Completed:        21st June 1994

                                                                XXX?

                                What?

‘A state is better governed which has but few laws and those laws strictly observed.’    Descartes  

Foreigners fail to understand Americans because they cannot comprehend the American love of legislation. What are we to make of a nation where Justices of the Supreme Court are better known than Cabinet Ministers? How can we fathom a nation that likes nothing better than to  curl up in bed with a new Statute?

For actuaries, pride of place at the top of the reading list is held by XXX and its sister, Regulation 147.

To the great American public, XXX is a logo on beer cans.                        

To we select few, it is Model  Regulation entitled  ‘Valuation of Life Insurance Policies - Special Rules’ known these many years as ‘Guideline XXX’.  Too many years and too boring has been the legal argument. Yet,  buried below  legal rock a thousand  feet thick runs a thin, precious vein of scientific gold.

At the bottom of the mine, what do we find? Consider a level benefit non-profit whole life insurance policy with very competitive level premiums for the first ten years, thereafter annually increasing premiums based upon attained age and ever more severely substandard mortality. How do we value this amalgam of term and whole life.  What reserve should be placed under it?

State  insurance valuation laws - following the ‘Standard Valuation Law’ (SVL) - specify the ‘Commissioners Reserve Valuation Method’  (CRVM) for policies  providing a level amount of insurance  and requiring the payment of  level premiums.  For such policies,  (modified) net premiums are to be an invariant percentage of gross premiums calculated on prescribed mortality.

The Commissioners Reserve method is a modification of  that known elsewhere by the name of its author, Dr. Zillmer. Here the good doctor’s work is termed the Full Preliminary Term reserve method.  Modification is made for  policies with high savings elements such as medium and short-term endowments. For such assurances,  fully Zillmerizing the net premium in the first policy year to produce a zero reserve at year end may be too radical. A number of Modified Full Preliminary Term reserve methods address this issue. Though interesting and complex, these modifications need not detain us. The  originators  believe in the ‘artichoke approach’ - spending too much time on the outside leaves instead of the core. Suffice it to note, by way of example, for whole life policies with premiums payable  over 20 years or more, CRVM and Zillmerized reserves are equal, both being below unmodified (net premium) reserves. For a twenty year endowment, CRVM reserves exceed (fully) Zillmerized reserves but are less than unmodified (net premium) reserves.

Under a regimen of  statutory valuation mortality tables reviewed irregularly and infrequently, it can too easily happen that a chasm opens up between valuation and pricing bases. And into this chasm scientific valuation principles have fallen. Consider the results of  statutory mortality being too heavy.  You can find gross premiums less than net premiums (on the statutory valuation basis)! A policy with net premiums exceeding gross is ‘deficient’ and additional deficiency reserves must be established.

Turn back to our combination of a term policy with whole life. Since gross premia are not level, Commissioners Reserve is not directly applicable. Law demands  reserves for policies that cannot be calculated employing CRVM be calculated by a method that is consistent with it. Literal interpretation of the law requires an insurer to maintain a constant ratio of net to gross premiums throughout the policy term (life).                 

In essence, we are concerned  with policies with initially low premiums that are guaranteed for some period (say 5,10 or 15 years) at competitive premium levels that ultimately go to a higher possible maximum premium that are non-competitive. Law permits the insurer to set artificially high gross premiums in later years, thereby deflating the ratio of net to gross. This maneuver may be needed to bring the net premiums below the gross! By proper selection of the ultimate level of premiums. the overall ratio of net to gross premiums  can be made less than one (non-deficient) when the policy is treated as a unit. This is known as the ‘ unitary reserve’ concept; the ‘unitary’ valuation method treats the policy as a unit. Reading this stuff causes the face to assume a demeanor simultaneously tragic and urgent - as if you have been shot in the stomach and are late for an appointment.  Artificially high gross premiums in later years gives rise to post-funding of benefits. A supple legal mind can design a policy with reserves as low as an insurer may desire. Very high premiums in later years expose these policies to risk from selective lapses by insureds who are able take out new policies at standard rates. Only substandard lives remain. Thus, over time the mortality of the survivors becomes severely substandard.

Actuarial science teaches that  policies at risk of  selective and deteriorating  decrements must be valued allowing for them. Law is not a branch of science. Using  a mortality deterioration model, an actuary may model such term/whole life policies. He (or she) can thus calculate deficiency reserves assuming -- for example -- that the policyholder  will take that action which would require the company to hold the largest reserve, and reserve for that contingency.  Similarly, the actuary  can perform calculations  to ensure that future sufficiencies do not offset earlier deficiencies. Such results may be scientific, but submitted as a statutory valuation they will expose the actuary to the searing anguish only litigation can deliver.

