assal xvii annual meeting the effects of ageing on the insurance operations

ASSAL XVII Annual Meeting

The effects of Ageing

on the Insurance Operations

Instituto de Seguros de Portugal

26/04/2006

Summary of the Presentation

A. General considerations on Mortality Risk (2-4)

B. Pricing and the Insurance Solvency Framework (5-9)

C. Supervisory Upgrading of Regulatory Standards (10-12)

D. Mortality Projections for Life Annuities (example) (13-

31)

E. Main Conclusions (32-33)

1

2

A. General considerations on Mortality Risk

In order to better understand the effects of ageing on the insurance operations we should perhaps start by tying to understand the manifestation of those effects on the populations of whole countries as they are also valid for the insured subsets of national populations:

A.1. Some features apparently valid for every population:

apparently stable and improving mortality trends observed over long periods of time seem to correspond to long periods of political stability and socio-economical development that generate a continuously upgraded standard of living, easy and quick access to good quality healthcare and a generous and widely spread social and/or private retirement system.

3

apparently unstable overtime mortality trends, with either abrupt decreases or improvements in life expectancy seem to correspond to periods of social, economical and political instability where some or all the above life improvement factors are suppressed to a larger or smaller extent.


A.2. Once identified a stable evolutionary mortality pattern, the larger the population, the smaller the volatility about the trend

4

Therefore:

Any disruption in the known life improvement factors of the populations or their cohorts may disrupt an apparently stable pattern of continuously improving mortality trends.

Where in presence of a factual or probable disruptive influence over the mortality pattern of a population, accrued prudential measures should apply to the projection and valuation of death or survival risk cash flows.

Mortality is subject to volatility and parameter uncertainty.


B. Pricing and the Insurance Solvency Framework

Mortality Risk affects the Insurance Operations in multiple ways, to an extent that depends on the nature and type of mortality risk of each insurance operation. It clearly affects:

the valuation of the Liabilities (corresponding to the Technical

Provisions) associated with the type of insurance operation;

the valuation of the Solvency Requirements set above the level of the Liabilities;

the Pricing of each Contract corresponding to a particular type of insurance operation;

and, as the costs associated with holding the financial means necessary to cover the Global Solvency Requirements need to be financed through premium inflows, it also affects:

5

In order to better understand the links between the Technical Provisions, the Solvency Capital Requirements and the Insurance Premiums some concepts and common sense notions may help:

Our basic Reference Framework is that of the Solvency II Project that, in turn, seeks to be aligned with the Accounting Framework of the IASB for the Insurance Sector.

B.1. Insurance Technical Provisions are deemed to represent the “Fair Value of Insurance Liabilities”, i.e. “the amount for which an asset could be exchanged or a liability settled (or transferred) between knowledgeable, willing parties in a arm’s length transaction. They may be interpreted as the sum of the Best Estimate (according to the foreseeable evolutionary trend, especially in the case of the Life Risk) and the Market Value Margin of the Cost of Risk.6



B.2. Solvency Capital Requirements above the level of Technical Provisions are deemed to enable an insurance undertaking to absorb significant unforeseen losses beyond the value of Technical Provisions and meet all obligations (taking into account all significant quantifiable risks and including the effects of parameter uncertainty linked to the volatility of the observed data about the evolutionary trend, especially in the case of the Life Risk) over a specified time horizon to a defined confidence level. In doing so, the Solvency Capital Requirements should limit the risk that the level of available capital deteriorates to a level below the value of Technical Provisions at any time during the specified time horizon.

7

B.3. Insurance Technical Provisions and the Cost of Solvency Capital Requirements The notions of Insurance Technical Provisions and Solvency


Capital Requirements are interlinked to the extent that the Cost of holding the Solvency Requirements above Technical Provisions (the Cost-of-Capital) should also be a component of the latter. Therefore:

8

Technical Provisions may be seen as the Market Cost of Risk, where some of the risks will be hedgeable (a fully diversified assets’ portfolio will exist that replicates the cash-flow structure and characteristics of the risky (liability) portfolio, its market value will

correspond to the value of hedgeable risks) and some other risks will be non-hedgeable (in which case their value may be assessed as the sum of (i) the Expected present value of future liability cash-flows for non-hedgeable risks; and (ii) a Market Value Margin for non-hedgeable risks, calculated as the present value of the cost of holding the future capital requirement for those risks)


B.4. Pricing of Insurance Operations Once established the logical relationship between the concepts and notions mentioned under B.1., B.2. and B.3., the link with B.4. is easily apparent:

In order to avoid Losses the Pricing of Insurance Products and Operations must equal or exceed the value of Technical Provisions at any time during the specified time horizon of the SCR.

