The New Pricing Paradigm

The ability to price personal lines insurance policies successfully, accurately matching rate with risk, is arguably the most important competency required of Canadian property and casualty insurers. Pricing each risk with surgical precision can provide substantial competitive advantage and long-term profitability. Over the past decade, a number of insurers have emerged as leaders in pricing sophistication — Progressive and GEICO in the United States, Intact Insurance in Canada and many insurers in the European Union. Due in part to advances in computing power, but more so due to highly competitive market forces that drive innovation, these companies have complemented conventional actuarial methods with data mining and analytical techniques to produce more stable and accurate rating structures.

These techniques, commonly referred to as “multivariate analysis” (MVA), are now being adopted by more and more Canadian insurers and are on the verge becoming part of everyday business practices. As Canadian insurers employ- ing these techniques become more sophisticated in their use and application, the performance divide between these innovators and their competitors will grow.

CURRENT P&C INDUSTRY PRICING

Company actuaries create rating structures that generate a premium for each risk in a given portfolio. For personal auto insurance this process usually includes:

• analyses of various policyholder type characteristics and their impact on claim risk (i. e. claim frequency and severity);

• industry reports and tables that reflect the most recent industry trends regarding claim risk; and

• corporate financial objectives and competitive market factors.

Strong analytical and statistical skills are required, in addition to a thorough knowledge of regulatory environments. At times, these two factors may in fact be at odds with each other in a very competitive environment.

Most insurers today employ the conventional approach to rate setting. This dates back to the 1960s, when data processing capabilities were limited. In the conventional approach, rating analyses are conducted on a univariate basis. In other words, they look at how changes in one characteristic result in differences in loss frequency or severity. Loss frequency and severity measures are determined for commonly-used characteristics like claim history (it has been well established, for example, that the longer it has been since a vehicle incurred a loss, the less likely the driver is to incur one in the future) and vehicle use (a vehicle driven for personal use is less likely to incur a loss than a vehicle used for business, presumably because the vehicle is simply on the road less).

Most industry practitioners use the driving record variable to establish “base” rates for each vehicle. Generally, driving record categories range from 01 to 06. Usually, they go up to “06,” or six years claims free, but with better and more reliable data capture, some companies have introduced 10-, 15-and 20-year driving record groups. Every risk starts off with the same “base rate” set for the driving record group within which they fall. Then another rating variable, let’s say driving class, is applied. A “differential” is applied to determine how the base rate for each driving record group will change with the application of the next rating factor. A differential value is the measure of the difference in observed (actual) claim losses for each different driving class compared to the overall average. How this process works is simplified in the following example of collision coverage. (Please See Figure 1 at the top of this page.) In Figure 1, you can see how the premium charged for the vehicle changes as the different rating characteristics are combined.

In this simplified example, there are only two driving class groups — 01 (personal use only) and 02 (business use only). As each rating variable is added (e. g. years licensed, FSA location, vehicle rate group, etc.), differentials for the variable are repeatedly used to adjust the vehicle premium, reflecting the risk represented by the values of each rating characteristic or factor used by the insurer to determine the premium for the risk. Each risk in a portfolio falls into a small group/profile that best reflects the losses anticipated by that profile.

These cross tab-type reports determine the variation of premium between policyholders. As more factors or variables are introduced into the cross tab reports, we observe more groups and a lesser number of policyholders within each group. In effect, the information becomes more granular, resulting in many different possible premium values across the policyholder base. This increase in the number of risk groups or categories results in increased granularity, greater discrimination between risks and more accurate pricing.

Ultimately, however, the number of different possible premium levels will be restricted by the number of groups included in the analysis.

MULTIVARIATE ANALYSIS AND PREDICTIVE MODELLING

Multivariate analytical techniques take a different approach to predicting risk, focusing on individual-level data so the estimate of risk is more granular. They take into account the effects (interactions) that many different characteristics (variables) of a risk have on one another. Hence the use of the term multivariate approach, as opposed to the univariate approach typically employed by most insurers today.

