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UBC Theses and Dissertations

Retail price competition in Canadian whole life insurance Mitchell, David Hoadley 1968

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R E T A I L P R I C E C O M P E T I T I O N C A N A D I A N W H O L E L I F E I N S U R A N C E by DAVID HOADLEY MITCHELL B.A. , Queen's University, 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION in the Department of COMMERCE AND BUSINESS ADMINISTRATION We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1968 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Briti s h Columbia, I agree that '-.he Library shall make i t freely available for reference and study, I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives„ I t is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of B r i t i s h Columbia Vancouver 83 Canada ABSTRACT Problems of pr ice ana lys is and pr ice comparisons at the reta i l l eve l in whole l i fe insurance are so complex as to be we l l beyond comprehension to the average purchaser. In addit ion to the in i t i a l d i f f icu l t ies ar is ing from the combination of savings and insurance protection which ex is t in whole l i fe insurance po l i c ies many var iables exhibi t inf luence in the ana lys is of reta i l whole l i fe insurance p r i ces . The determination of price is no easy task but is ably accompl ished by the leve l -p r i ce method which i s u t i l i zed in th is study. Compet i t ion , it i s often expressed, should function as a suff ic ient deterrent against the charging of excess ive p r i ces . From economic theory the concept of effect ive competit ion dictates that pr ices need not be completely uniform but that they ought not exhibi t substant ia l d ivers i ty and that they should be f l ex i b l e . The f lex ib i l i t y of pr ices in whole l i fe insurance is res t r ic ted , by the nature of the product, to changes on an annual b a s i s . Evidence from this s tudy, based on 1967 data, indicates that substant ia l price dispari ty between different companies is existent in various types of whole l i fe insurance po l i c ies offered in Canada . Competi t ion however, operates as we l l on var iab les other than p r i ce . The extent to which the existent pr ice dispari ty ref lects the costs of the added var iables is not completely c lear . Wh i le this study only v iews the price competit ion s i tuat ion at one point in t ime, and is therefore restr icted from the advantages i i i of conc lus ions based on broad foundations in t ime, it nevertheless appears evident that whi le no conc lus ions can be made here on competit ion as a who le , competit ion on the bas is of price alone is less than whol ly e f fec t ive . TABLE OF CONTENTS CHAPTER PAGE 1 INTRODUCTION 1 2 PRICE DETERMINATION IN LIFE INSURANCE 3 Methods of Determining Price 6 Level-Price Method 10 3 THE PRODUCT 19 4 METHODOLOGY; PROCEDURE - INITIAL 23 Responses 25 The Sample 26 The Data 27 5 ASSUMPTIONS (a) Interest Rate 29 (b) Mortality 31 (c) Lapsation 34 (d) Dividends . 35 PROCEDURE - INTERJACENT 37 6 COMPETITION 39 Perfect Competition 40 Conduct Requirements 43 Market Performance 44 7 THE RESULTS 47 8 INTERPRETATION OF RESULTS 55 9 CONCLUSION 71 V. PAGE SELECTED BIBLIOGRAPHY 74 APENDICES 77 LIST OF TABLES TABLE PAGE I Year ly Price Information (on a $1,000 Basis) of a Hypothet ica l Po l i cy Assuming Interest at 4% . . . . 14 II Responses to Quest ionnaires 25 III Price Results for $1,000 Whole Li fe Non-Par t ic ipat ing Po l i c ies 47 IV Price Results for $10,000 20 Payment Life Non-Par t ic ipat ing Po l i c ies 49 V Price Results for $10 ,000 Whole Li fe Part ic ipat ing Po l i c ies 51 VI Price Results for $10,000 20 Payment Li fe Part ic ipat ing Po l i c ies 53 VII Information on Rank Correlat ion between Premium and Price 57 VIII Price Di f ferent ia ls in the Extremes of the Arrays . . . 58 IX Information Relevant to the Three Standard Deviat ion Test 60 X Companies with Pr ices 1.5 Standard Deviat ions from the Mean 61 XI Relat ive Growth of Low Price Firms in Terms of the Amount of New Effected Insurance Po l i c ies on Whole Li fe Po l i c ies in Canada 66 XII Relat ive Growth of High Price Firms in Terms of the Amount of New Effected Insurance Po l i c ies on Whole Li fe Po l i c ies in Canada 68 XIII Structural Changes Amongst Ten Largest Firms in the Study 70 ACKNOWLEDGMENTS Pr imar i ly , expressions of gratitude in connection with this thesis must go to Dr . Peter A . Lusz t ig of the Facul ty of Commerce and Bus iness Administ rat ion. Or ig ina l ly the work was commenced as Research for Dr . Lusz t ig and subse-quently it became suitable thes is mater ia l . Fu l l gratitude must be expressed for h is patience and d i rect ion. Thanks should a l so be expressed to M r s . Caro l C larke and M r . A . G . Fowler of the U . B. C . Computing Department for their ass is tance in developing the computer program; and to M r s . Betty O ' N e i l l for her invaluable typing he lp . CHAPTER I INTRODUCTION The loss by premature death of a human l i fe is the loss of different values to a few,, some, or many people. Although a human l i fe may be possessed of mora l , soc ia l or other v a l u e s , most human l i ves are a lso possessed of an economic va lue . The economic value of a human l i fe is derived from i ts earnings capaci ty and the f inanc ia l dependence of other l i ves on that earning capac i t y . The bas is for l i fe insurance ex is ts when there ex is ts an economic value of a human l i f e . Li fe insurance is a device which enables an unreal ized potential of the economic value of a human l i fe to be rea l i zed in the event of death. As a means of compensating economic l o s s , l i fe insurance has grown and become a part of the ex is tence of most Canad ians . In fac t , re lat ive to the nat ional income, Canadians own more l i fe insurance than the people of any other country.' ' ' Total l i fe insurance in force in Canada is about twice personal d isposable income and annual premium payments absorb 3% of 2 d isposable income. Without further elaboration it i s evident that in Canada , people have c a p i t a l -i zed heav i ly their economic l i fe va lues , through the purchase of l i fe insurance, thus making the subject one of extreme importance in the ind iv idua l and Canadian Li fe Insurance Facts 1966 (The Canadian Li fe Insurance A s s o c i a t i o n , Toronto, 1966), p. 30. 9 Royal Commission on Banking and Finance (Queen's Printer, Ottawa, 1964) , p. 238. 2 ul t imately the nat ional in terest . A glimpse of the importance of l i fe insurance in Canada is ref lected in the net amount of l i fe insurance in force in Canada at the end of 1966 of $76,824 m i l l i o n . 3 Whi le the importance of l i fe insurance i s not usual ly quest ioned, however, a great deal of confusion appears to ex is t at the reta i l l eve l about the subject . The primary confusion appears to ar ise from the potential purchaser 's attempt to determine a meaningful pr ice to pay for a part icular type and amount of l i fe insurance. The asser t ion is often made that the determination of price in l i fe insurance i s suf f ic ient ly complex to be we l l beyond comprehension to the 4 potential purchaser. Further, the assert ion i s sometimes made that compe-t i t ion is suf f ic ient as protection against excess ive pr ices being charged to the purchaser .^ If these two statements are taken together, they ra ise an important quest ion . When it appears that price ana lys is in l i fe insurance may be confusingly complex to the purchaser, i s price competit ion neverthe-less e f fec t ive? The purpose of this thes is i s to examine this question as it relates to the Canadian whole l i fe insurance scene. Spec i f i ca l l y , , the purpose of this thes is i s to determine the ef fect iveness of reta i l pr ice competit ion in the Canadian whole l i fe insurance market. Report of the Federal Superintendent of Insurance, 1966 (Queen's Printer, Ottawa ) , V o l . 1, p. i i . ^ s e e , for example, S . Huebner and K. B lack , Jr. , Li fe Insurance (6th E d . , New York: App le ton-Century -Cro f ts , 1964), pp. 596-98. ^ s e e , for example, R. Mehr and R. Os ie r , Modern Li fe Insurance (3rd Ed . , New York: M a c M i l l a n C o . , 1961) , pp. 714-15. CHAPTER 2 PRICE DETERMINATION IN LIFE INSURANCE Before any in i t i a l attempt can be made to d iscuss price compet i t ion, it i s necessary to define and determine 'pr ice ' in l i fe insurance. The fo l lowing sect ions therefore, are devoted to that task . In the Introduction, brief reference was made to the economic value of a human l i f e . The economic value of a human l i fe is subject to certain elements of uncertainty, the most important of which is death. The protection against this element of uncertainty is the domain of l i fe insurance. Wh i le various def ini t ions of the term insurance are ava i lab le from different texts on the subject , two concepts appear to underly a l l such def in i t ions. Kulp 's def ini t ion readi ly summarizes the two concepts . He states that, insurance is a formal soc ia l device for the substi tut ion of certainty for uncertainty through the pool ing of haza rds . ^ The f i rst impl icat ion therefore i s that uncertainty is reduced. Secondly , the impl icat ion is that l osses are shared—that r i sks are poo led. Persons exposed to loss from a part icular source combine their r i sks and agree to share losses on some equitable b a s i s . Thus from the point of v iew of the ind iv idual insured, insurance is a device that makes it poss ib le for him to substitute a smal l def-ini te cost for a large but uncertain loss (up to the amount of the policy) , under C . A . Ku lp , Casua l t y Insurance (3rd e d . , New York: Ronald Press C o . , 1956) , p. 9. 4 an arrangement whereby the fortunate many who escape the loss w i l l help to compensate the unfortunate few who suffer loss. In whole life insurance the loss is actually an eventual certainty. That i s , whole life insurance provides for the payment of the face amount upon the death of the insured, regardless of when it may occur. The uncertain element in whole life insurance is the time at which the insured wi l l die. In whole life insurance, if premiums are to be paid through the lifetime of the insured, the insurance is known as 'ordinary life'; if premiums are to be paid only during a specified period, the insurance is known as 'limited payment life' . Both ordinary life and limited payment life are level premium plans; that i s , a fixed premium is paid up to a specified number of years. In simple terms, under the level premium plan, part of the premium paid by the policyholder in any year is used to pay the death claims of others who have died during the year. Most of the remaining portion of the premium however, goes into the creation of a reserve which must be accumulat-ed and maintained by the insurance company in order to meet definite future obligations—ultimately the certainty of the payment of the face amount of the policy. Each year as the policy continues in effect, the reserve increases until eventually it reaches the face amount. The company therefore is never at risk on the whole of the face amount. The amount of insurance protection offered by the company is the face amount of the policy less the policyholder's own accumulated excess payments—the reserve. Since the excess payments may be withdrawn by the policyholder at any time through the cash surrender, they can be regarded as a savings or investment account. Thus, ordinary life and limited payment l i f e , both level premium plans, do not provide only pure insurance protection, but rather a combination of decreasing insurance protection and increasing savings or investment, the two amounts being computed in such a manner that their sum in any year is equal to the face g amount of the policy. Figure 1 serves to illustrate the concept. FIGURE 1 f t Pro-tecrt ION tet&vv^ > In attempting to determine the price of the protection element in whole life policies, numerous problem factors become apparent. The time-shape of the savings element is one factor which is subject to manipulation by a company and may be used in attempting to improve a company's apparent relative price position. The so-called traditional method of price determination described later in this section is susceptible to such manipulation. Further, the 'steepness' of the dividend scale in participating policies may be manipulated In actual fact the cash surrender value is not equal to the reserve; it is somewhat less than the reserve. However for purposes of illustrating the concept of increasing savings and decreasing protection • this distinction need not be made. o This is in contrast to term insurance in which there is no savings ele-ment and in which protection is given for a limited period of time, as stated in the policy, usually for 5, 10, or 20 years, or to a stated age such as 65. 6 for similar purposes. The use by a few companies of certain policy forms which deviate from the general, such as, for example, the use of terminal dividends, further complicates the problem of price analysis. Because of the existence of these and other complicating factors which shall be discussed in depth later on, the proposition is often put forward that price analysis in life insurance is too complicated for the comprehension of the layman. Con-sequently, in attempts at extreme simplification, the two parts of the package in ordinary life insurance—protection and savings—are often grouped together in terms of discussing the cost of insurance and the premium rate is thus con-g sidered as the cost of insurance. Whether or not the premium rate is a reliable estimate of a policy's price of protection is a question with which this study shall concern itself. Despite the complications in life insurance price analysis, various methods have been developed and are in use. A brief discussion of some of these methods w i l l help to point out their shortcomings and wi l l lead to a description of the price analysis method utilized in this study. METHODS OF DETERMINING PRICE Textbook references either make no mention of the proper determination of the price of protection in life insurance or else they differ as to the proper compu-tation of such price. It is to be emphasized that the process of computing the see for example an Article in the Financial Post, Instant Estate?  