Pricing strategy combines five elements: financial pricing for equilibrium premiums based on the return on capital, underwriting cycles for competitive fluctuations, lifetime pricing to balance losses on new business with profits from renewals, class systems for optimal selection of low-cost risks, and multivariance class analysis.
● Financial pricing models determine the indicated equilibrium premiums for perfectly competitive markets. Traditional ratemaking uses nominal claim values and preset underwriting profit margins. Financial pricing models use fair values of expected losses and derive the underwriting profit margin from the target capital and the cost of holding capital. The equilibrium premiums are the anchor to which other pieces attach.
● Underwriting cycle analysis adjusts equilibrium premiums for short term competitive fluctuations. Financial pricing models assume a return on capital based on asset pricing models and the systematic risk of the insurance industry. Underwriting cycle analysis assumes the return on capital for the insurance industry varies with the phase of the underwriting cycle. Pricing actuaries use competitive dynamics to forecast the movement of the underwriting cycle and the needed adjustment to the equilibrium premiums.
● Lifetime pricing considers loss costs, acquisition expenses, lapse rates, and not-taken rates as policies move from new business to renewals. Traditional ratemaking and financial pricing models set rates by policy year. Lifetime pricing sets rates by cohort of business, including all renewals of that cohort. The pricing actuary sets rates for new business, based on lifetime losses, expenses, and lapses, along with the estimated price elasticity of demand.
● Class systems identify the influences on accident propensities. Traditional class ratemaking uses broad classes, such as age, sex, territory, and credit score, that may be proxies for the true influences on loss costs. Class systems considers the influences on aggressive behavior and risk-taking used in criminology, psycholody, and evolutionary biology to identify the optimal predictors of loss costs.
● Multivariate class analysis uses generalized linear models and minimum bias procedures to derive rate relativities. Traditional ratemaking uses one-way analyses to derive univariate rate relativities, ignoring correlations of the class variables and skewness of the loss distribution. Generalized linear models and minimum bias procedures adjust for correlations and skewness and they provide measures of statistical significance that affect the credibility of the analysis.
Marketing methods affect pricing. Aggregator web sites might limit the choice of rating variables. An insurer may wish to give discounts to young unmarried males if they have married parents living together or if they attended a high school without disciplinary problems. Some insurers use family scores and school scores, similar to credit scores, that combine several variables.
Rating systems also affect pricing. Telematics may allow insurers to use distance driven, time of day, and road hazards to rate the risk. The pricing, underwriting, and marketing departments must work together to select the optimal rating variables.
The five pricing elements must be integrated: the premium rates charged to the insured are determined from their combination. We customize the pricing analysis for the insurance products, the marketing methods, and the rating systems to ensure that all elements work together.
Financial pricing models
Financial pricing models combine discounted cash flows with target returns on capital. They derive equilibrium premiums that would prevail in perfectly competitive markets; these premiums serve as anchors to which the effects of underwriting cycles and imperfect competition are attached.
Capital markets are efficient: insurers with too much capital supporting their insurance portfolios earn returns below those expected on projects of similar risk, and insurers with too little supporting capital are downgraded by rating agencies and are unable to sell their insurance policies. To maximize long-term earnings, insurers estimate the capital that optimally supports the insurance portfolios. Insurers may hold more or less capital than the target (supporting) capital, but pricing models use the target capital. Insurers may raise prices slightly if they hold excess capital and are financially stronger, but the overall return on capital decreases.
Given the supporting capital and the expected return on that capital for the insurance industry, insurers derive the premium rates that provide this expected return. These premium rates are long-term benchmarks: in any year, the market rates may differ from the long-term benchmark because of stronger or weaker competition and short term fluctuations in estimated loss costs. To adjust for inflation and expense ratios, financial pricing models derive long-term target operating ratios for the book of business. The target operating ratio combined with the projected claim and expense cash flows gives the indicated premium rates.
The pricing actuary prepares long-term target operating ratios for each book of business linked to the insurer’s planning cycle, updated for changes in loss cost trends, interest rates, and expected returns on capital. The target operating ratio combines insurer cash flows with capital requirements, investment strategy, and tax law to derive the premium rates that maximize long-term profits. The pricing actuary must:
● Compute target capital for the book of business, based on the capital held by the insurance industry and rating agency capital formulas, sometimes refined by the insurer’s internal capital model.
● Estimate the expected return on this capital for relevant book of business, based on asset pricing models and the systematic risk of the business.
● Derive the optimal investment strategy for the book of business, based on corporate tax rates by asset class, asset-liability matching strategies for insurance, and volatilities for each type of asset.
