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The actuarial treatment of the disability risk in Germany, Austria and Switzerland
Insurance: Mathematics North-Holland
and Economics
131
13 (1993) 131-140
The actuarial treatment of the disability risk in Germany, Austria and Switzerland Giinther
Segerer
Miinchener Riickuersicherungs-Gesellschaft, Germany Received December Revised April 1993
Miinchen,
1992
Abstract: The general method used for the actuarial treatment of the disability risk in all three countries considered is the ‘method of decrement tables’, but there are some market specialities, especially simplifications. There are also considerable differences from country to country in the bases used for calculation. Keywords: Actuarial
treatment
of the disability
risk
1. Introductory remarks on the actuarial ment of the disability risk
treat-
The method used for the actuarial treatment of the disability risk in Germany, Austria and Switzerland, as well as in some other countries on the European continent, can be generally termed the ‘method of decrement tables’, because the policy values, premium rates and reserves are calculated in principle on the basis of the probabilities of various decrements as disablement or death in the active portfolio, recovery or death in the disabled portfolio. In contrast, the method applied in the US market is known as the ‘continuance method’ ’ in accordance with the continuance tables used for this purpose. What is typical of this method is that it is based on the probabilities of a risk of becoming disabled and remaining in the disabled portfolio for a certain
Correspondence to: Dr. G. Segerer, Miinchener Riickversicherungs-Gesellschaft, Kijniginstrasse 107, D-80791 Miinthen, Germany. ’ cf. ‘Bases of Premium Calculation in Disability Insurance Friendly Society Method, Continuance Method’, Munich Re 1985, pp. 17-27. 0167-6687/93/$06.00
0 1993 - Elsevier
Science
Publishers
length of time. The so-called ‘friendly society method’ ’ still used mainly in the UK bases its calculations on the probabilities of insureds being disabled over specific periods of time. The method of decrement tables used in Germany, Austria and Switzerland is based on the procedures also applied in life insurance. For the active portfolio, these tables show the mortality rates (= qza) and also the disablement rates (= i,>, both of which are dependent on age. The disabled portfolio, which is composed of all those risks that have been eliminated from the active portfolio through disablement, is in turn influenced by two elimination probabilities, namely the disabled mortality rate (= q:>, which usually differs from the mortality rate of active persons, and the recovery rate (= r,>. Both the disabled mortality rate and the recovery rate depend not only on the attained age of the insured but also on the length of time which has elapsed since disablement. As will be demonstrated in the following pages, however, some simplifications are generally made in the markets considered.
2. The disability
risk in Germany
If we compare the number of disability policies with that of whole life, endowment and term insurances, disability covers account for about 12%. Ten years ago this figure was only 8%. This rise in disability coverage can be explained by the fact that new life insurance policies are sold being increasingly with disability riders. The proportion is currently 30% but in some occupational groups it is much higher. Figure 1 shows how the sums insured under German disability covers have grown in the last few years. In contrast, Austrian life insurers are relatively hesitant about insuring the disability risk. While in some
2 cf. same publication,
B.V. All rights reserved
pp. 4-16.
132
G. Segerer
/Actuarial
treatment
of the sum insured under the main policy and is now, following a tariff reform, limited to 48% per year. For pension payments of more than 24% of the sum insured, however, premiums loaded with higher costs are charged.
companies the proportion of disability riders is as much as 5% of the number of life insurances, in others it is as small as only 1%. In Switzerland, on the other hand, whole life and endowment policies are sold almost exclusively with waiver of premiums in the case of disablement (assuming, of course, that the proposer’s state of health permits inclusion of the disability risk). Often the waiver-of-premium policies additionally provide for payment of a disability pension. But now we return to the German disability market. The disability products offered by German life insurance companies are, apart from a few minor differences, mostly standard in form, since all insurance products are subject to insurance supervision. This means that policy conditions and the technical structure of the tariff, including the actuarial basis, have to be submitted to the supervisory authority for approval in the form of a so-called business plan. In order to simplify the approval process, the supervisory authorities have published specimen business plans for disability insurance on which most products are based. However, with the implementation of the 3rd EC life insurance directive the tasks of the supervisory authority will probably be completely altered. In disability riders the premium for the main insurance is usually waived. In addition, a disability pension can be insured - this applies to approximately 60% of all disability policies in Germany - which used to be limited to 24% per year
%
Million
DM
of the disability risk
2.1. Definition of disability Both disability riders and separate disability policies cover the risk of occupational disability. The disability definition reads as follows: ‘The Insured shall be deemed to be suffering from total disability if, as a result of illness or bodily injury which must be medically demonstrable, he is expected to be permanently unable to practise his occupation or carry out another activity which can be performed by reason of his training and experience and which corresponds to his social standing. The Insured shall be deemed to be suffering from partial disability if the prerequisites specified above are expected to be met permanently to a certain degree only. If, as a result of illness or bodily injury which must be medically demonstrable, the Insured has for an uninterrupted period of six months been totally or partially unable to practise his occupation or carry out another activity which can be performed by reason of his training and experience and which corresponds to his social standing,
of
annual
benefit
600,
0
564%
1960
1965
1970
Fig. 1. Development
1975
of German
1980
disability
1985
rider.
1990
G. Segerer /Actuarial
treatment
133
2.2. Net premium formula
the continuation of this condition shall be deemed to be total or partial disability.’
The formula for the calculation of the net premium for a disability annuity of amount 1 is as follows (Figure 2):
Generally, companies pay the whole benefit insured in the case of a disability of 50%. Some companies offer their insured the option of partial benefits in the event of partial disablement. A proportion of the full benefits becomes payable in the case of a disability of 25% or 33%, for example, with full benefits becoming due for disabilities of 67% or 75% and over. German disability covers generally exclude the risks of war and civil commotion, active participation in criminal acts, intentional self-mutilation, motor racing and flying risks, either professionally or as a sport. In acknowledging disability claims under private life policies, the insurers are not generally bound to follow the decision of the authorities responsible for the payment of social security benefits if the insured is entitled to such a pension in addition. In particular, private insurers can reach their decision without having to make allowance for the current market employment situation and are therefore able to consider each case objectively on its merits alone. This means that the only aspects taken into account are the purely medical facts of the case and their probable effect in the opinion of the physicians on the insured’s ability to perform his own or another suitable occupation.