Here's the Only Wav. (April 13, 1968), pp. 23-4. 7 price of protection element of a l i fe insurance po l icy involves the making of various assumpt ions. For this reason, no s ingle pr ice figure can be es tab -l i shed as the pr ice; rather, any price figure that is determined must be accompanied by a statement of the method and assumptions used in computing that f igure. As has been d iscussed ear l ie r , in whole l i fe insurance there are two parts of the package—protect ion and sav ings—and any figure estab l ished as the pr ice of protection must be accompanied by an assumption about the 'p r ice ' of the sav ings . Conve rse l y , it i s poss ib le to make a statement about the pr ice of the savings only if an assumption i s made about the pr ice of pro-tect ion . This latter approach has been u t i l i zed from time to time in l i fe insurance price a n a l y s i s . One such use was made by M . A . L in ton 1 " 0 who made an assumption about the pr ice of protection and assumed that the pol icyholder invests each year in an alternate savings medium the difference between the price of pro-tect ion and the premium. Linton then computed the net rate of interest that would have to be earned on the yearly differences in the alternate savings medium in order to reach the po l i cy ' s cash value at a given point in t ime. For reasons that w i l l be expanded upon later in th is paper, an assumption of a common price of protection as between different companies presents several problems which decrease the va l id i ty of this approach. Consequent ly most see M . A . L in ton, "L i fe Insurance as an Investment" Li fe and Heal th  Insurance Handbook, e d . D. W . Gregg (2nd e d . , Homewood, 111.: Richard D. I rwin, Inc. 19 64) pp. 241-44. 8 price ana lys is methods attempt to determine the price of protection and make an assumption about the 'pr ice ' or 'opportunity cost ' of the savings element— the net interest rate at which the savings element could be invested by the pol icyholder in an alternate savings medium with safety comparable to that found in l i fe insurance. Of a l l the numerous methods of pr ice ana lys is in whole l i fe insurance, the s o - c a l l e d ' t radi t ional ' method has probably enjoyed the widest u s e . ^ Under this essen t ia l l y simple method the sum of the dividends payable during a given period (in the case of a part ic ipat ing pol icy) and the cash surrender value at the end of the given period (usual ly 20 years) is subtracted from the sum of the premiums payable during the per iod. The resul t ing figure i s then d iv ided by the number of years in the period in order to arrive at an 'average annual pr ice ' for the per iod. If the po l icy has a face amount of other than $ 1 , 0 0 0 . 0 0 , the average annual pr ice i s then div ided by the face amount (in thousands of dollars) to arrive at an average annual pr ice per $1,000 of face amount. Wh i le the t radi t ional method has the important attribute, of s impl ic i ty the combined effect of ignoring certain factors impairs i ts re l i ab i l i t y . To begin w i th , the tradit ional method ignores the fact that the amount of protection at any point in t ime, up to the end of the premium payment per iod , is not the face amount of the p o l i c y , but rather i s the difference between the face amount and the a descr ipt ion of the tradi t ional method can be found in R. W . Lord , "Ana lyz ing Contracts and C o s t s " , L i fe and Heal th Insurance Handbook, op. c i t . , pp. 227-37 . 9 savings element. As the amount of protection during the period cont inual ly decl ines., . and after the in i t i a l phase is a lways less than the face amount, this def ic iency in the tradi t ional method leads to an understatement of the p r i ce . Secondly , interest is ignored in the ca l cu la t i ons , and this a lso leads to an understatement of the p r i ce . The combined effect of disregarding both the interest factor and the decl in ing amount of protection in most level-premium po l i c ies on occas ion leads to the absurd conc lus ion that the average annual pr ice per $1,000 of face amount is negat ive. Another def ic iency of the t rad-i t ional method is that the price figure is appl icable only to the arbitrar i ly chosen period of a n a l y s i s . It provides no information on the price of pro-tect ion for other time periods . Another method which par t ia l ly a l lev ia tes the def ic ienc ies of the tradi t ional 12 method is descr ibed in Matteson and Harwood. This method does not ignore interest . This method accumulates the gross annual premium ( less dividends in part ic ipat ing pol ic ies) over a stated period (usual ly 20 years) at a given rate of in terest . The cash surrender value at the end of the stated period (usual ly 20 years) is then subtracted from the accumulated net payments as descr ibed in the preceding sentence. The result supposedly represents the net cost of the insurance protection to the pol icyholder during the stated per iod. Wh i le this method recognizes interest in part, it completely neglects W . J . Mat teson and E. C . Harwood, Li fe Insurance and  Annuit ies from a Buyer 's Point of V iew, (Great Barr ington, M a s s : American Institute for Economic Research, Annual) . 10 the t ime-shape of the cash surrender value pattern as we l l as the steepness of the div idend s c a l e . U t i l i z i ng this method one might be able to make price comparisons between companies, but only on a retroactive bas is—that i s , at the end of the stated period of yea rs , assuming no surrender option was exer -c i s e d . This method is not at a l l suff ic ient for the potential purchaser of a po l i cy who wishes to analyse and compare different company price pos i t ions . The potent ial buyer is pr imari ly interested in what the po l i cy is going to cos t . The relevance of what a part icular po l icy has cost in the past i s not l i ke l y to be s igni f icant because of changes in cost var iables companies u t i l i ze in e s t -ab l ish ing ra tes . The method next descr ibed—the one used in this study— gives most re l iab le indicat ions of the pr ices of protection for different po l i c ies between different companies. THE LEVEL-PRICE METHOD The method used in this study to determine the price of protection is the 13 ' l eve l - p r i ce ' method, which cons is ts in general of two s tages. The f i rst stage i s the ca lcu la t ion of year ly pr ices per $1,000 of protection and the second stage is the ca lcu la t ion of l eve l pr ices per $1,000 of protect ion. STAGE I - YEARLY PRICE CALCULATION The year ly price ca lcu la t ion may best be i l lust rated by an example. Assume This method i s descr ibed in an art ic le by Joseph M . Be l th , "Pr ice Competi t ion in Li fe Insurance" , Journal of Risk and Insurance, (September, 1966) , pp. 367-70. 11 that the pr ice of protection i s being computed in the 6th po l icy year of a whole l i fe non-par t ic ipat ing po l i cy which has a face amount of $10,000 a gross l eve l annual premium of $190.00 and cash surrender values of $510.00 and $645.00 at the end of the 5th and 6th po l icy years respec t ive ly . If the po l i cy owner should decide to discont inue the po l icy before paying the 6th annual premium, he would be ent i t led to receive the 5th year cash sur-render va lue . If he decides to continue the insurance for another year , he is in effect invest ing that amount in the po l i cy for a period of one year . Further, he is adding to it h is gross annual premium payable at the beginning of the 6th year . The sum of the cash surrender value at the end of the 5th year ($510.00) and the 6th year 's repmium ($190.00) equals the po l i cy owner's total i nves t -ment in the po l i cy at the beginning of the 6th year ($700.00). If the po l i cy owner should decide to discont inue the po l icy before paying the 6th year premium, the total investment ca lcu la ted in the foregoing paragraph could be p laced e lsewhere, at in terest , which for purposes of this i l lust rat ion 14 w i l l be assumed to be 4%. If the pol icyholder decides to discont inue the insurance the total investment would have grown by 4% by the end of the 6th year . The resul t ing figure may be considered the pol icyholder 's alternate investment fund at the end of the 6th po l i cy year . Thus total investment at The choice of an appropriate interest rate is not an easy task . D i scuss ion of this problem and determination of an appropriate interest rate to be u t i l i zed in this study is to be found in a later sec t ion . the beginning of the 6th year ($700.00) plus 4% interest ($28.00) equals alternate investment fund at the end of the 6th year ($728.00). If the pol icyholder continues the po l icy during the 6th year and then surrenders the po l i cy at the end of that year , he would receive the 6th year cash surrender va lue . The cost to the pol icyholder of cont inuing the protection during the 6th year is therefore the difference between h is alternate investment fund deter-mined in the preceding paragraph, and the 6th year cash surrender va lue . Thus the alternate investment fund at the end of the 6th year ($728.00) minus the cash surrender value at the end of the 6th year ($645.00) equals the cost of insurance protection for the year ($83.00). Wh i le the face amount of the po l icy remains $10,000 the amount of insurance protection is not constant. The amount of insurance protection is the di f fer-ence between the face amount of the po l i cy and the investment fund, which steadi ly increases as a result of the interest factor. If the po l icy owner decides to continue the insurance during the 6th year and immediately dies at the beginning of that year , h is estate would benefit to the extent of the face amount l ess the total investment at the beginning of the 6th year . If, however, h is death occurs at the end of the 6th year , h is estate would benefit to the extent of the difference between the face amount and the investment fund at the end of the 6th year. In determining the average amount of protection throughout the 6th year , the average s ize of the inves t -ment fund is considered as the arithmetic mean of the investment fund at the beginning and at the end of the year in quest ion. The average amount of protection is then the difference between the face amount and the average investment fund. Thus the face amount ($10,000) minus the average s ize of the investment fund during the year ($714.00) equals the average amount of insurance protection during the year ($9,286.00) . From the preceding ca lcu la t ions it i s now poss ib le to determine the cost per thousand dol lars of protection for the year under study. The cost of protec-t ion for the year ($83.00) d iv ided by the average amount of protection during the year expressed in thousands of dol lars (9.286) equals the cost per thous-and dol lars of the average amount of protection during the year ($8.94). It w i l l be noted that the i l lus t ra t ive example was a non-part ic ipat ing po l i c y . The introduction of annual dividends into the ca lcu la t ing process presents no spec ia l computational problems and can be handled quite e a s i l y . In ref -erring to the example, the cost of insurance protection for the 6th year was determined by subtracting the cash surrender value at the end of the 6th year from the po l icyholder 's alternate investment fund at the end of the 6th year . If the po l i cy i s par t ic ipat ing, the div idend payable at the end of the 6th year would be added to the cash surrender value at the end of the 6th year and the sum would then be subtracted from the pol icyholder 's alternate investment Wh i l e no detai led considerat ion has been given to the time d i s t r i -bution of po l icyho lder 's deaths over a year , the assumption of a normal distr ibut ion does not appear unreasonable and does not unduly complicate the ca lcu la t ing p rocess . 14 fund at the end of the 6th year . STAGE II - LEVEL PRICE CALCULATIONS Ca lcu la t ions respect ing only stage I of the l eve l pr ice method—that i s , ca lcu la t ion of the year ly pr ice—may be suff ic ient for certain purposes. However , because of the poss ib i l i t y of wide variat ions in the different yearly pr ices of a po l i c y , it i s desirable to reduce a ser ies of unequal year ly f igures to a leve l price per $1,000 of protect ion. Stage II of the l eve l price method— the reduction of various yearly pr ices to a s ingle leve l p r i c e - - i s more comp l i -cated than stage I and w i l l best be i l lust rated by an example. Assume the year ly price information for the f i rst three years of a hypothet ical po l icy as presented in Table 1. TABLE 1 Year ly Price Information (on a $1,000 Basis)  of a Hypothet ica l Po l icy Assuming Interest at 4% Po l icy Year Cos t of Protection Average Amount of Protection Cost per $1,000 of Average Amount of Protection 1 $ 20.11 $ 979.31 $ 20.54 2 6.38 979.31 6.51 3 5.15 966.10 5.33 In determining a single average cost over the 3 po l icy year per iod, it i s improper for several reasons to simply add the three cost per $1,000 of aver-age amount of protection f igures and divide by 3. In order to compute a 15 meaningful average cost for a period of years it i s necessary to keep in mind the nature of the yearly price f igures. They are simply ra t i os - -each cost per $1,000 of the average amount of protection is the rat io of the cost of protection to the average amount of protection for the year under study. Since the denom-inators of these rat ios change from year to year in whole l i fe p o l i c i e s , it i s necessary to weight the ratios by the average amount of protect ion. Employing the i l lus t ra t ive f igures, the average cost per $1,000 of protection weighted for the average amount of protection would be ca lcu la ted as fo l lows: ($20.54) (.97931) + ($6.51) (.97931) + ($5.33) (.96610) = $ 1 Q Q 2 (.97931) + (.97931) + (.96610) However , s ince the product of the cost per $1,000 of protection and average amount of protection for a given year i s ident ica l to the cost of protect ion, the same resul t would be obtained by combining in the numerator of the above ca l cu la t i on , the cost of protection for the three years as fo l lows: ($20.11) + ($6.38) + ($5.15) = $ 1 Q 8 2 (.97931) + (.97931) + (.96610) To this point , equal recognit ion has been given to the year ly price f igures regardless of the point in time at which they are incurred. It i s necessa ry , however, because of the time value of money, to give greater recognit ion to the cost nearer to the beginning of the ser ies than to those incurred later on . Thus , the three year average cost per $1,000 of protect ion, weighted for the average amount of protection and recogniz ing in terest , is ca lcu la ted by div id ing the present value of the ser ies of cost of protection f igures by the present value of the ser ies of average amount of protection f igures . The 16 ca l cu la t i on , assuming 4% interest i s as fo l lows: ($20.11) + ($6.38) (1/1.04) + ($5.15) ( 1 /1 .04 ) 2 (.97931) + (.97931) (1/1.04) + (.9661) (1/1 .04) •j = $11.02 The above three year average cost figure assumes that the pol icyholder w i l l survive to incur each of the single year c o s t s . However , there is a prob-ab i l i t y that the pol icyholder may die before incurr ing the price in the second and third po l icy years and hence mortality must be recognized in the leve l l i ng p rocess . This is accompl ished by further discount ing the single year costs that are to be incurred in the future. For purposes of this i l l us t ra t ion , the 16 1958 Commissioners Standard Ordinary Table of Mor ta l i ty sha l l be used . This Table gives the probabi l i ty of death at age 40 as .00353 and the prob-ab i l i ty of death at age 41 as .00384. The three year average cost per $1,000 of the average amount of protection weighted for the average amount of pro-tect ion and recogniz ing interest and mortality is then computed as fo l lows: (20.11)+(6.38)(l/1.04)(l.