Aggregate investment strategy, or the percentages of government bonds, corporate bonds, municipal bonds, and equities in the asset portfolio, is set by the investment department, reflecting expected yields by asset class, likely changes in the term structure of interest rates, and the credit risk or market risk by asset class.
The pricing actuary allocates the assets by book of business based on capital to asset ratios and tax law. To price business with a higher than average ratio of capital to assets, the investment portfolio should have a higher ratio of tax advantaged assets.
Financial pricing models use the underwriting cash flows (premium received, claims and expenses paid), the statutory reserve margins (equity in the unearned premium reserves and the implicit interest discount in the unpaid claim reserves), and the supporting capital for the business that is being priced.
The indicated premium from the financial pricing model is the long-term equilibrium price, which we combine with the short term price optimization relativity from the underwriting cycle analysis.
Indicated premiums depend on actuarial pricing models; the premiums charged to insureds depend also on market competition – the underwriting cycles that limit an insurer’s pricing discretion. In soft markets, insurers focus on retaining business that will be profitable in the long-run, but they must avoid excessive short term losses. In hard markets, insurers focus on maximizing profits, but they must avoid losing market share.
Underwriting cycles are industry phenomena, not patterns in an insurer’s own profits. They reflect synchronous rate changes by competing insurers, not fluctuations in any one insurer’s rate changes.
Pricing actuaries must evaluate industry patterns to discern if rates will likely increase or decrease and how quickly they may change. Few insurers can resist the strength of industry cycles, but equally few actuaries can project the cycles accurately.
Competitive strategy is like coalition building in parliamentary systems, except that agreements are discrete. Leading insurers periodically reveal their pricing expectations, by rate changes or by statements to the industry press, to test whether other insurers will follow. Experienced pricing actuaries understand the signals of their competitors and adjust their own pricing recommendations. Failure to accurately forecast market competition or to include competitive information in rate indications causes lags of six months to a year in pricing strategy, with market share losses in soft markets and income losses in hard markets.
An insurer’s own staff often differ on the course of the underwriting cycle. Actuaries and accountants see the losses on existing business and presume the cycle must turn up; underwriters and sales agents see intense competition and presume the cycle will turn down. In fact, the course of the cyle is best inferred from remarks by industry executives in the insurance trade press and rate filings by leading insurers.
Insurers make rational pricing decisions, even if their judgment is sometimes clouded by lack of information. Optimal pricing considers the probability distribution of industry price changes and models the long-run effects of each pricing strategy. Sound forecasts and quick but appropriate pricing can maximize profits from changes in the underwriting cycle.
Lifetime pricing of insurance contracts
Most property-casualty insurance shows losses for new business from high underwriting expenses, not-taken rates, lapse rates, and new business loss costs, with offsetting profits as the policies mature. Traditional ratemaking aggregates all business in the policy year and does not distinguish the loss-making versus profit-making phases of the policy lifetime. Insurers may think expanding books of business are unprofitable and contracting books of business are profitable, though each matches the expected returns for its phase.
Optimizing lifetime profits on a cohort of policies requires evaluating the elasticities of loss costs and lapse rates to new business premiums and underwriting selection. Actuarial pricing quantifies the actual vs expected profits for the cohort’s phase to assess the lifetime profitability of a book of business.
Pricing actuaries use the relations of premium rates, underwriting selection, and elasticities of demand. Senior executives know that raising premium rates in a competitive market reduces profits, especially if lower-quality (high-risk) consumers are more likely to seek insurance policies than higher-quality (low-risk) consumers. But they rarely know the price elasticities of demand for renewal business vs new business, since not all insurers track profitability by cohort. Raising premium rates for the entire book of business increases profits on renewal business for their remaining years but reduces the volume of new business and the lifetime profitability on the cohort of new business.
Lifetime pricing combines static and dynamic analyses. Static analyses consider the loss costs, acquisition expenses, lapse rates, and not-taken rates by policy year, but not the elasticities of these costs to premium rates and underwriting selection. If premium rates do not change, static analysis shows the expected lifetime return on new business, but if rates change, the loss costs, expenses, and lapse rates change. Static analysis is a critical first step, but it does not suffice for business strategy.
The price elasticity of demand for auto insurance is low for renewals and high for new business. If the insurer raises the premium rate for a renewal, the policyholder chooses between paying the higher rate or searching for an alternative insurance policy that may have a lower rate. The search is expensive and a lower rate may not be available, so the policyholder generally saves money by paying the higher rate on the renewal policy.
