The direct marketing of insurance

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH

ELSEVIER

European Journal of Operational Research 109 (1998) 541-549

Case Study

The direct marketing of insurance Keet Peng Onn, Alan Mercer * The Manugement School, Lanccrster Unicersity, Department of Munugement Science, Lancaster LA1 4 YX. UK

Received 8 July 1997: accepted 15 December 1997

Abstract An insurance company, like many in the financial services industry, will advertise a product in the press and some readers will avail themselves of it. Often the cost of an advertisement will exceed the income derived from the accepted respondents in the following years. It only becomes profitable if acquiring names into a database results in purchases in future years of the advertised and other, cross-sold products. Therefore evaluating advertising effectiveness requires the development of future lifetime values (LTVs), which vary over time between individuals for the different products. Real 0 1998 Elsevier Science examples include evaluating the media vehicle, size, content and frequency of advertisements. B.V. All rights reserved. Kr_~~vd.~: Marketing;

Insurance

1. Introduction A general (non-life) insurance company will typically sell buildings, home contents, motor and medical insurance to domestic customers. In recent years, there has been a major move to the direct marketing of insurance, rather than selling policies through the companies’ own offices or agents. The reader of a newspaper or magazine will see an advertisement and respond either by returning a coupon or by telephone to ask for a quotation. Respondents, who satisfy the insurance company’s underwriting criteria and present acceptable risks, are immediately sent a quotation

*Correspondingauthor. Fax: + 44-1524 844 885. 0377-2217/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved PIISO377-2217(98)00024-l

and their details are entered into a database. Those people who accept the quotation will be invited to renew their policy when it expires a year later. In the intervening 12 months, attempts will be made to sell different insurance products to selected individuals. For example, somebody having insured the contents of his home will have been asked for the renewal date of his current motor policy with a competing company. Then at the appropriate time, the home contents insurer will attempt to cross-sell motor insurance. Those people, who requested a quotation but did not respond positively, will be mailed on the anniversary of their first approach for several years ahead in further attempts to persuade them to switch insurance companies. Similarly there are individuals who once had a particular type of policy

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with the company but had cancelled it in favour of a competitor. These ex-policy holders will also receive unsolicited approaches, trying to reactivate the former policies, when they would have been due for renewal. The original advertisement may have attracted few respondents. Therefore their initial premiums in total might well have been exceeded by the cost of the advertisement. Indeed the situation would be even worse if the newly insured customer made claims during the first year. However, an insurance company hopes that its policy holders will remain loyal for many years and also take out other types of insurance. Then the new business will be profitable when judged over a time period of several years. Thus the cost effectiveness of an advertisement must be measured over the years following its appearance and this is equally true of the insurance company’s total marketing activities. Indeed, the purpose of the advertisement needs to be seen as generating new names for the database, each of which has the potential to provide the insurer with a net profit after the deduction of marketing costs and claims. This measure of how much a customer is worth to the insurance company during his total time in the database is called the lifetime value (LTV) of the individual. There is some confusion about the origins of the LTV concept in the insurance industry, possibly due to considerations of commercial confidentiality. Jackson (1989) claimed that the LTV of a policy owner was a new idea at that time but Blattberg et al. (1993) state that in-depth interviews carried out in a survey of US insurance companies revealed that it was first applied in the 1950s. Certainly, the literature in reputable journals on LTVs is very sparse. Sheppard (1990) illustrated the difference between the LTV model for a new book club and that for a catalogue mail order company, as well as listing areas of application. Sheppard also included planned promotions. However both he and Jackson segmented individuals into groups, each member of which was then assumed to behave in exactly the same way with respect to every marketing activity. The same parameter values were used for each individual within a segment, so that the LTV was assumed to be a concept related to generally defined segments. Yet for example,