-.00353)+(5.15)(l/1.04) 2(l.-.00353)(l.-.00384) (.97931)+(.979 31)(l/1.04)(l.-.00353)+(.9661)(l/1.04) T(l.-.00353)(l.-.00384) The above f igure, whi le recogniz ing several th ings , does not recognize that the pol icyholder faces a probabi l i ty that he w i l l discontinue the po l i cy before 1 7 incurr ing the price in either the second or third year. The recognit ion of lapsat ion in the leve l l i ng p rocess , because of i ts magnitude, is an important factor in the computat ion. For the purposes of this i l lust rat ion assume the = $11.04 16 a fu l l d iscuss ion of mortality and of the appropriate rates to be employed is to be found in a later sect ion of this study. In the above i l l u s -tration the actual mortality rates u t i l i zed are unimportant. The concept and ca lcu la t ion method recogniz ing mortal i ty, however, is not. 17 a fu l l d iscuss ion of withdrawal i s found in a later sec t ion . 17 probability of withdrawal in the first policy year i s .097 and .081 in the second policy year. The three-year average cost per $1,000 of protection weighted for the average amount of protection and recognizing interest, mortality and withdrawal i s then calculated as: (20.1 ]) + (6.38)(L4.04)(l.-.00353-.097)+(5.19(1/1.042(L-00353-.09^(l.-.OO384-081) (.9793D+(.9793D(l/L.04)(l.-00353-.097) + (. 9661)(0.O4^(l.-.OO353-.O97;(l.-.00384-081) Although stage I and stage II of the level-price method have been followed through step by step, no formulae have as yet been presented. The formulae for the computation of yearly and l e v e l prices per $1,000 of protection are as follows: Formulae for Price Calculations Explanation of Symbols: t A given policy year. x The first policy year in a series of n policy years, n A given number of policy years, beginning with x, and ending with x+n-1. i Annual interest rate (expressed as a decimal). v 1/(1+1). j Index of summation. m^x Probability of surviving and persisting from beginning of year x until beginning of year x+m. GAP t Gross annual premium payable at beginning of policy year t. VALt Cash value at end of policy year t (special case: when t+1, V A L t _ 1 = 0 ) . DIV-t Dividend payable at end of policy year t. FACE-t Face amount payable in event of death during policy year t. YPt Price of protection in policy year t. AMT-t Average amount of protection in policy year t (expressed in thousands of dollars). YPTt Price per $1,000 of protection in policy year t. L P n Level price per $1,000 of protection, weighted for amount of protection and recognizing interest, mortality, and lapsation, for n policy years. 18 Computation of Yearly Pr ices per $1,000 of Protect ion: Y P t = (GAP t + VAL t _ ! ) ( l + i) - (VAL t + DIV t) A M T t = j(FACEt) - (GAP t + V A L ^ ) (1 + . 5i)) (.001) YPT t = (YP t ) / (AMT t ) Computation of Leve l Pr ices per $1,000 of Protect ion: XC 1 ( Y P j H v ^ M j . A ) j - x x+n-1 £ (AMTj) (vi~ x) (j - x ^ ) j=x In the appl icat ion of the leve l price method to this s tudy, the formulae were s l ight ly modif ied to ease the burden of computation. For computational purposes the symbols in the formulae (v-*~x)(^_XZ^) were combined by use of a hand calculator and the resul t ing f igures for each of the 20 po l icy years were termed Z fac tors , which therefore combined the interest discount factor and the mortality and lapsat ion factors . A reproduction of the Z factors is to be found in Appendix A . CHAPTER 3 THE PRODUCT The determination of an exact ing def ini t ion of product in l i fe insurance is a part icular ly d i f f icu l t task . Ident ical contractual l i fe insurance coverage for two ind iv idua ls does not necessar i l y consti tute an ident ica l product. Although the contractual coverage may be i den t i ca l , the leve l of serv ice provided as we l l as the r isk of mortality may not be equa l . If product is def ined in this manner, however, ident ica l po l i c ies i ssued by any two different companies, or even by the same company through two different agents , would be different products and any comparisons would be imposs ib le . For pract ica l purposes insurance companies u t i l i ze c l ass rating systems that group ind iv iduals together and assume that a l l ind iv iduals within the group are of equal r i s k . Di f ferences in the serv ice prov ided, however, may be very r e a l , and probably cost more money to prov ide, therefore just i fy ing an addit ion to the price by a h igh-serv ice company. Service i s an example of an intangible aspec t , ref lect ing the terms and c i r c -umstances surrounding the purchase, which may appear t r i v ia l to the outside observer. To the buyer however, intangibles are important and he may be w i l l i ng to pay extra to get them. In a total assessment of product therefore, one must consider ' total product' and not just phys ica l product. 'Total product' as conceived by contemporary students of marketing embraces not just the phys ica l product i t se l f , but the diverse elements of a "package" inc lud ing dependabi l i ty , ava i l ab i l i t y , extent, and cost of serv ice prov ided, 20 credit supp l ied , as we l l as the other sat is fact ions the customer may derive 18 from purchasing from a given source. The problem of assess i ng the substance or t r iv ia l i ty of product differentiat ion is rendered doubly di f f icul t in deal ing with a service industry, such as insur -a n c e , in which the " p h y s i c a l " product is i tse l f par t ia l ly in tang ib le , a contract of insurance. In terms of whole l i fe insurance, such a contract is a contingent one in respect of when certain events w i l l mater ia l ize . Pr imar i ly , perhaps, the buyer of l i fe insurance is buying peace of mind. He probably hopes he is going to get nothing else out of the t ransact ion, except of course , cumulat ive savings in whole l i fe insurance p o l i c i e s . In the event of death of the insured however, the pol icyholder hopes that benefi ts w i l l be forthcoming expedient ly to the benef i c ia r ies . Such a contract , may of course , not be worth very much. It could be written by anyone; anyone with capaci ty to contract could write a va l i d po l i cy though he might v io late one of several statutes in doing so . If he didn't have the f inanc ia l capaci ty to meet h is contractual obl igat ions it would be wor th less . Canadian leg is la t ion in the f ie ld of insurance was f i rst prompted by an apparent need to l i cense insurance companies to see to it that they were able to meet their ob l iga t ions , and this remains the primary concern of the federal Department of Insurance (and, with respect to p rov inc ia l l y - l i censed comp-°E. J . M c C a r t h y , Bas ic Market ing: A Manager ia l Approach (Rev. E d . Homewood, 111.: I rwin, 1964), pp. 315-16. 21 a n i e s , of prov inc ia l departments as we l l . ) Presumably such regulat ion is required because buyers of insurance are unable to assess insurers ' f inanc ia l capac i t y . The buyer expects far more than mere solvency on the part of the insurer , however. He may want to have h is premium f inanced, he may want to change h is coverage at 2 a . m . on New Year 's morning. He wants the l i fe insurance benefi ts handled as qu ick ly as poss ib le with a minimum of personal i n c o n -venience to the bene f i c ia r ies . He may want some or a l l or more of these . Some of them are immediate, the others consti tute a bundle of contingent future serv ices which he may be hard put to evaluate a pr io r i . ^ •This total package of serv ices is provided partly by the company which writes the po l i cy and expedites it in the event of death and partly by the agent which se l l s i t . Wh i le cognizance ought to be taken of the total product concept and of the competit ive inf luence of the various intangibles assoc ia ted with that concept , it is extremely d i f f i cu l t , perhaps imposs ib le , and we l l beyond the scope of this study, to object ive ly evaluate the intangibles provided by each company and i ts agents. Theref ore, f or purposes of object ive compar ison, the product has been defined in th is study as one providing ident ica l coverage for i n d i -Just how to form a re l iab le appra isa l of h is potential future treat-ment by a company in the event of any one of the multitude of potent ia l ly poss ib le catast rophes, in the l ight of h is apparent inab i l i ty to determine whether it is f i nanc ia l l y able to treat him at a l l , remains a r isk to the p o l i c y -holder. viduals in the same rate c l a s s : i . e . for ind iv iduals of the same age at entry. Four types of $10,000 l i fe insurance po l i c i es ava i lab le in Canada to standard males at age 30 in 1967 are surveyed in this study. The four types of po l i c ies are as fo l lows: 1) Whole l i fe part ic ipat ing 2) Whole l i fe non-part ic ipat ing 3) 20 payment l i fe part ic ipat ing 4) 20 payment l i fe non-part ic ipat ing CHAPTER 4 METHODOLOGY PROCEDURE - INITIAL Hav ing determined the appropriateness of the leve l price method in appl icat ion to this study, the next procedural step was the gathering of data relevant to 20 the study. In i t i a l l y , it was thought that Stone and Cox would provide the necessary data. However , an ana lys is of this information revealed that in most instances cash surrender values and d iv idends, on the type of po l i c ies u t i l i zed in the s tudy, were only given for i l lus t rat ive po l i cy years such as years 1, 2 , 3 , 4 , 5 , 10, 15 and 20. Although with such information it would be poss ib le by an interpolat ion technique to estimate values for the years not reported, it was felt that the room for error would be too large to place any meaningful va l id i ty on the resu l t s . In v iew of the fact that it was poss ib le to obtain definite v a l u e s , i t was considered that the greater effort and expense in obtaining definite f igures would be just i f ied in a l lev ia t ing the poss ib i l i t y for errors that interpolat ion would create. Accord ing ly , in early 1967 i den t i -c a l quest ionnaires were sent to 102 federal ly registered l i fe insurance comp-anies operating in Canada . The names of the companies were obtained from Canadian Life Insurance Facts , 1966 publ ished by the Canadian Life Insurance Assoc ia t i on . The companies are therein segregated in terms of Canad ian , The Stone and Cox Life Insurance Tables are publ ished annual ly by Stone and C o x , L td . , Toronto, Ontario and i s considered a universal Canadian l i fe insurance rate manual . 