For new business, the applicant is already searching for an insurance policy, and search costs are similar for all the policies. If the premium rate is too high, the applicant will not take the policy, since other insurers offer similar benefits. The price elasticity of demand is high, and the insurer must decide whether a lower rate improves lifetime profitability. Lowering rates adds to the new business loss but it decreases lapse rates and not-taken rates and may improve lifetime profitability.
Insurers seek to maximize lifetime profits, but they rarely know the optimal rate level, as shown by the range of rates charged by insurers. If their currents rates are too low, a rate increase raises lifetime profits; if their current rates are too high, a rate decrease raises lifetime profits. Their current rates are the estimated optimal rates, so rate increases and decreases have equal likelihood of raising lifetime profits, after adjusting for loss cost trends. The claim severity trend, reflecting inflation, is positive and the claim frequency, reflecting vehicle safety, is negative; the overall trend from low inflation and technological innovations is close to zero.
Traditional ratemaking can be deceptive, leading to pricing recommendations that reduce lifetime profitability. Movements of the underwriting cycle, marketing innovations (such as aggregator web sites), new classification dimensions (such as family history and school scores), and entry or exit of competitors changes the elasticities for existing products. Pricing actuaries must periodically revalue lifetime profitability to set optimal rates.
The elasticity of underwriting selection on loss costs also affects business strategy. Underwriting selection has several forms: the decision by the underwriter whether to issue the policy, by the agent whether to accept the application, and by the insurer for what information to require in an online web site. Stringent underwriting selection reduces the expected loss costs but it is expensive and it reduces the volume of business. More lax underwriting selection increases the volume of business but may impair its quality. The pricing actuary must judge how each rating variable affects lifetime profitability.
Live agents can often judge if the applicant is too risky for the policy offered. Underwriting web sites might consider only age, sex, marital status, territory, credit score, and accident history. Insurers may misjudge the optimal level of underwriting selection.
● If they select business too cautiously, perhaps by insuring only applicants with clean driving records and good school and employment histories, less stringent underwriting selection may raise market share and lifetime profits.
● If they select business too cautiously, perhaps by ignoring family history and peer groups, more stringent underwriting selection may reduce loss costs and raise lifetime profits.
Maximizing lifetime profitability changes the pricing perspective from calendar years to cohorts. Traditional ratemaking may misjudge profits, since raising rates too high boosts short term profits but reduces market share and profits in future years. The traditional pricing analysis is unbalanced: the benefits of higher rates on renewal business profits is considered, but the damage of higher rates to market share is ignored.
The proper objective is to maximize the lifetime profit in the new cohort of business, considering both market share and expected profit in each year. This pricing objective is used for long duration policies, such as whole life insurance: maximize the lifetime profit at initial recognition of the cohort of policies from the new business and all renewals. The best auto insurers are adopting all actuarial tools that increase their profits.
The difference between long duration whole life insurance and short duration motor insurance is contractual (the legal obligations of the insurer to the policyholder), not economic (the expected cash flows between the insurer and the insured). A renewal of a whole life insurance policy is an extension of the original contract; the renewal of a motor insurance policy is a new contract. For the pricing actuary, this distinction is not relevant; the pricing analysis depends on the expected cash flows, not the legal obligations of the contract.
Ideal pricing uses elasticities of demand with respect to both premium rates and underwriting selection. Exact elasticities are not known for insurance contracts: sales agents and marketing personnel often consider the price elasticities to be higher (more elastic) than do underwriters and actuaries. The price elasticity of demand depends on the class of business (more elastic for low-income drivers) and phase of the underwriting cycle (more elastic during soft markets when insurers compete for new business).
Lifetime pricing combines modeling of the policy through all its renewals with judgment by experienced pricing actuaries for the effects of rate increases or decreases at each state of the policy’s life. Traditional ratemaking formulas give a fixed indication, but this figure is rarely correct. Lifetime pricing includes the essential variables to optimize long-term income.
Several types of rating variables are used for auto insurance. The traditional rating variables (age, sex, marital status, and territory) are shown on the insurance application and are used by all insurers, except where they are restricted by state regulation. Other rating variables (delinquencies, peer groups, family stability, education, employment) are especially important for high-risk drivers and are used by select insurers. Some rating variables are composites: a credit score combines several parts of a driver’s credit record. And some rating variables assess the type of vehicle (model, year, price, safety features) or its use (distance driven, business use).
Rating variables are used in their benefits exceed their costs. The most predictive rating variables, such as testosterone level, peer groups, and alcohol use, are too costly to measure, so we use proxies: age, sex, and marital status for testosterone level and aggressive behavior. Some proxies are crude: territory is a proxy for average attributes of its residents, such as education, income, and crime rates.