P* XR
of the disability risk
Xi
-i
x+tax+ry
where -i a x+f
=
+(al+64
+
andD,“” and Nf” result on the basis of an actuarial interest rate of 3.5% from the decrement formula -ix).
I,““+, =1,““(1 -q:‘)(l
For qza the values given in the mortality tables used for life insurance are taken (neglecting reduction factors), while i, represents the disability incidence rates which will be discussed in more detail later on. 2.3. Bases for calculation Since the tariff reform, which was started in 1990, new disability incidence rates have been introduced. They are based on the experience of the German market between 1983 and 1985 loaded by a safety margin of 20% for males and
=
I
n-4
Ill-1
1 aa
NX
aa - N x+m
x
t=o
D;+t.~x+t,~‘2.aix+1+112
n-1-
-
n-1
1
NX
~L+,+G=F+‘/*
- Nx+n
z
Dxit
+ 112
*I
t=o
Fig. 2. Net premium
x+
t
l
Ox+t Yr-
formulas
l
aix+t+112
for disability
n-t-112
insurance.
pi.ifGq
G. Segerer /Actuarial
134
treatment of the disability risk
Table 1 Comparison: Disability incidence rates. Incidence rates for benefits payable in case of total and partial disability per 1000. a Age
25 50 35 40 45 50 55 60
D Male
Female
1.4 1.5 1.8 2.6 3.8 7.8 19.6 42.6
0.8 1.4 2.2 3.3 5.5 11.6 22.2 44.1
A
CH
NL
1.1 1.2 1.9 3.1 4.6 9.1 22.5 54.4
1.1 1.3 1.7 2.4 4.0 6.6 10.6 18.2
6.0 7.5 9.4 11.8 14.8 18.7 23.5 29.5
particularly obvious if one compares the disability incidence rates for disability pensions with incidence rates for the waiver of premium benefit. Incidences for the latter are significantly lower. Therefore, it was decided to base the incidence rates on the quotient between benefit paid and benefit insured. Further, the data confirm that the disability incidence rates depend on the occupation of the insured. However, as the character of the work of certain professions changes over a long period of time and the insured can change his profession during the policy term, it was deemed appropriate to use individual extrapremiums, as in the case of medically substandard risks, rather than using a different calculation basis depending on the class of profession. Prior to the tariff reform, disability annuity values were approximated at 85% of the values for life annuities calculated according to the life insurance mortality tables. Since the middle of the 1970s Munich Re has been investigating the mortality and recovery rates of disabled. From this material statistics for males were provided to the German Life Association. The basis for Munich Re’s statistics were the reinsurance portfolios of several German life companies in the period from 1978 to 1983. These data show that mortality does not only depend on the age of the insured but also on the number of years elapsed since the insured became disabled (Figure 3). Mortality during the first years of disability and young ages is always
a D: rate of calculation basis 1990; CH: basic rate of GKM 80; A: rate of calculation basis Heubeck-Fischer; NL: rate according to KAZO 1990, reduced for class 2.
25% for females. Previously, American disability incidences dating from the years 1935 to 1939 were used. In Table 1, the new German incidence rates are compared with those of Austria, Switzerland and the Netherlands. The incidence rates used in the Netherlands look comparatively high, especially in younger age groups. However, it should be remembered that KAZO-rates are constructed for separate disability cover - highly significant in the Netherlands - with a quite different risk profile as experienced for rider policies. The German statistics confirm that the more the annuity benefit insured increases, the more the incidence of disability increases. This trend is
% of
active
life at
mortoliiy
IZOO-
age
disablement
‘OOO-
::.:_-“---------,
;i;:
~~___~~~~~~~~~~~~~~ ----___
-.-,
----_ ------_____
zoo60-
-
-
-------______
.-__
-‘-.,
---__.
----_-_-_ O-
1 st
2
nd
3 rd yeor
Fig. 3. Mortality
of the disabled
since
4
th
5
disablement
depending
on age and duration
6
th r,nd
th
following
since disablement.
G. Segerer /Actuarial
treatment of the disability risk
- non-recurring initial costs (2%/12% of the annual benefit insured in the case of rider/ separate policy), - collection and administration costs (6%/10%), - pension payment costs (also taken into consideration in the reserve calculation under ‘c’; generally 2% of the annual benefit insured).
significantly higher than the mortality rates used for the life insurance premium calculation. For higher ages and longer durations of disability, mortality approaches the normal insured mortality. Therefore, a five years select table, reduced by a safety margin of 20%, has been introduced as a basis for premium calculation. Since good statistical material for females is still not available, it is assumed in the premium calculation that the ratio between normal and disabled mortality for females is the same as it is for males. In young ages, recovery (Figure 4) is by far the most frequent reason for termination of the claim payment, i.e. the disability annuity. With increasing age and duration of disability, however, recoveries become less frequent. Therefore, a five years select table (reduced by a safety margin of 25%) has also been introduced for the recovery rates as the basis for the premium calculation. Due to a lack of statistical data, the same recovery rates are used for males and females.
2.5. Reserves Both the active life reserves and the disabled life reserves are calculated on the same bases as the net premiums, which means that the same result is obtained whether the reserve calculation method is retrospective or prospective. The corresponding prospective formulas are as follows: Active life reserves (for policies miums are being paid): ,I$-
,v:‘,
Fig. 4. Recovery
rate of the disabled
c)u$,,,
-px”“$a:“,,~.
= (I + +:+,E=iz/.
is the single premium correHere a:‘+,sponding to the annual premium p$,,, n--ml and c represents the percentage costs of pension payment. Companies can also set up late claims and IBNR reserves, if they have experience statistics to support them.
In the case of both disability riders and separate disability policies - with generally higher premium rates - the costs taken into account in the gross premium rates include
since
= (1+
for which pre-
Disabled life reserves (for policies which are currently paying out disability pensions):
2.4. costs
yeor
135
disablement
depending
on age and duration
and
following
since disablement.