24 Br i t ish or Foreign ownership and this segregation has been maintained in order that the ultimate price resul ts could be ava i lab le on this bas is of d i f ferent ia-t ion . Companies which it was known had ceased to write new bus iness in Canada as we l l as prov inc ia l l y incorporated companies operating under a prov inc ia l l i cense on ly , i . e . without federal reg is t ry , were exc luded , because of their l o ca l i zed and l imi ted inf luence on the total Canadian l i fe insurance re ta i l market. ^ The companies were assured that their names would be kept on a conf ident ia l b a s i s . Accord ingly the pr ice resul ts appear by company number, not name. A copy of the questionnaire is to be found in Appendix B. Specia l typing serv ices at the Univers i ty of Br i t ish Columbia were u t i l i zed in order that the quest ionnaires would appear as a personal ized communicat ion. Department stationery was used . As some of the or ig inal questionnaires were forwarded to the head of f ices of several of the foreign companies, responses continued o to be rece ived for approximately a two month period after the mai l ing date of the or ig inal quest ionnai res. Largely as a consequence of receipt of responses to the or ig inal quest ionnai res, certain problems became apparent. Fol low up letters were sent to f i f teen companies to ascerta in information relevant to the problems. These problems and the methods used to handle them are detai led in subsequent sec t ions . In Prov inc ia l companies accounted for only 6% of the l i fe insurance in force at the end of 1965 according to Canadian Life Insurance F a c t s , op. c i t . , p. 2 . addit ion second quest ionnaires were sent to 18 of the non-respondents to the or ig inal quest ionnaire. RESPONSES The number of respondents to the or ig inal questionnaire was 77, ind icat ing a response rat io of .755 . In view of the fact that companies were under no obl igat ion to respond, the response rat io obtained is part icular ly sat is fy ing and was no doubt at least par t ia l ly prompted by use of departmental stat ionery. However , not a l l repl ies received from companies were useful as input data. Table II g ives a breakdown of the reaction to the quest ionnai res. TABLE II RESPONSES TO QUESTIONNAIRES Total Number Number of Repl ies Not Non-Responses Quest ionnaires Usefu l Repl ies Usefu l Sent  1) 102 56 21 25 2) 18 4 1 13 Repl ies were not useful primari ly because the company had ceased to write bus iness in Canada or was involved in re- insurance on ly . Other repl ies were c l a s s i f i e d as not useful for a variety of reasons , such a s , (a) po l icy form deviat ion from the general form u t i l i zed in the leve l -p r i ce method, (b) assu r -ance that a copy of this study would be forwarded free of charge, and (c) un -w i l l i ngness to part ic ipate in a price comparabi l i ty study. Despi te some inevi table unwi l l ingness to part icipate on the part of a few companies, it i s 26 fel t that the insurance companies to whom questionnaires were sent , were extremely generous in their effort to provide the author with the appropriate information. Although the data from the companies is not con f iden t ia l , it appears that in some ins tances , considerable time and effort was expended in providing the same. Further, there was no assurance of any direct benefit to the companies for their effort in providing the information. THE SAMPLE Wh i l e 60 companies part ic ipated in the study, not a l l of these companies provided information on each of the four types of p o l i c i e s . The number of companies submitt ing information and thus being inc luded in the analyses on each of the four types of po l i c i es i s as fo l lows: Po l i cy Number of Companies Included Whole l i fe part ic ipat ing 40 Whole l i fe non-part ic ipat ing 44 20 pay l i fe part ic ipat ing 42 20 pay l i fe non-part ic ipat ing 41 In terms of premium volume, the 60 companies appearing in the study 22 accounted for 73.7% of the total Canadian l i fe insurance market in 1965. Although no s ta t i s t i ca l techniques have been appl ied in test ing the va l id i ty In terms of " insurance premiums and annuity considerat ions" from The Report of the Superintendent of Insurance for Canada , V o l . 1, 1965, pp. 40c , 66c, 72c. of the sample, it is considered that the overall sample consisting of almost 75% of the population, i s representative. Unfortunately, it i s not possible because of lack of data to determine the percentage of the market represented in each of the four po l i c i e s in the study. THE DATA -Certain problems of comparability with respect to the data became apparent as responses to the original questionnaires were received from the companies. In the participating policies a few companies issued terminal dividends or expressed the dividends as additions to the sum assured. These companies were excluded from the analysis as their number did not justify the consider-able task of rendering them comparable. The main problem experienced with the data concerned the waiver of premium provision. This i s a provision offered by some companies automatically or as an optional provision, which provides that if the insured suffers a total d i s a b i l i t y , the company w i l l waive any premium subsequent to the d i s a b i l i t y . The policy s t i l l continues in effect. The extent to which this provision increased the premium was ascertained by follow-up letters to four different companies. The replies from the four companies indicated very close agreement between the companies concerning the influence of the waiver of premium provision on the premiums for the various p o l i c i e s . S p e c i f i c a l l y , on the basis of this information, premiums on the few companies that automatically included the waiver of premium provision, were adjusted downward as follows: 28 Downward Premium Adjustment W h o l e l i f e par t i c ipa t ing 2. 6% W h o l e l i fe n o n - p a r t i c i p a t i n g 3.2% 20 pay l i fe n o n - p a r t i c i p a t i n g 1.4% 20 pay l i fe par t i c ipat ing 1.1% CHAPTER 5 ASSUMPTIONS The appl icat ion of the leve l -p r i ce method involves the making of certain assumpt ions. Wh i le an assumption is not , by i ts nature, imbedded in fac t , it ought to spring as far as i s poss ib le from reason. The assumptions made in the appl icat ion of the leve l -p r i ce method to this study are d i scussed in the remainder of this sec t ion . (a) Interest Rate The choice of an appropriate interest rate to be used in the study is of fa i r ly c ruc ia l importance. As aforementioned, any figure estab l ished as the price of protection element in a whole l i fe po l icy must be accompanied by an assumption about the price of the savings element. It was therefore necessary in u t i l i z ing the leve l -p r i ce method, to es tab l ish a price or opportunity cost of the savings element. In es tab l ish ing an appropriate interest rate it was assumed that Government of Canada long-term bonds represent an acceptable alternate savings medium to the buyers of $10,000 whole l i fe p o l i c i e s . Accord ing ly , the average interest y ie ld on long-term Government of Canada bonds was computed over a 10-year per iod , ending December, 1963. The resul t of this ca lcu la t ion indicated the average y ie ld to be 5.09%. However this figure is a before tax interest y ie ld to the investor in this savings medium. Since the interest bui l t into the savings element of a l i fe insurance po l icy is currently exempt from federal income tax , the tax bracket of the pol icyholder enters into the determination of an appropriate interest rate to be used in the 30 price ca l cu la t i ons . Considerable d i f f icu l ty was experienced in attempting to determine the average net income tax rate for persons buying any of the four $10,000 whole l i fe p o l -i c i e s . However , after careful considerat ion and consul tat ion with various i nd i v i dua l s , a general figure of something s l ight ly in excess of 20% was c o n -c luded as the most reasonable probabi l i ty . Accord ing ly , a spec i f i c average net income tax rate of 23% was u t i l i zed . Appl icat ion of this tax rate to the previously determined average y ie ld of long-term Government of Canada bonds resul ts in a rounded price of the savings element of 4%. This represents the net interest rate at which the savings element could be invested by the p o l i c y -holder in an alternate savings medium with safety at least comparable to that found in l i fe insurance. In l ight of the current plateau of re la t ive ly high interest rates in this country, an after tax rate of 4% on the savings element of a whole l i fe po l i cy may seem unduly conservat ive . It may be . However , at least two factors may tend to mitigate against this c r i t i c i sm . In the f i rst instance the vo la t i l i t y of Canadian interest rates in recent years may be expected to be reduced if international forces and si tuat ions s tab i l i ze and if domestic management both monetary and f i s c a l chooses appropriate remedies. Secondly , ind iv iduals purchasing $10,000 whole l i fe po l i c ies are not general ly heavy r isk takers insofar as their investment in the savings element of l i fe insurance is concerned. Information pub l ic ly ava i l ab le , as for example as contained in Stone and C o x , indicates the interest rate u t i l i zed by different companies in determining their cash surrender va lues . The 1965 edit ion of Stone and Cox indicates that the general average valuat ion interest rate u t i l i zed was 3 to 3 1/2%. The extent to which an upward change in the interest rate would affect the f ina l price of protection f igures becomes of importance in view of interest developments in Canada . Whi le it is recognized that differences in po l icy data, such as the t ime-shape of the savings element—the cash surrender value—between different company's p o l i c i e s , may change the relat ive price posi t ion of the po l i c ies if a different interest rate is u t i l i z e d , the change is not considered to be s igni f icant if the interest rate is moved 1% such as from 4% to 5 % . 2 3 (b) Mor ta l i ty As l i fe insurance may be loose ly thought of as a futures contract , it i s essen t ia l that best poss ib le est imates concerning relevant var iables in the future be made. Mor ta l i ty is one of the most relevant var iables in forecast ing for l i fe insurance purposes. Its re levance stems from the fact that accumu-lat ions to meet future obl igat ions—and therefore premium rates—are a l l based on the mortality experience of the insured l i v e s . Mor ta l i ty forecast ing is a problem in pred ic tab i l i ty . As with most other forecast ing problems, the va l id i ty of mortality forecasts depends upon two The resul ts reported in a U . S. ana lys is by Dr. Belth indicate only a s l ight shift in re lat ive price posi t ions in moving from 3% to 4% interest . See J . M . Be l th , op. c i t . , p. 373. 32 factors: (a) the accuracy of mortality s ta t is t ics underlying the es t imates, and (b) the number of exposure units or the volume of mortality experience u t i l i z e d . Wi th respect to the f i rs t factor, mortality s ta t is t i cs have been drawn from two general sources—the general population and insured l i v e s . For various reasons such as the poss ib i l i t y that general population mortality may not be whol ly ref lect ive of insured l i ves mortality and the lack of comp-arable detai led information in the general population mortality s ta t i s t i c s , v i r tua l ly a l l l i fe insurance companies today u t i l i ze mortality tables based on 24 the experience of insured l i v e s . Various mortali ty tables are presently in ex i s tence , several of which have 2 S been approved by the Canadian and Br i t ish Insurance Companies Ac t . In the course of attempting to determine the most appropriate table to be u t i l i zed in this study, several mortali ty tables were scru t in ized. For example, the Canadian Assured L ives '52- '56 Tab le , being based on re la t ive ly recent Canadian mortality experience appeared as a log ica l a l ternat ive. However , as it has not been approved by the Canadian and Br i t ish Insurance Company Act at the implementation of this study, it was d iscarded. The mortality table f ina l l y chosen for the study i s the 1958 Commissioners Standard Ordinary Table as it is based on re la t ive ly recent mortality exper ience, has been D . M . M c G i l l , Li fe Insurance, (Homewood, I l l ino is : Richard D. I rwin, 1959) , p. 134. 2 5 S e c t i o n 82 (2)(b) Third Schedule. approved by the A c t , and is in general use . The 1958 Commissioners Standard Ordinary Table is reproduced in Appendix C . Experience has conc lus ive ly proved that the rate of mortality among a group of recent ly insured l i ves i s lower , age for age , than that among pol icyholders who have been insured for some years . This result fo l lows from the fact that l i ves insured for ind iv idua l l i fe insurance are se lected at entry. That i s , through medical se lec t i on , or otherwise, the company sat is f ies i tse l f that the potent ial insured is an acceptable r i s k . As would be expected, the rate of mortali ty among such se lected l i ves is l ess than among a more general body of l i ves of the same age , for some years after entry. The dispar i ty in death rates between selected l i ves and pol icyholders who have been insured for some years , i s at i ts maximum during the f i rst year of insurance, thereafter gradual ly d imin ish ing . For pract ica l purposes it is general ly assumed in the 71 United States and Canada that the effect of se lect ion wears off after 5 years . In order to properly recognize the effects of select ion on a man age 30 at entry, the tabular rates given in the 1958 Commissioners Standard Ordinary Table have been adjusted in the f i rst f ive years . The adjustment was made 7 7 on the fo l lowing bas i s : mortality in the f i rst po l icy year is 50% of tabular , ^ ° D . M . M c G i l l , op. c i t . , p. 141; A . Pedoe, Life Insurance, Annuit ies and Pensions , (Toronto: Univers i ty of Toronto P ress , 1964.) p. 48. 7 7 This adjustment to show the effects of se lect ion i s found in R. E. Larson and E. A . Gaumni tz , L i fe Insurance Mathematics (New York: John W i l e y and Sons, 1951) p. 120. 65% in the second po l i cy year , 75% in the third po l icy year , 85% in the fourth po l icy year , 95% in the f ifth po l icy year , and 100% after f ive po l icy years . (c) Lapsat ion Since the pol icyholder faces a probabi l i ty that he w i l l discontinue the po l i cy before incurr ing the pr ice in any po l icy year subsequent to the f i r s t , lapsat ion must be recognized in the leve l ing p rocess . The posi t ion might be put that wheras a pol icyholder is presumed to lack control over the mortality aspec t , he can control h is own po l icy lapsat ion si tuat ion and therefore lapsat ion should be ignored in the ca lcu la t ion of the price of protection to the buyer. However various future elements and cont ingencies some of which are beyond the control of the pol icyholder such as diverse f inanc ia l developments may affect h is proc l iv i ty to lapsat ion of the po l i cy . As complete ignorance of lapsat ion—equiva lent to i ts recognit ion with zero lapse ra tes—is not appro-priate for the average po l icyho lder , although it might be appropriate for a given po l icyho lder , some account must be taken of lapsat ion in the pr ice 2 8 ca lcu la t ing p rocess . Although ind iv idua l companies usual ly ca lcu la te their own lapsat ion tables , 2 9 the Linton 'A' Table i s we l l known and has long been accepted as a standard. In consul tat ion with M r . M . H . Farrant, Actuary, of Farrant & Company, Indicat ions a re , that on ordinary insurance, over -a l l lapse ratios are about 3%. See for example D. M . M c G i l l , op. c i t . , p. 715. 