A common maxim is that rate relativities should be supported by actuarial data. But claim frequency data are not available for some rating variables, such as absence of the biological father from the home or the number of days the student was absent from school, yet these variables predict risky behaviors like delinquency, crime, alcohol use, drug use, and promiscuous sex, and they presumably predict auto accidents as well. Other predictors, such as peer groups, are inferred from claim studies, not pricing data. Adolescent male drivers have more auto accidents if they carry adolescent male passengers, before whom they are motivated to show risk-taking and aggressive behavior.
Collecting data is not always feasible. Inferring rate relativities from the effects on other risky behaviors may be an efficient pricing method. Criminologists relate delinquency and crime to (a) age, sex, and marital status (single, married, divorced); (b) family background, such as the absence of the father from the home; (c) neighborhood (urban, sub-urban, rural) and socio-economic status; (d) education (grades completed, school suspensions, days absent from school); (e) community involvement (church groups); and (f) employment.
Restricting rate relativities to those supported by actuarial pricing data ignores the information available from other disciplines. Criminologists and evolutionary biologists have examined influences on delinquency, crime, aggression, violence, and risk-taking. The effects of age, sex, and marital status on delinquency and crime are larger than the effects on auto accidents, for several reasons:
● Delinquency and crime are intentional, so they differ between young men who compete aggressively and women who avoid physical aggression. Auto accidents are unintentional; they reflect both aggression and risk-taking (which vary with age and sex) and from inadvertent acts of either men or women.
● The motor vehicle is the same regardless who is at the wheel. Young men are more likely than women to use guns and knives (criminal behavior), but men and women drive equally lethal cars.
● The young men who commit the worse crimes are the least likely to buy motor insurance.
The homicide frequency for young, urban men is much greater than the frequency for mature, rural women. The pattern of homicides by men vs women, by young men vs older men, and by unmarried men vs married men is similar to the pattern of auto accidents by sex, age, and marital status.
FBI statistics show crime rates along each class dimension (age, sex, territory) and for various combinations. (Territory means the location where the crime occurs, not where the criminal lives.) From the crime statistics, we derive the percentage of the one-way factors that are picked up by the two-way factors. Age, sex, and territory are party correlated, but not as much as family background, education, peer groups, and employment.
Predictive, measurable, and orthogonal
The variables for a class system should be predictive (accurate), measurable, and orthogonal.
Drinking habits, peer groups, and testosterone levels are accurate predictors of auto accidents, but they are hard to measure. Territory is easy to measure, but it reflects numerous attributes of the population and does not distinguish low-risks vs high-risks living in the same location. Territory is a proxy for ethnic group and socioeconomic status, which is correlated with the type of peer group, but it does not differentiate by person within the territory.
The sex, age, marital status and residence of a mature, middle-class mother or of a young unmarried male are easy to measure, and they are used by all auto insurers. Further segmenting the insurance applicants by credit score, school score, family structure, peer groups, employment, delinquencies, and education enables insurers to select the lower risk drivers.
Education, employment, and residence overlap; they are not orthogonal. The rate relativities for high school vs college graduate, blue-collar vs white-collar work, and population characteristics of the territory all measure socioeconomic class.
Scoring techniques combine overlapping variables. Credit history databases have hundreds of variables, all measuring similar personality attributes. The credit history variables include outstanding balances each month, the missed payments each year, and any defaults. The personality attributes that the variables measure are impulsiveness (people who shop impulsively have higher outstanding balances and are more likely to miss payments), income (poor people are more likely to build up credit card debt), and planning for the future (people with strict payment plans keep debt low).
Banks, home insurers, and auto insurers combine the data different ways. Banks are most concerned with past defaults and the ratio of income to debt. Insurers are more concerned with missed payments, which show indifference to future obligations.
Age, marital status, and number of children are correlated and should be combined into an age/family score. Each variable is correlated with accident frequency, but the correlation of the combined score is lower than the product of the individual rate relativities.
The absence of the father from the home, days absent from school, and delinquencies affect a young man’s association with peer groups that encourage intra-male competition for dominance and status by displaying risky behavior, including risky automobile driving. Each variable’s correlation with risky behavior is moderate, but the overall score from combining these variables predicts risky behavior well.
Minimum Bias and GLMs
Traditional ratemaking uses one-dimensional class systems, with rate relativities multiplied to determine the premium. This class ratemaking works if the class dimensions are independent and invariant: that is, the rate relativities for one dimension do not depend on the values along other dimensions. In practice, rate relativities are not invariant: the rate relativity for young drivers is greater for men than for women and is greater in urban territories than in rural territories.