136
G. Segerer
/Actuarial
treatment
The deferment period is the main reason for setting up IBNR reserves. Additionally, there are often cases with
The German disability tariffs contain safety margins that generally result in profits not only from interest but also on the risks themselves. At present, supervisory regulations require that at least 90% of profits be returned to the policyholders; for competitive reasons, this percentage is usually even higher. The main forms of profit sharing are a final dividend of x% of the disability premiums paid and/or an increase in the disability pension of, for example, 3% on that of the previous year. Forms of early profit distribution are becoming more popular nowadays than the final dividend; these include premium rebates or pension bonuses that are paid in addition to the insured pension in the event of disablement.
(a> delays in claims being reported, (b) situations in which the benefits to be paid are underestimated
initially, or
Cc)later changes in the amount of the benefits on account of an increase in the degree of disability. Prior to the tariff reform it was usual in separate disability insurance to set up an additional reserve for ‘latent’ disability cases. The purpose of this was to ensure that, if disability claims remained markedly below the estimated rate either owing to factors relating to the current economic cycle or purely by chance, a reserve amount would be set up equivalent to the amount that would have had to be set up in the event of a disablement rate of 70% of the calculated disability risk. The difference between the amount of this reserve and that of the total reserve set up on the basis of actual claims experience represented the latent disability reserve. 2.6. Premium adjustment /profit sharing Premium adjustment is possible in Germany only in the case of separate disability policies and, even there, only with the permission of the supervisory authorities, which is granted in the event of market-wide losses that are likely to be more than temporary.
Annual Maturity
net premium age 60
rate
for
of the disability risk
2.7. Change in calculation bases due to the tariff reform
Following the tariff reform the insurance companies were compelled to reorganize their reserves, since it had become necessary, owing to the steeper curve of the disability risk, to weight the reserves more heavily in the direction of the higher ages. The premium levels for new business also had to be changed considerably, the net premiums being increased for high ages at entry and ages at maturity and being decreased in some cases for low ages (Figure 5). The net premium for a risk with age at entry 20 and age at maturity 60, for example, is now only 80% of the former premium, whereas for an age at entry of 50 and an age at maturity of 60 it is now as much as 38%
1000
annual
Moles I
benefit Females
I 60
Age
at entry Fig. 5. Old and new premium
Age
rates.
at entry
G. Segerer /Actuarial Active duration
Life 40
reserve years
for
1000
annual
treatment benefit
of the disability risk Age
ot
entry
137
25.
1000
600
Pohcy mnew
year
I
basis
old
basis
Fig. 6. Active life reserves.
higher. Since the tariff reform, separate premium tables for women have also been introduced. Whereas the female rates used to be the rates for males plus a 50% loading across the board, they are now calculated on the basis of separate disability incidence rates and annuity values, with the result that most of the female rates have been reduced. The number of combinations of age and policy period for which the new premiums are lower is even greater for women than for men. Depending on the composition of their portfolio, it may be necessary therefore for some companies to set up additional reserves because, while the premiums for disability riders cannot be raised, the disability risk can be expected to be greater at the higher ages than was allowed for by the premiums calculated under the old tariff (Figure 6).
3. The disability
tion of disability many:
is similar
to that
used
in Ger-
‘An insured is considered to be disabled if, as a result of illness, bodily injury or debility of which medical evidence must be provided, he will probably be unable for the rest of his life to engage in his own occupation or in any other occupation for which he is trained or which requires an equivalent level of skill and knowledge. An insured is, in any case, regarded as being disabled if his ability to work has already been reduced uninterruptedly for at least six months or is expected to be reduced for life on account of his physical or mental condition to less than half of that of a physically and mentally sound person of similar education or training and with an equivalent level of skill and knowledge.’
risk in Austria
In Austria, disability cover is only offered in the form of riders to life policies. As a general rule, premiums for the main insurance are waived on disablement and - in very few cases - a pension of up to 30% of the sum insured annually may become payable in addition. 3.1. Definition of disability In Austria as well as in Germany occupational disability is insured. For that reason the defini-
The exclusions which preclude payment of a disability benefit are much the same as those of most German disability tariffs. 3.2. Net premium formula Nearly all Austrian formula for calculating ure 2):
companies use the same their net premiums (Fig-
G. Segerer /Actuarial
138
treatment
3.5. Reserves
where m is the period n is the period
of the disability risk
of cover and of pension payment.
Austrian companies set up the conventional active life and disabled life reserves, using the same actuarial bases as for calculation of the premiums. In addition they provide for an administrative costs reserve which is equivalent to 1% in all of the active and disabled life reserves.
3.3. Bases for calculation The disability incidence rates used in Austria are generally the Heubeck-Fischer figures (camp. Table 1). Although these are derived mainly from German social security statistics dating from the year 1934, they show what is still quite an acceptable age structure. The disabled mortality rates which form the basis of the disabled annuity values are also taken from the Heubeck-Fischer tables and are based on data collected on bank employees in the years 1928 to 1932. Due to a special social security situation, no recovery is taken into consideration. The actuarial interest rate used for the calculation of both the premiums and the reserves is 3%.
3.6. Premium adjustment /profit sharing Premiums are guaranteed for the entire policy period and may not be adjusted. There is no general rule in Austria governing the distribution of profits but some companies pass on interest profits on their disabled life reserves to recipients of disability benefits by increasing the amount of their pension.
4. The disability
3.4. costs
In Switzerland disability insurance can be bought both in the form of a rider to a life insurance policy and in the form of a separate disability cover. Disability riders providing for waiver of premiums for the main cover in case of occupational disability are always included but approximately half of the riders pay a pension as well. Pensions of up to 30% of the life sum insured annually are common; if a higher pension is desired, the policyholder must pay the higher
The costs allowed for in the tariff premiums differ from one company to the next. Some companies include in their calculations both administration and premium collection costs as well as pension payment costs for the period of pension payment, while other companies make allowances for administrative costs but not for premium collection or pension payment costs.