2 9 P u b l i s h e d by M . A . Linton in 1924 in the Record of the American  Institute of Ac tuar ies , Volume 13, p. 283. Vancouver, M r . Farrant stated that L inton's Rate ' C g iv ing higher lapse rates than the 'A' Table is perhaps most i l lus t rat ive of Canadian exper ience. H o w -ever , because the d ivers i ty between the Linton 'A' and ' C Tables is not excess ive and because it was considered that the lapse rates used ought to be conservat ive in order to take account of, to some extent, the element of control that the pol icyholder has over lapsa t ion , the Linton 'A' lapsat ion table was chosen for purposes of price ca l cu la t i on . The Linton 'A' Table i s repro-duced in Appendix D. (d) Div idends Div idends are paid on part ic ipat ing p o l i c i e s . Wi th the pr ice ana lys is of part ic ipat ing l i fe insurance p o l i c i e s , d iv idend information must be taken into account . A l imi tat ion inherent in the use of d iv idend information from l i fe insurance companies is that projected dividends are only estimates and are not guaranteed. The extent to which projected dividend estimates are re l iab le is quest ionable. A l l companies submitting div idend information did so on the bas is of their respect ive 1967 dividend s c a l e s . Since i l lus t rat ive div idend sca les are mere extensions of current assumpt ions, they create cost patterns that have not necessar i l y been del ivered to po l icy owners in the past and may probably not be del ivered in the future. On the other hand , actual d iv idend h is tor ies create cost patterns that have actua l ly been del ivered to po l i cy owners. The f igures therefore have some tangible meaning. A poss ib le approach to determining the re l iab i l i t y of a company's estimated future d i v i -dends is to determine the extent to which past estimates have approached 36 actual past d iv idends. However , complete dividend h is tor ies are very d i f f icul t 30 to obtain and do not appear in the trade pub l ica t ions . In many instances no div idend h is tor ies at a l l are reported for a given company. In those instances where some dividend information is g i ven , there ex is ts a 'b l ind spot' with respect to po l i c ies i ssued during the 19-year period immediately preceding the point at which the pr ice ana lys is is being performed. For example, i f an ana lys is i s being made in 1967, some 20 year dividend project ions for 1967 i s s u e s , based on the company's 1967 dividend sca le and some 20-year h i s t -ories for 1947 i ssues are avai lab le in the 1967 edit ions of the trade p u b l i c a -t ions; s im i l a r l y , some 20 year projections for 1966 i s s u e s , based on the company's 1966 div idend sca le and some 20 year h is tor ies for 1946 i ssues are ava i lab le in the 1966 ed i t ions . However , concerning po l i c ies i ssued during the period 1948 to 1966, only div idend projections are general ly a v a i l -able and such projections are based on the div idend sca le appl icable only in the respect ive years of i s s u e . The only information avai lab le in 1967 on a po l icy i ssued in 1960, for example, would be found in the 1960 edit ions of the trade publ icat ions and would be based on the company's 1960 div idend s c a l e . Whi le a few companies report ten year div idend h i s to r i es , a b l ind spot s t i l l ex is ts in respect of a 9 year period immediately preceding the time at which the ana lys is i s undertaken. Thus, the extreme di f f icu l ty of obtaining appropriate div idend history inform-such a s , for example, the Stone and Cox Li fe Insurance Tab les . 37 ation coupled with the fact that the c loseness of the re lat ionship between past div idend project ions and h is tor ies may very probably change (history i s un l ike ly to repeat i tse l f here) precluded any serious effort at determining the re l iab i l i t y of the div idend information provided by the companies. C o n s e -quently the div idend data presented by the companies was deemed acceptable to the price a n a l y s i s . This i s not to suggest , however, that the div idend information u t i l i zed was judged re l i ab le . It may or may not be . It is r ecog -n ized that the va l id i ty of the price resul ts on part ic ipat ing po l i c ies i s reduced because of part ia l dependence on div idend information whose re l iab i l i t y is somewhat quest ionable. However , for reasons such as company reputat ion, it is considered that federal ly registered companies would general ly not put to the publ ic exhorbitant and c lear ly unreasonable dividend pro ject ions. PROCEDURE - INTERJACENT Hav ing f ina l i zed the necessary assumpt ions, a computer program, incorpor-at ing the l eve l -p r i ce formulae and interest , mortality and lapsat ion data (appearing as Z factors) , was formulated with the ass is tance of the Univers i ty of Br i t ish Columbia Computing Department. The po l icy information appropriate to the study was coded and subsequently put on punched cards for use in the Univers i ty of Br i t ish Columbia I . B . M . computer. The punched cards were double checked for errors. A copy of the computer program u t i l i zed is to be found in Appendix E. Before the program was run through it was thought adv isab le to ca lcu la te by use of a hand calculator the leve l pr ice for a par t i -cular po l i c y . The po l i cy chosen was Number F42 Whole Li fe Par t ic ipat ing. Hand ca lcu la t ions of the l eve l -p r i ce method on one po l icy over a 20-^year period take approximately two hours. The result of $5.59323 subsequently-proved to be exact ly the result as computed through the use of the computer. Having made this f ina l check in the program, the rest of the po l i c ies were run through and the price resul ts obtained. CHAPTER 6 COMPETITION The assessment of the ef fect iveness of competit ion depends on what standards are to be app l i ed . Compet i t ion, monopoly and the various patterns in between, have received attention from scholars in a number of d i s c i p l i n e s , although economics ranks f i rst in g iv ing attention to the matter. The study of the work-ings of competit ive markets has const i tuted the main body of economic theory at least s ince the days of Adam Smith. The achievement of Smith lay in h is ana lys is of the workings of a system from which monopoly was excluded and in focuss ing attention on the posi t ive advantages of a competit ive system. Monopoly i s usual ly c r i t i c i sed because it leads to a higher price for the monopol ized ar t ic le than i s poss ib le under a more appropriate system. This enhancement of price i s achieved by restr ic t ion of output, re lat ive to what output would be under compet i t ion. If the latter is taken as an i d e a l , too l i t t le of the monopol ized commodity is produced and too much of those c o m -modit ies which are not monopol ized. This misdirect ion of productive efforts means that labor and cap i ta l (factors of production) are badly a l l oca ted . Where misdirect ion of the factors of production ex is ts such that certain commodities have a market price in excess of factor c o s t s , the a l locat ion of resources is sa id to be inef f ic ient . The importance of the ef f ic iency concept is that it creates the path down which one may move from an inef f ic ient a l locat ion of resources to an eff ic ient one, and give more of some desired product(s) to at least one member of soc ie ty . Ef f ic iency i s thus a necessary condit ion (although not necessar i l y by i t se l f sufficient) for attaining a posi t ion of maximum economic wel fare. PERFECT COMPETITION Unfortunately however, complete e f f ic iency is a rather Utopian concept. Complete ly ef f ic ient resource a l locat ion in an economy can be shown to be consis tent with only one type of market, which must be present throughout the economy. This type of market is usual ly ident i f ied as 'perfect competi t ion' It l i es at one extreme end of the sca le of types of monopoly—competit ion that economists have ana l yzed , and is almost un iversa l ly recognized as being unattainable in the real wor ld . However, it has value as an idea l type and standard, and thus merits cons iderat ion. Requisi tes for perfect competit ion are general ly considered to include the fo l lowing: (a) Homogeneity of product. The products or serv ices coming from the various producers in the industry are not differentiated in the minds of the buyers. (b) Perfect knowledge of al ternatives and foresight as we l l as an absence of uncertainty. See , D . S . W a t s o n , Price Theory and Its Uses , (Boston: Houghton M i f f l i n C o . , 1963) , p. 106. 41 (c) The ex is tence of a large number of buyers and se l lers such that it i s not worthwhile for anyone to exerc ise any sl ight control he may have over p r i ce . (d) Perfect mobi l i ty of resources. (e) Buyers are only economical ly motivated as are se l l e r s . Compe-t i t ion is on the bas is of price on ly . The foregoing requ is i tes , taken together, would produce an instantaneous mutual adjustment of supply and demand, resul t ing in an ef f ic ient use of resources at a l l t imes. Perfect competit ion dictates that there is no price dispar i ty for a given product. Wh i le the economic theor is t 's concept of perfect competit ion is an i d e a l , it is one which is v i r tual ly unattainable in the real wor ld . As an attainable standard, economistsjhave attempted to develop a standard of 'e f fect ive ' or 'workable' compet i t ion. Some idea of the re lat ionship between perfect and workable or effect ive competit ion is 32 ava i lab le in the fo l lowing statement: " 'Workab le ' or 'ef fect ive ' competit ion suppl ies no formula which can substitute for judgment. It suggests leads to data of s ign i f i cance , and a means of organizing data bearing on the question whether a given market of i tse l f is suf f ic ient ly competit ive in i ts structure and behaviour to be c l a s s i f i e d as workably compet i t ive. And it provides some benchmarks or cr i ter ia , representing somewhat different points of vantage, for the process of making that judgment." "Workable competit ion differs from pure and perfect competit ion in several w a y s . In the f i rst p l a c e , the two theories have different from the Report of the Attorney Genera l 's Nat iona l Committee to  Study the An t i -Trust Laws , March 31 , 1955 , U . S . A . 42 purposes. The theory of pure and perfect competit ion i s an instrument of theoret ical ana l ys i s ; the theory of workable competit ion seeks to provide a method for making necessar i l y less exact but more pract ica l rea l i s t i c judgment of actual market s i tuat ions. Secondly , to the. extent that the two theories are concerned with the same broad e lements- - the def ini t ion of the product and market, the number and relat ive s i ze of s e l l e r s , and condit ions of entry—the concept of workable competit ion posi ts a lesse r degree of 'per fec t ion ' . Thus perfect competit ion would require an extremely large number of se l l e r s . Cr i ter ia of workable compet i t ion, as is expla ined above, could be sa t is f ied by a lesser number of s e l l e r s , some of whom may we l l produce s igni f icant fract ions of total supp ly , provided they rea l ly compete and do not foreclose entry of new competitors , except by reason of their superior i ty. " There is some disagreement amongst economists concerning just what c o n s t i -tutes 'e f fec t iveness ' or 'workab i l i t y ' . The factors which are usual ly taken into account are the structural character is t ics of the industry, the way in which competit ion i s conducted and the performance which resul ts from the interact ion 33 of the structural and conduct fac tors . Structural factors may help determine whether ind iv idua l firms possess market power or are not l i ke l y to in the absence of c o l l u s i o n . Wh i le they can indicate the l i ke l ihood that market power e x i s t s , they cannot indicate i ts absence or whether it is exe rc i sed . Those who fee l the possess ion of market power is as serious as i ts exerc ise are probably l i ke l y to p lace great weight on structural fac tors . On the other hand , those who regard performance and resul ts as the va l i d object of concern are apt to regard structural facts as only one set of factors to be cons idered. Except for those whose concern is essen t ia l l y the possess ion of market power, a detai l ing of structural factors is found in C . W i l c o x , Publ ic  Po l i c ies Toward B u s i n e s s , (Homewood, 111., Richard D. I rwin, 1955), pp. 103-4. 