CORRESP ONDENCE, 



255 



CORRESPONDENCE. 



IN^SUEANCE VALUE. 



To the Editor of the Popular Science Monthly : 



IT is one of the most difficult things to 

 popularize mathematical science, either 

 abstract or applied. On this account, and 

 not for want of good intention, I have failed, 

 in my " Politics and Mysteries of Life In- 

 surance," to make myself understood on 

 some points, even by my able and candid 

 reviewer in The Popular Science Monthly 

 for May. The reviewer says : " If the hold- 

 er of a ' single - premium policy,' having 

 twenty or more years to run, becomes de- 

 sirous to surrender his policy at the end of 

 five years, he should get back from the 

 company, not only the * reserve,' but also 

 that portion of the ' insurance value ' that 

 has been set apart by the company to com- 

 pensate for the risk attached to the remain- 

 ing fifteen or more years of the policy's 

 term." 



This, I regret to be obliged to say, is not 

 quite correct. But I must confess it is not 

 an altogether unnatural inference from the 

 definition of "insurance value "^given on 

 page 12 of "Politics and Mysteries." "In- 

 surance value" is there spoken of as if it 

 were a sum " paid in advance." It is really 

 only a function of the sura so paid, not 

 a part of it. The " single premium," apart 

 from the margin added to defray office ex- 

 penses, that is, the net single premium, is 

 itself the reserve. The cost of the first 

 year's insurance, so far as it is done by the 

 company, comes from the interest of that 

 premium. It is the present value of so 

 much of the interest as is not needed to 

 make up the "self-insurance" or reserve 

 at the end of the year. And this reserve is 

 the net single premium at the party's pres- 

 ent age. And just so comes the cost of the 

 next year's insurance, so far as it is done 

 by the company. The " insurance value " 

 of the policy at the start is the present 

 value of all these costs, or partial interests, 

 discounted both by the interest and mortal- 

 ity rates. Consequently it is nothing to be 

 returned in addition to the reserve. On 

 the contrary, if the life is a good one, which , 



may be expected to live long enough to pay 

 more than the average toward death-claims, 

 something must be deducted from the re- 

 serve, which will bear some proportion to 

 the " insurance value " of the policy at the 

 time of surrender, to compensate the com- 

 pany for the loss of the future xoherewith to 

 make up the deficiencies of lives that are 

 not good. This is on the principle that, 

 other things being equal, the profitableness 

 of policies will be as their " insurance val- 

 ues." 



If we speak of "insurance value" as 

 being actually contained in the single pre- 

 mium (net), then the balance thereof is less 

 than the " self-insurance " or reserve. We 

 have no technical name for that balance. 

 Prof. Bartlett calls it {see " Politics and Mys- 

 teries," page 73), the fund which " works 

 at compound interest till it amounts to the 

 sum assured." But it is more, as will ap- 

 pear presently. 



The two new technical terms "self-in- 

 surance" and "insurance value," which I 

 have felt obliged to introduce into the dis- 

 cussion of this subject, cannot be well un- 

 derstood without noting their relation to 

 each other. 



Self -insurance is the amount in the 

 hands of the company at the end of a poli- 

 cy year, which the insured party has paid 

 beyond the normal cost of the past insur- 

 ance. In the fact of paying so much beyond 

 the normal or assumed cost, he insured 

 himself to that amount. And the law has 

 stepped in and made it emphatically a self- 

 insurance, by virtually forbidding the com- 

 pany ever to apply it to the payment of a 

 claim on any other policy. 



Insurance value — and I should have done 

 better by so defining it — is the present 

 value, discounting by the assumed rates 

 both of interest and mortality, of which the 

 policy may he expected to contribute toward 

 the payment of death-claims, including its 

 own, so far as that, when it occurs, shall 

 not be self-insured. 



This "insurance value" has of course 

 nothing to do with the margin arbitrarily 