Million
sfrs
of
annual
benefit
:OO7-p,
Fig. 7. Development
risk in Switzerland
of Swiss disability
rider.
G. Segerer /Actuarial
cost-loaded premium rate of the separate disability tariff. The development of the rider business over the last 30 years is shown in Figure 7. 4.1. Definition of disability Both total disability and partial disability are covered, the latter with correspondingly reduced benefits. Disability is usually defined as follows, with small differences from company to company: ‘Disability is the total or partial inability of the insured due to illness or accident to engage in his own occupation or in any other occupation that he may reasonably be expected to undertake in view of his situation in life, his knowledge and his abilities.’ The disability benefits are scaled according to the degree of disablement. Full benefits are granted if the disability is 66f% or more, whereas none are paid if the disability is less than 25%. A disability claim will be recognized if the insured has been at least 25% disabled throughout the entire deferment period. Due to the particular importance of group insurance in Switzerland it is necessary to sometimes differentiate between individual and group policies, e.g. deferment periods under individual disability policies may be 3 or 6 months whereas under group policies deferment periods from 2 to 36 months can be chosen. The number of exclusions provided for under Swiss disability policies is smaller than those customary in Germany and Austria, being limited to war, active participation in riots, intentional selfmutilation and serious criminal acts. 4.2. Net premium formula The formula for the calculation premiums is as follows (Figure 2):
of the
net
D, and N, are calculated on the basis of the standard mortality tables for life insurance with an actuarial interest rate of 3%. Since the simplification achieved by leaving cases of disablement out of consideration in the decrement process affects both the numerator and the denominator
treatment of the disability risk
139
of the premium formula, the inaccuracy that this introduces is small. g,,, reflects the mean degree of disability, which has to be taken into account in Swiss tariffs because of the payment of partial benefits, whereas the German and Austrian tariffs normally allow for full benefits only. g-values vary between 80% and 93%, being higher for females and higher ages. 4.3. Bases for calculation The current tariffs are based on statistically derived disability rates dating from the years 1971 to 1975 (Table 1). The figures in Table 1 were experienced for male insureds, whereas female rates were lower. In earlier observations the reversed result was achieved. Thus it was decided to use male rates for female insureds, as well. One reason for the comparatively low incidence rates is that Swiss private insurers work with special claims inspectors. They try to get as much information as possible by means of inquiries e.g. medical practitioners, employers or authorities. They also speak with the insureds, learn something about the social background of the insureds and finally they regulate claims. Additionally, the very low unemployment rate in Switzerland is very favourable with regard to the incidence rates. The annuity values are based on the recovery and disabled mortality rates determined simultaneously for fairly large age groups, being dependent on the duration of the disability. Subsequent calculations of the bases of calculations carried out at five-yearly intervals on a market-wide basis have not so far indicated the need for a tariff adjustment. The current premium rates are based on group insurance experience. With individual insurances the statistics show that the disability incidence rates are approx. 15-20% higher, but the recovery rates and the mortality rates for disabled persons in individual business are also higher than in group business. Therefore, it was decided to use the same premium rates in group and individual business. For reasons of tradition as well as simplification, the tariff premiums finally charged to the policyholders are scaled only according to age at maturity and are calculated by means of a
G. Segerer /Actuarial treatment of the disability risk
140
weighted average over the different ages at entry (examples in Table 2). The independence of the premium rates from the age at entry did at one time have a certain degree of actuarial justification, in that in disability insurance the net premium rates for a fixed age at maturity do not change very much as the ages at entry increase, because the product of increasing disability incidence rates and decreasing annuity values remains fairly constant. 4.4. costs In calculating the tariff premiums not only the net required premiums are used as a basis but safety loadings are added ‘to allow for the high degree of moral hazard involved in disability insurance’ and then commission, administrative and premium collection costs are taken into account. This all-inclusive method of calculating the tariff premiums, of which the net premiums make up about 60% (the remaining 40% being accounted for by cost and profit margins), is used to justify the charging of identical tariff premiums for both men and women and for both individual and group policies. 4.5. Reserves Reserves in Swiss disability insurance are set up only for the disabled cases, active life reserves being technically unnecessary owing to the fact that the tariff premium rates are independent of the ages at entry:
=
Age at entry
D a
AC
CH a
Disability 25 35 45 55
benefit
rider 46.20 66.60 103.20 156.60
38.00 56.00 77.00 84.00
40.00 40.00 40.00 40.00
Separate 25 35 45 55
disability
policy 53.80 76.10 116.70 176.00
a Profit participation. h Deferment period ’ Maturity age 60.
-
NL
70.00 lz 70.00 70.00 70.00
55.00 55.00 55.00 55.00
102.30 144.80 183.10 191.80
of 1 year.
0.3, increasing continuously disablement age 65.
until
it reaches
1 at
4.6. Premium adjustment /profit sharing The premiums are guaranteed under individual policies for the duration of the cover and under group policies for a certain number of years. In the event of a tariff increase, the new premiums may be charged only for new policies. Depending on claims experience, profits are distributed among the insureds. In individual insurance these usually take the form of a higher pension, in group insurance of a premium rebate.
er
The disabled life reserve takes into account both the recovery rate and the higher disabled mortality rate but would be expressed in terms of the corresponding life annuity value: tV; = l.O2a,+,A
((I-+)f(x)+$
where f(x)
Table 2 Disability tariffs with own occupation definition. Annual benefit also in case of partial disability. Maturity age 65, deferment period of 6 months. Annual gross premium for individual policies. 1,000 annual benefit - Males with white collar occupation.