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the factors which influence a customer’s decision to accept a cross-sold home contents policy are not necessarily the same as those which resulted in the original purchase of motor insurance. Thus the LTV should be an individual concept, even though it requires the collection and processing of large quantities of historical data to estimate the parameters, as acknowledged by Roberts and Berger (1989). Previous researchers defined the LTV of an individual as the present value of all future contributions to overheads and profit. However, Baptie (1989) recognised that an individual’s LTV starts from the moment his name is entered into the database and changes over time. Therefore at any point in time, the total LTV is the sum of the realised LTV and the expected future LTV. The realised LTV is defined as the net present value of the actual net profit generated from all activities from the time when the name entered the database to the present time. Since it consists of past events, the realised lifetime value (RLTV) is always accurate and readily calculated. The expected future lifetime value (ELTV) is the net present value of the expected net profit generated from all the future activities of an individual to the LTV horizon.

2. Individuals’ probabilities marketing activities

af responding to direct

The ELTV is calculated using a decision tree, with each branch representing the individual’s expected reaction to a promotion of the insurance company. Consequently the probabilities of the various reactions are required for the different individuals having distinct requirements and being exposed to a variety of promotions. Each type of insurance is a standard product, with a limited number of predefined options being available to people who fall into well defined categories. Any other respondents or those having requirements not covered by the standard policies are deemed not to qualify and are excluded from subsequent analyses. For example, a respondent to a newspaper advertisement for motor insurance can be classified according to age, gender, marital status, the

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residential neighbourhood, the availability of a telephone number and the number of days before the insurance is necessary. The product characteristics are the type of car and its year of manufacture, the area where it is normally kept, the number of drivers, the premium and the number of years without a claim. The direct marketing factors include the media, the response type, whether a telephone response can be made without charge and the creative treatment of the advertisement in terms of size, content and whether or not in colour. The numbers of levels of these factors result in there being of the order of lOI combinations, so that some grouping together is necessary to reduce the number to a realistically representative value. The responses of 16 800 people to 690 press advertisements for motor insurance were analysed with CHAID to segment the market such that the probability of taking out insurance was the same for each individual within a cell but different from the probabilities for all individuals in differof one ent cells.For example, the interpretation of the simpler cells was that if the individual responded by telephone when his renewal date was from one to three days away, the probability of purchasing motor insurance was 0.157. In this case, no other factor was important, although 13 factors were identified by CHAID for the complete tree diagram. Of the 13 factors, the most important factor was the number of days to renewal, followed by how a person responded. This is intuitively reasonable because if, for example, somebody with very few days left before the renewal is legally necessary replies by posting a coupon, the insurance company has little time in which to respond. Indeed one benefit from this analysis was that the company changed to providing all quotations over the telephone, whereas it had previously replied by mail to coupon respondents. Interestingly, neither the medium nor the creative treatment of the advertisement had any effect on the probability of buying motor insurance after an inquiry had been made. Obviously, they could have had a significant effect on the probability of responding to the advertisement in the first instance. Whatever the immediate operational benefits of this analysis were, the data illustrate the need for LTVs, because the overall probability

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of taking out motor insurance was 0.059, giving on average 1.45 new policy holders per advertisement. CHAID analyses were carried out for each type of additional motor cover, such as no claim discount protection, as well as for the initial purchase of home contents and medical insurance. The company attempts to cross-sell to each holder of one kind of policy all its other products, including buildings insurance. CHAID analyses of the probabilities of successful cross-selling yielded differing numbers of factors but the availability of a number to telephone and the size of the premium were invariably the two most important. Six weeks before an active policy is due to expire, the company sends a renewal invitation to the policy holder, with the exception of medical insurance. CHAID analyses were performed for each renewal separately for each type of insurance, so that the factors which affected the probabilities of renewal were identified. However because CHAID is model-free, it cannot project the retention rate beyond the last observed, which in the case of the available data was the fourth. Yet the LTV concept requires the estimation of the probabilities of renewal to the LTV horizon. Therefore a log-linear model was built for each type of insurance, in which the logarithm of the probability of renewal was assumed to be a linear function of the factors identified in the CHAID analyses for the individual renewals of a policy and the renewal number. For motor and buildings insurance, the probability of renewing a policy for the third and all subsequent years was 21% higher than for the first renewal to cover the second year. It was also 21% higher for the third year of contents insurance but rose to 30% for each following year. The interpretation is that policy holders who had renewed once were more likely to continue with the same insurer. Everyone who responds to a press advertisement for home contents insurance but does not accept the quotation is first mailed with promotional material and then contacted by telephone, if the number is known, shortly before the anniversary of the renewal date for each of the three years following the first approach. Similarly, efforts are made to reactivate any home contents policy in the period prior to its renewal for five years after