Valuation statutes  fail to consider the possibility of selective lapses. My reading of insurance laws  parallels my reading of Checkov - starting slowly then tapering off! Nonetheless, to allow for lapsation is inconsistent with Commissioners Reserve. Clearly,  since for statutory reserving, lapses have never been explicitly incorporated, to consider lapses is illegal. American actuaries are in the absurd position  that not only may they ignore the possibility of  selective lapses - but to allow for lapsation is illegal! This can result in  inadequate reserves for certain types of policies - including our example. Now we see why some offices write such policies!

Our term/whole life policy  may have negative  reserves, which are set to zero and the mid-policy year reserve is then 50% of the net premium. This is referred to as the ‘Unitary 2’ reserve. Some have felt that the mid policy year reserve should at least equal the cost of insurance to the next anniversary on the valuation basis and accordingly set a minimum reserve of 50% of  Cx . This has been called the ‘Unitary 3’ reserve.

Life, it often appears, is more and more a reassertion of old and somewhat tired themes; new topics of potential enquiry are lost amidst a regimen of  seeing old operas, patronizing new ethnic restaurants and making uncharitable comments on those not present.

Actuaries argue that a level benefit policy with level premiums for the first ten years followed by annual premiums based upon attained age (and increasingly substandard mortality)  thereafter should be supported by reserves at least as great  as those that would be held if the policy were  only a ten year policy. This is termed the ‘term’  valuation method. An insurer should not rely on the future collection of inflated gross premiums since it is unlikely that, for the vast majority of policies, those gross premiums will be collected! The policy is, in effect,  a term policy. This is an actuarial argument, not a legal one - and therefore irrelevant to the Standard Valuation Law.  Law is concerned not with the establishment of proper reserves but with  adherence  to the cook-book.

Under the term method, a composite term/whole life policy is treated as a series  of separate policies, each for one renewal period of the policy. Reserves are for the present term only, plus the present value of any future deficiencies (excesses of net premiums over gross). Since the net premiums for each period are calculated separately, large premiums at later durations do not avoid deficiency reserves  at early durations if early premiums are  too low.

Following the debate on legal aspects of policy valuation is disorienting. The style is reminiscent of ‘House Beautiful’ and other ‘shelter’  magazines in which impeccably dressed people drift through spotless mansions. Have the people who build these legal abstracts ever valued a policy?

The segmented reserve or unified method attempts to blend the features of the unitary method  - such as an invariant net to gross premium ratio - with those of the term method.  The segmented  method can be thought of as the unitary method modified to eliminate negative reserves or the term method modified to merge level-premium periods when necessary to provide for net premiums being a level percentage of gross premiums.

The  segmented  reserve method is based on a methodology  described by Stephen Beach in a paper  ‘Statutory Reserves for Nonlevel-Premium Policies’ published in Vol. XLII of ‘Transactions of the Society of Actuaries’.  Calculate net premiums  (under the unitary method) that are sufficient to provide for all future (guaranteed) benefits if the policy were to terminate at each possible future duration. The termination duration which results in the highest ratio of net premiums to gross premiums defines the length of the first policy term segment. To use a longer segment with a lower ratio of net to gross premiums will result in post-funding of benefits. To use a shorter segment with a lower ratio of net to gross premiums will result in inadequate pre-funding of benefits. Start at the end of the first segment, ignore time past and repeat the process to determine the length of the second segment  and the corresponding net premium ... and so on. The reserve at any  point is simply the present value of future benefits less the present value of future net premiums.

This approach has the merit of reducing to the normal valuation of a level  premium policy as a special case where the ratio of net to gross premiums is a monotonically increasing function of possible termination duration (starting from policy inception).

Segmented reserve method net premiums are  unitary method net premiums  for segments of the policy where each segment is as long as possible without generating negative reserves (or reserves less than the surrender value). There is an intellectual link to the Commissioners Annuity Reserve Valuation Method (CARVM) employed for policies where extra premiums buy extra benefits. In that method, the reserve is the greatest excess of the present value of future benefits over the present value of future guaranteed premiums. In the segmented method, net premiums are based on the greatest  ratio of future benefits  to future gross premiums. As such, both methods  use worst cases and do not allow future factors more favourable to the company to lower current reserves.

Segmented reserves are the excess, if any, of the present value, as of the valuation date, of all future (guaranteed) life assurance and endowment benefits to the (mandatory) expiry date of the policy over all future modified net premiums to such date. The modified net premiums within each segment of a policy must be a uniform percentage of the respective gross premiums within each segment except that Zillmerization is allowed for the first segment (only). The modified net premiums for subsequent  segments are net level premiums.

As I trudge ever deeper into the valley of advanced age, I find beauty in the brevity of a formula. A formula is worth a thousand words of prose flowing like cement. So we express the segmented method mathematically. For any policy, take our stand at policy inception and look forward to duration  t.   The value of the  duration t reserve  discounted back to inception is equal to  the discounted value of premiums less the cost of life cover. So:

                   _tE_x x _tV  =  { Σ P _j  x _jE_x}-A{x(1),t}                                                                              (1
                   _tE_x  x _tV  =  {Σ P _j x _jE_x } -  A{x(1),t}                       (1

employing the international actuarial notation with modifications:

  Summation is  of  ( P _j  x  _jE_x  ) over the range (j=0) to (j=t-1)

A{x(1),t} denotes the value at x of  1 payable on death between x and (x+t).