=0.3+0.7
(x - 15)2 5. .
f(x) is the age-dependent deduction factor. For the ‘largely theoretical’ disablement age of 15 it is
5. Concluding
remarks
It has been demonstrated that the disability insurance markets in Germany, Austria and Switzerland have related structures. This does not mean, however, that there are not also considerable differences from country to country in the numerical significance of disability insurance, in the bases used for calculation and in the resulting gross premium rates. The summary of gross premiums given in Table 2 for people with sedentary occupations and for an age at maturity of 65 is intended to illustrate this.
and Economics
131
13 (1993) 131-140
The actuarial treatment of the disability risk in Germany, Austria and Switzerland Giinther
Segerer
Miinchener Riickuersicherungs-Gesellschaft, Germany Received December Revised April 1993
Miinchen,
1992
Abstract: The general method used for the actuarial treatment of the disability risk in all three countries considered is the ‘method of decrement tables’, but there are some market specialities, especially simplifications. There are also considerable differences from country to country in the bases used for calculation. Keywords: Actuarial
treatment
of the disability
risk
1. Introductory remarks on the actuarial ment of the disability risk
treat-
The method used for the actuarial treatment of the disability risk in Germany, Austria and Switzerland, as well as in some other countries on the European continent, can be generally termed the ‘method of decrement tables’, because the policy values, premium rates and reserves are calculated in principle on the basis of the probabilities of various decrements as disablement or death in the active portfolio, recovery or death in the disabled portfolio. In contrast, the method applied in the US market is known as the ‘continuance method’ ’ in accordance with the continuance tables used for this purpose. What is typical of this method is that it is based on the probabilities of a risk of becoming disabled and remaining in the disabled portfolio for a certain
Correspondence to: Dr. G. Segerer, Miinchener Riickversicherungs-Gesellschaft, Kijniginstrasse 107, D-80791 Miinthen, Germany. ’ cf. ‘Bases of Premium Calculation in Disability Insurance Friendly Society Method, Continuance Method’, Munich Re 1985, pp. 17-27. 0167-6687/93/$06.00
0 1993 - Elsevier
Science
Publishers
length of time. The so-called ‘friendly society method’ ’ still used mainly in the UK bases its calculations on the probabilities of insureds being disabled over specific periods of time. The method of decrement tables used in Germany, Austria and Switzerland is based on the procedures also applied in life insurance. For the active portfolio, these tables show the mortality rates (= qza) and also the disablement rates (= i,>, both of which are dependent on age. The disabled portfolio, which is composed of all those risks that have been eliminated from the active portfolio through disablement, is in turn influenced by two elimination probabilities, namely the disabled mortality rate (= q:>, which usually differs from the mortality rate of active persons, and the recovery rate (= r,>. Both the disabled mortality rate and the recovery rate depend not only on the attained age of the insured but also on the length of time which has elapsed since disablement. As will be demonstrated in the following pages, however, some simplifications are generally made in the markets considered.
2. The disability
risk in Germany
If we compare the number of disability policies with that of whole life, endowment and term insurances, disability covers account for about 12%. Ten years ago this figure was only 8%. This rise in disability coverage can be explained by the fact that new life insurance policies are sold being increasingly with disability riders. The proportion is currently 30% but in some occupational groups it is much higher. Figure 1 shows how the sums insured under German disability covers have grown in the last few years. In contrast, Austrian life insurers are relatively hesitant about insuring the disability risk. While in some
2 cf. same publication,
B.V. All rights reserved
pp. 4-16.
132
G. Segerer
/Actuarial
treatment
of the sum insured under the main policy and is now, following a tariff reform, limited to 48% per year. For pension payments of more than 24% of the sum insured, however, premiums loaded with higher costs are charged.
companies the proportion of disability riders is as much as 5% of the number of life insurances, in others it is as small as only 1%. In Switzerland, on the other hand, whole life and endowment policies are sold almost exclusively with waiver of premiums in the case of disablement (assuming, of course, that the proposer’s state of health permits inclusion of the disability risk). Often the waiver-of-premium policies additionally provide for payment of a disability pension. But now we return to the German disability market. The disability products offered by German life insurance companies are, apart from a few minor differences, mostly standard in form, since all insurance products are subject to insurance supervision. This means that policy conditions and the technical structure of the tariff, including the actuarial basis, have to be submitted to the supervisory authority for approval in the form of a so-called business plan. In order to simplify the approval process, the supervisory authorities have published specimen business plans for disability insurance on which most products are based. However, with the implementation of the 3rd EC life insurance directive the tasks of the supervisory authority will probably be completely altered. In disability riders the premium for the main insurance is usually waived. In addition, a disability pension can be insured - this applies to approximately 60% of all disability policies in Germany - which used to be limited to 24% per year
%
Million
DM
of the disability risk
2.1. Definition of disability Both disability riders and separate disability policies cover the risk of occupational disability. The disability definition reads as follows: ‘The Insured shall be deemed to be suffering from total disability if, as a result of illness or bodily injury which must be medically demonstrable, he is expected to be permanently unable to practise his occupation or carry out another activity which can be performed by reason of his training and experience and which corresponds to his social standing. The Insured shall be deemed to be suffering from partial disability if the prerequisites specified above are expected to be met permanently to a certain degree only. If, as a result of illness or bodily injury which must be medically demonstrable, the Insured has for an uninterrupted period of six months been totally or partially unable to practise his occupation or carry out another activity which can be performed by reason of his training and experience and which corresponds to his social standing,
of
annual
benefit
600,
0
564%
1960
1965
1970
Fig. 1. Development
1975
of German
1980
disability
1985
rider.
1990
G. Segerer /Actuarial
treatment
133
2.2. Net premium formula
the continuation of this condition shall be deemed to be total or partial disability.’
The formula for the calculation of the net premium for a disability annuity of amount 1 is as follows (Figure 2):
Generally, companies pay the whole benefit insured in the case of a disability of 50%. Some companies offer their insured the option of partial benefits in the event of partial disablement. A proportion of the full benefits becomes payable in the case of a disability of 25% or 33%, for example, with full benefits becoming due for disabilities of 67% or 75% and over. German disability covers generally exclude the risks of war and civil commotion, active participation in criminal acts, intentional self-mutilation, motor racing and flying risks, either professionally or as a sport. In acknowledging disability claims under private life policies, the insurers are not generally bound to follow the decision of the authorities responsible for the payment of social security benefits if the insured is entitled to such a pension in addition. In particular, private insurers can reach their decision without having to make allowance for the current market employment situation and are therefore able to consider each case objectively on its merits alone. This means that the only aspects taken into account are the purely medical facts of the case and their probable effect in the opinion of the physicians on the insured’s ability to perform his own or another suitable occupation.
