annuity 30
Saving 07
-0.250
-0.225
-0.200
-0.175
-0.150
-0.125
-0.100
-0.075
-0.050
0.925 0.950 0.975 1.000 1.025 1.050 1.075
Lif
e L
iab
ilit
y (
£ b
illi
on
)
Annuity Liability (£ billion)
ρ=-50%
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
~£10bn of whole life coverage provides a material trend risk
hedge against a £1bn annuity book
Assuming independence: £60m of risk capital (£30m against
each book) can be pooled to give a diversified risk capital of
£42 million
SII permits a -25% correlation between longevity and
mortality trend risk: frees up an extra £6 million bringing the
diversified capital to £36 million
In current example economic risk capital falls to £30 million
(-50% correlation)
Trend Risk Hedge – from £60m of risk capital to £42m to £30m
14
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Hedging Shock Risk
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Pandemic Impacts Vary By Age
16
5-9
10
-15
15
- 19
20
- 24
25
- 29
30
- 34
35
- 39
40
- 44
45
- 49
50
- 54
55
- 59
60
- 64
65
- 69
70
- 74
75
- 79
80
-84
85
-90
90
-95
95
+
Eme
rgin
g in
fect
iou
s d
ise
ase
ex
cess
mo
rtal
ity
Flat
Young&Old
Middle Aged
0%
1%
2%
3%
4%
5%
6%
0 10 20 30 40 50 60 70 80 90 100 110 120
% o
f E
xp
os
ure
Age
Life Annuity
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Shock Mortality Losses Strongly Offset by Annuity Gains
17
-0.24
-0.24
-0.23
-0.23
-0.22
-0.22
-0.21
-0.21
-0.20
4.96 4.97 4.98 4.99 5.00
Lif
e L
iab
ilit
y £
bn
Annuity Liability £bn
annuity £5bn :£10bn life
0
1
2
3
4
5
6
7
0 2 4 6 8 10 L
ife
+ A
nn
uit
y R
es
erv
e £
m
Expected Annuity Liability £bn
p99.5 of annuity + life PV
annuity £Xbn : £10bn life
ρ=-98%
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
~£6m of risk capital held at the 1-in-200 level against shocks
on £10bn of whole life coverage
Conversely annuity book with liability of £5bn stands to gain
~£6m from a 1-in-200 pandemic
As annuity book grows > £6-7bn, begin to expect a gain in
the event of a pandemic
As annuity book reaches £10bn only negligible potential for
a pandemic loss remains
Solvency II framework doesn’t recognize shock hedge: life
cat module only applies to portfolios that are short mortality
Shock Risk Hedge – as Annuity PV approaches Parity with Life Cover, Shock Risk is Neutralized
18
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Combining Trend and Shock Risk
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
£1.2bn of annuity hedges
£10bn of life – hedge
dominated by trend risk
offset
Run-off Trend and Shock Risk
20
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40
Life
Lia
bili
ty £
bn
Annuity Liability £bn
annuity £1.2bn :£10bn life
ρ=-45%
0
10
20
30
40
50
60
70
0 0.5 1 1.5 2
Lif
e+
An
nu
ity C
ap
ita
l £
m
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2
Ca
pit
al R
ed
uc
tio
n
Expected Annuity Liability £bn
reserves at p95 of run-off
(includes future pandemics)
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
£1.6bn of annuity hedges
£10bn of life – hedge still
dominated by trend risk
offset
1-year Shock Risk with Run-Off Trend Risk
21
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80
Lif
e L
iab
ilit
y £
bn
Annuity Liability £bn
0
10
20
30
40
50
60
70
0.0 0.5 1.0 1.5 2.0
Lif
e +
An
nu
ity C
ap
ita
l £
mil
0
0.2
0.4
0.6
0.8
1
1.2
0.0 0.5 1.0 1.5 2.0
Ca
pit
al R
ed
uc
tio
n
Expected Annuity Liability £bn
reserves at p99.5 of shock (1st yr only)
& p95 of trend annuity £1.6bn :£10bn life
ρ=-45%
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Assuming £10bn of life coverage:
– Trend risk: optimally hedged by ~£1bn annuity book
– Shock risk: optimally hedged by >£10bn annuity book
– Trend + Shock Risk: optimally hedged by ~£1bn annuity book
Trend and Shock Risk Hedge – dominated by trend risk
22
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Risk Transfer Strategies
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Targeting an Optimal Mix of Mortality and Longevity Risk
24
Insurer with an over concentration of Longevity Risk is in a
strong position to digest complementary Mortality Risk and
vice-versa
Complementary risk can be acquired via reinsurance,
insurance linked securities etc. targeting an optimal mix of
mortality and longevity risk
Unwanted risk can be disposed of via the same mechanisms
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Risk Swap: 50% Reduction in Risk Capital … For Free!
25
Long Co.
Annuity Bk Life Book
Size (£bn) 2 0
Shock Capital (£m) - 0
Trend Capital (£m) 80 0
Total Risk Capital 80
Mort Co.
Annuity Bk Life Book
Size (£bn) 0 20
Shock Capital (£m) - 20
Trend Capital (£m) 0 67
Total Risk Capital 70
Long Co.
Annuity Bk Life Book
Size (£bn) 1 10
Shock Capital (£m) - 10
Trend Capital (£m) 40 33
Total Risk Capital 38
Mort Co.
Annuity Bk Life Book
Size (£bn) 1 10
Shock Capital (£m) - 10
Trend Capital (£m) 40 33
Total Risk Capital 38
150
76
Before Swap
After Swap
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Life and annuity are well diversified lines of business
Risk between each is correlated at < 0%
Solvency II recognizes the trend risk offset which can be
leveraged for regulatory capital reductions
In addition firms writing both annuity and life may be able to
free-up economic risk capital by looking holistically at trend
and shock risk across all lines of business
Risk swaps are a cost efficient method for attaining a more
efficient capital position
Conclusions
26
CONFIDENTIAL © 2012 Risk Management Solutions, Inc.
Hedge analysis techniques and
benefits are included in the RMS
whitepaper on Solvency II.
Now available on
rms.com/liferisks
RMS LifeRisks Solvency II Whitepaper
27