43 and for whom performance, no matter how good at a part icular point in t ime, is i r re levant , the object of concern is usual ly performance. C O N D U C T REQUIREMENTS Conduct requirements prescribe the type of behaviour by firms which is n e c -essary for competit ion to be ef fect ive. One such requirement is that firms in the industry behave independent ly, each seeking to increase i ts own prof i ts . It i s not necessa ry , however, that a l l firms behave in this manner. In spite of part ia l ca r te l i za t ion , competit ion may be effect ive if the non-col laborat ing firms in the industry are suf f ic ient ly la rge, numerous and aggress ive . Another requirement is that there be an absence of act ions which are de l iber -ate ly aimed at exc luding present or potential competitors or at restr ic t ing their ab i l i t y to compete. Act ions which are contrary to this requirement include the enlistment of the regulatory agencies of the state to help exclude potential compet i tors, predatory price cutting in selected markets, and the use of exc lus ive deal ing arrangements forcing buyers to buy a l l of their requirements from a s ingle source although part could be obtained equal ly we l l e lsewhere. Further, there must be evidence of act ive price competit ion in the market. Wh i le price need not be the only competit ive weapon u t i l i zed , if it i s the only one not used , the probabi l i ty of prevalent ineffect ive competit ion is h igh . A f ina l conduct requirement is the nature and extent of product di f ferent iat ion. In genera l , where product differentiation has given one firm a dominant market posi t ion from which it is enabled to destroy competit ion and prevent change, product differentiat ion is considered as contrary to effect ive compet i t ion. However , where product differentiation is based on real differences in prod-uct qual i ty (as opposed to subject ive differences) and where the relat ive market posi t ions of competitors are f lex ib le in response to a high rate of innovat ion, product differentiat ion is usual ly considered as contributing to the ef fect iveness of compet i t ion. The relevance of product differentiat ion is judged in the l ight of the performance of the market. MARKET PERFORMANCE Where the performance record of an industry in response to growing demand is one of ra is ing pr ices rather than increas ing output, the ef fect iveness of competit ion is suspect , unless natural resource l imitat ions prevent an increase in output. Where the record is one of introducing cost - reduc ing innovat ions, permitting the cutt ing of pr ices (relative to other commodities) and growing with the market, competit ion is most l i ke l y e f fect ive. In a perfect ly competit ive market, a l l producers are ' p r i ce - take rs ' . Price i s set by supply and demand in the market, and firms accept the going price or stay out of the market. This is feas ib le in a few situat ions such as where organized commodity exchanges ex i s t . No serious departure from the com-peti t ive idea l e x i s t s , however, where firms go through the motions of sett ing their own p r i ces , as long as the latter are responsive to the interplay of supply and demand. Where this is ef fect ive ly operat ive, the power of i n d i -v idual producers to set pr ices is largely i l l uso ry . The ex is tence of pr ice discr iminat ion is usual ly regarded as incompatible with effect ive compet i t ion. Price discr iminat ion is the charging of different pr ices for an ident ica l product under ident ica l condit ions of s a l e . It normally ar ises because ind iv iduals are able to exploi t dif ferences in ind iv idua l buyer 's demand curves for the product. It may a lso ar ise in certain si tuat ions where price is not se l f -ev iden t , where buyers are unable to determine the real price of the product. If strong competit ion were prevalent, pr ice discr iminat ion would not usual ly surv ive , unless certain non-pr ice factors were dominant. Perhaps the most unequivocal evidence of effect ive competit ion is to be found 3 4 in the re lat ionship between pr ice and marginal cos t . An absence of d i sc r im-ination in a competit ive context impl ies that pr ices for the products in an industry w i l l be proportional to their marginal c o s t s . From an ana lys is of the price and cost structure of an industry it i s poss ib le to determine the existence or non-ex is tence of d iscr iminat ion , and by imp l i ca t ion , the ef fect iveness of compet i t ion. This task is not only one of enormous magnitude, however, but i s often rendered impossib le in many industr ies because of lack of sat isfactory cost data for ana lys is . Another type of price performance regarded as incompatible with effect ive competit ion is the truly administered price where the price i s set and is Marg ina l cost may be defined as the cost of producing an addi t ional unit of a given product during a part icular per iod. tota l ly unresponsive to supply and demand for years at a t ime. Few markets of the truly administered pr ice ex i s t , however. In one sense ordinary l i fe insurance in Canada is an administered pr ice industry. Po l i cy data are e s t -ab l ished in trade publ icat ions unt i l rev ised annual ly . Such a form of pr ic ing detracts from the competit ive i d e a l . Thus, to an extent, the existence of even the form of administered pr ices in l i fe insurance, represents an attenuation of the competit ion from the perfect ly competit ive model . However , it is a mistake to infer from this that the mere existence of this form of administered pr ic ing is evidence that competit ion is inef fect ive. L i fe insurance i s in ef fect , so ld in a futures market on ly , s ince the coverage extends into the future. Pr ices primari ly ref lect expected costs not yet incurred. The frequency with which changes in expected costs are perceived as we l l as techn ica l and communication const ra in ts , dictate that annual price changes are the most expedient for the company. CHAPTER 7 THE RESULTS TABLE III PRICE RESULTS FOR $10,000 WHOLE LIFE  NON PARTICIPATING POLICIES Company Leve l Company Rank Company Rank Number Price by Leve l Pr ice Premium by Premium 1 $ 6.42500 20 $ 137.40 25 2 6.52049 22 131.50 17 3 5.01960 1 130.70 15 4 7.07141 36 138.60 31 5 6.70806 30 131.60 18 6 6.57528 26 132.60 20 8 6.41049 19 132.40 19 11 7.22532 38 139.60 33 13 6.14992 15 126.30 5 14 6.04204 11 140.50 35 15 5.55813 4 137.50 26 16 5.60322 5 124.00 1 18 9.31510 44 158.30 43 19 6.70154 29 128.30 8 20 6.54882 24 128.10 7 21 5.44384 2 124.50 2 23 7.47814 40 135.20 24 24 5.80565 7 128.70 10 25 6.51315 21 124.70 3 27 6.10143 13 128.50 9 28 5.54197 3 126.00 4 29 6.99195 33 138.20 29 31 6.13109 14 140.40 34 32 6.64045 28 134.60 23 33 6.19589 17 127.00 6 34 5.84050 8 130.60 14 36 6.93987 32 137.70 27 38 5.98105 10 128.90 11 F 2 6.78103 31 142.60 38 F 7 6.09761 12 138.50 30 48 TABLE IH(Cont'd.) Company Leve l Company Rank Company Rank Number Price by Leve l Pr ice Premium by Premium F 9 $ 6.56945 25 $ 130.00 12 F 10 7.24841 39 133.50 22 F 11 6.21470 18 137.80 28 F 14 5.98084 9 133.10 21 F 25 7.12663 37 152.60 41 F 26 8.32217 43 158.30 42 F 27 7.04671 35 141.50 36 F 31 8.23824 42 164.80 44 F 32 7.68909 41 144.50 40 F 50 6.59171 27 139.40 32 F 52 6.53768 23 143.30 39 F 55 6.15368 16 130.50 13 F 59 7.01439 34 142.20 37 F 64 5.70708 6 130.90 16 Total Number of Companies = 44 LEVEL PRICE PREMIUM Canadian Foreign Canadian Foreign Owned Owned Total Owned Owned Total Mean $ 6.40998 6.83246 6.56361 $ 132.94 141.47 136.04 Standard Deviat ion .799 .744 .806 7.103 9.630 9.120 Coef f ic ient of Variat ion 12.46% 10.89% 12.27% 5.34% 6.81% 6.70% 49 TABLE IV PRICE RESULTS FOR $10,000 20 PAYMENT LIFE NON PARTICIPATING POLICIES Company Leve l Company Rank Company Rank Number Price by Leve l Pr ice Premium by Premium 1 $ 8.73065 25 $ 216.40 25 3 8.14482 14 225.80 29 4 9,04058 29 217.50 27 5 9.40318 31 207.80 11 6 7.21606 4 202.90 6 8 9.98386 34 208.30 13 9 8.87358 27 216.80 26 11 8.67668 23 210.20 17 13 7.38706 6 204.30 8 14 7.96212 11 229.60 32 15 6.69625 2 213.70 21 18 .11.45197 39 237.10 35 19 7.13828 3 201.90 5 20 7.96153 10 209.00 14 21 6.41367 1 196.00 2 24 7.54565 7 188.50 1 25 7.36316 5 203.60 7 27 8.14305 13 196.60 3 29 8.48558 18 212.20 19 31 10.13617 35 241.70 36 32 9.93644 33 249.30 37 33 10.34412 37 226.10 30 36 8.79381 26 215.80 24 38 9.48601 32 231.80 34 F 2 8.32085 16 219.00 28 F 7 8.22364 15 199.80 4 F 9 8.62272 19 207.70 10 F 10 9.21873 30 209.00 15 F 11 8.40401 17 213.00 20 F 13 8.62927 20 214.10 22 F 14 7.60206 8 206.60 9 F 25 12.11006 41 257.40 39 F 26 11.20411 38 251.20 38 F 27 10.14301 36 226.80 31 50 TABLE IV(Cont 'd.) Company Leve l Company Rank Company Rank Number Price bv Leve l Price Premium by Premium F 31 $ 12.08589 40 . $ 282.80 41 F 32 8.92056 28 215.50 23 F 50 8.63475 21 210.40 18 F 52 8.70389 24 231.30 33 F 55 8.09180 12 209.70 16 F 59 8.64197 22 260.10 40 F 64 7.61105 9 208.00 12 Total Number of Companies = 41 _ T p\n?T D D T f T PRF1\ATTT1\/T. Canadian Foreign Canadian Foreign Owned Owned Total Owned Owned Total Mean $ 8.55476 9.12755 8.79226 $ 215.12 224.85 219.15 Standard Deviat ion 1.238 1.370 1.325 14.809 22.988 19.297 Coef f ic ient of Variat ion 14.47% 15.01% 15.07% 6.88% 10.22% 8.81% 51 TABLE V PRICE RESULTS FOR $10,000 WHOLE LIFE  PARTICIPATING POLICIES Company Level Company Rank Company Rank Number Price by Level Price Premium by Premium 2 $ 6.84763 29 $ 175.30 14 5 4.42039 5 172.20 9 6 6.43126 25 182.20 25 9 4.65251 8 167.60 4 10 9.00089 40 182.40 27. 11 6.86222 30 170.40 5 13 5.04511 10 178.90 19. 15 4.49998 6 179.00 20 16 5.12904 11 184.60 30 18 8.57224 38 170.60 7 20 4.61628 7 173.50 12 21 5.22219 14 178.00 18 24 4.79775 9 176.70 16 25 5.30817 17 156.00 2 27 5.20750 13 181.40 24 28 3.60793 1 • 172.00 8 29 7.17267 35 182.30 26 30 4.04561 2 173.20 11 31 5.87340 22 170.50 6 32 6.95080 33 183.50 29 33 8.68667 39 185.20 31 34 6.92871 32 176.20 15 38 7.04214 34 189.10 32 F 9 5.55828 19 215.10 39 F 11 4.10948 3 228.00 40 F 14 5.40840 18 172.30 10 F 21 5.28499 16 195.60 35 F 25 6.86279 31 196.50 36 F 26 6.61053 27 190.80 34 F 27 7.70257 36 189.10 33 F 29 5.93760 23 159.60 3 F 40 6.55912 26 179.90 22 F 41 5.74132 21 180.70 23 F 42 5.59323 20 202.80 37 F 43 6.68462 28 183.50 28 F 45 7.97176 37 204.50 38 TABLE V (Cont'd.) 52 Company Number Leve l Company Rank Price by Leve l Price Premium Company Rank by Premium F 52 F 58 F 62 F 65 6.36896 4.41085 5.28447 5.20069 24 4 15 12 177.60 148.00 174.30 179.00 17 1 13 21 Total Number of Companies = 40 -LEVEL PRICE - -PREMIUM-Canadian Foreign Owned Owned Canadian Foreign Total Owned Owned Total Mean $ 5.95309 5.95822 5.95527 $ 176.56 186.90 180.95 Standard Deviat ion 1.497 1.010 1.312 7.002 18.963 14.490 Coef f ic ient of Variat ion 25.15% 16.95% 22.04% 3.97% 10.15% 7.99% 0 53 TABLE VI PRICE RESULTS FOR $10,000 20 PAYMENT LIFE PARTICIPATING POLICIES Company Level Company Rank Company Rank Number Price bv Leve l Price Premium by Premium 2 $ 8.40131 23 $ 273.70 15 5 6.98451 16 277.20 18 6 7.79423 20 276.60 17 9 6.11485 9 266.40 9 10 11.96828 40 283.50 22 11 7.79047 19 240.20 2 13 6.33799 11 270.60 13 15 5.17553 4 271.00 14 16 6.30896 10 285.50 25 18 10.53311 33 266.70 10 20 5.74464 8 264.10 7 21 7.41648 17 286.50 26 24 5.57388 7 266.30 8 25 5.54476 6 231.40 1 27 6.43080 12 281.00 20 28 3.80455 1 292.00 29 29 8.11169 22 279.60 19 30 4.96500 3 262.10 6 31 6.84944 15 268.30 11 32 9.40803 30 289.80 27 33 10.00239 31 294.10 30 34 8.62195 26 270.50 12 38 10.78161 34 290.50 28 F 9 8.03801 21 308.40 33 F 11 10.85051 35 350.00 42 F 13 11.54299 39 284.00 23 F 14 6.75426 14 256.90 5 F 21 8.82031 28 324.00 39 F 25 10.87393 37 317.80 36 F 26 10.07317 32 324.40 40 F 27 10.85872 36 301.70 32 F 29 8.43966 24 298.40 31 F 33 9.36626 29 316.30 35 F 40 11.98859 41 313.50 34 F 41 11.38169 38 320.20 37 F 42 7.48603 18 322.20 38 F 43 8.59204 25 276.10 16 54 Company Number F 44 F 45 F 58 F 62 F 65 TABLE VI (Cont'd.) Leve l Company Rank Price by Leve l Pr ice 63030 2 58592 42 20348 5 66183 27 73112 13 4, 12, 5, 8, 6, Premium $ 244.50 328.20 242.30 281.20 284.60 Company Rank by Premium 4 41 3 21 24 Total Number of Companies = 42 LEVEL PRICE -Canadian Foreign -PREMIUM-Canadian Foreign Owned Owned Total Owned Owned Total Mean $ 7.42017 9.09889 8.17959 $ 273.37 299.72 285.29 Standard Deviat ion 2.032 2.212 2.274 Coef f ic ient of Variat ion 27.38% 24.31% 27.80% 15.034 28.932 25.973 5.50% 9.65% 9.10% CHAPTER 8 INTERPRETATION OF RESULTS Some information with respect to theories of competit ion has been presented in order to serve as a background in the interpretation of the resul ts of this study. From the resul ts of this study, several things seem apparent. Ind i -cat ions from the resul ts previously reported are that: as determined by the coef f ic ients of var iat ion -(a) for each of the four types of po l i c ies with the except ion of 20 payment l i fe non-par t ic ipa t ing , the relat ive price variat ion is greater amongst Canadian owned companies than amongst foreign owned companies. (b) for each of the four types of p o l i c i e s , the re lat ive premium var iat ion is greater amongst foreign owned companies than amongst Canadian owned companies. (c) re lat ive price variat ion is greater amongst the two types of part ic ipat ing po l i c ies than amongst the two types of non-part ic ipat ing p o l i c i e s . This resul t is perhaps to be expected s ince the pr ices of part ic ipat ing po l i c ies ref lect the companies' non-guaranteed 1967 dividend s c a l e s , whi le the pr ices of the non-par t ic ipat ing po l i c ies are based ent irely on contractual guarantees. (d) relat ive premium variat ion in each of the four types of po l i c ies i s substant ia l ly lower than the relat ive price var ia t ion. Further, (e) the mean leve l pr ices as we l l as mean premiums in each of the four types of po l i c ies are greater for foreign owned companies than for Canadian owned companies. One speculat ive reason for this occurrence is the p o s s i -56 b i l i t y of higher r isk attendent to foreign companies operating in Canada with consequent attempt at higher rates of return. The greater var iat ion in pr ices as opposed to premiums suggests the poss ib i l i t y that premium competit ion is being substi tuted for price compet i t ion. If premium competit ion is being substituted for price competit ion does it make any di f ference? Is the premium rate for a po l i cy a re l iab le measure of the po l i cy ' s p r ice? A scan ana lys is of the rank data as presented in the Results indicates no c lose pos i t ive correlat ion between premium and p r i ce . More detai led evidence supporting th is conc lus ion is found in the computation of Spearman's coef f ic ient of rank correlat ion as presented in Table VII. Leve l premiums are easy to compare, easy to obta in , and involve no c a l c u -lat ions on the part of the buyer. Accurate pr ices however, such as the price of protection determined by the leve l price method, are extraordinari ly d i f f i -cul t to determine. In addit ion to a lack of appropriate information confronting the buyer , such price ana lys is involves complexi t ies that place such ana lys is beyond the reach of the average buyer and perhaps beyond reach of the fa i r ly sophis t icated buyer. As a competit ive market approaches, although never a t ta ins , the idea l of perfect compet i t ion, the expectat ion is that the tendency w i l l be towards more uniform p r i ces . As this study indicates that there is much more uniformity amongst premiums than amongst pr ices and as the problems of price determination are subs tan t ia l , support is lent to the propo-si t ion that at least to an extent throughout the market competit ion is expressed on the bas is of premium. TABLE VII 57 Information on Rank Correlat ion between Premium and Price Type of Po l icy Spearman's coef f ic ient of rank correlat ion between price and premium *  Whole l i fe non-part ic ipat ing .6399 20 pay l i fe non-part ic ipat ing .6521 Whole l i fe part ic ipat ing .3381 20 pay l i fe part ic ipat ing .7171 * Ca lcu la t ions were performed on a hand ca lcu la tor . The computational formula used is found in C . G . Para dine and B. H . P. Rivet t , S ta t is t ica l