P* XR
of the disability risk
Xi
-i
x+tax+ry
where -i a x+f
=
+(al+64
+
andD,“” and Nf” result on the basis of an actuarial interest rate of 3.5% from the decrement formula -ix).
I,““+, =1,““(1 -q:‘)(l
For qza the values given in the mortality tables used for life insurance are taken (neglecting reduction factors), while i, represents the disability incidence rates which will be discussed in more detail later on. 2.3. Bases for calculation Since the tariff reform, which was started in 1990, new disability incidence rates have been introduced. They are based on the experience of the German market between 1983 and 1985 loaded by a safety margin of 20% for males and
=
I
n-4
Ill-1
1 aa
NX
aa - N x+m
x
t=o
D;+t.~x+t,~‘2.aix+1+112
n-1-
-
n-1
1
NX
~L+,+G=F+‘/*
- Nx+n
z
Dxit
+ 112
*I
t=o
Fig. 2. Net premium
x+
t
l
Ox+t Yr-
formulas
l
aix+t+112
for disability
n-t-112
insurance.
pi.ifGq
G. Segerer /Actuarial
134
treatment of the disability risk
Table 1 Comparison: Disability incidence rates. Incidence rates for benefits payable in case of total and partial disability per 1000. a Age
25 50 35 40 45 50 55 60
D Male
Female
1.4 1.5 1.8 2.6 3.8 7.8 19.6 42.6
0.8 1.4 2.2 3.3 5.5 11.6 22.2 44.1
A
CH
NL
1.1 1.2 1.9 3.1 4.6 9.1 22.5 54.4
1.1 1.3 1.7 2.4 4.0 6.6 10.6 18.2
6.0 7.5 9.4 11.8 14.8 18.7 23.5 29.5
particularly obvious if one compares the disability incidence rates for disability pensions with incidence rates for the waiver of premium benefit. Incidences for the latter are significantly lower. Therefore, it was decided to base the incidence rates on the quotient between benefit paid and benefit insured. Further, the data confirm that the disability incidence rates depend on the occupation of the insured. However, as the character of the work of certain professions changes over a long period of time and the insured can change his profession during the policy term, it was deemed appropriate to use individual extrapremiums, as in the case of medically substandard risks, rather than using a different calculation basis depending on the class of profession. Prior to the tariff reform, disability annuity values were approximated at 85% of the values for life annuities calculated according to the life insurance mortality tables. Since the middle of the 1970s Munich Re has been investigating the mortality and recovery rates of disabled. From this material statistics for males were provided to the German Life Association. The basis for Munich Re’s statistics were the reinsurance portfolios of several German life companies in the period from 1978 to 1983. These data show that mortality does not only depend on the age of the insured but also on the number of years elapsed since the insured became disabled (Figure 3). Mortality during the first years of disability and young ages is always
a D: rate of calculation basis 1990; CH: basic rate of GKM 80; A: rate of calculation basis Heubeck-Fischer; NL: rate according to KAZO 1990, reduced for class 2.
25% for females. Previously, American disability incidences dating from the years 1935 to 1939 were used. In Table 1, the new German incidence rates are compared with those of Austria, Switzerland and the Netherlands. The incidence rates used in the Netherlands look comparatively high, especially in younger age groups. However, it should be remembered that KAZO-rates are constructed for separate disability cover - highly significant in the Netherlands - with a quite different risk profile as experienced for rider policies. The German statistics confirm that the more the annuity benefit insured increases, the more the incidence of disability increases. This trend is
% of
active
life at
mortoliiy
IZOO-
age
disablement
‘OOO-
::.:_-“---------,
;i;:
~~___~~~~~~~~~~~~~~ ----___
-.-,
----_ ------_____
zoo60-
-
-
-------______
.-__
-‘-.,
---__.
----_-_-_ O-
1 st
2
nd
3 rd yeor
Fig. 3. Mortality
of the disabled
since
4
th
5
disablement
depending
on age and duration
6
th r,nd
th
following
since disablement.
G. Segerer /Actuarial
treatment of the disability risk
- non-recurring initial costs (2%/12% of the annual benefit insured in the case of rider/ separate policy), - collection and administration costs (6%/10%), - pension payment costs (also taken into consideration in the reserve calculation under ‘c’; generally 2% of the annual benefit insured).
significantly higher than the mortality rates used for the life insurance premium calculation. For higher ages and longer durations of disability, mortality approaches the normal insured mortality. Therefore, a five years select table, reduced by a safety margin of 20%, has been introduced as a basis for premium calculation. Since good statistical material for females is still not available, it is assumed in the premium calculation that the ratio between normal and disabled mortality for females is the same as it is for males. In young ages, recovery (Figure 4) is by far the most frequent reason for termination of the claim payment, i.e. the disability annuity. With increasing age and duration of disability, however, recoveries become less frequent. Therefore, a five years select table (reduced by a safety margin of 25%) has also been introduced for the recovery rates as the basis for the premium calculation. Due to a lack of statistical data, the same recovery rates are used for males and females.
2.5. Reserves Both the active life reserves and the disabled life reserves are calculated on the same bases as the net premiums, which means that the same result is obtained whether the reserve calculation method is retrospective or prospective. The corresponding prospective formulas are as follows: Active life reserves (for policies miums are being paid): ,I$-
,v:‘,
Fig. 4. Recovery
rate of the disabled
c)u$,,,
-px”“$a:“,,~.
= (I + +:+,E=iz/.
is the single premium correHere a:‘+,sponding to the annual premium p$,,, n--ml and c represents the percentage costs of pension payment. Companies can also set up late claims and IBNR reserves, if they have experience statistics to support them.
In the case of both disability riders and separate disability policies - with generally higher premium rates - the costs taken into account in the gross premium rates include
since
= (1+
for which pre-
Disabled life reserves (for policies which are currently paying out disability pensions):
2.4. costs
yeor
135
disablement
depending
on age and duration
and
following
since disablement.