We require there to be no negative reserves - or, more generally, that the reserve should exceed the cash surrender value (which is non-negative). From equation (1, we see that to make _tV greater than the cash surrender value _tSV, it is sufficient to ensure that

                                { Σ P _j  x  _jE_x  }    ≥  A{x(1),t}  + { _tE_x x  _tSV }                                                               (2

Return now to our hybrid  term/whole life policy. To achieve the inequality set out in (2,

we divide the policy into segments and set net premiums (P) for each segment to a constant percentage of the gross premiums. Let k be the ratio of net to gross premiums over the segment, t the length of the segment and m the beginning of the segment. We derive k  from a generalization of 2):

                                _mk_t  x  { Σ G_j  x  _tE_x+m }      =   A{[x+m](1),t}  +   [_tE_x+m  x _t+mV ]  -  _mV          (3

where G is the gross premium. The reserves used in equation (3 should be the minimum acceptable - zero or the cash surrender value.

To calculate the length of the first segment, we start with the first policy year  and compute  ₀k_t   (from (3  ) for all possible t.  That value of  t - say, m,  -  which yields the largest ₀k_t   is the final year in the first segment. To calculate the length of the next segment, we start with the mth policy year  and compute  _mk_t   for all possible t. Proceed as for the first segment ...and so on.

XXX muddies the water by defining a ’Levelized premium segmentation method’. This follows the segmented reserve method except that the method of dividing a policy into segments for valuation purposes is defined crudely. The length of a particular levelized premium segment is to equal the minimum value of t for which G(t) exceeds R(t), where G(t) is the ratio of gross premiums per mille excluding policy fee) from one policy year to the next  and R(t) is the ratio of the valuation mortality rates from one policy year to the next. If premiums are level or stepped, G(t)<R(t) for each step, with the reverse inequality arising at the steps.

The somnolent prose rambles on to define deficiency reserves not as the present value of the excess (if any) of  net premiums over gross.  Rather, we are told, if gross premiums are always greater than modified net premiums, no deficiency reserve is required. If deficiency reserves are required, they are ‘calculated for each policy as the excess , if any, of  quantity A over the basic reserves. The quantity A is obtained by recalculating the basic reserves’ using minimum valuation standards allowable for deficiency reserves and by  replacing the modified net premium by the gross premium in any year in which the modified net premium exceeds the gross premium. 

The NAIC  hopes to adopt the XXX model regulation in 1994.

Where does Regulation 147 come in?

Like Europe,  America is a Union of states.  As in Europe, some states are ‘fast track’, others ‘slow track’. Some go for ‘opt-outs’. In the words of a minor British Prime Minister, member states can decide “in their own way and at their own speed”.  US insurers  live in a  “multi-speed, multi-track” union. As befits the ‘Empire State’, New York has its own track - in this case New York Regulation 147. (Part 98 of Title 11 of the Official Compilation  of Codes, Rules and Regulations of the State of New York.)

Casting aside my preferred mode of investigation (idle speculation), I opened  Regulation 147 at random, to read:

"Basic Reserves’ means reserves calculated in accordance with the principles of section 4217 of the Insurance Law, as interpreted by this Part. ‘Commissioners Reserve Valuation method’ means the method defined in section 42178(c)(6) of the Insurance Law or, in the case of policies subject to section 98.6 of this part, as set forth in section 98.6 of this part, based on section 4217(c)(6)(C) of the Insurance Law.” 

Have standards of written English really declined this far? Not even in the US will this raw legalese reach the ‘best-seller’ list. It is comforting to know some folk are  even worse communicators than actuaries!

To be  fair to Regulation 147, for yearly renewable term insurance, at least,  deficiency reserves are the present value of the excess (if any) of  net premiums over gross. At last, a sensible definition! XXX declines to follow this useful lead.

Legal draftsmen have not forgotten how to shock readers of  XXX  with  a few ill-chosen words.  In ‘Section 3.  Applicability’ we read ‘This regulation shall apply to all individual life insurance policies, with or without nonforfeiture values, issued on or after the effective date of this regulation...’  Say that again?  The law has been emasculated!  In a debate that has bored us these many years, speaker after speaker asserted the inadequacy and inappropriateness of valuation methods. So much ink spilled on the need to ensure policyholders’ security!  Now we are told those inadequate and inappropriate valuation methods may continue to be used for existing policies! We are all guilty until proven influential.

Americans  must put more emphasis upon the observance of law rather than upon its evasion.  Quantity of laws is mistaken for quality of laws. If you laid all our laws end to end, there would be no end.  After all, despite laws against murder, Washington D.C. - the greatest law factory the world has ever seen -  is also the world’s murder capital.

  ‘The more corrupt the state, the more numerous the laws.’(Tacitus)