Methods  for Technologists (London, England: Engl ish U n i -vers i t ies P ress , 1966), pp. 212-3 . The unre l iab i l i ty of premium as a measure of a po l i cy ' s price is revealed by the rank correlat ion evidence in relat ion to the fact that if total posi t ive correlat ion were present—if the premium and price rank orders were iden t i ca l— Spearman's coef f ic ient of rank correlat ion would be equal to one. At least a general def ini t ion of an excess ive price is necessary in at tacking the quest ion of the ef fect iveness of price compet i t ion. From economic theory, in a perfect ly competit ive market an excess ive price would be one which exceeded marginal cos t . Whi le i t i s not appropriate to consider the Canadian l i fe insurance industry in extensive re lat ionship to perfect compet i t ion, c o n -c lus ions respect ing the ef fect iveness of competit ion could be reached if appl icable cost data were ava i l ab le . Unfortunately, however, in respect to this study, the road is c losed here. Moreover , such a cost ana lys is if performed on only a handful of companies may give mis leading resu l t s . For 58 example, i f the sample inc luded ineff ic ient companies, these companies could just i fy pr ices that buyers might consider c lear ly excess ive in relat ion to the pr ices charged by eff ic ient companies. A more feas ib le poss ib i l i t y for this study, in defining an excess ive p r i ce , is to make comparisons between price figures in the various arrays. Whi le this comparison is to a large extent sub jec t ive , it can a lso be reasonable. In making comparisons one poss ib i l i t y i s to look at the pr ices in the extremes of the arrays.Table VIII indicates the existent price dif ferentials given by such a compar ison. TABLE VIII Price Di f ferent ia ls in the Extremes of the Arrays Type of Po l icy Company Price Ranking (1 = lowest) Companies with a Price at least Double Number Percentage 20 Pay Li fe Non-Par t ic ipat ing 1 0 0 20 Pay Li fe Part ic ipat ing 1 2 3 4 5 6 7 8 9 10 24 14 12 10 10 5 5 4 1 0 57.1 33.3 28.6 23.8 23.8 11.9 11.9 9.5 2.4 0 Whole Li fe Non-Par t ic ipat ing 1 0 0 59 TABLE VIII (Cont 'd.) Type of Po l icy Company Price Ranking (1 - lowest) Companies with a Price at least Double Number Percentage Whole Li fe Part ic ipat ing 1 2 3 4 5 6 7 5 3 3 1 1 1 0 12.5 7.5 7.5 2 .5 2 .5 2 .5 0 No premium was double the lowest ranking premium in any one of the four types of p o l i c i e s . The greater pr ice dispari ty evident from the foregoing table in the two part ic ipat ing types of po l i c ies may be attributed to the unguaranteed prov-is ions . It appears that for the part ic ipat ing po l i c ies s tud ied, the evidence suggests the ex is tence of excess ive p r i ces . The price dispari ty suggested by Tables VIII and K between ident ica l contractual products is of such a degree as to render, from a subject ive a n a l y s i s , the pr ices in the extreme high price end of the two ar rays , e x c e s s i v e . However , the comparison of pr ices in the extremes of an array may seem to exaggerate price d i f ferent ia ls . Another approach to the determination of the poss ib i l i t y of ex istence of excess ive pr ices is to exclude for comparative purposes the few pr ices in the extremes of the array, and compare pr ices within the main body of pr ices in the array. The body or group of pr ices u t i l i zed may be defined as ly ing within 60 a certain distance from the mean. If a distance of three standard deviat ions is es tab l ished as appropriate the pr ices inc luded in the group could be c o n -sidered as those ly ing within 1.5 standard deviat ions to each side of the mean. Whether or not the group should be defined by boundaries equidistant from the mean depends on the skewness of the price d is t r ibut ion. The resul ts of this study indicate a sl ight skewness to the right of the mean for three of the four types of po l i c ies s tud ied. The extent of the skewness is not s igni f icant how-ever; consequently the three standard deviat ion test sha l l be appl ied in d i r -ect ions equidistant from the mean. Information pertinent to this type of a n a -l y s i s i s found in Table IX. TABLE IX Information Relevant to the Three Standard Deviat ion Test P R I C E Pr ices 1.5 Standard Type of Po l icy Lowest Highest Deviat ions from the Mean Whole Li fe Non-Par t ic ipat ing $ 5.01960 - 9.31510 $ 5.35533 - 7.77189 Whole Li fe Part ic ipat ing 3.60793 9.00089 3.98687 7.92367 20 Pay Li fe Non-Par t ic ipat ing 6.41367 12.11006 6.80484 10.77969 20 Pay Li fe Part ic ipat ing 3.80455 12.58592 4.76827 11.59091 Revelat ions respect ing the s ize of the price group determined by the three standard deviat ion test are given in Table X . TABLE X Companies with Pr ices 1.5 Standard Deviat ions from the Mean Percentage of Type of Po l icy Number of Companies Wi th in Group Number of Companies in Companies the Sample Beyond Group Beyond Group Whole Li fe Non-Par t ic ipat ing 40 4 10.0 20 Pay Li fe Non-Par t ic ipa t ing 35 6 17.1 Whole Li fe Part ic ipat ing 35 5 14.3 20 Pay Li fe Part ic ipat ing 37 5 13.5 It seems very un l ike ly that a buyer of, for example, the 20 payment l i fe non-part ic ipat ing po l i cy studied here, would pay $10.78 for the po l icy if he is aware of the fact that the price is $10.78 and that an alternative i s ava i lab le at $6 .80 . From the information in Table X this conc lus ion can be extended to the other three types of po l i c ies as w e l l . In each case the price dispari ty appears to be large enough as to render pr ices 1.5 standard deviat ions above the mean, e x c e s s i v e . Wh i le the absolute difference between the pr ices given may appear s m a l l , these figures are pr ices "per year per $1,000 of protect ion" . When the purchase invo lves many units of protection over many yea rs , the d i f -ference amounts to a large sum. For example, extending the 20 payment l i fe non-par t ic ipat ing figures of $6.80 and $10.78 to the face amount of the po l icy ($10,000) and the appropriate time period (20 years) , the fu l l pr ices are $1 ,360 . and $2 ,156 . Quite c l ea r l y , the magnitude of the foregoing higher p r i ce , in relat ion to the lower p r i ce , for an ident ica l contractual product, 62 renders the higher pr ice e x c e s s i v e . To the extent that excess ive prices ex is t in whole l i fe insurance in Canada it appears that pr ice competit ion is not whol ly e f fect ive. The va l id i ty of the foregoing sentence, however, hinges on the extent of the existence of e x c e s -s ive p r i ces . G i v e n , by the resul ts of this study, that substant ia l price dispar i ty ex is ted in Canadian whole l i fe insurance in 1967, the question ar ises as to the causes of such d ispar i ty . One poss ib le explanation is that the pr ice dispar i ty i s not r ig id but only ref lects competit ive company pr ice po l i cy in an annual state of f l ux . Adherents to this explanat ion would prob-ably purport that the evident price dispari ty in 1967 would be extens ive ly different, in terms of magnitude and company rank by p r i ce , in any other year . The idea l condi t ion in determining the true nature of the price dispari ty would be to perform the same price ana lys is on the same l i fe insurance po l i c ies at another point in t ime. Such an undertaking would in a l l l i ke l ihood lead to unequivocal conc lus ions respect ing the causes of the 1967 price d ispar i ty . Unfortunately however the ana lys is at another point in time is beyond the scope of this study. Consequent ly , increased stress sha l l be p laced on the price information as it i s and on some other var iables relevant to conclus ions respect ing compet i t ion. Before leav ing the explanat ion that the price dispari ty is ref lect ive only of a competit ive si tuat ion in a constant state of d isequi l ib r ium, it appears to the author that two factors mitigate against acceptance of such an explanat ion. In the f i rs t i ns tance , the potent ial to perpetuate price dispari ty in whole l i fe insurance is cons iderab le , in view of the fact that p r i ce , being shrouded by complex i ty , is v i r tua l ly indeterminable to the average buyer. Secondly, i l lus t ra t ive information concerning the magnitude of the pr ice dispari ty has been presented in Tables VIPI andIX. The immensity of the pr ice dispari ty over a period of one year therein indicated would appear to suggest that the d i s -parity is not ind icat ive of effect ive competit ion in part ia l d isequi l ib r ium. The extent of the price dispar i ty i s just too substant ia l to lend much credence to such an exp lanat ion. Another explanat ion for the price dispari ty and one which appears to the author as more feas ib le is that the pr ice dispari ty inc luded evidence of excess ive pr ices that would not prevai l i f competit ion on the bas is of price were more e f fec t ive . Ef fect iveness is a matter of degree, however, and whi le pr ice competit ion respect ing only the contractual product: does not appear whol ly e f fec t ive , other factors become operative in considerat ion of the total product. Price in l i fe insurance is to some extent unique in i ts complexi ty and in the confusion it generates. Consequent ly , various sources have st ressed the importance of non-pr ice factors in the purchase of l i fe insurance. Competi t ion therefore may be found to operate on var iables other than price such as product d i f ferent iat ion, conven ience, service and sa lesmanship. Convenience and the serv ices provided by the agent could we l l be very dec is ive factors in the dec is ions of many buyers . Some information on the importance of sa lesman-ship and serv ice is provided in the fo l lowing excerpt of the Canadian Li fe Insurance Off icers Assoc ia t ion Submission to the Royal Commission on Banking 64 35 and F inance . Life insurance has a lways had to be s o l d . Mos t people require some persuasion to put aside for tomorrow a dollar which is ava i lab le to be spent today. This is the cont inuing task of l i fe insurance represent-a t i ves . A l s o , in the face of the complexi t ies of l aw , taxat ion and estate adminis t rat ion, the ta i lor ing of l i fe insurance programs to changing needs requires continuing service as w e l l . Non-pr i ce competit ive var iables are part icular ly d i f f icul t to measure s ince they are often in tangib le . The extent to which price dif ferentials ref lect the cost of added.serv ices and other var iables is not at a l l c lea r . Wh i le an ana lys is of this part icular aspect is beyond the scope of this s tudy, the factor of the high magnitude in the pr ice dispari ty may attenuate the proposit ion that competit ion in the total product is whol ly e f fec t ive . Although considerat ion of the total spectrum of factors in assess ing compe-t i t ion is not poss ib le here , attention sha l l be given to some general ly accepted relevant factors in order to resolve whether or not they have a bearing on other indicat ions in this study. A cr i ter ion general ly considered necessary for ef fect ive competit ion is freedom of entry and ex i t . That i s , the market should be such that new competit ive inf luences may enter without undue restr ic t ion if they so desire; s imi lar ly no competit ive inf luence should be ef fect ive ly locked in to the market such that i ts freedom to exit is prohibi ted. Entry into the Canadian l i fe insurance industry and the requisi te federal registry (except for p rov inc ia l l y l i censed companies) is not part icular ly easy because of sub-stant ia l deposit requirements by the federal government. However , for a The Canadian Li fe Insurance Off icers Assoc ia t i on , Submission to  the Royal Commiss ion on Banking and F inance , Toronto: July, 1962. company which possesses the resource capaci ty to meet these requirements entry is prohibited only by the nature of the l i fe insurance product i t se l f . Entry into the l i fe insurance industry requires substant ia l resources in terms of labor , pr imari ly for the sales funct ion, and cap i t a l . Unt i l sa les are expanded to the point where the law of large numbers takes effect and to where sa les are suf f ic ient to generate reserve capac i t y , substant ia l c a p i t a l , in reserves to meet cont ingenc ies , is required. In the context of ef fect ive competit ion a completely stat ic si tuat ion over a period of time where no firms exi t or enter the market would l i ke l y indicate competit ion is not funct ioning e f fec t ive ly . A market si tuation where the number of firms i s not stat ic and where there is some turnover and growth of firms in the market, would appear to support a conc lus ion that competit ion is e f fec t ive . Some information respect ing the ease of entry cr i ter ion is ava i lab le from the Federal Superintendent's Reports. For the year 1961 there was a net posi t ive change of one new federal ly registered company (Acadia Life) operative in the Canadian l i fe insurance marke t^ 5 . For the year 1963 the net change was an 37 increase of f ive new companies operative in the market. For the year 1964 Report of the Superintendent of Insurance for Canada 1961, V o l . 1, p. v i i . ^ 7 Report of the Superintendent of Insurance for Canada 1963, V o l . 1, p. v i i . there were four new registrants including Allstate L i f e , Family L i f e , and 38 Federated L i f e . Two companies exited from the market. In 1966 there were 39 no new entrants or exits in the market. Bearing in mind the resource require-ments and the fact that there are over 100 federally registered l i f e insurance companies in Canada, the foregoing entry-exit information reveals nothing contrary to the proposition that effective competition e x i s t s . Another factor often appraised in attempts to determine the effectiveness of competition i s the growth behaviour of the low price firms in the market. Information respecting this factor i s presented in Tables XI. and'XII, 40 TABLE XI Relative Growth of Low Price Firms  in Terms of the Amount of New Effected Insurance Policies on Whole Life Policies in Canada Type of Policy Whole Life Non-Participating  Company Number 3 21 28 15 16 Rank by Price 1 2 3 4 5 Change in Rank by Amount of New Effected Insurance 1961-64 1964-66 + 37 - 1 0 - 7 - 1 3 0 0 3 1 38 Report of the Superintendent of Insurance for Canada 1964, Vol. 1, pp. v i i - v i i i . 