9

C. Supervisory Upgrading of Regulatory Standards

10

One of the present concerns of ISP is that, once the new IFRS Standards and the EU Insurance Directive are adopted, no Life Business Technical Provisions fall below the Fair Value of Insurance Liabilities.• As the IASB’s concept of Fair Value of Insurance Liabilities has

not yet produced a stable definition, ISP is presently taking the corresponding SOLVENCY II Working Concept as a reference, which, for the moment, means:

The Financially Discounted Value of the Liabilities’ Cash-Flows corresponding to a 75% confidence level according to the Term Structure of the Yield Curve corresponding to AA rated corporate bonds.

Working Concept of Fair Value of Insurance Liabilities


• Projecting the cash-flows of Insurance Liabilities at a 75% confidence level requires that the specific characteristics of each insurance contract are taken into account, namely if the contract is “With Profits” or “Without Profits”, if it possesses Lapsation and Surrender Options, a Guaranteed Interest Rate, etc.

• One of the least complicated exercises of Liability Cash-Flow Projection at a 75% confidence level corresponds to the case of a “Without Profits”, Immediate Life Assurance Annuity contract, where only the value of the Periodic Payoff, the Projected Mortality Rate (by age and sex) and the Term Structure of Interest Rates are involved.

11


As this issue is specially important to Pension Schemes, we propose to briefly illustrate how that may be done in respect of the most important element in the valuation the Mortality Projection

12

D. Mortality Projections for Life Annuities (example)

Mortality Table

0,000

0,100

0,200

0,300

0,400

0,500

0,600

0,700

0,800

0,900

1,000

0 5

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

105

age (x)

Pro

b. o

f 1

ind

ivid

ual

of

age

x)

Dyi

ng

ove

r 1

year

= q

(x)

tgx

tgx

tgx

xq

x

The cathets of the triangles should be taken

One should take into account the fact that In graph tg determine the value of To

In their correct scale

Mortality Table

0

100.000

200.000

300.000

400.000

500.000

600.000

700.000

800.000

900.000

1.000.000

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

105

age (x)

l(x)

= N

º in

div

idu

als

aliv

e at

ag

e (x

)

x

xh

h

xh

h

xx lh

d

h

q

dx

qd

00limlim hxxxh lld

xx

x

xh

hx

hxx

h

xhx

h

x llh

dl

h

ll

h

ll

dx

ld

000limlimlim

xx

x ldx

ld

with

The force of mortality (x) may be expressed as the first derivative of the rate of mortality (qx ):

13

D. Mortality Projections for Life Annuities (example)If a mortality trend follows a Gompertz Law, then

tkxtx e

hence tk

x

tx e

, then

x

txtk

ln and also

x

tx

tk

ln1

If mortality were static, then the complete expectation of Life would be

dzek

ee k

zk

x

o x

x

Z

1

1, or, in summary

k

kf

e

x

x

o

with

11

1

!ln

nZ nn

n

k

kdze

x

xkz

x

where ...5772157,0 Is the Euler constant 14

15

Let us suppose now, that for every age the force of mortality tends to dim out as time goes by, in such a way that an individual which t years before had age x and was subject to a force of mortality x , is now aged x+t and is subject to a force of mortality lower than x+t (from t years ago). The new force of mortality will now be: e

tr

txt

tx

Where translates the annual averaged relative decrease in the force of mortality for every age

er

If we further admit another assumption, that the size relation between the forces of mortality in successively higher ages is approximately constant over time, i.e.:

etk

xtx

and etkt

xt

tx

then eeee

trk

x

tktr

x

tktx

ttx

hence

etrk

xt

tx

John H. Pollard –“Improving Mortality: A Rule of Thumb and Regulatory Tool” – Journal of Actuarial Practice Vol. 10, 2002



eeeeeee tk

x

tktxtr

x

tktxtrtk

x

ttxtrk

The prior equation also implies that:

x

txtr

lnwhere hence, finally

x

tx

tr

ln1

16


Mortality Tables

0,000

0,100

0,200

0,300

0,400

0,500

0,600

0,700

0,800

0,900

1,000

0 5 10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

10

0

10

5

11

0

age (x)

Pro

b.

