CHAPTER XVI THE RESERVE By BRUCE D. MUDGETT One of the most difficult subjects for the layman to understand in connection with the administration of a life-insurance company is the existence of the enormous assets possessed by the different companies and the reasons why these funds must be held. That a single company should hold over half a billion dollars strikes many persons as unnecessary and as an opening to the possible misuse of such funds. The fact is not generally known, or clearly understood, that a major portion of these assets represents liabilities held by the company for its policyholders and subject to call by them at any time upon the surrender of their policies. This portion of the funds is held in trust by the company and is known as the reserve. Financial Importance of the Reserve. The Insurance Year Book for 1914 shows that thirty-four companies doing business in New York State in 1913 held on December 31 of that year total admitted assets amounting to $4,351,042,584 and of this sum $3,677,450,917, or over 84 per cent., was held as reserve. A comparison of the total admitted assets and the reserves of the five largest life-insurance companies in the United States is also furnished in the following table: These figures likewise show that 80 to 90 per cent. of the total funds held by these companies is included in the reserve. The possession of these vast resources justifies a careful analysis of the sources and purposes of the reserve. The Origin of the Reserve. The life-insurance reserve arises as a result of the method of paying premiums. In the three chapters immediately preceding, an analysis of net or mortality premiums has been undertaken and the statement is there made that life-insurance policies may be purchased by a single cash payment or by annual premiums paid during life. The fact was demonstrated furthermore that mortality rates increase with increasing age and that the annual cost of insurance therefore augments rapidly with advancing age. This results in the creation of a surplus from the annual level premiums paid in the early policy years when mortality costs are low, and this surplus is available in the later years of high mortality when premiums are inadequate. The purpose of this fund is to average the varying yearly costs so that the burden of insurance premiums can be carried at all times. These level premiums thus bring into the possession of the company, funds which are not used immediately to pay policy claims but which must be accounted for by the company and placed to the credit of the policyholder until needed at some future date. In like manner when a policy is purchased by a single premium this premium becomes the total contribution of the insured toward claims paid under contracts of this class, and in the early years of the policy contract a large share of this single premium must still be in the possession of the company. Definition and Purpose of the Reserve.-In Chapters XIII to XV, premium rates were computed on the assumptions that a specified rate of interest would be earned on funds in the possession of the company and that the mortality experienced among policyholders would be at the rate shown in the American Experience table. If these assumptions are realized in practice the premiums will be adequate. From the standpoint of premiums there are two ways of viewing the re serve. It may be considered as the difference between the premiums collected in the past and the policy claims paid that is, the surplus premiums on hand at any given time; or it may be looked upon as that fund which together with future premiums to be collected, if any, will enable the company to pay future estimated claims. The former is called the unearned premium reserve, or the reserve is said to be valued retrospectively, that is, looking backward to past accumulations; the latter is the reinsurance reserve, or the reserve is valued prospectively looking forward to future requirements. The word "reserve," however, has come to have a technical meaning in life insurance, due to the fact that most of the states have passed laws requiring some definite method of valuing this fund, and when the term is now used this technical or legal reserve is ordinarily meant. - The legal reserve required by state laws to be held is invariably the prospective reserve, or the fund which with future premiums, if any, based on assumed rates of interest and mortality will pay estimated future claims. If the actual experience of a company as regards interest and mortality exactly coincides with the expected or assumed experience the reserve fund will always be the same whether valued as unearned premium or as a reinsurance fund, but such coincidences do not occur in practice. If premiums are redundant the unearned premiums will be greater than the legal reserve; if they are inadequate the surplus left from them after payment of claims accrued will be less than the legal requirement. That the legal reserve shall be determined on the basis of future requirements is necessary because of the fact that the life-insurance contract is written for a long term and cannot be cancelled by the company and the premium rates can never be changed. Therefore, the assumptions as to future interest earnings and mortality must be made on a safe basis, and the reserve must be valued with one object in mind, viz, the continued solvency of the company. The state, in establishing a method of valuing life-insurance contracts, sets certain standards of interest and mortality that can safely be realized and then says, in effect, that any company is solvent if on the basis of estimates made with these standards its future premiums plus its reserve fund will enable it to pay all claims. The standards set by state law in most instances are a 32 per cent. interest rate and mortality according to the American Experience table. This fixes the minimum reserve required, but a company may usually value its liabilities by a higher standard if it so chooses. Many companies to-day value their reserves on new policies on a 3 per cent. interest basis and thus hold a larger reserve than required by law. The solvency of a company is thus guaranteed if the assumptions made are adequate, and years of experience with insurance under American conditions have shown that they are. Method of Calculating the Reserve.- Inasmuch as the legal reserve looks to future requirements, and is based on the assumption that a certain interest rate will be earned and must provide for mortality equal to that of the American Experience table, these factors must form the basis for calculating reserves on any policy. Likewise since insurance may be purchased by a single or by an annual level premium, reserves will differ according to the method of paying premiums, for in the latter case credit may be taken for premiums still due. Suppose therefore it is desired to calculate the reserves on a whole-life policy for $1,000 issued at age 45, based on the American Experience table and 3 per cent. interest and paid for by a single premium. The net single premium for this policy was found in Chapter XIII to be $504.58493. The simplest method of showing the operation of the reserve on this policy will be to make the assumption that a company insures a group of 74,173 persons, the number living at age 45 according to the mortality table, and trace the disposition of the entire fund contributed by them, showing how the total fund paid at the start is increased year by year through interest accretions and decreased at the same time by payment of death losses occurring within the group. According to the table, therefore, 74,173 persons will insure at age 45 and each will pay to the company $504.58493, giving the company a fund of $37,426,578.013 at the beginning of the first year of insurance. This sum is paid at the beginning of the year and, since death claims are assumed to be paid at the end of the year, will earn interest for one year before any claims for death payments will be made upon it. Three per cent. of the above sum is $1,122,797.340 and this added to the original sum gives a fund of $38,549,375.343 at the close of the year. Death claims for $828,000 are now due and when paid leave a net surplus of $37,721,375.34. ́This latter sum represents the funds belonging to policyholders still living from among the original group, or 73,345, and if the insurance were cancelled at this time and the share of each returned to him there would be available $514.30 for each policyholder. In continuing the insurance, however, this $37,721,375.343 again earns interest and the process here described is repeated for the second year. The accompanying table, showing the net reserves on a single premium policy at age 45, traces the operation of the fund for the group until at age 96 they will all have died according to the mortality table, and in the last column shows the reserve standing to the credit of the individual policyholder for each of the fifty-one years of insurance. The table shows the total sum on hand at the beginning of each year of insurance, the amount of interest earned during the year, the total of these two amounts, the death claims paid during the year and the reserve fund remaining at the close of the year for the group as a whole and the pro-rata share belonging to each survivor. Since this policy is paid for by a single premium, this individual reserve constitutes the total sum available per policyholder for the payment of future claims and therefore must equal the net single premium at each age later than forty-five for a wholelife policy at that age. If these figures are correct the terminal reserve at age 94 (i.e. the reserve at the end of the year) will be the net single premium at age 95 and this sum increased at 3 per cent. interest for one year will just equal the amount payable at the close of age 95, for the mortality table shows that the last person of the group insured will certainly |