Multivariate techniques have been mastered by data miners across academic (e. g. scientific research) and business (e. g. marketing and risk management) environments as a way to predict behaviour. While these techniques were developed more than 60 years ago (they evolved from statistical tools designed to improve bombing accuracy in World War II), advances in computing technology have made them more accessible. Marketers, for example, use predictive modelling — a form of multivariate analysis — to create measures of the likelihood that a customer will respond to a promotional offer such as magazine subscriptions, for example. Banks use these tools to create measures, such as credit scores, of whether a client will be able to meet lending obligations for a loan or mortgage.

Similarly, property and casualty insurers can use predictive models to predict claim behavior. Essentially, predictive models identify the characteristics that best predict risk; produce a scoring equation that can be maintained and updated; and calculate a score that represents the expected losses for each risk in the portfolio. (Please see Figure 2 below.)

Figure 2 shows how the scoring model or mathematical equation is composed of the fewest number of characteristics or variables possible (usually 10 to 15), each of which are responsible for a discrete “amount” of the expected loss behavior that, when added together, account for 100% of the expected losses for the risk.

A simple way of looking at this approach is to consider each characteristic in a model equation as though it were a different piece of a pie. The entire pie represents the sum total of the “expected loss” amount. (Please see Figure 3.)

In Figure 3, the pieces of the pie — each piece represents a different characteristic of an auto insurance risk identified by the model — fit together to form a whole, perfectly shaped pie. In other words, the set of variables in the equation are the optimal combination that provides the most accurate measure of the expected losses. At first glance, it might appear that by adding more information (e. g. adding another piece to the pie), one could generate an even more accurate assessment of the risk. But the statistical processes account for the relationships between different characteristics, so that the addition of another characteristic to the pie would only distort its shape and not add any additional
value in accurately measuring risk.

In our experience, multivariate or predictive modelling techniques provide even more granularity and better understanding of the differences between individual risks than conventional approaches used by most insurers today. This is achieved because risk measures produced by predictive modelling outcomes are produced for each individual risk rather than by group differentials. In essence, the techniques enable more accurate matching of rate with risk. Those relatively few insurers in Canada employing these methods are able to acquire business by offering lower rates for risks that the general market is overpricing; in addition, they charge higher prices to avoid taking on risks that the general market is underpricing. The overall benefits of this result include:

• better risk selection and pricing;

• reduced underwriting expenses; and

• improved underwriting results.

The ability of multivariate analytical techniques to improve rating accuracy is ultimately determined by how much better these measures predict losses compared to the premium assigned to a risk — vehicle or property — using the conventional rate-setting paradigm.

RESULTS FROM CASE STUDIES

Illustrated at right is an example of actual observed results for a portfolio of homeowner’s policies. Figure 4 shows a Homeowners Claims Risk Scoring Model produced for a Canadian insurer. Each policy in the portfolio was scored at its effective date. The score represents the expected losses on the policy in the policy year. Each policy was ranked from highest risk (score) to lowest risk (score).

Figure 4 depicts the percentage of actual losses on policies in the portfolio that occurred after the policy effective date. Based on the model’s prediction of losses, policies with the highest 20% of scores generated 46% of total losses; policies in the lowest 20% of scores accounted for only 6.8% of losses

Based on the premium charged for each policy, however, the policies with the highest 20% of premium produced 32% of all losses and those policies with the lowest 20% of premium produced 15.2% of losses.

The shaded area between the green line (reflecting model’s predicted losses) and the red line (showing the insurer’s current premium charged for each policy) represents the “lift” or increased accuracy in loss prediction produced by the model over the insurer’s current rating structure. The shaded area essentially represents losses for which existing rates are not accounting.

CONCLUSION

The application of data mining tools and multivariate modelling techniques can substantially improve current rating structures for property and casualty insurers. As a result of their capability, multivariate modelling techniques have gained traction and are becoming an industry standard. The primary challenge is the effective use of these tools. Insurers must become more familiar with these techniques and adopt them as a daily part of doing business