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per cent, and even more, is sometimes used instead of ten. This correction is not, however, the only one needed. And for our recent American companies, and for all who are receiving a large number of new members, there is another of the highest importance.

It is well known, by the universal experience of life companies, that the inortality in the early years of insurance is much less than afterwards. This is especially observed in the first year, when the insured have just been examined by the company's physician and pronounced perfectly sound. The influence of selection extends for several years after the first. At the later years the mortality is higher than the average. The abandonment of their policies by the strong and the hearty, and the purchase of such by the company, makes the mortality among the older members much above the average. These two influences are of great importance. They indicate most clearly that it is wrong to count as earnings all the gains that appear to be made in the earlier years of insurance. The mortality will be below the average at first, and the gains from this source must be husbanded to meet the future losses when the mortality will be above the average. That time will be sure to arrive, sooner or later, and even if it should never come, the large profits of the first years being expected when the contract was made and the premium fixed, belong to the whole contract, and should be distributed over the whole time.

If a fire insurance were taken in May for twelve months, as the risk is less for the summer than the winter, half the premium is not earned in six months. In a marine risk, if the vessel has been spoken near the distant port wbither she is bound, the underwriter should not regard the premium as nearly earned, for the most hazardous part of the risk is yet to be incurred. So a life insurance company, knowing that its losses in the first year will be small, ought not to count all the apparent gains, from a mortality below the average, as real earnings, but should reserve a part of them to meet future excesses above the average. Even if those excesses shall never arrive, the first year's apparent gains do not belong to that year, but should be distributed among all the years.

It is no answer to this to say, that the reserve is sufficient to meet the future mortality according to the tables ; because, on account of forfeiture by the best lives, the future losses will probably exceed the average; and because the mortality, as made up in the actuaries' table, is an average of the first and all subsequent years; and because, in making the contract, a small mortality was expected the first year, and the premium being the same for the whole life, is made to represent an average for the whole time.

This point being very important, we will illustrate it still farther. Suppose a company to insure a man at thirty, for a single premium, after a careful and satisfactory examination of his constitution, health, and habits. They would earn a certain portion of the money received if the insured should live till he was thirty-one; if he should survive another year the portion earned would be still larger; if he should be alive at the end of ten years the gains would increase every year. He may now be helpless, his constitution gone, his habits ruinons; or his health may be as good as when he first took out his policy. But this uncertainty makes the risk at forty greater than it was at thirty, and if he survives till he is forty-one the earnings will be greater than in the first year after

insurance, not only because he is older, but also because of the uncertainty as to his general health and habits.

Some of our companies make an allowance for this, under the name of a deterioration of life, and this phrase expresses not only the object but the appropriateness of this allowance.

The statistics furnished by the London offices, from which the actuaries' table was constructed, give us the means of judging of the extent of this diminution of mortality during the earlier years of insurance. The following table is deduced from Mr. Higham's discussion of these statistics, in Vol. I. of the Assurance Magazine. The first column contains the chance of dying in one year, according to the actuaries' table; the second, the same chance deduced from the deaths during the first year of assurance; the third, from the deaths during the second year of assurance; and the fourth, from those lives in which the influence of selection was exhausted :

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In the actuary's report of the Mutual Life of New York, this experience is presented in a different form :

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The regularity of these differences, the large numbers from which they are derived, the fact that most of them were obtained from the Equitable society—where lives, not policies, were considered-make the results worthy of much confidence. They show most conclusively that the mortality during the first year of insurance is a third or a fourth less than the average, and that in the latter years, after selection no longer betters the probabilities of living, the chance of dying is nearly one-half greater than the

average. The following has been furnished us by one of our American offices :Mortality in the first year of insurance..

.00426 Expected by the Carlisle table...

.01150 Mortality after the first year..

.01277 Expected by the Carlisle table..

.01361 This, and other experience of our American companies, confirms the results of the English life offices.

After the first year the effect of selection, though sensible, is not of much importance. For ten or twelve years it exerts a favorable influence, and after that the mortality is regular and far above the average. From this, it follows that the apparent gain in the first year should be dis

tributed mainly among the last years of insurance. As the reserve for the first year is nearly equal to the risk for that year, being nearly half the net premium, it is evident that an increase of one-fourth of the first year's reserve will represent very nearly the saving from the diminished mortality of the first year. The following formula, for calculating the reserve or reinsurance fund, modifies, therefore, the one before given so as to introduce this correction for the first year's diminished mortality; and as the multiplies, 1 + a decreases slowly at first and rapidly afterwards it distributes the saving among all the subsequent years, reserving most of it for the latter years of iife, which is exactly what is required by the experience of the English life offices. The formula is

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To give an example of this mode of calculation we will use the same age and table as before. The net premiums at twenty-nine, thirty, and thirtyseven are $171, $175 50, and $215 40. If the policy issued at the age of thirty had been running seven years, p for m, increased by ten per cent, would be $193 05; p for m + it would be $236 94, and p for m -1

$188 10, and p for m * = $191 81. The difference of $191 81 and $236 94, or $45 13 being multiplied by 16,666, which is 1 + a for 37, gives $752 14 as the correct amount needed for reinsurance. The method of net premiums gives only $664 97. The percentage of diference would be larger for two or three years, and less for more than seven.

We have not hitherto made any reference to the defective premiums charged by some companies, and we would now remark that, unless the rates are thirty per cent higher than the Carlisle or the actuaries' four per cent tables, the methods above explained will not give satisfactory and reliable results. The object of the formula is only to determine what portion of the past payments appropriately belong to future risks and contingencies; but if the future payments are not sufficient to meet the hazards for which they are devoted, the company's safety will be endangered from this source, as well as from the other. Nor does this difficulty exist only when the whole table of rates for every age is insufficient, but also when the premiums for particular ages are too low. In the rates of the “ International,” for example, the loading ranges from 9 to 62 per cent. For those ages when the additions are too small to meet expenses and contingencies, something must be reserved out of capital or former accumulations to meet the deficiency.