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its cancellation. At the time of the analyses, no da-

the expected total claim cost must be included in

ta were available beyond two years but CHAID and log-linear analyses were carried out, as for renewals, because of the need to project the results forward for three and five years. The availability of a telephone number and the size of the premium were again the most important factors. As would be expected, because the people being contacted were not current policy holders, the chance of responding to the second approach was 40% less than the probability a year earlier. At the anniversary mailing, unconverted respondents were offered an inducement to take out home contents insurance. The chance of success when the offer was a reduction of &15 in the premium was only 10% of the probability when the promotion was a free smoke detector.

the calculation of an individual’s ELTV. Because the insurance industry has been preoccupied with the setting of premium tariffs, claims is a well researched topic. Hossack et al. (1990) justified the separate estimation of claim frequency and claim size. Beard et al. (1984) modelled the claim frequency with the Poisson distribution, whilst the gamma distribution was used for the claim size by Brockman and Wright (1992), who showed that

3. Individuals’

availabilities

for promotions

and

claims

Apart from people not responding to the insurance company’s marketing activities, some individuals whose names are in the database will be unavailable for promotions for reasons such as death, change of address and simply not wishing to be contacted. Therefore the probability of being unable to contact an individual, given that his name is still in the database, must be extrapolated to the LTV horizon. Consequently the hazard function, as described in Elandht-Johnson and Johnson (1979), was fitted to personal characteristics and direct marketing factors. However, product characteristics were not used, being replaced by the product responsible for the individual’s name entering the database. This factor was statistically significant, together with many personal characteristics like age and the individual’s residential neighbourhood (ACORN) classification. The newspaper read by the person was also very significant and the baseline hazard function was linearly dependent on time. Consequently the probability of being available for promotions at any time could be calculated for a specific individual. Every claim made by a policy-holder reduces the profitability of the insurance company, so that

the multiplicative model was the most appropriate for incorporating the factors of the expectation. The estimation problems caused by non-constant variances were overcome by using joint modelling, as advocated by McCullagh and Nelder (1989). As for the premiums in the response probabilities, the claims were discounted to the beginning of 1992 for interest and inflation. Many factors were found to affect the claims, as a result of which the insurance company reviewed its pricing policy. The

most important influences on claim frequency were the ages of the policy holder and vehicle for motor, location and size of property for home contents and age for buildings insurance. The factors most influencing the size of claim were the type of car and the property location for both home contents and buildings insurance.

4. Expected product sold

future

lifetime

values

if only

one

The expected lifetime value calculations are complex and therefore most easily appreciated by first assuming that the insurance company sells only one product. Thus the complications due to cross-selling are avoided and the individual has a binary choice of buying or not buying the policy. For example, in the second year the decision tree has four branches, two of which stem from whether or not a policy bought in the first year is renewed. The other two branches are due to whether or not the individual, who did not purchase in the first year, bought insurance in the second year as a result of the anniversary mailing. Hence if m represents the number of years in the database, there would appear to be 2”’ possible However the company only sends outcomes.