of

1in

div

idu

al a

ged

(x

) D

yin

g o

ver

the

per

iod

of

1 y

ear

= q

(x)

tkxtx e

trx

tx e

tTqx

Tq x

tTx

Tx

The practical application of the theoretical concepts involving the variables k and r may be illustrated in the graph bellow:

17

D. Mortality Projections for Life Annuities (example)In order to increase the “goodness of fit” of the mortality data by using the theoretical Gompertz Law model involving the variables k and r, it is sometimes best to assume that r has different values for different age ranges (we may, for example, use r1 for the younger ages and r2 for the older ages)

Mortality of insured lives of the survival-risk-type of life assurance in Portugal: 2000-2002 (Males )

-0,0100

0,0100

0,0300

0,0500

0,0700

0,0900

0,1100

0,1300

0,1500

20 23 26 29 32 35 38 41 44 47 50 53 56 59 62 65 68 71 74 77 80 83 86 89 92 95 98

xq

age

upper boundary

Observed mortality rates

lower boundary

mortality trend projected

from 1997 to 2001

ee

yearsrxyearskSplineGompertz

x

1997200150202050201997

20

2

21

21

001

ee

yearsrxyearskSplineGompertzx

19972001100513610051199736

2

21

21

001

18


19

As may be seen, the previous graph illustrates several features related to the Portuguese mortality of male insured lives of the survival-risk-type of life assurance contracts (basically, endowment, pure endowment and savings type of policies) for the period between 2000 and 2002: The mortality trend for the period 2000-2002 (centred in 2001) is adequately fitted to

the observed mortality data and has been projected from the Gompertz adjusted mortality trend corresponding to the period between 1995 and 1999, with k=0.05 for the age band from 20 to 50 years and with k=0.09 for the age band from 51 to 100 years. The parameter r, which translates the annual averaged relative decrease in the force of mortality for every age assumes two possible values; r=0.05 for the age band from 20 to 50 years and r=0 for the age band from 51 to 100 years:

Some minor adjustments to the formulae had to be introduced, for example, the formula for the force of mortality for the age band from 51 to 100 years is best based on the force of mortality at age 36, multiplied by a scaling factorthan if it were directly based on the force of mortality at age 51:

eeyearsrxyearskSplineGompertz

x

19972001100513610051199736

2

21

21

001

199736 2

1 Spline

e

3650


20

Further to that, some upper and lower boundaries have also been added to the graph. Those boundaries have been calculated according to given confidence levels in respect of the mortality volatility (in this case and ) calculated with the normal approximation to the binomial distribution, with mean and volatility

%9,991 %1,01

xxx qEE xxxx qqE 1

10

1%1.0@

x

x

xxxxxvel forconfid. lex q subject to

E

qqEqEq

x

The upper boundary may, therefore, be calculated as:

10

1%9.99@

x

x

xxxxxvel forconfid. lex q subject to

E

qqEqEq

x

And the lower boundary may be calculated as:

Those approximations to the normal distribution are quite acceptable, except at the older ages, where sometimes there are too few lives in , the “Exposed-to-risk”

xE

D. Mortality Projections for Life Annuities (example)As for the rest, the process is relatively straightforward:

From the Exposed-to-Risk ( )at each individual age, and from the observed mortality ( ) we calculate both the Central Rate of Mortality ( ) and the Initial Gross Mortality Rate ( ) and assess the Adjusted Force of Mortality ( ) using “spline graduation”

xE

x xmxq

Splinex 2

1

We then calculate the parameters for the Gompertz model that producein a way that replicates as close as possible the

Gompertzx 2

1 Splinex 2

1

The details of the process are, perhaps, best illustrated in the table presented in the next page;

This process has been tested for male, as well as for female lives, so far with very encouraging results, but we should not forget that we are only comparing data whose mid-point in time is distant only some 4 or 5 years from each other and that we need to find a more suitable solution for the upper and lower boundaries at the very old ages.

21

Mortality of insured lives of the survival-risk-type of life assurance in Portugal: 2000-2002 (Males)

-0,0050

0,0000

0,0050

0,0100

20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70

xq

ages


23

24

Mortality of the Beneficiaries and annuitants of Pension Funds in Portugal2000-2002 (Males)

-0,0010

0,0040

0,0090

0,0140

0,0190

0,0240

0,0290

0,0340

20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70

xq

ages

As may be seen in the graph below, between the young ages and age 50 there are multiple decrement causes beyond mortality among the universe of beneficiaries and annuitants of Pension Funds. That impairs mortality conclusions for the initial rates, which have to be derived from the mortality of the population of the survival-risk-type of Life Assurance