39 Report of the Superintendent of Insurance for Canada 1966, Vol. 1, pp. 1A -2A. ^ uThe Growth data portrayed in Tables XI „ XII and XIII i s based.on the TABLE XI (Cont'd.) Change in Rank by Amount of New Type of Policy Rank by Price Effected Insurance 1961-64 1964-66 20 Payment Life Non-Participating  Company Number 21 15 19 6 25 1 2 3 4 5 + 1 7 5 6 3 0 - 3 - 5 + ' 4 - 2 Whole Life Paricipating 28 30 11 58 5 1 2 3 4 5 + + 0 1 1 4 2 0 - 1 0 - 1 + 1 20 Payment Life Participating 28 44 30 15 48 1 2 3 4 5 0 - 4 + 1 - 7 - 4 0 - 4 - 1 - 3 - 1 Total net rank change for above firms 1961 - 1966 = -25 amount of "New effected Insurance P o l i c i e s " on whole l i f e insurance in Canada found in the Report of the Superintendent of Insurance for Canada, 1961, Vol. 1, pp. 2A-12A; 1964, Vol. 1, pp. 2A-8A, 10A-14A; 1966, Vol. 1, pp. 2C-8C , 10C-16C. 68 TABLE XII Relative Growth of High Price Firms  in Terms of the Amount of New Effected Insurance Po l i c i e s on Whole Life Policies in Canada Type of Policy Whole Life Non-Participating  Company Number Rank by Price Change in Rank by Amount of New Effected Insurance 1961-64 1964-66 18 F 26 F 31 F 32 23 44 43 42 41 40 + + 7 3 5 2 2 + 0 3 1 7 3 20 Payment Life Non-Participating F F 25 31 18 26 33 41 40 39 38 37 + 3 5 7 3 3 2 1 0 3 5 Whole Life Participating 10 33 18 45 27 40 39 38 37 36 + + + 5 3 7 3 6 1 5 0 0 5 20 Payment Life Participating F F F F 45 40 10 13 41 42 41 40 39 38 + + 0 - 1 - 1 - 2 - 3 Total net rank change for above firms 1961 - 1966 = -29 The general expectation, where effective competition on the basis of price exists, is that low price firms would grow in terms of sales volume, relative to high price firms. Evidence from TablesXI and XII gives contrary indications to this expectation. Both the very high and very low price firms exhibited net negative growth behaviour of almost the same magnitude over the period 1961 to 1966. The evidence of the low price firms is even more startling when it is considered that one firm accounted for the vast majority of positive rank changes. If this one firm was excluded from the evidence the low price firms would have fared far worse than the high price firms. While this evidence appears to support conclusions that competition on the basis of price alone is not effective, caution must be exercised. The computed prices are based on 1967 data while the sales growth behaviour is studied over the period 41 1961 - 1966. As discussed in a previous section, although the extent of the consistency in prices over years is not clear, the opinion of the author is that extensive price fluctuations by an individual company are very much the exception if in fact they occur at a l l . Table Xn provides some information on market rank changes within the ten companies participating in the study having the largest amount of new insur-ance policies effected. Comparable sales growth data subsequent to 1966 is not as yet available from publications. 70 TABLE XIII Structural Changes Amongst Ten Largest Firms in the Study Rank by amount of new Insurance Policies Company Number Effected on Whole Life Insurance in Canada 1966 1964 1961 24 1 1 1 F 43 2 2 2 28 3 3 3 F 52 4 4 4 20 5 6 7 11 6 5 5 5 7 8 6 F 9 8 11 11 25 9 7 8 30 10 9 10 It is evident from TableXEHthat while the positions of the largest four companies remained constant throughout the period, rank changes were experienced by the remaining firms in Table XHI. In terms of the total competitive picture—not only competition on the basis of price—this representation of company mobility does not appear contrary to the proposition that competition is effective. s C H A P T E R 9 C O N C L U S I O N The pr i ce ev idence deve loped in th is study and any ind ica t ions to w h i c h the ev idence p o i n t s , are b a s e d on the l e v e l - p r i c e method of pr ice a n a l y s i s . The appropriate recogni t ion made by this method of the var ious complex factors operative in whole l i fe insurance pr ice a n a l y s i s , e s p e c i a l l y in comparison to other pr ice determination methods , renders the l e v e l - p r i c e method a v a l i d and r e l i a b l e measure . The average buyer of whole l i fe insurance i s faced with numerous problems in any attempt that he may make to determine meaningful pr ices for var ious p o l i -c i e s . The l a c k of a v a i l a b l e p o l i c y information as w e l l as the complex i t i e s i n v o l v e d in pr ice determination in a l l probabi l i ty prec lude the average buyer from an awareness of the pr ice he pays when he buys l i fe insurance as w e l l as an awareness of the pr i ce s of a v a i l a b l e a l t e r n a t i v e s . In consequence t h e n , whether or not the buyer purchases on the b a s i s of premium rather than pr ice is not c l e a r . N o l a c k of c l a r i t y ex i s t s however in the re la t ionsh ip of premium to p r i c e . The premium is not a r e l i a b l e measure of a p o l i c y ' s p r i c e . The subs tant ia l pr ice d i s p a r i t y , between i d e n t i c a l contractual produc t s , evident in the resul ts of this study support the c o n c l u s i o n respec t ing the buyer 's general l ack of awareness of p r i c e . The pr ice d i spar i ty i s a l s o of such magnitude as to ind ica te the c o n c l u s i o n that compet i t ion on the b a s i s of pr ice alone is l e s s than w h o l l y e f f ec t ive . This c o n c l u s i o n is further s u p -72 ported by growth evidence of the high and low price firms—the net relative growth of the low and high price firms being almost identical and of a negative character. Although the evidence points to the existence of substantial price disparity it does not appear to the author that the price disparity is evidence of price discrimination. A requisite for price discrimination is that conditions of sale are identical. The conditions of sale in whole life insurance, particularly as perceived by the buyer, differ widely. Intangibles operative in the sale of whole life insurance assure a stature not otherwise generally reached, because of the apparent neglect of price as a meaningful factor to the buyer. The extent to which the price disparity reflects the cost of added services and other non-price variables involved in the total product concept is not at a l l clear. The effect of other than price variables does not appear insignificant, however; non-price variables seem to be important competitive factors. Evidence not inconsistent with effective competition as a whole is found in the entry and exit behaviour of firms in the market as well as in structural changes amongst the larger firms participating in this study. The extension of conclusions here to competition as a whole is not possible with the limited information with which this study deals. Indeed, it is per-haps venturesome to conclude that price competition alone is less than completely effective when the analysis is undertaken at only one point in time. However, the nature of the evidence appears to the author to support this conclusion despite the limitations in the analysis. 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"Life Insurance as an Investment," Life and Health Insurance Handbook. Homewood, Ill inois: Richard D. Irwin, 1964, 2nd Ed. Lord, R. W . "Analyzing Contracts and Costs ," Life and Health Insurance  Handbook. Homewood, Illinois: Richard D. Irwin, 1964, 2nd Ed. MacLean, J. B. Life Insurance. Toronto: McGraw-Hi l l , 1957. Matteson, W . J. and Harwood , E. C . . Life Insurance and Annuities  From a Buyer's Point of View. Great Barrington, Mass: American Institute for Economic Research, Annual. McCarthy, E . J. Basic Marketing: A Managerial Approach. Homewood, Il l inois: Richard D . Irwin, 1964, Rev. Ed. M c G i l l , Dan M . Life Insurance. Homewood, Illinois: Richard D . Irwin, 1959. Mehr, R. I. andCammack, E . Principles of Insurance. Homewood, Illinois: Richard D. Irwin, 1961, 3rd Ed. Mehr, R. I. and Osier, R. W . Modern Life Insurance. New York: The MacMil lan Company, 1961, 3rd Ed. Minrath, W . R. Handbook of Business Mathematics. Toronto: D . VanNostrand, 1959. Paradine, C . G . andRivett, B. H . P. Statistical Methods for Technologists. London, England: English Universities Press, 1966. Pedoe, A. Life Insurance, Annuities and Pensions. Toronto: The University of Toronto Press, 1964. Purdy, H . L . Evidence of Dr. H . L . Purdy at the Public Hearings of the Royal  Commission on Automobile Insurance. Victoria, 1967. Report of the Superintendent of Insurance for Canada. Ottawa: Queen's Printer, Vol . 1, 1961, 1962, 1963, 1964, 1965, 1966. Richardson, F . B. and Hartwell, John M . "Lapse Rates" , Transactions of the  Society of Actuaries , III (1951) pp. 338-74. Richmond, Samuel B . Statistical Analysis. New York: Ronald Press , 2nd Ed. , 1964. Royal Commission on Banking and Finance. Ottawa: Queen's Printer, 1964. Salyzyn, V. "The Competition for Personal Savings Deposits in Canada," The Canadian Tournal of Economics and Political Science, XXXII #3 August, 1966. Stone and Cox Life Insurance Tables 1965. Toronto: Stone and Cox, 1965. Watson, D . S. Price Theory and Its Uses. Boston: Houghton Mifflin Company, 1963. Wi lcox , C . Public Policies Toward Business. Homewood, Illinois: Richard D . Irwin, 1955. APPENDIX A Z FACTORS Po l i cy Year Factor 1 1. 2 .86051 3 .77246 4 .69993 5 .63802 6 .58326 7 .53474 8 .49173 9 .45353 10 .41865 11 .38674 12 .35717 13 .32975 14 .30432 15 .28075 16 .25891 17 .23841 18 .21896 19 .20057 20 .18322 The present value f igures used in computing the Z factors are taken from Wi l l i am R. M in ra th , Handbook of Business Mathemat ics . D . Van Nostrand C o . , Inc. , Toronto 1959. APPENDIX B T H E UNIVERSITY OF BRITISH C O L U M B I A V A N C O U V E R 8 , C A N A D A F A C U L T Y O F C O M M E R C E A N D BUSINESS A D M I N I S T R A T I O N February 13, 1967. Dear The - \: "J has been included i n the sample i n a research project presently being c a r r i e d out i n the D i v i s i o n of Finance, Faculty of Commerce, Un i v e r s i t y of B r i t i s h Columbia. Your assistance i n providing the following informa-t i o n , relevant to your company, would be greatly appreciated. Current information concerning the following p o l i c i e s f o r 1 to 20 years i n c l u s i v e : 1. Assume $10,000 str a i g h t l i f e p a r t i c i p a t i n g p o l i c y issued at age 30. Request information re:-(a) Annual premium (most favorable c l a s s i f i c a t i o n ) . (b) Cash surrender values per $1,000 of face amount i n each of the f i r s t 20 p o l i c y years. (c) Annual dividends i n each of the f i r s t 20 p o l i c y years as projected i n Stone & Cox. 2. Assume $10,000 s t r a i g h t l i f e non-participating p o l i c y issued at age 30. Request information r e : -(a) Annual premium (most favorable c l a s s i f i c a t i o n ) . (b) Cash surrender values per $1,000 of face amount i n each of the f i r s t 20 p o l i c y years. 3. Assume $10,000 20 pay l i f e p a r t i c i p a t i n g p o l i c y issued at age 30. Request information re:-(a) Annual premium (most favorable c l a s s i f i c a t i o n ) . (b) Cash surrender values per $1,000 of face amount i n each of the 20 p o l i c y years. (c) Annual dividends i n each of the 20 p o l i c y years as projected i n Stone & Cox. 4. Assume $10,000 20 pay l i f e n on-participating p o l i c y issued at age 30. Request information re:-(a) Annual premium (most favorable c l a s s i f i c a t i o n ) (b) Cash surrender values per $10,000 of face amount i n each of the 20 p o l i c y years. - 2 - 79 Please be assured that your Company w i l l not be i d e n t i f i e d . Enclosed i s a return envelope for your convenience. Yours t r u l y , D. H. M i t c h e l l Research A s s i s t a n t D i v i s i o n of Finance DHM/dl APPENDIX C 1958 COMMISSIONERS STANDARD  ORDINARY MORTALITY TABLE Probabi l i ty Adjusted to Show Age of Death Effects of Select ion 30 .00213 .00107 31 .00219 .00142 32 .00225 .00165 33 .00232 .00197 34 .00240 .00228 35 .00251 36 .00264 37 .00280 38 .00301 39 .00325 40 .00353 41 .00384 42 .00417 43 .00453 44 .00492 45 .00535 46 .00583 47 .00636 48 .00695 Source: D. M . M c G i l l , L i fe Insurance (Homewood, I l l i no is : Richard D. I rwin, I n c . , 1959), pp. 158-9. 81 APPENDIX D THE LINTON 'A' LAPSATION TABLE Policy Year Probability of Lapse During Year 1 .104 2 .065 3 .056 4 .050 5 .047 6 .044 7 .041 8 .038 9 .037 10 .036 11 .036 12 .036 13 .036 14 .036 15 .036 16 .037 17 .039 18 .041 19 .043 APPENDIX E 82 S F C P T R A N C L I F E I N S U R A N C E 1 . . . R E A L L E V F . 2 I N T E G E R K , G , F , F . 3 C WENS ION V A L ( 5 C } , D I V ( 5 C ) , Z { 5 0 ) , A N T ( 5 C ) , Y P T { 5 0 ) , Y P { 5 0 ) L I M P E N S I G N T I T L E ( 6 ) 5 R E AC ( 5 , 1 7 ) N 2 6 1 7 F C R V A T ( I 1 C ) ~? R E A C ( 5 , 2 1 ) N 1C 2 1 F O R M A T ( 2 I 1 C ) 1 i R !: A C ( 5 » 2 2 ) ( Z ( G ) , G = 1 , N ) 1 2 C C 1 5 F = 1 , M 2 1 3 R E A C ( 5 , 3 2 ) T I T L E 14 3 2 F G R N A T ( 6 A 6 ) 1 5 . R E A L ( 5 , 2 C ) A N I N , F A C E , G A P 16 2 C F O R M A T { 3 F 1 0 . 5 ) 1 7 R E A C ( 5 , 2 2 ) ( V A L ( N ) , P = 1 , N ) 2 C R E A C { 5 , 2 2 ) ( r i V ( K ) , K = l , N ) 2 1 2 2 F C R N A T ( 8 F I C . 5 ) 2 2 B = 1 . + A K I N 2:3 C C 1 6 I = 1 , M 2 4 L = I — 1 2 5 I F ( I . E C - 1 ) GO TO 1 9 2 6 X •= ( G A P + V A L ( L ) ) * 8 2 ? W = G A P + V A L ( L ) 3 C GC TO 2 5 2 1 1<5 X = ( G A P ) * B 3 2 '.v= G A P 3 3 2 5 Y= V A L ( I ) + D I V ( I) 3 4 Y P { I ) = X — Y 3 5 A . V T U ) = ( ( F A C E ) - ( W ) * ( 1 . +0 . 5 * A N I N ) ) * 0 . 0 0 1 3 6 1 6 Y P T ( I ) = ( Y P { I ) ) / A M T ( I ) 3 7 WR I T E - ( 6 , 3 3 ) T I T L E A C 3 3 F C R N A T ( 6 A 6 ) 4 1 l-v R I T E ( 6 , 3 0 ) G A P 4 2 3 G F C R i V A T ( F L C ' 5 ) 4 3 WR I T E ( 6 ? 14 ) ( Y P T ( I ) , I = 1 , N ) 4 4 1 4 F C R N A T I 8 F 1 0 . 5 ) 4 5 S U M A = G . C 4 6 su<ve = c c 4 7 N 1 =. N + 1 5 C C C 4 0 E •= 1 , M 5 1 J = HI - E 5 2 S U N1 A = S L1 i v A + Y P ( J ) * Z ( j ) ^ ^ S U C ' E = S U . V B + A i v T ( J ) * Z'( J ) _ _ 5 4 " 4 C C O N T I N U E L E V F = S U M A / S U H D 5 6 W R I T E ( 6 , . 1 2 ) L E V P 5 7 1 2 F O R M A T S I X , F 1 2 . 5 ) 6 C 1 5 C C N T T N U E 6 1 S T O P < 6 2 E N D 

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