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third kind which makes a negative contribution that cannot be ignored. The first kind consists of four branches, irrespective of the horizon. The individual first buys the policy in year 1, 2, 3 or 4, respectively and then renews it every year following. The reason for only four branches is that anniversary mailings cease after three unsuccessful promotions. Each branch of the second kind starts with the individual taking out insrrance in year 1, not renewing it for one year but reactivating the policy for the following year, so that it is in force in year h. Hence there are (h - 2) branches of the second kind. The third kind of branch, on which the company loses money because of the costs of unsuccessful reactivation promotions, begins with the customer purchasing insurance in year 1 and then renewing it each year for not more than (h - 2) years, after which all reactivation attempts are unsuccessful. There are (h - 2) branches until year 7, then the number remains at five, because successive reactivation promotions are undertaken for only five years. Thus due to the company’s policy on anniversary mailings and reactivation promotions, together with some customer behaviour being seen from the data to be very unlikely, there are (h + 7) main branches to be calculated when h 3 7. Also, the expression for IIh has a general form for h 3 9, because analyses of the renewal data indicated that the probabilities of renewing and reactivating a home contents policy are constant after the third and second promotions, respectively. Moreover the terms in the resulting expression for ELTVh, form finite geometric series in these two probabilities if it can be assumed that the probability of being available for promotions and the real discount rate reduce at fixed rates. These assumptions were shown to be valid and are included in the calculation of the values of the ELTVh using main branches, given in Table 1, for h=9 and 10.

anniversary mailings to those who never purchased, for three years after the name entered the database, so that the number of outcomes is rewhen m exceeds four. Similarly atduced by 2”‘mm4 tempts to reactivate lapsed policies are made only for the five years after the policy was not renewed, thereby reducing the number of possible outcomes by (m - 7) 21nm7,when m is greater than six. Therefore when m 3 8, the total number of possible outcomes if only one product is sold is 2”’- 2”p4 - (m - 7)2”p7. which is 0(103) for

m =

1C and 0(106) for m = 20.

Previous researchers have taken an arbitrary LTV horizon but this is obviously unsatisfactory in a real situation, where decisions based on lifetime values will be made. It is therefore necessary to calculate the ELTV with an horizon of h years, ELTVh, for different values of h using the probabilities, premiums, costs and claims determined from the earlier analyses, together with interest and inflation rates. In principle, this is simple because ELTVh = ELTVh_, + l-I/,. where IIh is the net present value of the expected net profit from year h in the database. Table 1 gives the results of calculations for a real life example of a respondent to an advertisement for home contents insurance. The value of II,0 is not sufficiently small to be ignored, so that a more distant horizon must be considered. Although the number of branches becomes extremely large, very few contribute significantly. These are termed the main branches and defined by contributing more than l&O.01( to the ELTV calculation. Examination of the home contents data quickly reveals that there are two kinds of branch, which make a positive contribution to the ELTV, and a

Table I Expected

lifetime values for different

nh ELTV,, ELTV,, (main branches

horizons 1

h

14.75 14.75 only)