Overlapping class dimensions, such as credit score, age, territory, education, and income, use multivariate statistical models and scoring systems. Credit score, territory, education, and income are proxies for attributes of the driver that affect risk-taking. Estimating relativities separately for each rating variable and multiplying them overcharges high-risk drivers and undercharges low-risk drivers. Instead, we use two methods:
● Orthogonal class dimensions use multivariate minimum bias procedures or generalized linear models.
● Correlated class dimensions are consolidated by scoring systems, used for credit rating, socioeconomic class, and family structure.
Orthogonal class dimensions are not correlated but the relativities may not be invariant by class dimension.
Illustration: Age and sex are not correlated: the percentage of drivers who are male vs female does not differ by age, so knowing that a driver is male doesn’t indicate his age. (In previous generations, men drove than women did; at older ages, more women remain healthy, so the percentage of women drivers rises with age. These cohort and mortality effects are less material for rate relativities now, as auto use is similar by sex.) But the relativities are not invariant: age relativities differ by sex, and sex relativities differ by age.
● The rate relativity for young vs mature drivers is higher for men than for women.
● The rate relativity for men vs women drivers is higher for young drivers than for adult drivers.
The rate relativities reflect both risk-taking and random accidents:
Testosterone: The difference in testosterone levels between young persons and middle-age persons is greater for men than for women. The difference in testosterone reflects the mating strategies for men vs women; it is a human universal, though it is suppressed or induced by social patterns. Male mating strategies induce young men to compete aggressively for access to women; female mating strategies induce young women to choose mates who provide low-risk paternal care. Middle-age persons, especially if they are married, do not compete aggressively for members of the opposite sex, so testosterone levels decline with age and marriage after late adolescence. See the class variables section for the effects of testosterone and mating strategies on motor insurance rate relativities.
Additive factors: Testosterone levels and mating strategies affect risk-taking and aggressive behavior, shown by the incidence of violent crime by age and sex, which are higher than the age and sex relativities for auto accidents. Many auto accidents stem from causes besides risky driving, such as road hazards, worn out brakes, and cell phone distractions, that affect men and women similarly (additive factors) and reduce the rate relativities. Combining the rate relativities by multiplicative models, additive models, and scoring systems is the key to multivariate analysis.
Rate relativities are multiplied for independent class dimensions, but the relativities must be quantied holding all other attributes constant. For instance, vehicle type measures the damage caused by a given accident; sex, age, and marital status measure the accident propensity of the driver. Vehicle type and driver attributes are correlated: young unmarried male drivers are more likely to drive sports cars than are middle-age, married female drivers, and inner-city residents have older cars than suburban residents have. Rate relativities for vehicle type are computed either by holding driver attributes constant or by adjusting for driver attribute in the loss costs by vehicle type. Once the rate relativities are computed, they are applied multiplicatively.
Some rating variables measure the same attributes. Credit scores use dozens of variables, such as average debt outstanding, payments overdue, and ratios of debt to income. School scores use quality of the school, the student’s grade point average, and disciplinary actions against the student, such as suspensions. Scores combine the information into a single figure for the rating variable.
Multivariate analyses include regression, generalized linear models, and minimum bias procedures. Multiple regression can be done on spreadsheets and needs little special training, but it assumes normal distributions and additive effects. For multiplicative models of rate relativities, we use the logarithms of the variables.
Generalized linear models allow a range of distributions (not just normal distributions) and show additive and multiplicative effects, but they require statistical expertise to derive the rate relativities and to interpret them.
Minimum bias procedures give the same results as generalized linear models for the most common insurance scenarios (multiplicative models with Poisson distributions) and they are more easily understood.
Pricing actuaries forming rating systems require a combination of three traits: statistical expertise, underwriting experience, and keen understanding of human behavior.
● Statistical expertise adjusts rate relativities for probability distributions, mathematical vs additive models, and correlations among class dimensions. Generalized linear modeling is done separately for accident frequency vs average severity, which have different probability distributions.
● Underwriting experience is the effect of each rating variable on loss costs and the interrelations of the class dimensions. Vehicle type and distance driven differ by many driver attributes; the pricing actuary must tease apart the effects on loss costs.
● Auto accidents stem from human behavior. Many accidents by young unmarried male drivers result from risk-taking and other aggressive behavior, which are amplified or suppressed by social norms for the interactions of males and females. Peer groups that emphasize “male scoring” raise accident frequency; social norms that emphasize marriage and abstinence suppress accident frequency.