The true table of mortality, or the closest approximation to it we can have, should also be made the basis of the calculations.

The formula we have given above is not, therefore, proposed as complete, since the proper mode of calculation must have reference to the real premium charged, and to the approximate mortality of the assured. The consideration of these we will postpone for a subsequent article. VOL. XLIII. —NO. I.

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Art. III.-BRAZIL: ITS TRADE AND FINANCES.

The course of events is rapidly bringing the countries of the American continents into closer connection, and the vast empire of Brazil, with its great resources, is, at no distant day, to contribute a large portion of our commerce. All that throws light upon the actual position of that interesting country, becomes, therefore, important to the commercial public. We therefore lay before our readers the accompanying translation of a letter which was addressed to the Brazilian Minister of Finance, in reply, partly, to questions (which are given) addressed to the eminent firm of Maxwell Wright & Co. by the Minister, and partly to separate questions, which do not appear, addressed to Robert Clinton Wright, Esq., by the principal law officer of the Treasury Department.

The American reader must lear in mind that in Brazil the quotations of exchange are the reverse of those in New York, and that exchange is said to be rising there when in the United States it would be said to be declining. And he must not, therefore, be startled to find arguments based upon a declining exchange which he has always been accustomed to refer to an advancing exchange. And if he shall tind any expressions in reference to crisis which may seem to bim paradoxical-as, for instance, “a crisis arising from the legitimate movement of the foreign trade”—he will remember that, in the view of the writer, the crisis of 1857, which shook the world, was brought about by a half-dozen stock gamblers in New York; that it came like a clap of thunder from a clear sky, and was no less a phenomenon than this—that it was the result of senseless panic, and that so long as credit shall constitute an element of trade, it must own panic as its twin sister; that panic, owing no allegiance to reason, may arise with or without a cause, and therefore that it is not paradoxical to say that “ crises may arise in the course of the legitimate movement of trade,” involving alike the prudent and the inprudent, those who trust to instinct and those who build on reason, in ove common ruin. It must never be forgotten that all of credit that enters into price is the subject of collapsethe food of panicthe only source of crises :

Question 1. How are exchange operations made in the market of Rio de Janeiro ?

Answer. As regards foreign exchange, operations are made by the offer and purchase of bills of exchange, at a conventional usance, but for the most part at 90 days' sight upon various foreign markets. The business is generally done through the agency of brokers. It may be observed that the quotation of exchange in the Rio market is always based upon the value of the money of the country. It is the money of the country that is quoted, which is not the case in some other markets. For instance, in the markets of the United States the foreign moneythe money

in which the bill is drawn-is quoted, and not the money of the country. As a consequence, a rise or fall of exchange in Brazil and in the United States convey diametrically opposite ideas. A rise of the exchange in Brazil is considered favorable to the country; a rise of the exchange in the United States, on the contrary, is considered unfavorable to the country.

Question 2. What determines amongst us, as a general rule, the course of Exchange

Answer. The daily exchange with foreign countries amongst us, as well as in all countries, is determined by what Raguet terms the “balance of payments "—an expression used by bim in contradistinction from the more comprehensive term “ balance of trade." By the “balance of payments” is understood that sum which a city or a nation may be bound to pay at a given time; and the daily course of the foreign exchange, that is, the daily fluctuations which are observable, is determined by the relatior existing between the sum of obligatory payments and the sum of exchange offering in the market upon foreign countries--this last sum representing, as a general thing, the operations then effected in the products of the country. What we have stated is the legitimate basis of the daily course of exchange, of its daily fluctuations everywbere. Nevertheless, it cannot be affirmed that this is absolutely the only element of the daily course of exchange. There enter into it, also, various moral and speculative influences which defy any mathematical conclusion. Drawers, as well as takers, of exchange speculate upon the future. It is difficult, nay impossible, to form any positive judgment upon the commercial condition of a country from the daily quotation of exchange, because it is not given to any human intelligence to embrace and estimate all the elements-positive, moral, and speculative-by which this is determined. But, notwithstanding this great unreliability of the daily course of exchange, all economists

agree in the opinion that the exchange —that is, its general tendency-should serve as a barometer to the intelligent merchant; that it should, on this account, be left as free as the ebb and flow of the tide, and in no manner subjected to disturbance by governmental interference.

Thus far we have been dealing with the daily course of exchange upon the hypothesis of a sound circulating medium, one either of metal or which maintained a par with metal. Wbat we have said is referable to the general intelligence as to the causes which determine the course of exchange, and it must be borne in mind that, in this case—that is, upon the hypothesis of a sound circulating medium-be the daily fluctuations what they may, the exchange cannot, for any great length of time, rule at a point above or below par, exceeding the cost of transporting the precious metals.

We shall nowo take a somewhat broader view of the subject.

For the most part, merchants, contenting themselves with a knowledge of the simple practice of their profession, give themselves little trouble to fathom the science of money, so intimately linked with that profession, and upon which depend their fortunes—the favorable or unfavorable result of their enterprises. The simple practical merchant is not, therefore, the safest counselor in matters of monetary science. general rule, the course of exchange is considered amongst merchants to be a simple question, as depending absolutely and solely upon the relation existing between the imports and exports. There could not be a more erroneous ojinion.

This opinion is not positively correct even when referable to a sound circulating medium, for it is well known that, even upon that hypothesis, money is inore or less abundant according to the greater or less activity of credit trade, and that this element of the greater or less abundance of the circulating medium, although sound in itself, and although this greater or less abunda ice may be purely relative, exercises a very mani

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