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2 24.64 39.39

3 20.81 60.20

4 17.95 78.15

5 15.13 93.28 93.30

6

I

8

9

10

12.49 105.77 105.81

10.07 115.84 115.88

8.07 123.91 123.95

6.24 130.15 130.10

4.73 134.88 134.75

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A comparison of the total and main branches values of ELTV,, in Table 1 indicates that the assumptions made to reduce the complexity of the calculations have a negligible effect on the overall accuracy, so that general expressions may be used. For home contents and h 3 9, this is ELTV,, = 149.15 - (24.970 + 0.029h)(0.755)hP* and similar expressions are available for other types of insurance. Fig. 1 illustrates how the values of ELTVh change with the horizon for home contents, motor and medical insurance. For practical purposes, the horizons were taken to be the values of h by which ELTV,, had reached 95% of their asymptotic values. Obviously the horizons depend on the parameters used and each individual has a different set of parameter values, so that the horizon for each product differs between individuals. However it is impractical to have different horizons for different individuals, so that the values were calculated for a random sample of 200 names in the database. The longest was chosen for each product, giving 12, 18 and 16 years for home contents, motor and medical insurance, respectively. Whilst the definition in this study for a main branch uses an arbitrary value of contributing more than l&O.01/ to the ELTV calculation, an upper bound to the contribution of each branch can be found for any horizon. Hence the cut-off contribution required to estimate the ELTV with a specified accuracy could be determined, rather than using an arbitrary value. When an individual’s name enters the database, the RLTV will be zero. Each year, this respondent to the original advertisement will decide whether or not to buy insurance, so the value of RLTV must be updated according to precisely which actions have been taken. Moreover, the actions taken aflect the individual’s status and hence the insurance company’s promotions, so that the probabilities of future actions will be changed. In principle, this requires that the horizon should be re-estimated but that would be too complex for a practical system, so that the same constant rolling horizon is used. The status of a respondent is determined by first categorising the individual according to whether he has never bought

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insurance, currently has insurance or previously purchased insurance but does not currently have a policy. Second, each individual is classified further by the number of planned promotions outstanding. For example, anybody whose name has been in the database for four years and has never taken out a policy will have a zero ELTV, because the insurance company limits the number of anniversary mailings to three, the last being at the beginning of the fourth year. Essentially, the same method as was used to determine the horizon is employed to calculate the ELTV of an individual, whose status and number of outstanding promotions are known. All the branches are evaluated when planned promotions are outstanding, after which the main branches are projected to the horizon.

5. The complexities of real lifetime value systems for insurance marketing In reality, the direct marketing of insurance is most profitable when a respondent to an advertisement for one type of product subsequently takes out a policy for a different cross-sold product. Thus companies sell several types of policy, thereby increasing dramatically the numbers of branches in the decision tree. For example, if a company sells only two types of insurance, the number of possible outcomes after m years in the database is 4” - 4”~~ -- (m - 7)4”’ ~7 - 2mm4 if m > 8. The value of 4 is due to a customer being able to hold both products, either the response or cross-sold product, or neither. The additional term 21nmm4 results from the company stopping anniversary mailings and cross-selling promotions to individuals, who hold only either the response product or the cross-sold product after four years in the database and have not responded to the promotional activities. The method of determining the horizon and the individual lifetime values is necessarily the same for many as for one product; use all the branches until the planned promotions have been carried out and then use only the main branches. Obviously the number of main branches increases with the number of products sold. For example, cross-selling motor insurance to the previously cited

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respondent to a home contents advertisement increases the number of main branches from 25 to 8 1 for the motor horizon of 18 years. However, there would only be 69 main branches, if those involving only home contents insurance were terminated at the home contents horizon of 12 years, and the difference in the ELTV would be only 0.09%. Therefore in the real system, the horizon for a main branch is taken to be the longest of the products featured on the branch. An added advantage of this approach is that the introduction of a new product has no effect on horizons of existing products. The status of an individual whose LTV is to be calculated is determined as for a single product, except that the outstanding promotions are divided into the number planned for each product. A real LTV system needs to be updated regularly. When an individual responds to a planned activity of the insurance company, expectations are realised, so that both the RLTV and ELTV require changing. In theory, this should be done immediately after the event but in practice it takes place monthly. An annual update is necessary because the total LTV is discounted to the present time and the probabilities of being available for promotions also change. It is quite usual to update the parameters at the same time, using estimates from analyses of all the specially recorded outcomes of the planned promotions, and then to modify every individual’s ELTV. Whilst the variances of these parameters can be readily calculated at that time, using them to determine the variances of the ELTVs is fraught with difficulty, because of the complexity of the ELTV expressions and consequential correlations between terms. The insurance company is now considering introducing some form of regular contact with its policy holders, such as a newsletter. Then this increased level of contact will have an effect on the ELTVs. However, to date only those infrequent contacts, as described, have taken place.