136
G. Segerer
/Actuarial
treatment
The deferment period is the main reason for setting up IBNR reserves. Additionally, there are often cases with
The German disability tariffs contain safety margins that generally result in profits not only from interest but also on the risks themselves. At present, supervisory regulations require that at least 90% of profits be returned to the policyholders; for competitive reasons, this percentage is usually even higher. The main forms of profit sharing are a final dividend of x% of the disability premiums paid and/or an increase in the disability pension of, for example, 3% on that of the previous year. Forms of early profit distribution are becoming more popular nowadays than the final dividend; these include premium rebates or pension bonuses that are paid in addition to the insured pension in the event of disablement.
(a> delays in claims being reported, (b) situations in which the benefits to be paid are underestimated
initially, or
Cc)later changes in the amount of the benefits on account of an increase in the degree of disability. Prior to the tariff reform it was usual in separate disability insurance to set up an additional reserve for ‘latent’ disability cases. The purpose of this was to ensure that, if disability claims remained markedly below the estimated rate either owing to factors relating to the current economic cycle or purely by chance, a reserve amount would be set up equivalent to the amount that would have had to be set up in the event of a disablement rate of 70% of the calculated disability risk. The difference between the amount of this reserve and that of the total reserve set up on the basis of actual claims experience represented the latent disability reserve. 2.6. Premium adjustment /profit sharing Premium adjustment is possible in Germany only in the case of separate disability policies and, even there, only with the permission of the supervisory authorities, which is granted in the event of market-wide losses that are likely to be more than temporary.
Annual Maturity
net premium age 60
rate
for
of the disability risk
2.7. Change in calculation bases due to the tariff reform
Following the tariff reform the insurance companies were compelled to reorganize their reserves, since it had become necessary, owing to the steeper curve of the disability risk, to weight the reserves more heavily in the direction of the higher ages. The premium levels for new business also had to be changed considerably, the net premiums being increased for high ages at entry and ages at maturity and being decreased in some cases for low ages (Figure 5). The net premium for a risk with age at entry 20 and age at maturity 60, for example, is now only 80% of the former premium, whereas for an age at entry of 50 and an age at maturity of 60 it is now as much as 38%
1000
annual
Moles I
benefit Females
I 60
Age
at entry Fig. 5. Old and new premium
Age
rates.
at entry
G. Segerer /Actuarial Active duration
Life 40
reserve years
for
1000
annual
treatment benefit
of the disability risk Age
ot
entry
137
25.
1000
600
Pohcy mnew
year
I
basis
old
basis
Fig. 6. Active life reserves.
higher. Since the tariff reform, separate premium tables for women have also been introduced. Whereas the female rates used to be the rates for males plus a 50% loading across the board, they are now calculated on the basis of separate disability incidence rates and annuity values, with the result that most of the female rates have been reduced. The number of combinations of age and policy period for which the new premiums are lower is even greater for women than for men. Depending on the composition of their portfolio, it may be necessary therefore for some companies to set up additional reserves because, while the premiums for disability riders cannot be raised, the disability risk can be expected to be greater at the higher ages than was allowed for by the premiums calculated under the old tariff (Figure 6).
3. The disability
tion of disability many:
is similar
to that
used
in Ger-
‘An insured is considered to be disabled if, as a result of illness, bodily injury or debility of which medical evidence must be provided, he will probably be unable for the rest of his life to engage in his own occupation or in any other occupation for which he is trained or which requires an equivalent level of skill and knowledge. An insured is, in any case, regarded as being disabled if his ability to work has already been reduced uninterruptedly for at least six months or is expected to be reduced for life on account of his physical or mental condition to less than half of that of a physically and mentally sound person of similar education or training and with an equivalent level of skill and knowledge.’
risk in Austria
In Austria, disability cover is only offered in the form of riders to life policies. As a general rule, premiums for the main insurance are waived on disablement and - in very few cases - a pension of up to 30% of the sum insured annually may become payable in addition. 3.1. Definition of disability In Austria as well as in Germany occupational disability is insured. For that reason the defini-
The exclusions which preclude payment of a disability benefit are much the same as those of most German disability tariffs. 3.2. Net premium formula Nearly all Austrian formula for calculating ure 2):
companies use the same their net premiums (Fig-
G. Segerer /Actuarial
138
treatment
3.5. Reserves
where m is the period n is the period
of the disability risk
of cover and of pension payment.
Austrian companies set up the conventional active life and disabled life reserves, using the same actuarial bases as for calculation of the premiums. In addition they provide for an administrative costs reserve which is equivalent to 1% in all of the active and disabled life reserves.
3.3. Bases for calculation The disability incidence rates used in Austria are generally the Heubeck-Fischer figures (camp. Table 1). Although these are derived mainly from German social security statistics dating from the year 1934, they show what is still quite an acceptable age structure. The disabled mortality rates which form the basis of the disabled annuity values are also taken from the Heubeck-Fischer tables and are based on data collected on bank employees in the years 1928 to 1932. Due to a special social security situation, no recovery is taken into consideration. The actuarial interest rate used for the calculation of both the premiums and the reserves is 3%.
3.6. Premium adjustment /profit sharing Premiums are guaranteed for the entire policy period and may not be adjusted. There is no general rule in Austria governing the distribution of profits but some companies pass on interest profits on their disabled life reserves to recipients of disability benefits by increasing the amount of their pension.
4. The disability
3.4. costs
In Switzerland disability insurance can be bought both in the form of a rider to a life insurance policy and in the form of a separate disability cover. Disability riders providing for waiver of premiums for the main cover in case of occupational disability are always included but approximately half of the riders pay a pension as well. Pensions of up to 30% of the life sum insured annually are common; if a higher pension is desired, the policyholder must pay the higher
The costs allowed for in the tariff premiums differ from one company to the next. Some companies include in their calculations both administration and premium collection costs as well as pension payment costs for the period of pension payment, while other companies make allowances for administrative costs but not for premium collection or pension payment costs.