25

In general, the mortality rates derived for annuitants have to be based on the mortality experience of Pension funds’ Beneficiaries and Annuitants from age 50 onwards but, between age 20 and age 49 they must be extrapolated from the stable trends of relative mortality forces between the Pension Funds Population and that of the survival-risk-type of Life Assurance.

e

tttxttx T

2006008.005.0000144446.065.1

Ages 2040 :

Annuitants (Males)

etttx

ttx txT

2006008.005.0000144446.0

400654.065.1

Ages 4149 :

e

tttxttx T

20060075.009.0000044994.0

Ages 50 :

Where T is the Year of Projection and 2006 is the Reference Base Year


e

tttxttx T

2006008.0028.0000211957.0415.1

Ages 2034 :

Annuitants (Females)

etttx

ttx txT

2006008.0028.0000211975.0

3510495.0415.1

Ages 3544 :

e

tttxttx T

20060075.009.0000033095.0

Ages 45 :

Where T is the Year of Projection and 2006 is the Reference Base Year

The above formulae roughly imply (for both males and females) a Mortality Gain (in life expectancy) of 1 year in each 10 or 12 years of elapsed time, for every age (from age 50 onwards).

26

Annuitants

As was mentioned before, for assessing the mortality rates at the desired confidence level we may use the following formulae:

21

21

211

x

x

xq

levelconfidencedesiredthatsuchiswhere

E

qqEqEq

x

xxxxxlevelconfidencex

α α

α

Φ

0,1

max@

In our case ()=75% which implies that 0.67285

Now, to use the above formulae we need to know two things: The dynamic mortality trend for every age at onset, and the numeric population structure.


27


28

In order to calculate the trend for the dynamic mortality experience of annuitants we need to use the earlier mentioned formulae and construct a Mortality Matrix:


29

As explained before, knowing the Stable Population Structure of our cohort of annuitants enables us to estimate the parameter uncertainty of the trend to a chosen degree of approximation or (in other words) to a chosen confidence level, using the formula:

levelconfidencedesiredthatsuchiswhere

E

qqEqEq

x

xxxxxlevelconfidencex

α α

α

Φ

0,1

max@

Strictly speaking, if we assume a normal distribution for the deviations about the trend, the confidence level of an annuity for age x is somewhat less than the value of an annuity for age x calculated from the qx set to the same confidence level. This is because, for successive ages, the deviations about the trend flow both above and below the trend and the annuity reflects the value of a multi-year survival probability. However, calculating the value of the annuity from the the qx set to the required confidence level allows us to estimate the parameter uncertainty of the trend, which is a necessary step for assessing the Solvency Capital Requirement.


30

0

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

0 9 18 27 36 45 54 63 72 81 90 99 108

Population Structure of Pension Funds Beneficiaries and Annuitants (Males: Exposed-to-Risk) Projection for 2006

ages

3-year Exposed-to-Risk

20 year Moving Average for the 3-year Exposed-to-

Risk

1-year Exposed-to-Risk (stable

structure)

In order to calculate a Stable Population Structure we need to smoothen the averaged proportionate structures from several years experience

We are now able to project the dynamic mortality experience for different ages at onset and for different confidence levels

31


E. Main Conclusions

32

E.1. In modern Risk-based Solvency Systems (like the ongoing

Solvency II Project) the dynamic aspects of mortality affect both: the Pricing of the Insurance contracts,

the Valuation of Technical Provisions and the Solvency Capital Requirements above the

Technical Provisions.

E.2. In the near future, all aspects of Insurance Valuation and Management will be influenced by the analysis of dynamic evolutionary trends and the volatility about the trend (especially

in the Life Assurance Business) based on stochastic modelling techniques.

E. Main Conclusions

33

E.3. As the size of volatility of risks about their dynamic trends depends on the size of the Portfolio of Risks , as does size of parameter uncertainty:

the size and the extent of risk diversification of the Portfolio of Risks will influence the amount of Solvency Capital Requirements (and hence the Cost-of-Capital and the Technical Provisions), becoming elements of critical importance to preserve the capacity of insurance undertakings to remain competitive in their markets.

taking a pro-active attitude today in order to create solutions and avoid those future problems will very likely increase the probability of survival for many insurance undertakings.

assal xvii annual meeting the effects of ageing on the insurance operations

Documents

insurance premiums

insurance operationsinstituto

insurance sector

insurance technical

type of mortality risk

mortality projections

solvency capital requirements

global solvency requirements