6. Applications The design and installation of a real LTV system is a major undertaking and only when it has

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been completed can the full benefits be derived. In particular, an insurance company wishes to know whether its marketing investment, in order to expand the database, is sound. Progress can be assessed by monitoring the total ELTV for all the individuals in the database. Meanwhile, other questions posed by management can be answered with data for samples of individuals, although the statistical accuracy is less good than will be obtained from the whole system. A weighted analysis of variance (ANOVA) was carried out on the total LTVs of a sample of 60 individuals, divided equally between people who had entered the database by responding to an advertisement in the Daily Express, the Daily Mail or the Sun. All the total LTVs were calculated when each respondent had been in the database for the same length of time and the parameters appertaining at the time were used. The weights were necessary to reflect the differences in the variances of the ELTVs. The results were significant at the 10% level, with the Daily Express having the highest average total LTV. The insurance company’s advertisements in the Daily Express had all covered four columns but some had a height of 25 cm, whereas others were 10 cm. An ANOVA for 20 respondents for each size indicated that there was no significant difference in the total LTV. The free smoke detector and the &15 reduction, which had different effects when offered in anniversary mailings to unconverted respondents also featured in press advertisements. However, an ANOVA for a sample of 30 individuals, who had taken out a policy as an immediate consequence of an advertisement in the Sun, showed that the contents featuring the offers had no significant effect on the total LTV, thereby indicating the need to understand fully the complex behaviour of respondents in the direct insurance market. An individual’s opportunities to see (OTS) an advertisement during the campaign when his name entered the database was calculated from his known readership habits. Analyses for a sample of 40 people demonstrated that the total LTV was a significant, quadratically increasing function of the OTS. Although advertisements appeared every week, the content was changed at least every three months, so that no wear-out or saturation

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effects were included. This would certainly be necessary if an indication of an optimum advertising schedule were required, rather than simply looking for the influence of OTS. Thus it appears that the factors most likely to have an effect on the total LTV were the particular newspapers and the weight of advertising, rather than the advertisements themselves. Analyses of the “what-if’ type can also be carried out. For example, a paired comparisons test on data for 25 individuals found that the ELTV would be reduced, significantly at 5% level, if the number of cross-selling promotions and anniversary mailings were each reduced from three to two. Similarly, a weighted discriminant analysis on a sample of 250 motor insurance respondents was undertaken to identify which factors, if any, could be used to distinguish between positive and negative contributions to the total LTV resulting from cross-selling home contents insurance. The discriminant function was 0.87 (Availability

of telephone number)

_ 0.31 (Size of premium) - 0.42 (Home contents insurance rating area). This result, which is in agreement with those of the CHAID analyses, allows the company to target individuals for cross-selling, because the higher an individual’s value of the discriminant function,

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the more likely is the person to purchase home contents insurance.

Acknowledgements

The authors are deeply indebted to the management of the insurance company in which the research was undertaken and where the system continues to be implemented. For reasons of commercial confidentiality, its identity is not divulged but its financial support above all deserves to be recognised.

References Baptie. R.. 1989. Towards Strategic Marketing. M.Sc. dissertation, Lancaster University. Beard, R.E.. Pentikainen, T., Pesonen, E.. 1984. Risk Theory The Stochastic Basis of insurance. Chapman & Hall. Cambridge. Blattberg, R.C., Petrison, L.A., Wang, P., 1993. Database marketing: Past, present and future. Journal of Direct Marketing, 73-8 I. Brockman, M.J.. Wright, T.S., 1992. Statistical motor rating: Making effective use of your data, paper presented to The Institute of Actuaries, 27 April 1992. Elandht-Johnson, R.C., Johnson, N.L., 1979. Survival Models and Data Analysis. Wiley, New York. Hossack. I.B., Pollard. J.H., Zehnwirth, B., 1990. Introductory Statistics with Applications in General Insurance. Cambridge University Press, Cambridge. Jackson, D.R., 1989. I51 Secrets of Insurance Direct Marketing Practices Revealed. Nopoly Press, Wilmington.