Million
sfrs
of
annual
benefit
:OO7-p,
Fig. 7. Development
risk in Switzerland
of Swiss disability
rider.
G. Segerer /Actuarial
cost-loaded premium rate of the separate disability tariff. The development of the rider business over the last 30 years is shown in Figure 7. 4.1. Definition of disability Both total disability and partial disability are covered, the latter with correspondingly reduced benefits. Disability is usually defined as follows, with small differences from company to company: ‘Disability is the total or partial inability of the insured due to illness or accident to engage in his own occupation or in any other occupation that he may reasonably be expected to undertake in view of his situation in life, his knowledge and his abilities.’ The disability benefits are scaled according to the degree of disablement. Full benefits are granted if the disability is 66f% or more, whereas none are paid if the disability is less than 25%. A disability claim will be recognized if the insured has been at least 25% disabled throughout the entire deferment period. Due to the particular importance of group insurance in Switzerland it is necessary to sometimes differentiate between individual and group policies, e.g. deferment periods under individual disability policies may be 3 or 6 months whereas under group policies deferment periods from 2 to 36 months can be chosen. The number of exclusions provided for under Swiss disability policies is smaller than those customary in Germany and Austria, being limited to war, active participation in riots, intentional selfmutilation and serious criminal acts. 4.2. Net premium formula The formula for the calculation premiums is as follows (Figure 2):
of the
net
D, and N, are calculated on the basis of the standard mortality tables for life insurance with an actuarial interest rate of 3%. Since the simplification achieved by leaving cases of disablement out of consideration in the decrement process affects both the numerator and the denominator
treatment of the disability risk
139
of the premium formula, the inaccuracy that this introduces is small. g,,, reflects the mean degree of disability, which has to be taken into account in Swiss tariffs because of the payment of partial benefits, whereas the German and Austrian tariffs normally allow for full benefits only. g-values vary between 80% and 93%, being higher for females and higher ages. 4.3. Bases for calculation The current tariffs are based on statistically derived disability rates dating from the years 1971 to 1975 (Table 1). The figures in Table 1 were experienced for male insureds, whereas female rates were lower. In earlier observations the reversed result was achieved. Thus it was decided to use male rates for female insureds, as well. One reason for the comparatively low incidence rates is that Swiss private insurers work with special claims inspectors. They try to get as much information as possible by means of inquiries e.g. medical practitioners, employers or authorities. They also speak with the insureds, learn something about the social background of the insureds and finally they regulate claims. Additionally, the very low unemployment rate in Switzerland is very favourable with regard to the incidence rates. The annuity values are based on the recovery and disabled mortality rates determined simultaneously for fairly large age groups, being dependent on the duration of the disability. Subsequent calculations of the bases of calculations carried out at five-yearly intervals on a market-wide basis have not so far indicated the need for a tariff adjustment. The current premium rates are based on group insurance experience. With individual insurances the statistics show that the disability incidence rates are approx. 15-20% higher, but the recovery rates and the mortality rates for disabled persons in individual business are also higher than in group business. Therefore, it was decided to use the same premium rates in group and individual business. For reasons of tradition as well as simplification, the tariff premiums finally charged to the policyholders are scaled only according to age at maturity and are calculated by means of a
G. Segerer /Actuarial treatment of the disability risk
140
weighted average over the different ages at entry (examples in Table 2). The independence of the premium rates from the age at entry did at one time have a certain degree of actuarial justification, in that in disability insurance the net premium rates for a fixed age at maturity do not change very much as the ages at entry increase, because the product of increasing disability incidence rates and decreasing annuity values remains fairly constant. 4.4. costs In calculating the tariff premiums not only the net required premiums are used as a basis but safety loadings are added ‘to allow for the high degree of moral hazard involved in disability insurance’ and then commission, administrative and premium collection costs are taken into account. This all-inclusive method of calculating the tariff premiums, of which the net premiums make up about 60% (the remaining 40% being accounted for by cost and profit margins), is used to justify the charging of identical tariff premiums for both men and women and for both individual and group policies. 4.5. Reserves Reserves in Swiss disability insurance are set up only for the disabled cases, active life reserves being technically unnecessary owing to the fact that the tariff premium rates are independent of the ages at entry:
=
Age at entry
D a
AC
CH a
Disability 25 35 45 55
benefit
rider 46.20 66.60 103.20 156.60
38.00 56.00 77.00 84.00
40.00 40.00 40.00 40.00
Separate 25 35 45 55
disability
policy 53.80 76.10 116.70 176.00
a Profit participation. h Deferment period ’ Maturity age 60.
-
NL
70.00 lz 70.00 70.00 70.00
55.00 55.00 55.00 55.00
102.30 144.80 183.10 191.80
of 1 year.
0.3, increasing continuously disablement age 65.
until
it reaches
1 at
4.6. Premium adjustment /profit sharing The premiums are guaranteed under individual policies for the duration of the cover and under group policies for a certain number of years. In the event of a tariff increase, the new premiums may be charged only for new policies. Depending on claims experience, profits are distributed among the insureds. In individual insurance these usually take the form of a higher pension, in group insurance of a premium rebate.
er
The disabled life reserve takes into account both the recovery rate and the higher disabled mortality rate but would be expressed in terms of the corresponding life annuity value: tV; = l.O2a,+,A
((I-+)f(x)+$
where f(x)
Table 2 Disability tariffs with own occupation definition. Annual benefit also in case of partial disability. Maturity age 65, deferment period of 6 months. Annual gross premium for individual policies. 1,000 annual benefit - Males with white collar occupation.
=0.3+0.7
(x - 15)2 5. .
f(x) is the age-dependent deduction factor. For the ‘largely theoretical’ disablement age of 15 it is
5. Concluding
remarks
It has been demonstrated that the disability insurance markets in Germany, Austria and Switzerland have related structures. This does not mean, however, that there are not also considerable differences from country to country in the numerical significance of disability insurance, in the bases used for calculation and in the resulting gross premium rates. The summary of gross premiums given in Table 2 for people with sedentary occupations and for an age at maturity of 65 is intended to illustrate this.